By W.H.L., GPT-5.6 Sol, Claude Opus 5

Graduality: A Feature Catalog of Gradual AGI

W.H.L., GPT-5.6 Sol, Claude Opus 5

Publication Version · v1.0

August 18, 2026

Version history

Version	Status	Change
v0.8	Analytical basis	Peer-reviewed technical reconstruction. CDT v2 and IMC v2 remain repaired post-pilot FirstCoder analyses awaiting a clean independent rerun.
v0.9	Publication preparation	Added division of labor with the reader-facing catalog, confidence parity, corpus freeze, reader navigation, the shared individuation example, and model-coding clarification. No G-register definition, CDT v2 assignment, IMC v2 assignment, or derived topology changed.
v1.0	Publication version	Integrity and production pass: controlled-vocabulary normalization, corpus-freeze clarification, section-placement repair, front matter, cross-table navigation, subscript typesetting of all notation for plugin-free rendering, and copy-edit normalization of spelling and dashes. Analytical content and assignments remain unchanged from v0.8.

Abstract

What does gradual mean in Gradual AGI? Across eight installments, the research program accumulated an increasingly rich apparatus involving capability and realization, relative clocks, synchronization, heterogeneous adoption, multidimensionality, observation, revisability and governance. This paper reconstructs that apparatus as a versioned feature catalog and asks which structures constitute graduality, which characterize or explain particular regimes, and which have identifiable historical antecedents. The principal result is semantic thinning under theoretical enrichment, conditional on transformation individuation. Once an individuation rule I fixes the relevant transformation, the recoverable phenomenal minimum is that its realization is not exhausted by a single event; slowness, smoothness, monotonicity, scalarity, homogeneity and uniformly small increments are not universal requirements. A repaired Corpus-Deployment Test (CDT v2) identifies three positive-premise configurations across four selected source passages, and IMC v2 grades their evidential force. Both repaired tests are post-pilot FirstCoder analyses and have not yet received the clean independent rerun specified in Appendix B. Within that provisional topology, the two Independent/NotEmbedded routes (#2 and #3; n = 2) share only G002, potential-realization separation, which also appears in three of four selected source passages overall. G002 is therefore the strongest presently observed candidate for a non-question-begging explanatory core under the current coding, not an independently reproduced explanatory primitive and not a semantically necessary condition. Papers #4 and #7 remain valid deployment routes, but their Embedded scopes prevent independent corroboration of non-point-exhaustion; paper #1 is an Unresolved/Embedded diagnostic but remains a direct textual anchor for rejection of singular arrival. Phenomenal gradualness is also separated from graduality as a principle of information-responsive iteration with preserved revisability. Historical analysis locates antecedents and blocks imported readings of gradual as necessarily slow or smooth. Validation remains object-specific and mixed: repaired targets, CDT v2 and IMC v2 do not inherit independent status from superseded versions.

1. Introduction

Gradual AGI began as a contrast. The first installment rejected the picture of artificial general intelligence as a sudden breakthrough, a single system, or one dated moment, and instead described a civilizational process that deepens, widens, diffuses and becomes realized over time. Seven subsequent installments carried that contrast into different problems: abundance, synchronization, dynamical modeling, optimization, empirical testing, governance, and governance measurement. In doing so, the series accumulated a vocabulary of potential and realization, relative rates and lag, heterogeneous adoption, multidimensional state spaces, partial ordering, iteration, revisability, observation and contestation. The phrase Gradual AGI became more precise, but also more crowded.

That history creates a problem of interpretation. If every later structure is treated as part of one expanding definition, gradual comes to mean too much. If only the original point-event contrast is retained, the series appears to have spent eight papers elaborating ideas that do not belong to its central term. The difficulty is not resolved by asking what gradual ordinarily means. Historical usage is itself heterogeneous: degree, staging, continuity, pace, accumulation, diffusion, punctuation, qualification and political gradualism belong to different lineages and impose different connotations. A reader can therefore import slowness, smoothness, continuity, small steps or normative delay into Gradual AGI without any of those meanings having been asserted by the series.

This paper addresses that problem by treating the published series as its primary corpus and asking a deliberately internal question:

What has “gradual” or “graduality” meant across the Gradual AGI series?

The historical record plays a secondary role. It supplies the initial representational vocabulary with which the endogenous corpus is examined, and it supplies interpretive guardrails against familiar readings that the series may not share. It is not a benchmark against which the series is expected to converge. The catalog therefore explains Gradual AGI from the inside; history helps locate it from the outside.

Division of labor with the reader-facing catalog. The published What “Gradual” Means in Gradual AGI: A Feature Catalog carries the exposition: the nine features in plain language, reader guardrails, examples, aliases, and current evidence-status notes. The present paper is deliberately the technical companion. It preserves the historical scaffold, source normalization, analytical tests, versioning, disagreements, repairs, and validation states needed to audit those public claims. Readers seeking the meaning first should begin with the catalog; readers seeking derivation and reproducibility should use this paper.

Series navigation

Paper	Short title	Graduality-related move
#1	Epistemic Extension	Rejects one breakthrough or arrival moment; introduces Depth/Width, uneven persistence, and Cumulative Insight.
#2	Abundant Resources	Separates capability emergence from societal realization and spread through infrastructure and society.
#3	Synchronization	Adds Ceiling/Floor/Slope, relative clocks, and iterative technological-civilizational co-development.
#4	Ceiling, Floor, and Slope	Formalizes assimilation rate, lag, thresholds, heterogeneous adoption, and multiple dynamical regimes.
#5	Optimization framework	Introduces principled graduality as information-responsive iterative revisability rather than slowness.
#6	Optimization tests	Operationalizes multi-agent and non-stationary optimization and revision under formal and empirical contact.
#7	Governance framework	Uses multidimensional partial ordering; permits local jumps within piecewise realization; separates phenomenon from principle.
#8	Governance measurement	Separates observables from underlying properties and adds measurement, revision transparency, and observation infrastructure.

This table is a navigation aid. Section 5.1 provides the fuller analytical chronology and explains how the installment-level formulations enter the reconstructed apparatus.

Reader’s map

If you mainly want…	Read…
The semantic claim and the two definienda	§§1.2, 3.10–3.11, and 7.1–7.3
How the catalog and instrument were built and repaired	§§2–4
The series-level synthesis	§5 and §7
Independent coding, disagreements, and validation limits	§6
The complete audit trail and retest rules	Appendices A–B

1.1 Research design

The study reconstructs eight published installments. Extraction precedes normalization: raw source formulations are first recorded without requiring them to belong to one conceptual type, and are then normalized under a Source-Role Rule that distinguishes a feature from a mechanism by the work it performs in its source. The resulting endogenous register contains nine stable records, but those records are not treated as nine peer components of one definition. They include seven PositiveFeatures, one Constraint and one Explanandum, with analytical Role and Locus recorded at provenance level rather than treated as intrinsic properties of an entry.

The eight installments constituting the endogenous corpus are listed under Primary Corpus in the References and identified as papers #1–#8 throughout.

Corpus Freeze. This study snapshots the published texts of papers #1–#8 as archived and coded for the present reconstruction, with a corpus cutoff of August 17, 2026. Where a public article carries no explicit version label, the frozen source copy retained for coding controls the analytical object. Those frozen source copies are retained as versioned study artifacts under the reproducibility protocol in Appendix B.15. The reader-facing companion published on August 17, 2026 is explanatory material and is not part of the coded eight-paper corpus. Subsequent edits to any installment—including later revisions of paper #8—or later series installments create a new corpus version and require explicit regeneration of affected derived views; they do not retroactively alter the results reported for this frozen eight-paper corpus.

A separate historical reference register contains 25 selected conceptions drawn from lexical, philosophical, mathematical, physical, geological, evolutionary, social, institutional, political and decision-theoretic lineages. Those entries supplied an initial five-coordinate scaffold—Degree, Mode, Tempo, Magnitude and Relation—but the scaffold is not privileged over the endogenous object. When the series’ multidimensional and partially ordered states could not be represented without forcing them into Degree or Mode, State Structure was added post hoc. Relation was later decomposed into structural, temporal and observational forms; Direct Signature was separated from Modulation; Tempo was tightened to rate or rate-like quantity; and provenance Locus was split so that State and Process could vary independently.

The method is therefore intentionally revision-sensitive. Stable IDs preserve the genealogy of a record while immutable versions preserve what a test actually saw. Analytical results are pinned to those versions, and a derived view becomes stale when a load-bearing input changes. The catalog does not treat revision as an editorial afterthought: revision is part of the evidence about whether the representational instrument fits its object.

Sources → Versioned Entries + Provenance → Faceted Catalog → Versioned Tests → Definienda

1.2 Main findings

The first result is that the series contains two definienda rather than one. Phenomenal gradualness concerns how an individuated transformation is realized. Principled graduality concerns how action should remain adaptive under uncertainty. The same lexical root therefore names two objects of different logical type.

For the phenomenal use, reduction produces a deliberately thin conditional minimum. In plain language: once we have fixed which transformation we are talking about, it is phenomenally gradual if its realization is not exhausted by one event. Let I denote an individuation rule determining which realized changes belong to the same transformation X, and let C_{X | I} denote their ordered temporal support. Then:

Grad_P(X | I) ⇔ ∃ t₁,t₂ ∈ C_{X | I} : t₁ < t₂

equivalently, |C_{X | I}| ≥ 2. The condition denies one rival picture once the transformation has been fixed: its realization is not exhausted by a single event. It does not require slow change, smoothness, mathematical continuity, bounded increments, homogeneous development, scalar ordering or one particular relation between clocks.

Individuation Dependence. The predicate is thin; classification is not. Different individuation rules can change which realized changes belong to X, and therefore change whether the condition is satisfied. Section 3.10 gives a worked same-history example in which a capability threshold, domain-level realization, and wider civilizational assimilation yield different gradualness verdicts because they are different transformations.

Individuation Motivation Check. The two-stage formulation creates a second circularity risk: I itself could be selected because the resulting object already secures non-point-exhaustion. IMC v2 therefore separates two questions. ScopeMotivation asks whether the source would still track the same transformation boundary if it expected the phenomenal result to be point-exhaustion. ExtensionEmbedding asks whether that boundary itself entails or substantially builds in temporally extended realization. The distinction permits independently motivated scopes to remain explicitly entangled with extension rather than forcing one omnibus verdict.

The second definiendum is principled graduality. The Optimization framework defines graduality as an optimization principle rather than a speed measure:

Grad_Pr(Π) = InformationResponsiveIteration(Π) ∧ PreservedRevisability(Π)

The two branches are not inferred from one another:

Grad_P(X | I) ⇏ Grad_Pr(Π)

The endogenous corpus does not reduce to one universal positive generator. CDT v2 identifies three positive-premise configurations across four selected source passages: {G002, G003} in papers #2 and #4, {G002, G005} in paper #3, and {G007} in paper #7. IMC v2 grades that topology: the two Independent/NotEmbedded routes (#2 and #3; n = 2) share only G002, potential-realization separation, which also appears in three of four selected source passages overall. Under the current FirstCoder analysis, G002 is therefore the strongest presently observed candidate for a non-question-begging explanatory core without becoming semantically necessary. CDT v2 and IMC v2 are repaired post-pilot tests and have not yet received the clean independent rerun specified in Appendix B; the topology and the n=2 inference are therefore provisional at the present validation state.

Finally, the reconstruction replaces the inherited seven-layer conception with a faceted architecture and treats revision and validation as part of the epistemic record. The independent pilot is model-based; repaired targets do not inherit validation from superseded versions; and raw disagreement is preserved rather than replaced by post-adjudication agreement.

1.3 From layers to facets

A third result concerns the architecture used to describe graduality. The inquiry began with seven apparent layers: Constitutive, Relational, Descriptive, Epistemic, Normative, Distributive and Procedural. The reconstruction shows that the list combined objects of different logical types. Constitutive content belongs to a definiens produced by reduction; Descriptive and Epistemic identify analytical Roles; Distributive and much Procedural content identify Loci; Relational content belongs partly to coordinate metadata and partly to regime characterization; Normative content divides between a principled definiendum and the conditions that justify it.

The replacement is a faceted catalog rather than another hierarchy:

normalized object ≠ provenance Role ≠ Locus ≠ coordinate reach ≠ definiens

The Facet Decomposition Finding (§4.1) explains why a compact definition and a rich theory can coexist without contradiction. The catalog stores explanatory, relational, distributive, epistemic and institutional machinery even when reduction excludes that machinery from minimum phenomenal membership.

1.4 Argument structure and equifinality

The endogenous corpus also does not reduce to one universal generator of phenomenal gradualness. The repaired Corpus-Deployment Test identifies three positive-premise configurations across four selected source passages: {G002, G003} in the Abundant Resources and Ceiling/Floor/Slope arguments, {G002, G005} in Synchronization, and {G007} in Governance. No positive generator is common to all four.

Route₂ ∩ Route₃ ∩ Route₄ ∩ Route₇ = ∅

The resulting claim is argument-level equifinality across four selected source passages, not four independent theories or a universal causal law. IMC v2 grades that topology and reveals a stronger positive pattern: the two Independent/NotEmbedded routes (#2 and #3; n = 2) intersect only at G002, potential-realization separation, which also appears in three of four selected source passages overall. Under the current FirstCoder coding, G002 is the strongest presently observed candidate for the series’ non-question-begging explanatory core. The clean subset is too small to establish a universal explanatory primitive, G002 remains semantically non-necessary, and neither the repaired CDT v2 topology nor the IMC v2 grading has yet been independently rerun. Their status is therefore provisional pending the clean retest specified in Appendix B.

1.5 Reliability under instrument revision

The reconstruction is accompanied by a model-based independent-coding pilot because several of its claims depend on the catalog instrument rather than directly on source wording. The raw pilot reproduces seven of nine endogenous Direct Signature sets exactly, while historical Direct Signatures reproduce at a substantially lower exact-set rate. Those figures are not collapsed into one coefficient. The pilot also exposes defects in the validation instrument itself: an over-constrained Tempo instruction, a provenance item that combined two source operations, and a Corpus-Deployment Test that still offered the phenomenal explanandum as a candidate generator. Its primary validation target is instrument determinacy under a frozen, prompt-separated application; it is not an estimate of human inter-rater reliability.

Those failures change the paper. Two endogenous Signature disagreements are adjudicated in favor of the independent assignments; two Role disagreements are adjudicated in favor of the first-coder assignments; the Optimization provenance is split into process-level and decision-level occurrences; and the Corpus-Deployment Test is versioned and redesigned. The resulting validation map is therefore mixed by construction. Some objects are IndependentlyCoded, some Adjudicated, some remain FirstCoder after target repair, and historical Tempo reliability is non-evaluable from the original pilot.

same target + disagreement → adjudication

changed target or rule → new version, not retroactive validation

The methodological contribution is not a claim that the catalog is globally validated. It is a rule for refusing that simplification. Validation attaches to versioned objects, and a derived result cannot inherit stronger evidentiary status than its load-bearing inputs. The instrument first changes when the endogenous object does not fit it; it changes again when an independent reader exposes coding boundaries and malformed targets. Both forms of contact narrow what the paper is entitled to claim.

1.6 Contributions and scope

The paper makes four contributions. First, it supplies a provenance-sensitive endogenous feature catalog of the eight-paper Gradual AGI series and reconstructs the semantic work accumulated by the phrase rather than assuming that later vocabulary simply thickens one definition. Second, it separates transformation individuation, phenomenal membership and the richer apparatus that explains or characterizes realization, and adds a source-level motivation check so that individuation is not treated as innocent merely because it precedes predicate application; it also distinguishes the phenomenal branch from principled graduality. Third, it replaces an inherited layer taxonomy with a faceted architecture that separates object identity, Role, Locus, coordinate reach, Standing, reduction and justification. Fourth, it makes revision and validation part of the method: changes to the object, coding rule, provenance grain or analytical test propagate through versioned records rather than being absorbed silently into prose.

The contribution is reconstructive and compositional rather than a claim to have invented the underlying primitives. Partial ordering has established formal antecedents, and the conjunction of information-responsive adjustment with preserved future flexibility has an exact conceptual antecedent in adaptive-policy theory. The question here is how these and other structures were assembled, differentiated and made to perform distinct theoretical jobs inside the Gradual AGI program.

IMC v2 is likewise a post-review FirstCoder test limited to the four current CDT-v2 routes plus paper #1 as a diagnostic case; its revised two-dimensional coding has not been independently rerun. And although the paper makes transformation individuation explicit, it does not supply a domain-general individuation rule: the endogenous corpus instead fixes relevant transformations argumentatively and source-relatively.

1.7 What follows

Section 2 reconstructs selected historical conceptions as a representational scaffold and as reception control, without treating them as a convergence benchmark. Section 3 turns to the eight-paper endogenous corpus, constructs the G register, records instrument failures and revisions, separates two definienda, and performs the logical, source-deployment and definitional reduction tests. Section 4 formalizes the versioned faceted catalog and its propagation rules. Section 5 answers the interpretive question directly: what Gradual AGI means in the full sense accumulated across the series. Section 6 reports the independent-coding pilot, leakage diagnosis, adjudications, redesigned CDT and remaining reliability limits. Appendix A carries the full catalog, provenance, revision ledgers, modal metadata, antecedent classifications and derived views; Appendix B freezes the coding rules, boundary tests and validation protocol.

Section 7 discusses the theoretical and methodological implications of the reconstruction. Section 8 states its limits. Section 9 concludes. Throughout, one asymmetry governs interpretation: the endogenous series is the object to be explained; historical knowledge supplies vocabulary, context and guardrails, but does not decide what Gradual AGI means.

2. Historical Graduality: Representational Scaffold and Interpretive Context

This section reconstructs selected historical conceptions associated with graduality before turning to the Gradual AGI series itself. Its purpose is not to determine what the series must mean by gradual, and it does not construct a benchmark against which the endogenous corpus is expected to converge. The primary object of this paper is the use of gradual and graduality across the published Gradual AGI installments. History enters in two narrower but important roles.

First, the historical reconstruction supplies a representational scaffold. Distinctions repeatedly encountered across lexical, philosophical, mathematical, physical, geological, evolutionary, social, institutional, political and decision-theoretic lineages were abstracted into an initial coordinate vocabulary for describing forms of graduality. That vocabulary is subsequently brought into contact with the endogenous corpus in §3 and is revised when it fails.

Second, the historical reconstruction supplies interpretive context. Readers bring established connotations to the phrase Gradual AGI: slow change, smooth change, continuous change, small steps, staged reform, or even respectable delay. The selected history makes those associations visible so that they can be distinguished from claims the series actually makes. In that sense the historical material functions partly as reception control: it helps prevent familiar meanings of gradual or gradualism from being imported into the research program without argument.

This division of labor is a post hoc clarification. Earlier analytical passes treated the historical and endogenous registers more symmetrically than the research question required and generated several cross-register comparisons from that symmetry. The present architecture does not retain convergence, divergence, parity or coordinate-frequency difference as an objective in its own right. The chronology of that correction, including the later independent-coding result for the historical register, is reported in §6 rather than rewritten as if the asymmetry had been fixed from the outset.

2.1 Selection and admission discipline

The historical reconstruction is selective rather than exhaustive. A lineage is admitted when it contributes a distinct conception, mechanism, contrast or candidate feature that changes how graduality can be represented. Historical importance alone is insufficient. The objective is not an intellectual history of every use of gradual or gradualism, but a disciplined set of distinctions capable of doing analytical work later in the paper.

Historical Admission Rule. Admit a candidate when a historically attested distinction directly changes the structure, value or applicability of at least one analytical axis and is not fully represented by an existing candidate. A cause, mechanism or representation is kept separate when it affects an axis only indirectly.

The reconstruction distinguishes axes from features. An axis is a dimension along which a process, state or relation can be characterized; a feature is a historically attested structure occupying or constraining one or more such dimensions. The first pass yielded five axes:

Axis	Schematic object	Initial historical function
D — Degree / scale	x	Level, extent or rank of a state or property.
M — Mode	path / transition form	How change proceeds: staged, continuous, punctuated, direct, cumulative.
T — Tempo	dx/dt	Rate or pace of change.
Δ — Magnitude	|Δx|	Size of an individual increment or transition.
R — Relation	rx/ry, τx/τy, ordering	Relation among processes, states, rates, clocks or units.

These five axes are an instrument abstracted from the historical material, not a definition of graduality. Section 3 will show that the instrument is incomplete: multidimensional and partially ordered endogenous states cannot be represented faithfully without adding State Structure S, and the generic Relation axis later requires decomposition. That failure is methodologically useful because it makes clear that the historical scaffold is revisable rather than authoritative.

Several provisional historical candidates were also retired or merged during normalization. Actualization, generic Trajectory and Adaptation were not retained as independent features; Rate/tempo was reclassified as an axis rather than a feature; and a separate Intermediacy candidate was merged into multi-stage succession. Stable historical IDs are retained in the revision ledger so that these changes remain auditable.

2.2 Lexical lineage: step, degree, pace and rank

The lexical history already resists a single reading. Latin gradus denotes a step, degree, rank or stage and can also support a sense of pace. The family therefore contains both discrete and scalar associations before any philosophical theory is added. A graduated scale divides a range into marks; a progression can move by stages; a degree locates a state within an ordering. None of those meanings by itself entails slowness.

The earliest noun use of graduality recorded in the Oxford English Dictionary is associated with Thomas Browne’s Pseudodoxia Epidemica (1646), in the phrase “graduality of Opacity and Light” (Oxford English Dictionary, s.v. “graduality, n.”; Browne, 1646). The example is important less for priority than for structure: graduality can denote gradation between qualities rather than a temporal claim about slow change. The adjective and noun also have distinct histories, so etymology is treated as connotative evidence rather than a source of necessary conditions.

2.3 Philosophical and mathematical lineages

Classical philosophy supplies several distinctions that later become separable in the catalog. Aristotle’s analyses of change, potentiality and actuality distinguish a thing’s capacities from their realized states and examine continuous change without making Aristotle a historical “gradualist” in the modern doctrinal sense (Aristotle, Metaphysics, Book IX; see also Physics, Book VI). The relevance here is structural: potential and realization, continuity and transition can be distinguished without being collapsed into one concept.

The sorites tradition supplies a different problem. Incremental variation can coexist with indeterminate classification: neighboring cases may differ only slightly even when no unique boundary determines where a predicate begins to apply. That history motivates keeping gradedness, limited increments, threshold structure and boundary vagueness conceptually separate. A process can be graded without having a vague boundary; it can have a threshold without proceeding by small steps.

Leibniz’s principle of continuity and the maxim commonly rendered as natura non facit saltus supply a canonical continuity lineage. Darwin later appealed to a closely related anti-jump formulation in evolutionary argument (Leibniz, 1996; Darwin, 1859). The historical lesson is not that graduality equals mathematical continuity. It is that continuity is one historically important strengthening of gradual change.

Hegel’s treatment of quantity, quality and nodal transition provides the converse caution (Hegel, 2010, “Measure”). Graded quantitative variation can culminate in qualitative transition. The existence of a threshold or regime change therefore does not by itself negate an extended gradual process. A historical account of graduality must be able to represent both continuous variation and qualitative transition without forcing one to exclude the other.

Mathematics enters here as a formalization lineage rather than a doctrine of graduality. Continuous functions, discrete sequences, ordered sets and threshold mappings provide precise ways to represent possibilities already visible in the historical record. The paper therefore does not identify graduality with mathematical continuity. A constant function is continuous without realizing a transformation; a discrete sequence can realize an extended process; and a threshold can map graded input into categorical output.

2.4 Metrology and physical timescale

Metrology contributes two distinctions often blurred in ordinary language: resolution and discretization. A graduated instrument may reveal finer distinctions when resolution increases, while a measuring convention may represent a continuous or graded underlying quantity in discrete bins. The representation can therefore look stepped even when the represented object is not, or look smooth because coarse measurement suppresses local structure.

Physical reasoning adds relative timescale. Whether a forcing is experienced as slow, fast or quasi-static depends on the response timescale of the system being driven. A useful generic ratio is χ = τ_response / τ_forcing. The same external change can therefore be gradual relative to one process and abrupt relative to another. Smooth forcing can also produce abrupt response near a phase transition. This history separates rate, relative rate, scale and regime transition rather than treating them as synonyms.

2.5 Geological and evolutionary lineages

Geology made accumulation and deep time central to explanations of large observed change. Lyell’s uniformitarian program emphasized the explanatory power of processes operating over long periods, but uniformitarianism should not be reduced to the claim that every geological rate is slow or constant. Gould’s later decomposition of Lyellian uniformitarianism into methodological assumptions and substantive hypotheses is useful precisely because it separates commitments about explanatory method from claims about actual geological rate and state (Lyell, 1830; Gould, 1987).

Evolutionary theory makes the separations sharper. Darwin’s emphasis on slight successive variations supplies an incremental lineage, but later evolutionary work shows that gradual evolution need not imply a constant rate or the absence of stasis. Eldredge and Gould’s punctuated-equilibria framework explicitly juxtaposes long intervals of relative stasis with comparatively concentrated episodes of change (Darwin, 1859; Eldredge & Gould, 1972). The resulting conceptual space distinguishes increment size, tempo, temporal distribution, stasis and punctuation.

Evolution also supplies heterogeneous development. Different traits, lineages or components can change at different rates rather than in lockstep. A global process may therefore be gradual while containing local punctuations, asynchronous components and variable rates. That possibility later becomes important as an interpretive guardrail: local discontinuity does not automatically settle whether a larger transformation is gradual.

2.6 Social, institutional, political and decision lineages

Social theory supplies lag and diffusion. Ogburn’s cultural lag distinguishes changes in material conditions from slower adaptation in non-material culture. Rogers’ diffusion framework describes adoption spreading progressively across a heterogeneous population (Ogburn, 1922; Rogers, 1962). In both cases aggregate graduality can arise from many discrete unit-level events. The population-level path should therefore not be confused with the micro-level form of each adoption decision.

Institutional language contributes graduation, qualification and authorization thresholds. A person or organization may move through graded requirements before acquiring a new standing; an authorization may activate only once a defined condition is met. These cases distinguish graded substrate from institutional classification and show why threshold crossing can be embedded within a larger staged process.

Political gradualism supplies the strongest reception-control warning. Elizabeth Heyrick’s Immediate, Not Gradual Abolition (1824) makes “gradual” a contested political strategy rather than a neutral description of tempo. Later disputes over gradual reform, Brown II’s instruction to proceed with “all deliberate speed,” Martin Luther King Jr.’s criticism of the demand to “Wait,” and Fabian gradualism all show that gradualism can denote staged reform, strategic pacing or indefinite postponement (Heyrick, 1824; Brown v. Board II, 1955; King, 1963; Shaw, 1889). The normative evaluation of gradualism therefore cannot be read directly from the descriptive meaning of gradual.

Decision theory supplies a related but distinct procedural lineage. Lindblom’s 1959 account of successive limited comparisons replaces one comprehensive decision with repeated bounded adjustments (Lindblom, 1959). That structure is historically close to incrementalism, but it does not by itself require that later decisions be responsive to newly acquired information or that earlier commitments preserve meaningful future options. Those stronger conditions matter later when the Gradual AGI series develops a principled use of graduality.

2.7 The historical reference register

The selected history is normalized into the following active reference register. The register is not a list of necessary conditions for graduality, and it is not a benchmark against which the endogenous series should match. Its entries preserve historically attested distinctions that either supplied the initial coordinate vocabulary or remain useful for interpreting what readers may mean when they encounter the word gradual.

ID	Normalized candidate	Primary lineage	Interpretive contribution
H001	Scalarity / gradedness	Lexical / metrological	Degrees can vary without reducing the property to binary presence.
H002	Intermediated / multi-stage succession	Lexical / institutional	A transformation can proceed through intermediary stages.
H003	Resolution / granularity	Metrological	Observed distinctions depend on representational or measurement grain.
H004	Measurement discretization	Metrological	A graded substrate can be represented in discrete bins or steps.
H006	Boundary indeterminacy / vagueness	Philosophical	Graded series need not determine one uniquely sharp category boundary.
H007	Threshold structure	Philosophical / institutional	A qualitative or classified state may change at a threshold.
H008b	Continuity	Philosophical / mathematical	Continuity is one historically important strengthening, not a universal requirement.
H009	Regime transition	Philosophical / physical	Graded variation can coexist with qualitative transition.
H010	Incrementality / limited step size	Evolutionary	Small successive changes are one form of gradual transformation.
H013	Relative timescale	Physical	Pace is meaningful relative to another characteristic timescale.
H014	Lag	Physical / social	Related processes can be temporally offset.
H015	Accumulation	Geological	Large change can arise through persistence and compounding.
H016	Scale dependence	Physical / metrological	Apparent graduality can change with temporal, spatial or observational scale.
H017	Heterogeneous development	Evolutionary	Components can develop at different rates rather than in lockstep.
H019	Stasis	Evolutionary	Extended intervals can exhibit little or no net change.
H020	Punctuation	Evolutionary / geological	Change can be concentrated in episodes separated by stasis.
H021	Normative staging	Normative-political	A reform can be deliberately introduced through stages.
H022	Institutional qualification	Institutional	Standing can be attained through graded requirements or stages.
H023	Authorization threshold	Institutional	Permission can activate once a defined condition is reached.
H024	Asynchrony	Physical / social	Related processes can be out of phase or non-coincident.
H025	Diffusion	Social	Population adoption can spread progressively through discrete unit events.
H026	Distributed realization	Social	Realization can be spread across units, domains or locations.
H027	Rate variability	Geological / evolutionary	The rate of change can vary across phases.
H028	Selected tempo	Normative-political	Actors can deliberately choose or constrain pace.
H029	Incremental decision procedure	Decision-theoretic	Decision-making can proceed through repeated limited adjustments.

The table preserves stable IDs for provenance and revision tracking, but the entries should not be read as homogeneous components of one definition. Some describe path form, some concern observation or classification, some concern social distribution, and some are explicitly normative or procedural. That heterogeneity is one reason the later catalog architecture uses multiple facets rather than treating the historical register as a flat taxonomy.

2.8 Interpretive guardrails for “Gradual AGI”

The historical reconstruction earns its place in the paper most directly by preventing familiar connotations from becoming unstated premises. The selected lineages support several distinctions that must remain open until the endogenous corpus is examined:

Guardrail	Historical reason
Gradual ≠ slow	Historical uses include degree, staging, continuity and classification as well as pace. Slowness is one possible association, not the lexical or conceptual minimum.
Gradual ≠ smooth	Punctuation and regime transition show that local discontinuity can coexist with an extended process.
Gradual ≠ continuous	Mathematical continuity is a strong formal property; staged and discrete processes can also be gradual in ordinary and institutional senses.
Gradual ≠ small-stepped	Incrementality is historically important but separable from duration, distribution, threshold and rate.
Graduality ≠ political delay	Normative gradualism can denote strategic staging or postponement; descriptive gradualness does not entail an endorsement of delay.
Aggregate graduality ≠ micro-level continuity	Diffusion can be smooth at population scale while consisting of discrete individual adoptions.

These are not conclusions about the Gradual AGI series. They are constraints on how the historical record may be used when reading it. Section 3 asks the endogenous question independently: which of these associations, if any, the published series actually adopts, rejects, transforms or leaves merely compatible.

Individuation guardrail. One further reception risk is not itself a historical conclusion. Readers may arrive with AGI already individuated as one capability threshold or one arrival event. The endogenous reconstruction treats that transformation boundary as a separate analytical choice. A reader who fixes the narrower boundary may therefore disagree with the series before the gradualness predicate is ever applied.

The historical reconstruction supplies two things carried forward: an initial representational scaffold and reception-control guardrails around inherited meanings of gradual. It does not determine what Gradual AGI means, predict that the endogenous corpus should reproduce the historical register, or make historical frequency a measure of theoretical importance.

Fine-grained historical coding becomes load-bearing only where it affects the instrument or a specific interpretive claim. Section 3 therefore treats the eight published installments as the primary corpus and permits the endogenous object to revise the historical instrument when that instrument fails.

3. Graduality Already Present in Gradual AGI

Section 2 used historical material to build an initial representational scaffold and to identify interpretive guardrails around the word gradual. This section turns to the paper’s primary object: what the eight published Gradual AGI installments themselves have meant by gradual, graduality, and the structures repeatedly associated with those terms.

The reconstruction is endogenous. Historical candidates do not determine admission into the present register, resemblance to a historical conception does not count as evidence of inheritance, and no convergence with the historical reference register is expected. History matters here only where its coordinate vocabulary is used as an instrument or where a later interpretive claim requires historical context. The reconstruction therefore proceeds as follows:

published corpus → raw extraction → normalization → source-deployment tests → conceptual separation tests → candidate definiens

This order matters because the series did not begin with a settled definition that later papers merely instantiated. Paper #1 describes AGI as a gradual civilizational process rather than a sudden breakthrough or single system, emerging as epistemic Depth and social Width develop over time. The synchronization papers shift attention to the relation between technological possibility and realized civilizational assimilation. The Optimization framework then gives graduality an explicitly different role, defining it as iterative refinement through observation, learning and feedback rather than as a speed claim. The Governance framework later supplies a series-wide definition of AGI as an expanding region on a partial order rather than a dated event.

The object of this section is therefore not to impose consistency retrospectively. It is to determine what structures survive when the published uses are reconstructed together, which structures explain graduality without constituting it, and which minimal definitions remain after those distinctions are tested.

3.1 Extraction and normalization

Each installment from #1 through #8 was read for explicit or implicit structures bearing on graduality. Extraction preceded normalization. Raw records were allowed to duplicate one another, disagree across papers, and include objects that later proved to be mechanisms, representations, assumptions, observables or boundary conditions rather than features.

The raw ledger contains, among other structures, process rather than event, epistemic gradients, uneven development, cumulative insight, distributed widening, growth versus spread, technical versus societal emergence, potential–realization separation, mismatched clocks, lag, reciprocal adaptation, Ceiling–Floor separation, heterogeneous adoption thresholds, non-constant synchronization, punctuated transitions, multidimensionality, repeated revision, observational dependence, non-stationarity, partial ordering, exposure-conditioned realization and measurement-induced changes in representation.

Normalization asks a different question. A recurring structure is not admitted as a feature merely because it appears often or helps explain something else. Its classification follows the role it plays in the source.

Endogenous Admission / Source-Role Rule. Retain a normalized structure when the source treats its presence or absence as constitutive, descriptive, explanatory, operational, epistemic, or boundary-setting for gradual, graduality, or Gradual AGI. Exclude a mere antecedent mechanism when its only source role is to cause or mediate another admitted structure and the source does not itself treat that mechanism as part of its graduality-relevant account. Admission does not imply centrality, necessity, universal explanatory use, or membership in a definiens.

This distinction proved necessary almost immediately. Infrastructure-mediated delay, threshold heterogeneity, absorption capacity, metastability and exposure all bear strongly on how gradual realization occurs, but their principal source role is explanatory or conditioning. They therefore do not become features merely because they can generate gradual outcomes.

Accumulation supplies the converse example. G009 was initially demoted during normalization on the ground that accumulation looked like a mechanism. Re-reading its source role reversed that judgment. Paper #1 names Cumulative Insight as a dimension of epistemic Depth itself: contributions increase Depth when they persist, interact and compound rather than disappear as isolated achievements. Accumulation therefore belongs in the endogenous register because the source treats it as descriptive of the state being characterized, not merely as an antecedent cause.

Stable identifiers are preserved through such revisions. An ID denotes the genealogy of a normalized record, not an immutable first classification.

3.2 The endogenous graduality-relevant register

Normalization produced nine stable endogenous records. Later tests show that they do not occupy the same analytical level, so the register should not be read as nine peer candidate components of a definition.

ID	Canonical label	Current direct signature	Provenance-indexed role(s)	Current standing
G001	Extended / non-pointlike realization	—	Phenomenal	Explanandum
G002	Potential–realization separation	{S, RS}	Structural/Generative	PositiveFeature
G003	Relative-rate / temporal asymmetry	{T, RT}	Phenomenal	PositiveFeature
G004	Heterogeneous realization	{S, RS}	Structural/Generative	PositiveFeature
G005	Iterative revisability	{M}	Phenomenal in #3; Principled in #5	PositiveFeature
G006	Local discontinuity compatible with global graduality	—	Compatibility/Boundary	Constraint
G007	Multidimensionality / partial order	{S, RS}	Structural/Generative	PositiveFeature
G008	Observational partiality	{RO}	Epistemic	PositiveFeature
G009	Accumulation / compounding	{M}	Phenomenal	PositiveFeature

The signature column reports the current direct-signature audit, not every coordinate visible in a source passage. G001 and G006 receive no positive feature signature: G001 is now the phenomenal explanandum candidate, whose coordinate location is stated separately in §3.10.3; G006 is a compatibility constraint rather than a positive feature. Under G-R5, T is reserved for rate or rate-like temporal quantity; temporal extension, succession, iteration and synchronic heterogeneity do not qualify by themselves. T is therefore absent from G001, G004 and G005.

The table also uses the controlled metadata vocabulary formalized in §4. Standing is entry-version metadata; Role is provenance-indexed. Earlier descriptive labels such as dynamic, compositional, Generator and Qualifier are not retained as controlled values. This metadata normalization creates or deletes no G-ID.

The appropriate interpretation is therefore an endogenous graduality-relevant register. Membership records that the series treats a structure as constituting, generating, qualifying, operationalizing or revealing graduality. Membership alone does not establish that the structure belongs in the eventual definiens. The table reports the current post-pilot entry versions: independently challenged assignments are either adjudicated and versioned or retained with their unresolved validation status, as reported in §6.

3.2.1 Three diagnostic records

The full nine-entry register is carried in the table above and documented at provenance level in Appendix A. Three records require discussion here because their treatment changes the subsequent analysis rather than merely documenting the catalog.

G001 — Extended / non-pointlike realization. G001 was first normalized as Processuality: AGI unfolds through time rather than being exhausted by a single arrival event. Sufficiency testing showed that formulation was too broad. Mere persistence can describe stasis, and an arbitrarily long delay can precede one instantaneous transition. G001 was therefore narrowed to Extended / non-pointlike realization. After G-R3 it is treated as the phenomenal explanandum rather than a peer positive feature.

G005 — Iterative revisability. The same normalized iterative structure performs different work in different sources. In Synchronization it is Phenomenal: Gradual AGI is characterized as reciprocal iterative adaptation. In Optimization it is Principled: graduality concerns information-responsive refinement while meaningful capacity for later revision is preserved. G005 therefore demonstrates why Role must be provenance-indexed rather than intrinsic to an entry.

G007 — Multidimensionality / partial order. G007 rejects automatic scalarization and permits vector-valued or partially ordered states with incomparability. It matters twice. Methodologically, it cannot be represented faithfully by the original Degree/Mode instrument and therefore forces the State Structure coordinate introduced in §3.3. Substantively, the Governance argument uses the partial-order structure to individuate AGI realization as expansion of a region rather than one local threshold transition.

The remaining six records require no separate derivation here: their current definitions, provenance and revision histories are carried in Appendix A and enter the analytical tests below through the G-register table.

The register is versioned. G-R1 through G-R7 preserve changes in admission, Standing, labeling, coordinate rules and post-pilot coding rather than overwriting earlier states. Appendix A.8.3 carries the complete endogenous revision ledger. The main text discusses only revisions that alter an argument or analytical instrument below.

3.3 Instrument failure and repair

The endogenous register was not merely coded with the instrument inherited from §2; it tested that instrument. Three kinds of failure matter to the main argument. First, G007 exposed a missing distinction between state-space structure, occupied degree and transition mode. Second, direct coordinate content had to be separated from effects on observation or representation, and generic Relation had to be typed. Third, Tempo had to be restricted to genuine rate-like content. Post-pilot disagreement subsequently sharpened the newest coordinate boundary. Full historical and endogenous revision ledgers are retained in Appendix A.8.

3.3.1 State Structure: the object changes the instrument

The history-derived scaffold initially contained five coordinates: Degree D, Mode M, Tempo T, Magnitude Δ and Relation R. That coordinate system failed when applied to G007. A multidimensional or partially ordered state cannot be represented faithfully as Degree alone, because Degree presupposes an already specified structure within which a position can be located. Nor is multidimensionality a transition Mode: a vector-valued or partially ordered state can exist at one time without saying anything about the path through it. G007 therefore exposed a scalar assumption in the five-axis instrument, and State Structure S was added post hoc.

S : (𝒳, ≼, representation structure)

D : X_t ∈ 𝒳

M : γ : t ↦ X(t) ∈ 𝒳

State Structure specifies the admissible space and its ordering; Degree specifies an occupied position in that already-specified space; Mode specifies a path through it. Scalar versus vector and total versus partial ordering therefore belong to S; occupied value belongs to D; staged, continuous or punctuated transition belongs to M.

Methodological result. An endogenous object could not be represented faithfully by the inherited instrument. The instrument was revised rather than the object forced into the existing taxonomy.

3.3.2 Signature, modulation and typed relations

The State Structure repair exposed two additional coding problems. First, some entries appeared to carry coordinates only because they changed how an underlying quantity was observed, resolved or classified. Direct Signature and Modulation are therefore separated:

Sig(E_i) = coordinates directly asserted or constrained by E_i

Mod(E_i) = coordinates whose apparent value, classification or resolution E_i alters

Second, generic Relation R conflated structurally different objects. It is therefore decomposed into:

R_S = structural relation;  R_T = temporal relation;  R_O = observational relation

These distinctions remain because they separate kinds of structure used by the endogenous analysis, not because historical and endogenous relation frequencies are compared. Because the historical register supplied the original instrument, these rule changes were propagated to it; Appendix A.8.2 preserves H-R1 through H-R5 and their validation status.

3.3.3 Tempo tightening

The inherited instrument also over-read temporal extension as rate. The current rule reserves T for a rate or rate-like temporal quantity:

T = rate or rate-like temporal quantity

Mere duration, succession, iteration or synchronic heterogeneity is insufficient. Applying this rule removes T from G001, G004 and G005; only G003 directly carries Tempo:

T_G = 1/9

The repair matters substantively because rate remains prominent in Synchronization and CFS while failing to become a generic property of the endogenous feature register. Theoretical prominence is therefore not the same as semantic or coordinate ubiquity. Because the Tempo rule originated in a shared instrument, the revision was also propagated to the historical register; Appendix A.8.2 records that audit.

3.3.4 Post-pilot endogenous repairs

The independent pilot produced two Direct-Signature disagreements concentrated on the newest coordinate boundary. Both survived source-level review as overcoding in the first-coder register.

G004: {S, D, R_S} → {S, R_S}

G-R6 removes Degree from G004. Heterogeneous realization requires structured cross-unit difference but no particular occupied degree.

G008: {S, R_O} → {R_O}

G-R7 removes State Structure from G008. Observational partiality is constituted by the relation between object and representation; a particular state-space structure is not required.

These are adjudicated dispositions on comparable pilot targets. The repaired rules have not themselves been independently rerun. G-R7 also matters downstream: it dissolves the former exact correspondence between State-Structure signatures and failed DH1 cases, as §3.5.1 records.

3.4 The magnitude result

A targeted audit was required because paper #1 describes Depth as advancing “incrementally.” Taken alone, that wording could suggest that Gradual AGI requires small steps.

The rest of the published record does not support that interpretation. Paper #1 defines cumulative insight through persistence, interaction and compounding rather than through a bound on increment magnitude. Paper #5 distinguishes gradual drift from punctuated shifts and allows both. Paper #7 is decisive: its account permits discontinuous capability jumps and says gradualness arises from progressive piecewise expansion rather than from smooth capability growth.

Δ ∉ Sig(G_i)   for every current positive endogenous feature record G_i

Magnitude result. No current positive endogenous feature signature requires individual changes to have bounded or small magnitude.

The result does not say that increments never occur. Nor does it erase the earlier use of incrementally. That wording remains part of the provenance history as an early local formulation subsequently generalized by later installments.

permitted ≠ required

Small increments are permitted. They are not constitutive.

3.5 Logical Independence Test

The first reduction attempt treated the endogenous records as if they were peer candidates and asked whether G001 might be a common root. The pre-specified hypothesis was:

DH1:  ∀i ∈ {2,…,9},  G_i ⇒ G001

The test used minimal logical instantiation: can G_i, under its normalized minimum, be coherently instantiated while G001 is absent? A single coherent counterexample defeats the arrow.

Under the then-current normalization, DH1 failed. Potential–realization separation can be represented at one time. Heterogeneous realization can exist in one cross-section. A multidimensional or partially ordered state can exist synchronically. An observation can fail to identify an underlying state in one measurement.

G002 ⇏ G001;   G004 ⇏ G001;   G007 ⇏ G001;   G008 ⇏ G001

At that stage G003, G005, G009 and the then-positive formulation of G006 were treated as necessarily temporal. The exact entailment graph from that initial run is not carried forward unchanged. G-R2 subsequently reclassified G006 as a compatibility constraint rather than a positive feature; G-R3 reclassified G001 from peer feature to explanandum; and G-R4 narrowed G001 from generic Processuality to extended realization. The first LIT is therefore retained principally as a diagnostic result in the genealogy of the instrument, not as a final dependency graph over the revised register.

3.5.1 Why the apparent State Structure correlation does not survive

An earlier version of the register made the four failed DH1 cases coincide exactly with the four signatures then carrying S. That correspondence initially looked like independent confirmation. The post-pilot repair G-R7 removes S from G008, so the exact coincidence no longer exists. The failure is informative: the apparent validation depended partly on an over-broad signature assignment.

State Structure does not logically imply synchronic instantiability. A partially ordered state space might itself be required to expand monotonically through time. The equivalence below is false in general:

S ⇔ synchronically instantiable

Three of the four failed DH1 cases remain state-structural under the current register: G002, G004 and G007. G008 does not. Its failure of DH1 follows from the fact that observational partiality can be instantiated synchronically through an observation relation, not from State Structure. The LIT therefore cannot be treated as a coordinate-validation test.

The earlier State Structure / DH1 coincidence is retained only as a normalization-sensitive artifact in the revision history, not as independent convergent validation.

3.5.2 What the LIT does and does not establish

The LIT tests identity, minimal entailment and irreducibility. It does not establish how a source actually uses a structure in an argument for gradualness.

That distinction becomes decisive. A potential–realization decomposition may be logically instantiable at one moment while being used in the corpus only as part of a temporally extended assimilation argument. A second dependency test is therefore required.

3.6 From feature identity to deployment role

The LIT also exposed a broader ontological problem. The endogenous register was initially treated too much like a flat set of features.

G002 can structure the state space on which realization occurs. G007 can determine the ordering properties of that state space. G008 concerns what can be inferred from observation. None need itself describe the phenomenal form of change in the same sense as accumulation or relative-rate asymmetry.

The correct response is not to require temporality for admission into G. Admission follows source role, not a demand that every endogenous structure describe change through time. The historical reconstruction had already made visible several relevant synchronic structures, but that observation is contextual rather than a requirement of register symmetry.

Instead the reconstruction distinguishes feature identity from analytical role. The principal roles are:

• Phenomenal — describes what the gradual phenomenon or transition is like.
• Structural / generative — supplies a structure that generates, conditions or makes gradual realization possible.
• Principled — specifies how an actor or system should proceed.
• Epistemic — specifies how graduality is observed, represented, measured or identified.
• Compatibility / boundary — states what graduality permits, does not require, or where an account ceases to apply.

Role(G_i, p)

Role is provenance-indexed, with p denoting a source occurrence. G005 proves why: the same normalized iterative structure is phenomenal in paper #3 and principled in paper #5.

This result also reveals a distinction that the corpus itself had already published but that the earlier catalog architecture had not given enough weight.

3.7 Two definienda: gradual and graduality

The series uses the same lexical root for two analytically distinct objects.

The first is phenomenal gradualness: a property of how AGI emerges or becomes realized. The second is principled graduality: a property of how an agent or civilizational optimization process should remain adaptive under uncertainty.

Paper #1 gives the first use its foundational form by treating AGI as a gradual civilizational process rather than a sudden event. The CFS and synchronization papers continue that use by describing Gradual AGI through civilizational assimilation and relations among technological and social clocks. Paper #5 then supplies the second use explicitly: graduality is an optimization principle, not a measure of speed; its content is iterative refinement through observation, learning and feedback.

Grad_P ≠ Grad_Pr

This is not merely a lexical observation. The two concepts have different subjects and different justificatory structures.

Phenomenal: How is a transformation realized?

Principled: How should action remain revisable under uncertainty?

Whether the two share a deeper primitive is addressed in §5 as a program-level synthesis rather than assumed here.

3.8 Corpus-Deployment Test

Minimal logical instantiation cannot determine how a published argument uses a structure. The Corpus-Deployment Test therefore asks a source-relative question: in a passage that explicitly defines or derives gradualness, which structures are load-bearing for the conclusion actually stated?

The original CDT passage set was fixed before its first-coder ablation judgments, but the independent pilot exposed two defects in that instrument: G001 had been offered as a candidate generator even after becoming the explanandum, and several targets were paraphrased rather than pinned to the narrowest exact source span. CDT v2 is therefore explicitly post-pilot. Its exact source spans and revised routing rule are versioned before the new judgments reported below. A passage qualifies only if it explicitly defines gradual, graduality or Gradual AGI; states why AGI is gradual or derives gradualness from named structures; or narrows the concept by contrast with threshold arrival, slowness, smoothness or another candidate interpretation. Mere occurrence of the word gradual remains insufficient.

Corpus-Deployment Load-Bearing Rule. A structure is coded load-bearing only where removing it causes the source argument, in the form actually stated, to lose its conclusion. Mere co-occurrence in the same passage, model or installment does not establish dependence.

After the independent pilot exposed defects in the original candidate routing and passage grain, CDT v2 identifies four especially clear phenomenal argument forms from exact published source spans. G001 is routed as the explanandum rather than a candidate generator, and G006 is reported separately as a compatibility constraint:

Paper #2:  G002 + G003  ↝  gradual societal emergence   [G006 exercised as a compatibility constraint]

Paper #3:  G002 + G005_phen  ↝  synchronizing co-evolution

Paper #4:  G002 + G003  ↝  assimilation-rate gradualness

Paper #7:  G007  ↝  piecewise domain gradualness   [G006 exercised as a compatibility constraint]

These are source-level deployment relations, not logical implications. They should also not be read as four independent theories. The series is cumulative. A later passage may omit an earlier structure while the paper containing it still inherits that structure elsewhere. Paper #7, for example, retains potential–realization separation as a foundational property of its governed object even though the specific paragraph deriving gradualness from partial ordering does not invoke it.

The route topology must be recomputed after the CDT v2 repair rather than inherited from the original table. Across the four passages there are now three distinct positive-premise configurations: {G002, G003} in papers #2 and #4, {G002, G005} in paper #3, and {G007} in paper #7. No positive generator is common to all four passages. Argument-level equifinality therefore survives, but the earlier appearance of four distinct route configurations does not. The result remains FirstCoder because the repaired candidate set and exact source spans have not themselves been independently rerun.

Route₂ ∩ Route₃ ∩ Route₄ ∩ Route₇ = ∅    (CDT v2; FirstCoder)

three positive-premise configurations across four passages; no universal positive generator

CDT v2 remains a post-pilot FirstCoder result. The independent return invalidated the old route table as a reliability target but did not independently code the repaired candidate set and source spans. Section 6 reports that distinction explicitly.

Individuation Motivation Check (IMC). Holding I fixed during N_D testing prevents a counterexample from changing the transformation boundary while removing a candidate feature, but it does not establish that the source’s choice of I was independent of the desired verdict. IMC v2 therefore treats scope selection and extension embedding as separate dimensions rather than one categorical judgment.

ScopeMotivation asks: if the source expected the eventual phenomenal result to be point-exhaustion rather than gradual realization, would its substantive problem still require the same transformation scope I_p? Code Independent, NotIndependent or Unresolved. ExtensionEmbedding asks whether the definition of I_p itself entails or substantially encodes realization across more than one temporal location. Code Embedded, NotEmbedded or Unresolved.

The separation is intentional. Independent motivation does not imply that extension is absent from the object definition, and extension embedding does not by itself show that the scope was selected to win the gradualness dispute.

Source	Transformation scope Ip	ScopeMotivation	ExtensionEmbedding
#1 Epistemic Extension (diagnostic)	Depth/Width co-emergence; Width as persistent social presence	Unresolved	Embedded
#2 Abundant Resources	Societal spread and realization of intelligence	Independent	NotEmbedded
#3 Synchronization	Coupled technological-civilizational realization through transformative adoption	Independent	NotEmbedded
#4 Ceiling, Floor, and Slope	Civilizational assimilation process linking Ceiling and Floor	Independent	Embedded
#7 Governance	Expansion of realized AGI across a multidimensional partial order	Independent	Embedded

IMC v2 is more cautious than v1. Paper #1 remains the warning case: ScopeMotivation is Unresolved and Width embeds extension. Papers #4 and #7 are Independent/Embedded; papers #2 and #3 are Independent/NotEmbedded. Evidentially, #2 and #3 therefore provide the cleanest source-level support in which non-point-exhaustion is not already built into the transformation boundary. #4 and #7 remain valid CDT deployment routes, but their Embedded scopes prevent them from serving as independent corroboration of non-point-exhaustion. IMC grades the evidential use of a route; it does not invalidate the route analysis. All five assignments remain FirstCoder.

3.9 G001 as explanandum rather than peer feature

The CDT changes the ontology of the G register. The principal phenomenal arguments repeatedly terminate in approximately the same claim: AGI realization is extended, progressive or piecewise rather than exhausted by one arrival event. That is the structure G001 names.

G001 therefore does not behave like a sibling generator. It functions as the phenomenal explanandum that other records help explain. This revision is logged as G-R3.

{G002, G003, G004, G005, G007, G009} ↝ Y,   with Y ≈ G001

G006 constrains acceptable descriptions and G008 qualifies observation of the object. The strongest conclusion at this stage is therefore not that one hidden generator underlies the series. It is that the phenomenal explanandum is more stable than any one explanation for it. Successive installments enrich the explanans while retaining the point-event rejection.

3.10 Reduction of phenomenal gradualness

The reduction that follows concerns membership rather than individuation: it asks what makes an already-fixed transformation gradual, not which transformation is under discussion. Because the two questions are easily conflated, one concrete illustration is worth stating first. Consider one history. An AI system crosses a major medical-reasoning threshold in a single release. If the question is when the system acquired that capability, the relevant transformation is the capability crossing, and it may be sudden. If the question is when that capability became realized across medicine, the transformation includes adoption across specialties, hospitals, regulators, insurers, and patients, and the same underlying history may be gradual. If the question concerns wider civilizational assimilation, the object is broader again. These are not three verdicts about one fixed transformation; they are three differently individuated transformations.

That freedom is not unlimited. A transformation boundary should be fixed by the research or policy question rather than widened after the answer is visible merely to obtain a gradual verdict. And if the chosen scope already defines the transformation as extended across domains, institutions, or time, that built-in extension cannot then be offered as independent evidence that realization is extended. IMC v2 (§3.8) operationalizes these two source-level checks as ScopeMotivation and ExtensionEmbedding. An Embedded scope can still be a legitimate analytical object; it simply carries less independent corroborative force for non-point-exhaustion.

The original primitive test combined Generality, Upstreamness, Irreducibility and Necessity. That remains appropriate for explanatory primitives. Once G001 was reclassified as explanandum, however, Upstreamness became category-inappropriate for a candidate definition. A definiens need not causally or explanatorily precede the phenomenon it defines.

GUNI_E = Generality + Upstreamness + Irreducibility + Necessity

GINS_D = Generality + Irreducibility + Necessity + Sufficiency

GINS_D is explicitly post hoc. It was introduced after the preceding analysis showed that the original test conflated explanans and definiendum. Its results are reported as instrument-revised reduction results, not as independently pre-specified confirmation.

3.10.1 Corpus-constrained definitional reduction

The necessity test requires a methodological commitment. If necessity were tested against the definiens that the reduction is supposed to discover, the procedure would be circular. The separating cases instead ask whether competent use of the predicate gradual can coherently apply when a candidate structure is absent, or fail when a proposed condition is present.

Corpus-Constrained Definitional Reduction. The published corpus supplies the candidate structures, their source roles, and the contrast class against which phenomenal gradualness is repeatedly asserted, especially the single exhaustive arrival event. Necessity and sufficiency are then adjudicated by conceptual separation: competent use of the predicate determines whether a candidate belongs to the meaning of gradual rather than merely to the series’ explanation of its subject matter.

A further condition is required for definitional testing. Competent application of gradual presupposes some answer to what counts as the transformation under consideration. Let I denote that individuation rule. Definitional necessity tests therefore hold I fixed: a candidate structure fails N_D when it can be removed while the same individuated transformation remains a competent instance of gradual realization. A counterexample may not manufacture a negative verdict by changing the transformation boundary at the same time that it removes the candidate feature.

What is the transformation?  ≠  Given that transformation, is its realization gradual?

Holding I fixed addresses circularity inside the N_D counterexample. It does not establish that I itself was chosen independently of the desired gradualness verdict. IMC v2 in §3.8 addresses that separate source-level risk.

Two necessity questions must consequently be separated:

N_C(G_i): Is G_i necessary within the corpus’s explanation of why AGI is gradual?

N_D(G_i | I): Holding I fixed, is G_i necessary for competent application of the predicate gradual?

CDT addresses N_C locally within source arguments. GINS_D uses N_D. Neither supersedes the other.

3.10.2 N_C and N_D produce different verdicts

The distinction is empirically and conceptually consequential. Across the four selected CDT v2 source passages, the current load-bearing counts are shown below. The N_D judgments hold the source-relative individuation rule I fixed.

Candidate	NC: load-bearing in four selected CDT passages	ND: necessary to gradual?
G002 Potential–realization separation	3/4	No
G003 Relative-rate / temporal asymmetry	2/4	No
G004 Heterogeneous realization	0/4	No
G005 Iterative revisability	1/4	No
G007 Multidimensionality / partial order	1/4	No
G009 Accumulation / compounding	0/4 as an isolated load-bearing premise	No

The N_C frequencies are CDT v2 FirstCoder descriptive results and are not treated as validated graph centrality. Even so, the contrast is informative: potential–realization separation remains load-bearing in three of the four selected source passages while remaining non-constitutive of what gradual means.

The N_D counterexamples are conceptual separation tests conditional on fixed individuation. A transformation can be gradual without a typed potential-realization decomposition; a single process can be gradual without comparison to another clock; a homogeneous object can change gradually; a deterministic non-learning process can realize change gradually; scalar gradual change is coherent; and successive states may replace rather than compound earlier states. None of these counterexamples changes the transformation boundary while removing the tested candidate.

No G002–G009 structure is universally necessary to phenomenal gradualness as such.

This is not a claim that those structures are unimportant to Gradual AGI as a substantive theory. It is a claim about semantic constitution rather than explanatory centrality.

The G003 verdict is correspondingly limited to phenomenal membership. Its revised 2/4 CDT incidence records source-level explanatory use, not definitional necessity. Relative-rate asymmetry remains central to synchronization and CFS regime characterization without becoming part of DFN001; §5 returns to that distinction when synthesizing the full sense of Gradual AGI across the series.

G009 illustrates the distinction between catalog admission and reduction survival. Its 0/4 N_C score and negative N_D verdict do not remove it from the register: G009 remains because the Source-Role Rule identifies Cumulative Insight as a feature in paper #1. The later tests show only that accumulation does not become a universal generator or constitutive condition across the corpus.

3.10.3 G-R4: from Processuality to extended realization

As anticipated in §3.2.1, the sufficiency stage is what forced G-R4. The earlier label Processuality admitted both stasis and delayed singleton transitions. The counterexamples state the reason for that refinement:

X(t) = c  ⇒  temporal persistence without transformation

C_{X | I} = {t*}  ⇒  a transformation exhausted at one realization point

Let I determine which realized changes belong to transformation X, and let C_{X | I} denote the ordered temporal support of those changes. The minimal phenomenal condition is:

Grad_P(X | I) ⇔ ∃ t₁,t₂ ∈ C_{X | I} : t₁ < t₂

equivalently, |C_{X | I}| ≥ 2

This formulation exposes rather than solves the individuation problem. If I groups a distributed history into one transformation, the predicate is evaluated over that larger object. If I individuates its local components separately, some of those components may be point-exhaustive. DFN001 therefore supplies a phenomenal membership condition only conditional on the transformation boundary.

Individuation Dependence. Phenomenal gradualness is thin conditional on I. The complete classification of a history as gradual depends jointly on individuation and membership.

3.10.4 The definiens is deliberately contrastive

The earned phenomenal membership condition is thin. Its primary content is the denial of one rival picture once transformation scope is fixed: the relevant transformation is not exhausted by one arrival event.

The condition does not determine whether the path is slow, continuous, smooth, scalar, cumulative, homogeneous or composed of small increments. Almost all of the richer machinery developed by the series concerns how non-pointlike realization is individuated, generated, structured, observed or governed rather than adding further universal conditions to the phenomenal predicate itself.

The appropriate description is therefore a minimal contrastive membership schema. Its thinness is a result of reduction, not an assumption with which the reconstruction began.

3.11 Reduction of principled graduality

Principled graduality follows a different analytical route. Paper #5 defines graduality directly as an adaptive process of iterative refinement through observation, learning and feedback, explicitly separating it from a speed claim. The same paper explains that successive observations should inform later decisions without requiring irreversible commitments made under incomplete knowledge.

The definition can therefore be reduced to two constitutive requirements.

3.11.1 Information-responsive iteration

The decision or policy process must admit successive updating:

π_t+1 = Φ(π_t, Y_t)

where Y_t denotes information becoming available after π_t, and Φ is genuinely responsive to that information. A predetermined sequence that would execute identically regardless of Y_t is temporally staged but does not satisfy the published concept. Iteration and information-responsiveness therefore form one constitutive condition rather than two independent clauses.

3.11.2 Preserved revisability

Earlier action must leave meaningful capacity for later alteration. Let R(π_t) denote the substantively feasible revisions remaining after policy state π_t. Then, over the portion of the process where adaptive updating remains relevant:

R(π_t) ≠ ∅

This does not mean every consequence must be reversible. It means the procedure does not exhaust its meaningful future options by construction before later information can matter.

Grad_Pr(Π) = InformationResponsiveIteration(Π) ∧ PreservedRevisability(Π)

Speed again does not enter. A procedure may update quickly and remain gradual in this principled sense. A deliberately slow but irrevocably precommitted procedure need not.

3.12 Constitution, justification and the is–ought firewall

The conditions that justify principled graduality must be kept separate from its constitution.

Paper #5 gives the justification explicitly. If the optimization landscape is nonconvex, if operational understanding of the long-term objective evolves, if stakeholders hold heterogeneous local goals, and if civilization operates under persistent uncertainty, irreversible one-shot optimization becomes difficult to justify. Iterative refinement can incorporate information as it arrives.

These conditions are not themselves parts of the definiens. They are justificatory antecedents. The same source then states that the argument is conditional. A bounded, stable and well-characterized problem may offer little for continued iteration to improve. Stakeholder convergence can remove much of the coordination benefit. High delay cost can outweigh the informational benefit of waiting.

Grad_P(X | I) ⇏ Grad_Pr(Π)

The fact that AGI may arrive gradually does not establish that actors ought to proceed gradually. Instead:

{nonconvexity, evolving understanding, heterogeneous goals, uncertainty, delay conditions} ↝ Grad_Pr

The normative conclusion therefore depends on decision conditions, not on inference from a phenomenal description. This separation is stronger than a methodological warning imposed by the present paper. It is already present in the published source argument.

Section 3 leaves three outputs. First, phenomenal gradualness reduces to an individuation-relative membership schema: once a source-relative rule I fixes the relevant transformation X, gradualness denies that its realization is exhausted by one event. The corpus does not make slowness, smoothness, continuity, bounded increments, heterogeneity or multidimensionality universal constituents of that predicate.

Second, principled graduality is a distinct definiendum requiring information-responsive iteration and preserved revisability. Its justification depends on decision conditions rather than on the phenomenal claim.

Third, CDT v2 retains three positive-premise configurations across four selected source passages, with no positive generator common to all four; that repaired topology remains FirstCoder. Multidimensionality is not necessary to the phenomenal predicate once I is fixed, but in the Governance argument G007 is load-bearing partly because it helps fix I by individuating AGI as expansion across a multidimensional region. The results separate semantic constitution, individuation and explanatory centrality and expose why the inherited seven-layer scheme cannot survive as one taxonomy. Section 4 formalizes the resulting architecture, §5 interprets its series-level meaning, and §6 reports the validation record.

4. From Layers to Facets: The Catalog Architecture

Section 3 leaves two outputs that should not be collapsed. The first is a thin pair of definienda. The second is a much richer apparatus of features, constraints, explanatory structures, provenance-specific roles, coordinate assignments and revision history. This section specifies the architecture needed to keep those outputs distinct. It also makes explicit an asymmetry clarified in §§2–3: the Gradual AGI corpus is the primary object of reconstruction, while the historical register supplies the initial representational scaffold and selected interpretive context. The catalog can store both registers without treating them as peer populations that are expected to converge.

4.1 Why the layer architecture does not survive reconstruction

The inquiry began with a seven-layer conception of graduality: Constitutive, Relational, Descriptive, Epistemic, Normative, Distributive and Procedural. Sections 2 and 3 show that these distinctions were relevant but not commensurable. Constitutive content concerns what belongs in a definiens. Descriptive and Epistemic identify analytical roles. Distributive and much of Procedural content identify sites at which a structure operates. Relational content concerns coordinate structure and, in the endogenous corpus, the characterization of gradual regimes through rates, clocks and lag. Normative content separates again: part belongs to a principled definiendum, while the conditions justifying that principle remain antecedent conditions rather than constituents.

The resulting correction is therefore not another layer taxonomy. It is a faceted catalog in which different questions are represented by different fields:

normalized object ≠ provenance Role ≠ Locus ≠ coordinate reach ≠ definiens

The repeated corrections in §3 instantiate the same general problem. Axis was separated from feature; State Structure from Degree and Mode; Direct Signature from Modulation; feature identity from mechanism; Role from Locus; membership from characterization; and constitution from justification. The seven-layer scheme flattened these distinctions into one apparent hierarchy. The catalog architecture instead preserves them as facets whose logical types remain explicit.

This is also why the eventual definiens is not another catalog field. The catalog retains the multidimensional apparatus accumulated across the series; the definiens is obtained only after reduction over that apparatus.

Facet Decomposition Finding. The original seven-layer scheme does not survive reconstruction as a taxonomy of one logical type. Its subject matter survives, but decomposes across distinct analytical facets: normalized catalog object, provenance-indexed Role, Locus, coordinate reach, Standing, reduction to a definiens, and justificatory conditions. These facets cannot be collapsed into one hierarchy without losing distinctions used in admission, interpretation, testing or reduction.

Individuation is not introduced here as an additional catalog facet. The revised phenomenal analysis distinguishes transformation individuation from predicate membership, but the present corpus establishes individuation principally as a source-level analytical operation. In the Governance derivation, G007 helps fix transformation scope through the expanding partial-order region; that function is presently recoverable from provenance, source span and analytical-test records. A dedicated Individuation field would require evidence that it preserves an additional non-reconstructible distinction across the catalog.

The individuation result reinforces the same general lesson: theoretical work performed by a structure need not coincide with the lexical constitution of the predicate it helps apply.

Register-Asymmetry Rule. H and G may share a catalog schema without sharing an inferential role. No cross-register frequency, parity or divergence claim is retained merely because the schema makes it computable. A cross-register view must be tied to an explicit instrument question, interpretive guardrail or antecedent question; otherwise it is descriptive metadata rather than a substantive result.

4.2 Faceted, versioned architecture

The body of the paper needs only the architecture’s commitments; Appendix B carries the field-by-field operational definitions. The catalog separates stable identities from versions so that a change in definition, Standing, source grain, coding rule or analytical test does not silently overwrite the object on which an earlier result depended.

Five object types are sufficient. Entry versions store normalized identity, definition, Standing, Direct Signature and Modulation. Provenance records attach a version to an exact source occurrence and carry Role, Locus, evidence and validation state. AnalyticalTest objects store frozen inputs, rules and verdicts for LIT, GINS_D, CDT and IMC. Definienda are outputs of reduction rather than catalog fields. Revision records preserve changes and their triggers.

Field Commitment Rule. A distinction warrants an independent field only when it can vary independently of existing fields and is used by an analytical operation that would otherwise lose information. That rule is why Role, Locus and Standing remain separate. G005 can retain one normalized identity while taking different source Roles; G002 and G007 can share structural signatures while occupying different Loci; and G001/G006 require Standing to distinguish Explanandum and Constraint from positive-feature records with empty signatures.

Individuation is not added as a catalog field. In the present corpus it is a source-level operation recoverable from provenance and analytical-test records. IMC v2 is therefore a versioned AnalyticalTest over source transformation scopes, not an Entry facet.

The same discipline governs revision and validation. A changed target begins a new version; it does not inherit independent coding from its predecessor. Derived views become stale when a load-bearing input changes and must be regenerated. Validation states remain categorical histories—FirstCoder, IndependentlyCoded and Adjudicated—rather than points on a single reliability scale.

The architecture can therefore be represented compactly:

Sources → Versioned Entries + Provenance → Faceted Catalog → Versioned Tests → Definienda

and, when an input changes:

Revision → VersionMismatch → StaleFlag → Re-audit → ViewRegeneration

The Validation-Inheritance Rule follows directly: a derived claim must preserve the material validation limitations of the inputs on which it depends. This is why the post-pilot G004/G008 repairs, the redesigned CDT v2 and the newly revised IMC v2 cannot be promoted by reference to coding performed on earlier target versions.

The resulting architecture is deliberately asymmetric across registers. H and G can share a schema without becoming peer comparison populations. H supplied the initial coordinate scaffold and reception-control context; G is the primary endogenous object. Cross-register aggregates are retained only when they answer an explicit instrument, antecedent or interpretive question. Appendix A preserves the revision ledgers and derived metadata; Appendix B freezes the coding and retest rules.

5. What “Gradual AGI” Means Across the Series

The preceding sections now support a simpler question than the historical-endogenous comparison used in earlier drafts: what does the phrase Gradual AGI mean when the eight published installments are read together? The answer is not recovered by asking whether the endogenous register resembles the historical one. The Gradual AGI series is the primary object. History supplied an initial vocabulary with which to describe it and remains useful for guarding against imported connotations, but the meaning reconstructed here is endogenous to the series.

Across the eight installments, gradual and graduality do not perform one invariant job. The earliest papers use gradual primarily to reject a singular arrival event and to describe development distributed across epistemic depth, social presence and civilizational adoption. The synchronization papers then make potential, realization, relative rate and lag explicit. The Optimization framework gives graduality a second, principled use concerned with iterative revision under uncertainty. The Governance framework subsequently states the phenomenal/principled distinction directly and adds a partial-order account under which local capability jumps remain compatible with globally extended realization. The final governance companion adds an epistemic caution: the representation by which a governing process is observed can change without the underlying object changing in the same way.

The resulting architecture is therefore not a thick definition assembled by adding every later concept to every earlier one. It is better described as a thin phenomenal minimum, a richer apparatus for characterizing and explaining how realization unfolds, and a separate principle governing how actors proceed when conditions remain uncertain and revisable.

thin phenomenal minimum + rich characterization apparatus + distinct principled graduality

5.1 Reading the phrase from inside the series

The series did not begin from a settled definiens. Its uses of graduality were progressively made more explicit as different problems came into view. The Series navigation table in §1 gives the compact reader map; the chronology here is the fuller analytical view used by the reconstruction. That chronology matters because later precision should not be projected backward as if every distinction had been present in paper #1. The catalog instead treats each installment as adding, separating or operationalizing a piece of the apparatus.

Installment	What the source adds	Work performed in the accumulated meaning
#1 Epistemic Extension	Rejects AGI as a sudden breakthrough, single system or moment. Introduces Depth and Width, uneven development, persistence and cumulative insight.	Phenomenal starting point: extended civilizational realization; accumulation and recurrence become salient.
#2 Abundant Resources	Separates cognitive emergence from societal emergence and distinguishes growth of intelligence from its spread through infrastructure and society.	Makes capability versus realization and distributed adoption harder to collapse.
#3 Synchronization	Distinguishes Ceiling, Floor and Slope; treats transformative adoption as reciprocal adaptation across successive cycles.	Adds potential-realization separation, relative clocks and iterative co-development.
#4 Ceiling, Floor, and Slope	Formalizes civilizational assimilation rate, threshold-gated coupling, heterogeneous adoption, residual lag and multiple dynamical regimes.	Turns rate, lag and synchronization into regime-characterization machinery rather than a minimum definition.
#5 Optimization framework	Defines graduality as iterative refinement through observation, learning and feedback while preserving adaptability; explicitly rejects slowness as the point.	Introduces principled graduality.
#6 Optimization tests	Operationalizes heterogeneous, multi-agent and non-stationary optimization and treats revision under falsification as part of the apparatus.	Shows how principled graduality behaves under formal and empirical contact without making it the phenomenal definition.
#7 Governance framework	States a series-wide AGI definition using a multidimensional partial order and explicitly distinguishes gradual as phenomenon from graduality as principle.	Clarifies that local jumps are compatible with extended, piecewise realization.
#8 Governance measurement	Shows that observables can be non-monotone and that measurement, revision transparency and observation infrastructure alter what can be inferred.	Adds an epistemic layer around the already-reconstructed phenomenon and principle.

This chronology explains why several features recur without becoming synonyms. Potential-realization separation is not the same claim as relative-rate asymmetry; heterogeneous realization is not the same as multidimensionality; iterative revisability is not the same as extended realization; and observational partiality does not itself make a process gradual. The phrase acquires its full sense through the interaction of these distinctions, not through their collapse into one list of necessary conditions.

5.2 The phenomenal meaning: individuation first, membership second

The strongest common phenomenal commitment is contrastive. Paper #1 rejects AGI as a sudden breakthrough or single moment and instead tracks an epistemic and civilizational transformation that develops over time. Paper #7 later sharpens the same contrast by allowing local capability jumps while individuating AGI realization as progressive expansion across domains.

That chronology exposes two analytical operations that the earlier reconstruction had compressed into one. Before asking whether a transformation is gradual, an account must specify what counts as the transformation. Let I denote that individuation rule. Once I fixes X, the phenomenal membership condition is:

Grad_P(X | I) ⇔ ∃ t₁,t₂ ∈ C_{X | I} : t₁ < t₂

The predicate itself remains deliberately permissive. It asks only whether the realization of the individuated transformation is exhausted by one event. But the resulting classification is sensitive to I. A coarse individuation can group domain-by-domain changes into one extended transformation; a finer individuation can treat individual domain transitions as separate transformations, some of which may be point-exhaustive.

thin phenomenal predicate ≠ trivial phenomenal classification

The semantic predicate does not require slowness, smoothness, continuity, small increments or homogeneous change. But deciding what object receives that predicate can require substantial theory.

The Governance framework makes this especially visible. Its multidimensional partial order does not become part of the lexical meaning of gradual. Instead, it helps individuate the relevant transformation as expansion of a realized region across dimensions. Local jumps can then occur inside that larger transformation without exhausting it.

That distinction would be vacuous if the series simply chose transformation boundaries because they were extended. IMC v2 therefore separates the source problem behind the boundary from the boundary’s own temporal content. The four CDT-v2 scopes are Independent on ScopeMotivation; #4 and #7 are also Embedded, while #2 and #3 are NotEmbedded. Paper #1 remains Unresolved on motivation and Embedded on extension. The later individuation result is therefore not licensed by treating independent motivation as equivalent to a verdict-free object definition.

5.3 The apparatus around the phenomenal minimum

A thin minimum does not make the surrounding theory thin. Most of what distinguishes the Gradual AGI program appears not in the membership condition for the word gradual but in the apparatus used to explain, characterize, observe and govern gradual realization. That distinction resolves an apparent tension in the series: rate, synchronization, heterogeneity and partial order can be central theoretical commitments even when none is required for every competent use of the phenomenal predicate.

Four clusters organize that apparatus.

Structural separation. The series repeatedly distinguishes possibility from realization. The Ceiling marks frontier capability or potential; the Floor marks durable civilizational realization. The governance papers preserve the same type distinction between capability potential and dated, located outcomes. This prevents a benchmark result from being treated as though its social realization had already occurred, and prevents the absence of observed realization from proving the absence of potential.

potential ≠ realization

Dynamical characterization. Once potential and realization are separated, the question becomes relational: how quickly and under what conditions does one become the other? The synchronization and CFS papers answer with relative rates, lag, threshold-gated coupling and multiple convergence regimes. Paper #4 explicitly reframes Gradual AGI as a civilizational assimilation-rate problem, but that does not make a particular rate part of DFN001. Rate characterizes which gradual regime obtains; it does not determine phenomenal membership once I is fixed.

membership ≠ characterization

Distributed realization. The series also resists treating civilization as one unit occupying one state. Capabilities, institutions, professions and populations can realize AI at different times and to different extents. Heterogeneous adoption can therefore generate a gradual aggregate even when local units change discretely. The same point appears at several scales: epistemic contributions recur unevenly across domains; social adoption spreads through infrastructure and institutions; governance acts at multiple points of purchase; and the partial-order framework permits domain-by-domain expansion rather than one globally scalar crossing.

State structure and ordering. Papers #5-#7 make multidimensionality explicit. Where no defensible scalar aggregation rule exists, states or trajectories may be only partially ordered. This does not itself constitute gradualness: a partially ordered state can exist synchronically. Its importance is instead architectural. It changes what it means to say that AGI has ‘advanced’ and blocks the assumption that one universal line can identify one arrival moment. In the Governance argument, this structure also performs individuation work: it determines that the relevant object is region expansion across the partially ordered space rather than any one local threshold transition. This interpretive function is not introduced as a new catalog Role or Locus; it is a source-level consequence of how G007 structures the argument.

Epistemic mediation. The later papers add another distinction: the state of the world and its observable representation are not identical. Scale, measurement, revision transparency and observation infrastructure can change what appears in the record. The governance measurement paper’s non-monotone observables make the point concrete: a count can fall while specificity or stringency rises. The catalog therefore retains observational partiality as part of the full apparatus even though observation is not a constituent of phenomenal gradualness.

Programmatic aspect	Representative endogenous structures	Question answered
Phenomenal membership	Extended / non-pointlike realization	Does the transformation count as gradual at all?
Structural	Potential-realization separation; multidimensional / partial-order state structure	What kinds of states and relations make realization intelligible?
Dynamical	Relative rate, lag, synchronization, regime change	Which gradual regime obtains and how does realization follow capability?
Distributive	Heterogeneous realization across domains, institutions and populations	Where and across whom does realization occur?
Epistemic	Observational partiality, scale, measurement and representation	What can be inferred from the available record?

Note: These synthesis labels are descriptive programmatic aspects, not controlled catalog Role, Locus, Standing, or coordinate values.

This is the principal sense in which Gradual AGI is richer than the thin phenomenal definition. The phrase names a research program about extended realization whose central questions concern the gap between potential and realization, the relative clocks governing that gap, the heterogeneous distribution of adoption, the structure of the state space, and the limits of observation. Post-pilot adjudication changes two coordinate assignments without changing that architecture: G004 loses Degree but remains a state-structural relation across heterogeneous units, while G008 loses State Structure and remains an observational relation. The repaired CDT v2 also no longer treats G004 as load-bearing in the four selected source passages; that is a claim about argument dependency, not about whether heterogeneous realization belongs in the catalog or in the programmatic meaning summarized here.

5.4 Principled graduality: a second use of the same root

The Optimization framework introduces a second use that must not be folded into the phenomenal one. There graduality is explicitly defined as an optimization principle, not a measure of speed. Successive observations should be able to change later decisions, and earlier decisions should not exhaust meaningful future options before later information can matter.

The reduction in §3 expresses that source commitment as two jointly necessary conditions:

Let Π = {π_t} denote the decision or policy process, with π_t its state at time t.

Grad_Pr(Π) = InformationResponsiveIteration(Π) ∧ PreservedRevisability(Π)

π_t+1 = Φ(π_t, Y_t)

R(π_t) ≠ ∅

The first condition excludes a merely pre-scripted sequence. A policy that unfolds in stages but would execute identically regardless of new information is iterative only in a weak temporal sense. The second excludes a process whose early choices close every meaningful revision path even though nominal iteration continues. Revisability here is not reversibility: some consequences can be irreversible while the decision procedure still preserves substantively different future choices.

This principled branch is justified on separate, conditional grounds. Paper #5 motivates it where objectives are heterogeneous, the optimization landscape may be non-stationary or non-convex, understanding evolves, and uncertainty persists. Those conditions explain why revisable iteration may be preferable to one-shot commitment; they are not extra constituents of the definiens.

constitution ≠ justification

The two uses of graduality therefore share a lexical root but not a logical type. A phenomenally gradual AGI process can unfold under a rigid policy that never revises. A highly revisable decision procedure can govern preparation for an event whose realization is itself discrete. The attempted master unification by ‘anti-point-exhaustion’ is therefore only a family resemblance.

Grad_P(X | I) ⇏ Grad_Pr(Π)

The Governance framework already states this firewall in substantive terms: gradual as a phenomenon concerns how AGI arrives, while graduality as a principle concerns how to act given uncertainty around that arrival. Post-pilot provenance repair makes the Optimization side more precise without changing the principle: the source contains a process-level definition of iterative refinement and a narrower decision-level consequence in which later observations inform future decisions while irreversible commitment is avoided. Both are Principled occurrences. Nothing in the phenomenal claim establishes that slower action is normatively superior.

5.5 Historical guardrails: what the phrase does not mean by default

History is most useful at this stage not as a benchmark to be matched but as reception control. The word gradual carries established associations that a reader can easily import into Gradual AGI. Section 2 shows why those associations should be separated before the endogenous claims are interpreted.

Guardrail for reading Gradual AGI	Why the guardrail matters
Not necessarily slow	Historical graduality includes degree, staging, accumulation, diffusion and classification as well as pace. The series itself makes rate relational and explicitly rejects slowness as the point of principled graduality.
Not necessarily smooth	Punctuation and threshold transitions are historically compatible with longer processes. Paper #7 directly permits local capability jumps inside piecewise global realization.
Not necessarily continuous	Mathematical continuity is a strong path property, not the lexical minimum. The endogenous minimum requires more than one realization location, not a continuous trajectory.
Not necessarily small-stepped	Incrementality is one historical form. The series later permits discontinuous local change and therefore does not impose a universal bound on Δ.
Not equivalent to political gradualism	Historical gradualism can mean staged reform, strategic pacing or delay. Principled graduality instead requires information-responsive iteration and preserved revisability; a slow irrevocable program can fail it.
Not opposed to thresholds	Thresholds can occur within extended realization. The question is whether the relevant transformation is exhausted by one threshold event, not whether thresholds exist.
Not necessarily one capability-threshold transformation	The series increasingly tracks societal realization, synchronization, assimilation or multidimensional region expansion rather than identifying the relevant transformation with one capability crossing. A reader who fixes X as a single threshold event may therefore disagree at the level of individuation before the gradualness predicate is applied.

These guardrails do not require fine-grained historical H-versus-G frequency comparisons. Their function is conceptual and textual: they prevent one familiar sense of the word from silently becoming a necessary condition of the series’ use. Accordingly, the historical modal crosswalk and coordinate frequencies are relegated to Appendix A as descriptive and instrument-genealogy material rather than treated as the main result of this section.

5.6 Antecedents and intellectual location

The catalog also helps calibrate novelty without making novelty its organizing question. Two targeted antecedent checks were retained because the reconstructed apparatus could otherwise make familiar structures look proprietary merely because they have been given a place inside Gradual AGI.

For G007, the relevant formal ingredients are older than the series. Partial ordering and incomparability belong to established order theory, and multidimensional or Pareto-style comparison long predates this application (Hausdorff, 1914; Pareto, 1906). The result is therefore a broader formal antecedent, not a formal innovation claim. What the series contributes at most is the placement of that structure inside a particular account of AGI realization and governance; the targeted search does not establish literature-wide priority for that application.

DFN002 requires a stronger concession. The conjunction of information-responsive adjustment and preserved future flexibility already appears in adaptive-policy theory. Walker, Rahman and Cave (2001) provide an exact conceptual antecedent at the level tested here; experimentalist governance and Dynamic Adaptive Policy Pathways supply closely related recursive and operational forms (Sabel & Zeitlin, 2008; Haasnoot et al., 2013). Lindblom’s successive limited comparisons, learning-by-doing, and real-options traditions supply constituent antecedents without by themselves reproducing the full two-part conjunction (Lindblom, 1959; Walters & Holling, 1990; Arrow & Fisher, 1974; McDonald & Siegel, 1986).

Reconstructed object	Prior location	Classification	Implication
G007: multidimensionality / partial order	Early order theory; multiobjective and Pareto-style ordering	Broader formal antecedent	No formal novelty claim for partial ordering itself.
DFN002: information-responsive iteration + preserved revisability	Walker, Rahman & Cave (2001); related experimentalist and adaptive-pathway frameworks	Exact conceptual antecedent	No conceptual-priority claim for the abstract decision structure.
Incremental decision procedure	Lindblom (1959)	Constituent antecedent	Successive adjustment is close but does not by itself guarantee both information-responsiveness and preserved revisability.
Learning / optionality components	Adaptive management; real-options and irreversibility traditions	Constituent antecedents	Each supplies one side of the conjunction more strongly than the other.

The appropriate conclusion is level-specific:

conceptual antecedent ≠ application identity ≠ series-level contribution

The paper therefore does not need Gradual AGI to have invented the primitives it uses. Its contribution is reconstructive and compositional: identifying how several familiar and unfamiliar structures were assembled across eight installments, separating semantic membership from regime characterization and principled action, and making their provenance and revision history explicit.

5.7 The full sense of “Gradual AGI”

Read across the series, Gradual AGI combines a thin phenomenal membership condition with additional theory that individuates the transformation, characterizes realization, mediates observation and supplies a distinct principle of revisable action.

Programmatic aspect	Meaning in the accumulated series	Catalog location
Phenomenal	Conditional on I, realization of X is not exhausted by one event.	DFN001; G001
Individuation	Source argument fixes what realized changes count as X; scope motivation and extension embedding are tested separately.	Source scope; IMC v2; G007 in #7
Structural / dynamical	Potential-realization separation, partial ordering, relative clocks, lag and synchronization characterize regimes.	G002; G003; G007
Distributive / processual	Realization may differ across domains; accumulation and iteration describe ways extended realization can unfold.	G004; G005; G009
Epistemic	Observed measures or classifications may only partially represent underlying state or change.	G008
Principled	Action is gradual when later information can revise later action and meaningful future options remain open.	DFN002; G005 Optimization provenance
Negative guardrails	The phrase does not by itself mean slow, smooth, continuous, small-stepped, threshold-free, or one capability-threshold transformation.	Historical context + endogenous commitments

These labels are descriptive programmatic aspects, not new controlled Role, Locus, Standing or coordinate values. The synthesis is intentionally asymmetric: the phenomenal predicate is thin, while classification and explanation remain theoretically substantive. Section 6 turns to the reliability and version status of the coded objects supporting the finer claims.

6. Independent Coding and Instrument Reliability

The preceding reconstruction contains two kinds of claims that require different kinds of support. Some are direct textual claims: paper #1 rejects a singular arrival event; paper #5 defines graduality as iterative refinement rather than a speed measure; paper #7 explicitly distinguishes the phenomenon from the principle. Others depend on the catalog instrument: whether a normalized entry directly carries State Structure or Degree, whether a source occurrence is Phenomenal or Structural/Generative, which Locus it immediately occupies, and which structures are load-bearing in a source-level ablation. This section tests the second class.

The pilot produced mixed agreement and exposed three instrument defects: Tempo leakage, compound provenance grain, and G001 misrouting in the original CDT. The response is object-specific adjudication and versioning rather than one manuscript-level coefficient.

same target + disagreement → adjudication

changed target or rule → new version, not retroactive validation

6.1 Validation design and pilot result

Validation attaches to target versions, not to the manuscript as a whole. The model-based blinded pilot received frozen normalized definitions, source material and coding rules without the first-coder assignments or downstream aggregates. Its purpose was assignment reproducibility conditional on the supplied reconstruction, not independent rediscovery of the ontology.

The return was mixed. Historical Direct-Signature exact-set agreement was 12/25 (48.0%). Endogenous exact-set agreement was 7/9 (77.8%); among PositiveFeatures it was 5/7 (71.4%), while positive-feature coordinate cells agreed on 54/56 (96.4%). Provenance Role agreement was 4/6 (66.7%) and Locus agreement 5/6 (83.3%). These numbers describe different target classes and are not collapsed into one coefficient.

A chronology disclosure is necessary. The decision in §§2–5 to treat G as primary and H as an instrument/reference register was recognized after the independent return, whose historical agreement was lower than its endogenous agreement. The reframing is retained because it follows from the research question, not because H performed poorly, but the sequence creates an obvious risk of convenient demotion. This section therefore reports the historical pilot result without softening it and does not recompute agreement after the reframing. The asymmetry was recognized late; the historical reliability failure is a separate fact.

Disagreement exposed G004/G008 overcoding, two Role disputes, the compound G005 provenance target, CDT misrouting, and Tempo leakage. Each case is handled below under the same-target/adjudication versus changed-target/versioning rule.

The resulting rule is simple: same target plus disagreement permits adjudication after both assignments are frozen; changed target or changed rule creates a new version and resets the validation state. Accordingly, the post-adjudication catalog is not reported as 9/9 independent agreement. Pilot V1 remains 7/9 exact-set on endogenous records.

CDT v2 and IMC v2 postdate the pilot and therefore remain FirstCoder; IMC v1 does not validate the repaired two-dimensional v2. Appendix B records the leakage, target-repair, metric and clean-retest rules.

6.2 Targeted endogenous adjudication

Adjudication was restricted to endogenous disagreements that bear directly on what the paper says Gradual AGI means. The published source passages, rather than the packet paraphrases, were used as the adjudicative basis.

Target	First coder	Independent	Disposition	Reason	Current state
G004 Direct Signature	{S, D, RS}	{S, RS}	{S, RS}	G-R6. Heterogeneity survives changes in occupied degree; D was overcoded.	Adjudicated
G008 Direct Signature	{S, RO}	{RO}	{RO}	G-R7. Observational loss is constituted by RO; S is not independently required.	Adjudicated
G005 Role, paper #3	Phenomenal	Structural/Generative	Phenomenal	The source directly says Gradual AGI should be understood as an iterative process of mutual learning.	Adjudicated
G003 Role, paper #4	Phenomenal	Structural/Generative	Phenomenal	The source directly reframes Gradual AGI as a civilizational assimilation-rate problem.	Adjudicated
G007 Locus, paper #7	State	State	State	Exact agreement on the partial-order/state-space occurrence.	IndependentlyCoded
G002 Locus, paper #2	Relation	Relation	Relation	Exact agreement on the potential-realization relation occurrence.	IndependentlyCoded

The directly comparable adjudications divide evenly by facet rather than by coder. Both Signature disagreements were resolved in favor of the independent assignment: G004 loses D and G008 loses S. Both Role disagreements were resolved in favor of the first-coder assignment: the paper #3 G005 occurrence remains Phenomenal and the paper #4 G003 occurrence remains Phenomenal. Adjudication was author-led rather than performed by a third adjudicator. The dispositions were not chosen to balance those outcomes: the Signature cases were decided by the frozen coordinate boundary tests applied to the normalized definitions, whereas the Role cases were decided by the grammatical and theoretical work performed by the exact published source occurrence.

The Optimization G005 Locus is not adjudicated to either Process or Decision as one record. The old item is superseded. At repaired provenance grain, the source contains a Principled/Process definition of iterative refinement and a narrower Principled/Decision consequence in which later observations inform later decisions while premature irreversible commitment is avoided. Those new Locus records are FirstCoder because no independent coder received the split targets.

G001 is handled similarly. The pilot’s State assignment was made on a paraphrase that combined the expanding-region derivation with the later phenomenal definition. The narrowed G001 target is the sentence defining the phenomenon as extended, non-instantaneous and piecewise over time. The current Locus is Process, but the repaired target has not been independently recoded and therefore remains FirstCoder.

6.3 The redesigned Corpus-Deployment Test

The original CDT is preserved as Pilot V1 but not promoted. Once G001 is removed from the candidate-generator set and the source passages are pinned more narrowly, two of the four first-coder routes change. The independent pilot had already supplied the diagnostic pattern: papers #3 and #4 substantially reproduced the original positive-feature routes, while papers #2 and #7 rejected G004 and treated G006 as the relevant compatibility constraint.

Source	Original first-coder route	Independent pilot signal	Current CDT v2
Paper #2	G002 + G004	Pilot: G002 + G003; G006 constraint	CDT v2: G002 + G003; G006 constraint
Paper #3	G002 + G005	G002 + G005	G002 + G005
Paper #4	G002 + G003	G002 + G003	G002 + G003
Paper #7	G007 + G004	Pilot: G007; G006 constraint	CDT v2: G007; G006 constraint

The revised positive-feature incidence is therefore G002 = 3/4, G003 = 2/4, G004 = 0/4, G005 = 1/4, G007 = 1/4 and G009 = 0/4. This changes a derived claim but not the definitional reduction. G004 remains an admitted and theoretically important distributive feature; it simply is not load-bearing in these four selected source passages under CDT v2. No candidate becomes necessary to competent phenomenal gradualness.

The equifinality result survives the redesign, but its form changes. CDT v2 contains three distinct positive-premise configurations across four passages: {G002, G003} in papers #2 and #4, {G002, G005} in paper #3, and {G007} in paper #7. No positive generator is common to all four passages. The intersection of the four route sets is therefore empty, so argument-level equifinality survives. What does not survive is the appearance of four distinct route configurations. This recomputed result remains FirstCoder because CDT v2 has not been independently rerun.

⋂_k Route_k = ∅   (CDT v2; FirstCoder)

CDT v2 is not IndependentlyCoded. The candidate routing and source spans changed after the pilot, so the new judgments are a new FirstCoder analytical-test version. Treating the pilot as though it had validated CDT v2 would violate the version rule the catalog was built to enforce.

6.4 What can and cannot be promoted

Object or claim	Current evidentiary state	Reason
Direct textual phenomenal/principled distinction	DirectSource / textually anchored	Direct source wording anchors the two branches.
G002/G007 Locus separating case	IndependentlyCoded	Relation versus State reproduced while Signature/Role were held constant.
G004 Direct Signature	Adjudicated	G-R6: {S, RS}.
G008 Direct Signature	Adjudicated	G-R7: {RO}.
G005 #3 Role; G003 #4 Role	Adjudicated	Exact source wording adjudicated after comparable disagreement.
G005 Optimization split Loci; G001 narrowed Process locus	FirstCoder, repaired targets	New target grain created after Pilot V1.
CDT v2 routes and NC counts	FirstCoder, new test version	Candidate routing and exact source spans changed after Pilot V1.
IMC v2	FirstCoder, new test version	v1 omnibus verdict was decomposed into ScopeMotivation and ExtensionEmbedding; revised rule has not been independently rerun.
Historical Direct Signatures	Mixed / not promoted register-wide	48% exact-set agreement; disagreement clusters at S/D and RS boundaries.
Historical Tempo	Non-evaluable from Pilot V1	Pilot rule leaked the disputed boundary.

The evidentiary endpoint is mixed. DirectSource and IMC answer different questions: paper #1’s Unresolved/Embedded IMC result limits scope-independent corroboration but does not weaken its textual status as an explicit rejection of singular arrival. IMC grades why and how a source scope supports the phenomenal claim; DirectSource records what the source explicitly says. CDT v2 and IMC v2 remain FirstCoder clean-retest targets.

6.5 Limits of model-based independence

The independent coder was model-based rather than human. Prompt-level blinding establishes that the return did not receive first-coder assignments or derived aggregates; it does not establish independence of training provenance, model family, latent priors or error-generating process. The exercise is therefore described as model-based independent coding, not human inter-coder reliability or statistically independent replication. In that limited sense the exercise tests whether the frozen instrument elicits stable assignments under a new application, not whether a population of human coders would agree.

Agreement also reflects rule tightness and target quality. Tempo leakage is the limiting case: convergence is uninformative when the instruction effectively supplies the intended boundary. Conversely, zero Unresolved responses do not establish reliability; two coders can experience a target as determinate and still assign it differently.

A clean next packet should prioritize the repaired S/D and R_S boundaries where they remain load-bearing, the split G005 provenance targets, G001’s narrowed Process locus, CDT v2 and IMC v2. For IMC v2 the coder must receive frozen source scope and problem context, but not the current motivation or embedding assignments. The same coder who completed Pilot V1 cannot restore blindness to the earlier repaired cases.

The methodological result is correspondingly narrow: object contact can revise the instrument, reader contact can revise the target or coding rule, and neither kind of repair licenses retroactive agreement. Validation follows the current versioned object.

7. Discussion

The reconstruction produces an initially counterintuitive result. The meaning of gradual becomes thinner as the theory around Gradual AGI becomes richer. Across the eight installments, additional distinctions accumulate: potential and realization, relative clocks, lag, heterogeneous adoption, partial ordering, observation, iteration, revisability and governance. Yet reduction does not turn those additions into an increasingly long list of necessary conditions. It does the opposite. The phenomenal minimum stabilizes around one contrast—realization is not exhausted by a single event—while most later structures move outward into explanation, characterization, observation, distribution or action.

That result is not a retreat from the series’ substantive claims. It clarifies their division of labor. A theory can be highly structured without requiring every structure it uses to be part of the lexical meaning of its organizing term. The important question is therefore no longer how many dimensions can be packed into a definition of graduality. It is which structures define membership, which distinguish regimes of gradual realization, which explain why those regimes arise, which mediate observation, and which govern action under uncertainty.

7.1 Thin semantics, individuation and rich theory

The central result is semantic thinning under theoretical enrichment. Conditional on an individuation rule I, phenomenal gradualness requires only that the realization of X not be exhausted by a single event. Rate, smoothness, continuity, scalarity, increment size and homogeneity remain available for regime characterization without becoming universal membership conditions.

That thin predicate does not make classification trivial. Individuation precedes membership: I fixes which realized changes belong to X, and Grad_P(X | I) is then evaluated over that object. A narrow capability-threshold individuation and a broader domain-by-domain realization individuation can therefore produce different verdicts without disagreeing about the conditional predicate itself. Some apparent sudden-versus-gradual disputes are consequently individuation disputes and should be tested at that level before the predicate is treated as contested.

The same move creates a circularity risk. IMC v2 finds papers #2/#3 Independent/NotEmbedded, papers #4/#7 Independent/Embedded, and paper #1 Unresolved/Embedded. Independent motivation therefore does not imply that extension is absent from the object definition. These FirstCoder results grade the evidential force of source-relative individuation without changing DFN001.

G007 illustrates the division of labor. Multidimensionality is not necessary to DFN001 once I is fixed, yet in Governance it helps determine that the relevant transformation is expansion of a realized region across a partial order rather than one local capability crossing. A structure can thus be dispensable to predicate membership while remaining load-bearing for individuation or explanation.

7.2 Many routes, one phenomenal explanandum

CDT v2 sharpens a second feature of the program: the series does not rely on one universal positive generator of gradual realization. The four selected source passages contain three positive-premise configurations:

#2, #4: {G002, G003}     #3: {G002, G005}     #7: {G007}

Route₂ ∩ Route₃ ∩ Route₄ ∩ Route₇ = ∅

Across all four selected source passages the route intersection is empty, so argument-level equifinality remains a valid description of CDT v2. IMC v2 reveals a more informative graded pattern. Only papers #2 and #3 are Independent/NotEmbedded, and Route₂ ∩ Route₃ = {G002}. Within this clean but very small subset (n = 2), potential-realization separation is therefore the only shared positive structure supporting a non-point-exhaustive realization argument without extension already being built into the transformation scope. G002 is also the most recurrent positive premise across the selected CDT v2 source passages, appearing in three of four. This does not make G002 part of the phenomenal definiens: N_D(G002 | I) = No. Nor does n = 2 establish a universal explanatory primitive. It identifies G002 as the strongest presently observed candidate for the series’ non-question-begging explanatory core. The four-passage empty-intersection result is not reproduced by the clean subset, so equifinality remains a topology result over all four selected source passages. Both the route topology and the IMC grading remain FirstCoder.

G007’s load-bearingness admits a more precise reading. The partial-order structure does not add a clause to DFN001; it helps fix the Governance transformation scope as expansion of a realized region rather than one local capability crossing. G007 can therefore fail semantic necessity while remaining load-bearing for individuation. Because the #7 scope is Embedded, that route remains part of the source-deployment topology but does not independently corroborate non-point-exhaustion.

G007 → I_Governance → Grad_P(X | I_Governance)

CDT consequently captures both explanatory and individuation dependence. IMC v2 then determines how much independent corroborative force a route can carry once its transformation scope is inspected.

source-relative individuation + stable conditional predicate + variable explanans

7.3 Phenomenal gradualness and principled graduality

The second definiendum is more than a terminological complication. It reveals that the series eventually asks two distinct questions with the same lexical root.

Phenomenal gradualness asks how a transformation is realized. Principled graduality asks how an actor or system should proceed when information, objectives and feasible choices remain unsettled. The Optimization framework makes the latter use explicit, and the governance framework later states the distinction directly. The catalog therefore resists the temptation to unify the two merely because both involve extension through time.

Grad_P(X | I) ⇏ Grad_Pr(Π)

The principled definiens is:

Grad_Pr(Π) = InformationResponsiveIteration(Π) ∧ PreservedRevisability(Π)

This formulation places the normative weight on learning and option preservation rather than on delay. A rapid sequence of revisable, information-responsive decisions can satisfy the principle. A slow sequence that merely executes a fixed plan or closes every meaningful future option can fail it. The distinction is especially important because political uses of gradualism often carry precisely the opposite connotation: waiting, staging, or postponement can be defended simply because it is gradual. The series’ principled usage does not license that inference.

The separation also blocks an is-ought shortcut. The phenomenal claim that AGI is likely to be realized through an extended process cannot by itself justify slower development, incremental governance or staged deployment. The normative argument depends instead on conditions such as uncertainty, evolving understanding, heterogeneous objectives, nonconvexity and the cost of irreversible commitment. Those conditions can be present even if the phenomenon governed is not gradual, and they can be absent in some parts of a process that is.

constitution ≠ justification

For the research program, this is a productive split. It allows future work to challenge the descriptive thesis and the decision principle independently. A finding that some capability transition is highly discontinuous need not refute principled revisability. A finding that fast irreversible action is optimal in a well-characterized setting need not refute phenomenal gradualness elsewhere.

7.4 The Facet Decomposition Finding

Section 4.1 established the Facet Decomposition Finding: the original seven-layer conception contained relevant distinctions but not distinctions of one logical type. The Discussion-level consequence is broader than bookkeeping. A definiens, a source Role, a Locus, a coordinate property and a justificatory condition cannot be placed on one flat taxonomic level without obscuring how they relate.

definiendum ≠ Role ≠ Locus ≠ coordinate ≠ justificatory condition

The faceted architecture preserves the content while changing its ontology. Constitutive content becomes an output of reduction rather than a peer catalog layer. Relational content is distributed between typed coordinate relations and rate-sensitive regime characterization. Descriptive and Epistemic content become provenance-indexed Roles. Distributive content becomes a Locus. Normative content separates into the principled branch and the conditions that justify it. Procedural content is distributed across Process, Institution, Decision and Intervention loci and the Principled Role.

The individuation result reinforces rather than expands that ontology. The present corpus shows that a structure can help fix transformation scope without becoming part of the phenomenal predicate, but that function is recoverable from source provenance and analytical-test records. The paper therefore does not create an Individuation facet merely because the distinction is theoretically useful.

This matters beyond the present series because conceptual frameworks often accumulate heterogeneous dimensions under one heading. Before treating a multidimensional framework as one taxonomy, the relevant question is whether its dimensions are of one logical type. If they are not, adding layers may create apparent completeness while making reduction and validation harder.

7.5 History, antecedents and novelty

The historical register is most useful as reception control and antecedent location, not as a benchmark population. It blocks inherited assumptions that gradual must mean slow, smooth, continuous, small-stepped or politically gradualist, while also showing that many primitives used by the series have prior conceptual lineages.

That antecedent control narrows the novelty claim. The series need not have invented multidimensionality, partial order, incremental decision, optionality or adaptive learning to make a contribution. Its contribution is reconstructive and compositional: it assembles these structures around a specific distinction between transformation individuation, phenomenal membership, regime characterization and principled action, then makes their provenance and revision history explicit. Structural antecedent, application identity and series-level contribution are different claims and are reported separately.

7.6 Methodological and programmatic implications

The catalog’s methodological contribution is not the final choice of eight coordinates or nine endogenous entries. It is the discipline of allowing the object and an independent reader to change the instrument while preserving the history of those changes. G007 forced State Structure into the scaffold; G-R6/G-R7 repaired endogenous signatures; the pilot exposed target-grain and leakage problems; CDT v2 corrected routing; IMC v2 then corrected an omnibus individuation verdict by separating motivation from extension embedding. Each repair narrows what later claims may inherit.

That discipline also sets the empirical agenda. Future studies of gradual AGI should report two separable decisions: the individuation rule assigning observed changes to one transformation, and the phenomenal verdict conditional on that rule. Where individuation is theoretically substantive, a motivation/embedding check should accompany the membership test rather than being hidden in prose. Rate, heterogeneity, observability and synchronization can then be measured as regime properties without being mistaken for lexical necessities.

The programmatic conclusion is correspondingly modest. Gradual AGI is not one universal mechanism, one speed thesis or one sequence of small increments. It is a research program organized around realized transformation that is not point-exhaustive once the relevant transformation is fixed, together with a richer apparatus for specifying that transformation, explaining its realization and preserving revisability under uncertainty. The present catalog makes those jobs independently contestable.

8. Limitations

The catalog is an auditable conceptual reconstruction, not a universal theory of graduality. Its strongest claims are series-internal: they concern what the eight-paper Gradual AGI corpus requires, permits, distinguishes and progressively adds. Four limitations determine how far those conclusions can be generalized.

8.1 Corpus scope and historical coverage

The endogenous corpus is deliberately bounded. It consists of the eight published Gradual AGI installments because the research question asks what gradual and graduality mean inside that series. The resulting claims should therefore not be read as representative of AGI research generally. A structure can be absent from the series without being absent from the wider literature, and a distinction can be central to this research program without being central to other accounts of AGI.

The historical register has a different limitation. It was selected to expose candidate structures across multiple lineages and to control imported interpretations such as slowness, smoothness, scalarity and small-step necessity; it was not constructed as an exhaustive intellectual history. Its coordinate counts are therefore descriptive metadata, not prevalence estimates. Antecedent searches are also asymmetric: finding a prior structure can defeat a structural-novelty claim more readily than failing to find one can establish novelty. Historical material constrains interpretation and locates antecedents; the phenomenal minimum is reconstructed principally from the endogenous corpus and its reduction tests.

8.2 Coding independence and validation

The study does not provide independent human replication of the catalog. Its independent-coding pilot is model-based. The pilot covered the complete active historical and endogenous Direct-Signature targets together with selected provenance, Corpus-Deployment Test and Locus targets. Validation is assignment-level rather than a blanket property of an entry or manuscript, and the controlled states FirstCoder, IndependentlyCoded and Adjudicated record different procedural histories rather than points on a scalar reliability scale.

Prompt separation establishes that the independent run did not receive first-coder assignments or derived aggregates. It does not establish independence of training provenance, model family, learned examples or error-generating process. Adjudication likewise does not erase the disagreement that made adjudication necessary. The strongest methodological claim is therefore procedural: disagreements, target repairs and validation states are retained, and derived conclusions inherit the material limitations of their load-bearing inputs. Further triangulation with human or cross-family model coders would test a property this design does not reach—error independence across coders—rather than replacing the present instrument-determinacy test.

8.3 Version repair and unreproduced targets

A repaired target is not automatically validated by a judgment on its predecessor. This matters because several late revisions changed entry boundaries, coordinate assignments, candidate routing or provenance grain. G001 moved from peer feature to explanandum and was narrowed to extended realization; G005 Optimization provenance was split into process-definition and decision-consequence records; CDT v2 changed both candidate routing and source spans; G004 lost Degree under G-R6; and G008 lost State Structure under G-R7.

The G-R7 case illustrates why propagation discipline matters. An earlier version of the paper observed an exact correspondence between the four failed DH1 cases and the four candidates whose signatures then carried State Structure. Once G008 lost S, that coincidence disappeared. The appropriate response is not to reinterpret G008 so that the old pattern survives; it is to record the old correspondence as a version-sensitive artifact. The same rule applies to validation. A changed target begins at the validation state warranted by the changed object, rather than inheriting independent agreement from a superseded version. Some repaired assignments and the redesigned CDT therefore remain FirstCoder.

8.4 No domain-general individuation rule

The paper makes transformation individuation explicit but does not solve it generally. DFN001 is conditional on an individuation rule I, and the endogenous corpus supplies that rule source-relatively through the transformation each argument tracks. No domain-general criterion is established for deciding when realized changes belong to the same transformation.

Possible criteria include causal continuity, persistence of an organizing objective, common initiating lineage, functional integration, stakeholder recognition or a shared state transition. Scale and resolution further complicate the choice: what appears as one transformation at one grain can decompose into several at another.

The resulting limitation is therefore narrower than before. The paper does not claim a universal theory of transformation identity. It claims that phenomenal membership can be made thin conditional on explicit individuation, and that disagreements about individuation must not be misreported as disagreements about the predicate itself.

The present motivation check is also limited. IMC v2 covers the four current CDT-v2 routes plus paper #1 as a diagnostic case. It separates independent scope motivation from extension embedding, but both dimensions remain FirstCoder and the five cases do not establish a domain-general individuation criterion. A clean retest packet for CDT v2 and IMC v2 is specified in Appendix B but was not executed for the present submission. The decision is deliberate: this version reports the completed reconstruction with its object-specific validation states rather than treating packet specification, or coding on superseded targets, as validation. CDT v2 and IMC v2 therefore remain auditable FirstCoder results awaiting independent rerun.

9. Conclusion

This paper asked what gradual means across the eight installments of Gradual AGI. The answer is thinner than the theory accumulated around the term, but it is not trivial.

The phenomenal result is conditional on transformation individuation. Let I specify which realized changes belong to transformation X. Then:

Grad_P(X | I) ⇔ ∃ t₁,t₂ ∈ C_{X | I} : t₁ < t₂

Once the transformation is fixed, phenomenal gradualness requires only that its realization not be exhausted by a single event. It does not universally require slowness, smoothness, continuity, monotonicity, scalar progression, homogeneous realization or small increments.

The phenomenal predicate is thin; phenomenal classification is not. Before the predicate can be applied, an account must determine what transformation is being tracked. Different individuation rules can assign the same underlying history differently. The surrounding theory can therefore matter without entering the predicate: it may help determine the boundary, scale or structure of the object to which the predicate applies.

The Governance partial-order argument makes that distinction especially visible. G007 is not necessary to the phenomenal predicate once I is fixed, but it is load-bearing in the selected Governance passage because multidimensional region expansion helps specify what counts there as AGI realization. This suggests that some disagreements commonly framed as gradual versus sudden may partly concern transformation individuation. A capability-centered account and a domain-by-domain realization account can disagree over what constitutes the relevant AGI transition even while accepting the same conditional criterion for whether an already-individuated transformation is gradual.

IMC v2 grades rather than erases the source-level support. Papers #2 and #3 are Independent/NotEmbedded, and their intersection is {G002}; within that clean but small subset (n = 2), potential-realization separation is the only shared positive premise supporting non-point-exhaustion without extension already embedded in the transformation scope. G002 also appears in three of four selected CDT-v2 source passages overall, making it the strongest presently observed candidate for a non-question-begging explanatory core under the current FirstCoder analysis, not a semantically necessary condition. Papers #4 and #7 are Independent/Embedded, so they remain deployment routes but not independent corroboration of non-point-exhaustion. Paper #1 is Unresolved/Embedded, which limits scope-independent support but does not alter its DirectSource status as an explicit rejection of singular arrival.

That result preserves the substantive importance of the wider apparatus. Potential-realization separation, relative clocks, lag, heterogeneous adoption, multidimensional ordering and observational partiality need not be lexical constituents to perform theoretical work. They can explain a regime, characterize it, determine where realization occurs, mediate what is observed, or help individuate the transformation itself. Semantic thinning therefore does not entail theoretical thinning.

The second definiendum remains distinct. Principled graduality concerns action rather than phenomenal realization:

Grad_Pr(Π) = InformationResponsiveIteration(Π) ∧ PreservedRevisability(Π)

Its justification depends on conditions such as uncertainty, evolving knowledge, heterogeneous objectives, nonconvexity and irreversible commitment—not on an inference from the claim that AGI itself is gradual.

The historical register limits inherited readings and locates antecedents rather than supplying a benchmark for the series. The validation exercise likewise limits the strength of finer reconstruction claims: CDT v2 and IMC v2 remain FirstCoder, repaired targets do not inherit validation from superseded versions, and model-based independent coding does not establish independent human replication.

The resulting picture is therefore not one universal mechanism of Gradual AGI. It is a stable conditional phenomenal contrast embedded in a richer, revisable theoretical apparatus. The central distinction is now threefold:

individuation ≠ membership ≠ characterization

alongside the separate distinction:

constitution ≠ justification

The feature catalog makes those divisions explicit while preserving the genealogy of how the series arrived at them.

References

Primary Corpus — Gradual AGI Series

1. W.H.L. & ChatGPT. (2026, January 19). Gradual AGI as Epistemic Extension. Champaign Magazine.

2. W.H.L. & GPT-5.5. (2026, June 11). Gradual AGI as Abundant Resources. Champaign Magazine.

3. W.H.L. & GPT-5.5. (2026, June 29). Gradual AGI as Synchronization for Transformative Adoption. Champaign Magazine.

4. W.H.L. & Claude (Sonnet 5). (2026, July 4). Ceiling, Floor, and Slope: A Falsifiable Dynamical Model of Synchronization for Gradual AGI. Champaign Magazine.

5. W.H.L., Claude Sonnet 5, & GPT-5.5. (2026, July 22). Gradual AGI as Optimization: A Conceptual Framework. Champaign Magazine.

6. W.H.L. & Claude (Sonnet 5, Opus 5). (2026, July 24). Gradual AGI as Optimization: Formal Models and Empirical Tests. Champaign Magazine.

7. W.H.L. & Claude (Opus 5). (2026, August 3). Gradual AGI as Contestation: A Framework for Governance. Champaign Magazine.

8. W.H.L., Claude Opus 5, & GPT-5.6 Sol. (2026, August 11). Gradual AGI as Contestation: Measuring Governance Under Empirical Contact. Champaign Magazine.

Reader-Facing Companion

W.H.L., GPT-5.6 Sol, & Claude Opus 5. (2026, August 17). What “Gradual” Means in Gradual AGI: A Feature Catalog. Champaign Magazine.

Historical and External References

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Appendix A. Catalog, Provenance, Revision, and Derived Views

This appendix carries the versioned records that are intentionally compressed in the main text. It is not a second results section. The endogenous G register is the primary catalog object. The historical H register is retained because it supplied the initial representational vocabulary and because selected historical distinctions remain useful for reception control. Cross-register counts reported here are descriptive metadata only; they are not tests of convergence, divergence, or historical validation of Gradual AGI.

Validation labels refer to particular versioned objects, not to the manuscript as a whole. Where the independent pilot exposed a defective target and the target was subsequently changed, the repaired object does not inherit the validation state of its predecessor.

A.1 Coordinate, standing, and validation legend

Code	Coordinate	Meaning
S	State Structure	Structure, ordering, dimensionality, or representation of the admissible state space.
D	Degree	Occupied level or position inside an already specified state space.
M	Mode	Path or transition form.
T	Tempo	Rate or rate-like temporal quantity.
Δ	Magnitude	Size of an increment or transition.
RS	Structural relation	Relation among levels, units, dimensions, or states.
RT	Temporal relation	Relation among rates, clocks, lags, or trajectories.
RO	Observational relation	Relation between an underlying object and its measurement or representation.

Sig(E) records coordinates directly asserted or constrained by an entry. Mod(E) records coordinates whose apparent value, classification, or resolution is changed without the entry specifying the underlying coordinate itself. Standing is one of PositiveFeature, Constraint, or Explanandum. ValidationState is FirstCoder, IndependentlyCoded, or Adjudicated; DirectSource is used below for claims anchored directly in published wording rather than coder assignment.

A.2 Historical reference register

The 25 active H entries preserve historically attested distinctions selected under the admission rule in §2. Stable IDs are not reused. Retired historical IDs H005, H011, H012 and H018 and the merged H008a remain in the revision genealogy but are not active entries.

ID	Normalized candidate	Primary lineage	Interpretive contribution
H001	Scalarity / gradedness	Lexical / metrological	Degrees can vary without reducing the property to binary presence.
H002	Intermediated / multi-stage succession	Lexical / institutional	A transformation can proceed through intermediary stages.
H003	Resolution / granularity	Metrological	Observed distinctions depend on representational or measurement grain.
H004	Measurement discretization	Metrological	A graded substrate can be represented in discrete bins or steps.
H006	Boundary indeterminacy / vagueness	Philosophical	Graded series need not determine one uniquely sharp category boundary.
H007	Threshold structure	Philosophical / institutional	A qualitative or classified state may change at a threshold.
H008b	Continuity	Philosophical / mathematical	Continuity is one historically important strengthening, not a universal requirement.
H009	Regime transition	Philosophical / physical	Graded variation can coexist with qualitative transition.
H010	Incrementality / limited step size	Evolutionary	Small successive changes are one form of gradual transformation.
H013	Relative timescale	Physical	Pace is meaningful relative to another characteristic timescale.
H014	Lag	Physical / social	Related processes can be temporally offset.
H015	Accumulation	Geological	Large change can arise through persistence and compounding.
H016	Scale dependence	Physical / metrological	Apparent graduality can change with temporal, spatial or observational scale.
H017	Heterogeneous development	Evolutionary	Components can develop at different rates rather than in lockstep.
H019	Stasis	Evolutionary	Extended intervals can exhibit little or no net change.
H020	Punctuation	Evolutionary / geological	Change can be concentrated in episodes separated by stasis.
H021	Normative staging	Normative-political	A reform can be deliberately introduced through stages.
H022	Institutional qualification	Institutional	Standing can be attained through graded requirements or stages.
H023	Authorization threshold	Institutional	Permission can activate once a defined condition is reached.
H024	Asynchrony	Physical / social	Related processes can be out of phase or non-coincident.
H025	Diffusion	Social	Population adoption can spread progressively through discrete unit events.
H026	Distributed realization	Social	Realization can be spread across units, domains or locations.
H027	Rate variability	Geological / evolutionary	The rate of change can vary across phases.
H028	Selected tempo	Normative-political	Actors can deliberately choose or constrain pace.
H029	Incremental decision procedure	Decision-theoretic	Decision-making can proceed through repeated limited adjustments.

A.3 Historical instrument coding and independent-pilot comparison

The table below separates the current first-coder instrument view from the model-based independent pilot. Exact-set Match means the two Direct Signature sets were identical in the raw pilot; Disagree means at least one coordinate differed. The raw historical exact-set result is 12/25 = 48.0%. Tempo agreement is not interpretable as clean reliability evidence because packet v0.1 disclosed the disputed exclusion boundary too explicitly.

ID	Current first-coder Sig	Mod	Independent-pilot Sig	Pilot modal vs DFN001	Raw exact-set
H001	{S}	—	{D, S}	Permitted	Disagree
H002	{M}	—	{M, S}	Required	Disagree
H003	{S}	{D, Δ}	{RO}	Orthogonal	Disagree
H004	{S}	{D, M}	{RO}	Orthogonal	Disagree
H006	{S}	—	{S, RS}	Permitted	Disagree
H007	{S, M}	—	{D, S}	LocallyPermitted	Disagree
H008b	{M}	—	{M}	Permitted	Match
H009	{S, M}	—	{M, S}	LocallyPermitted	Match
H010	{M, Δ}	—	{Δ, M}	Permitted	Match
H013	{T, RT}	—	{RT, T}	Permitted	Match
H014	{RT}	—	{RT}	Orthogonal	Match
H015	{M}	—	{M}	Permitted	Match
H016	{RO}	{D, M, T, Δ}	{RO}	Orthogonal	Match
H017	{S, T, RS}	—	{RT, T}	Permitted	Disagree
H019	{M}	—	{D}	LocallyPermitted	Disagree
H020	{M}	—	{M}	LocallyPermitted	Match
H021	{M}	—	{M}	Permitted	Match
H022	{S, M, RS}	—	{D, S}	Orthogonal	Disagree
H023	{S, RS}	—	{D, S}	Orthogonal	Disagree
H024	{RT}	—	{RT}	Orthogonal	Match
H025	{M, RS}	—	{M}	Permitted	Disagree
H026	{D, RS}	—	{S, RS}	Required	Disagree
H027	{T}	—	{T}	Permitted	Match
H028	{T}	—	{T}	Permitted	Match
H029	{M, Δ}	—	{M}	Permitted	Disagree

Current historical relation typing in the first-coder view is R_S on H017, H022, H023, H025 and H026; R_T on H013, H014 and H024; and R_O on H016. H-R3’s R_S assignments to H022 and H023 are not independently reproduced. H017 remains a live relation-typing disagreement: the first-coder view is structural, while the pilot coded R_T.

The current first-coder Tempo view retains direct T only on H013, H017, H027 and H028. H-R4 removed direct T from Stasis, Punctuation, Diffusion and Distributed realization. H-R5 then removed Degree from H017 while retaining Tempo. These are instrument-maintenance records, not cross-register findings.

A.4 Historical modal crosswalk

The first-coder modal analysis was originally reported in grouped form rather than as a row-by-row modal register. It was subsequently demoted from the main argument because history is not a benchmark population. The grouped first-coder view is preserved here together with the raw independent-pilot assignments that challenged one of its negative conclusions.

Historical form/group	First-coder modal disposition	Reason
Multi-stage succession; nonconstant continuity	Permitted; can be a stronger form	When genuinely instantiated, multiple realization locations are built into one transformation.
Incrementality / limited step size	Permitted, not sufficient alone	One small step may still exhaust the transformation at one realization event.
Stasis	LocallyPermitted	A plateau can occur inside a gradual transformation but cannot constitute the global transformation by itself.
Punctuation; diffusion; heterogeneous development; variable rate	Permitted	These specify path form, distribution, or rate regime beyond the minimum without contradicting DFN001.
Measurement, classification, institutional, and procedural candidates	Orthogonal where the role does not concern phenomenal membership	These concern observation, categorization, qualification, authorization, or action rather than minimum phenomenal membership.
Incompatible admitted H candidates	None identified by the first-coder view	No admitted historical conception was coded as requiring point-exhaustion as the meaning of gradual transformation.

The first-coder ‘no Required historical candidate’ view is not independently reproduced. The pilot coded H002 Multi-stage succession and H026 Distributed realization as Required. Because Required is a necessity claim, the repaired modal instruction makes the entailment direction explicit:

Required(H_i, DFN001 | I) ⇔ (DFN001 | I) ⇒ H_i

No adjudication of H002 or H026 is performed in the main study. The disagreement limits the historical modal crosswalk; it does not alter DFN001, which is reduced from the endogenous corpus.

A.5 Endogenous G catalog

The G register is the primary endogenous catalog reconstructed from the eight published installments. Standing and Direct Signature are properties of the current entry version; Role and Locus are provenance-indexed and can vary across source occurrences.

ID	Canonical label	Normalized definition	Standing	Current Sig	Role(s)	Validation / locus note
G001	Extended / non-pointlike realization	One transformation’s realization is distributed across more than one ordered location/event rather than exhausted by one arrival event.	Explanandum	—	Phenomenal	Primary locus: Process on the narrowed #7 definition; repaired target remains FirstCoder.
G002	Potential–realization separation	Capability possibilities and dated, located realized outcomes are maintained as distinct typed levels joined by a mapping.	PositiveFeature	{S, RS}	Structural/Generative	Relation; independently reproduced in paper #2.
G003	Relative-rate / temporal asymmetry	The relevant structure concerns relative rates or clocks rather than absolute slowness.	PositiveFeature	{T, RT}	Phenomenal	Relation; paper #4 Role adjudicated Phenomenal after pilot disagreement.
G004	Heterogeneous realization	Units, populations, institutions, or domains may occupy different realization states simultaneously.	PositiveFeature	{S, RS}	Structural/Generative	G-R6 adjudicated; Degree removed.
G005	Iterative revisability	A process undergoes repeated adjustment in light of subsequently acquired information; its source role varies by occurrence.	PositiveFeature	{M}	Phenomenal in #3; Principled in #5	Paper #3 Process; #5 split into Principled/Process definition and Principled/Decision consequence.
G006	Local discontinuity compatible with global graduality	Local jumps or punctuations are compatible with globally extended gradual realization; smoothness is not required.	Constraint	—	Compatibility/Boundary	Constraint location reported separately from positive signatures.
G007	Multidimensionality / partial order	The relevant state is multidimensional and may permit incomparability rather than requiring scalar total ordering.	PositiveFeature	{S, RS}	Structural/Generative	State; independently reproduced in paper #7.
G008	Observational partiality	An observable or representation need not identify the underlying theoretical property and may lose distinctions.	PositiveFeature	{RO}	Epistemic	Observation; G-R7 adjudicated; S removed.
G009	Accumulation / compounding	Contributions persist, interact, and compound rather than remaining isolated.	PositiveFeature	{M}	Phenomenal	Retained under Source-Role Rule; principal source paper #1.

A.6 Endogenous genealogy across the eight installments

Installment	Principal G contribution	Source-level contribution to the catalog
#1 Epistemic Extension	G001, G004, G007, G009	Point-event rejection; uneven/domain-specific development; Depth/Width multidimensionality; Cumulative Insight.
#2 Abundant Resources	G002, G003; G006 first compatibility use	Cognitive versus societal emergence; different technological and societal clocks; cognitive discontinuity compatible with gradual societal emergence.
#3 Synchronization	G003, G005	Ceiling/Floor/Slope relation; successive cycles of reciprocal adaptation; Gradual AGI as iterative mutual learning.
#4 Ceiling, Floor, and Slope	G003 formalized; G004; G006; G008 precursor	Assimilation rate, threshold-gated heterogeneous adoption, multiple regimes, measurement-window and population-mixture cautions.
#5 Optimization framework	G005 explicit; G006; G007 generalized	Graduality as iterative refinement under preserved adaptability; drift/punctuation compatibility; non-scalar multidimensional optimization.
#6 Optimization empirical tests	G004, G005, G007 operationalized	Heterogeneous multi-agent optimization; iteration under non-stationarity; scalar-to-tensor and multi-objective structure.
#7 Governance framework	G001, G002, G003, G005, G006, G007	Phenomenal/principled distinction; governed-object potential/realization separation; partial-order derivation; piecewise domain expansion; rate differences.
#8 Governance measurement	G007, G008; G005 revision use	Vector-valued governance profile; observable/latent distinction; measurement-induced representation change; governance by revision.

The genealogy records where a normalized family becomes explicit or materially changes role. It is not an exhaustive occurrence count. Application-only occurrences are recorded separately in §A.7.1 and may enter derived installment views without entering a card’s visible genealogy. Appendix B carries the coding rules by which raw source formulations are normalized into these families.

A.7 Principal provenance Role/Locus records

Prov. ID	Source	Target occurrence	Role	Locus	Current state	Note
P-A	#2 Abundant Resources	G002 / capability vs societal realization	Structural/Generative	Relation	IndependentlyCoded	The distinction joins potential capability to later societal realization.
P-B	#3 Synchronization	G005 / iterative mutual learning	Phenomenal	Process	Adjudicated Role; Process independently reproduced	The source directly says Gradual AGI should be understood as an iterative process of mutual learning.
P-C	#4 Ceiling, Floor, and Slope	G003 / civilizational assimilation rate	Phenomenal	Relation	Adjudicated Role; Relation independently reproduced	The source directly reframes Gradual AGI around the rate at which civilization assimilates capability.
P-D1	#5 Optimization	G005 / iterative refinement definition	Principled	Process	FirstCoder – repaired target	Narrow process-level definition created after the pilot exposed an over-broad combined occurrence.
P-D2	#5 Optimization	G005 / later observations inform decisions	Principled	Decision	FirstCoder – repaired target	Narrow decision-level consequence; does not inherit the combined pilot item’s status.
P-E	#7 Governance	G007 / partial-order state-space derivation	Structural/Generative	State	IndependentlyCoded	Partial ordering and expanding region supply the source’s derivation of gradualness.
P-G001	#7 Governance	G001 / extended, non-instantaneous, piecewise phenomenon	Phenomenal	Process	FirstCoder – repaired target	Pilot State assignment was made on a broader paraphrase mixing the state-space derivation with the phenomenal definition.
P-F	#8 Governance measurement	G008 / vector-valued observable profile	Epistemic	Observation	IndependentlyCoded	The occurrence concerns what the governance record represents and what it fails to identify.

A.7.1 Application-only provenance backplane

These records capture operationalization, reuse, or application of an already-established feature without treating the occurrence as a genealogical change. Reader-facing card trails therefore use Genealogy only, while installment-level derived views use Genealogy plus Applied in. The subtype prevents a later application from being mistaken either for a new feature meaning or for no provenance at all.

Source	Feature	Subtype	Application-only use
#6 Optimization empirical tests	G004	Applied in	Heterogeneous multi-agent optimization operationalizes heterogeneous realization without changing G004’s meaning.
#6 Optimization empirical tests	G005	Applied in	Iteration under non-stationarity and revision under falsification apply iterative revisability under formal and empirical contact.
#6 Optimization empirical tests	G007	Applied in	Scalar-to-tensor and multi-objective structure operationalize the existing multidimensionality feature.
#7 Governance framework	G003	Applied in	Relative-rate differences are carried into the governance account of piecewise realization; this reuses the relative-rates structure without materially changing it.
#8 Governance measurement	G005	Applied in	Governance by revision applies iterative revisability as an ongoing mode of governance.
#8 Governance measurement	G007	Applied in	The vector-valued governance profile applies the existing multidimensionality structure to governance measurement.

Propagation rule — introduced in v0.8. A correction retained only in working metadata does not count as propagated. After any change to a card, provenance record, or technical-basis version, every dependent derived view must be regenerated from the current authoritative backplane and its version stamps updated before the view is treated as current. This rule was made explicit after the G003/#7 application record existed in working metadata while the reproducible backplane remained stale.

A.8 Revision ledgers

Revision-prefix legend: I-R = instrument revision; H-R = historical-register revision; G-R = endogenous G register revision; V-R = validation/target repair; REV-L = Locus-schema revision. Existing identifiers are preserved rather than renamed for cosmetic uniformity.

A.8.1 Instrument revisions

Revision	Change	Trigger	Effect
I-R1	Five-axis historical scaffold → six-axis scaffold	G007 could not be represented faithfully under {D,M,T,Δ,R}; State Structure S was added.	Post-hoc instrument revision.
I-R2	Direct Signature separated from Modulation	H003, H004 and H016 appeared multi-coordinate because they altered observation/representation rather than directly specifying underlying values.	Creates Sig(E) versus Mod(E).
I-R3	Generic R decomposed	Structural, temporal and observational relations were conflated.	RS, RT and RO replace generic Relation as coded distinctions.
I-R4	Tempo rule tightened	Temporal extension, succession, iteration and synchronic heterogeneity had been over-read as rate.	T reserved for rate or rate-like temporal quantity.
REV-L1	State/process Locus split	Static state-space claims and process/trajectory claims could vary independently.	Creates distinct State and Process Locus values.
V-R1	Provenance grain repair	The paper #5 validation item combined a process-level definition with a decision-level consequence.	Split G005 Optimization provenance into P-D1 and P-D2.
V-R2	CDT routing repair	G001 was offered as a candidate generator after becoming the explanandum; source spans were also too paraphrastic.	Creates CDT v2 with exact source spans and G006 routed as a constraint.
I-R5	IMC v1 introduced	Individuation-relative DFN001 exposed scope-selection circularity.	Created one FirstCoder motivation verdict over source-level transformation scopes.
I-R6	IMC v1 → IMC v2	v1 conflated independent motivation with whether the scope itself embeds extension.	Creates separate ScopeMotivation and ExtensionEmbedding dimensions; v1 verdicts are superseded and do not validate v2.
I-R7	Authoritative-backplane regeneration rule	The G003/#7 application record existed in working metadata while the reproducible application-only backplane remained stale.	A dependent derived view is current only after regeneration from the authoritative backplane; version stamps on dependent artifacts must be propagated with the change.

A.8.2 Historical register revisions

Lifecycle note. H005, H011, H012 and H018 are retired historical IDs and H008a is a merged ID. They remain reserved in the genealogy, are not reused, and do not enter current derived views.

Revision	Change	Trigger	Current status
H-R1	H015 Accumulation: {M, Δ} → {M}	Accumulation specifies compositional/process structure, not limited step magnitude.	FirstCoder instrument repair.
H-R2	H003/H004/H016 reassigned under Sig/Mod	Representation effects had been coded as direct coordinate content.	H003 Sig {S}, Mod {D,Δ}; H004 Sig {S}, Mod {D,M}; H016 Sig {RO}, Mod {D,M,T,Δ}.
H-R3	RS added to H022 and H023	Institutional qualification and authorization were read as connecting differentiated levels/states.	Not independently reproduced in Pilot V1.
H-R4	Historical Tempo propagation audit	G-R5 changed the Tempo rule and made inherited H Tempo views stale.	T retained on H013,H017,H027,H028; removed from H019,H020,H025,H026.
H-R5	H017 Degree disambiguation	Rate heterogeneity had been conflated with different attained degree.	D removed; current first-coder view retains {S,T,RS}; relation typing remains unadjudicated after pilot disagreement.

Historical repair detail. H-R4 and H-R5 are retained here rather than in the main argument because they are propagation and disambiguation records generated by revisions to the shared instrument. Their purpose is reproducibility of historical derived views, not a substantive H-versus-G comparison.

A.8.3 Endogenous register revisions

Revision	Change
G-R1	G009 restored from mechanism demotion after application of the Source-Role Rule.
G-R2	G006 relabeled from Non-smooth transition structure to Local discontinuity compatible with global graduality and reclassified as a compatibility constraint.
G-R3	G001 reclassified from peer feature to phenomenal explanandum after the Corpus-Deployment Test.
G-R4	G001 relabeled from Processuality to Extended / non-pointlike realization after sufficiency testing showed mere temporal persistence was too broad.
G-R5	Tempo tightened to rate or rate-like temporal quantity; T removed from G001, G004 and G005.
G-R6	G004 Direct Signature {S,D,RS} → {S,RS}; adjudication removed Degree.
G-R7	G008 Direct Signature {S,RO} → {RO}; adjudication removed State Structure.

A.9 Derived coordinate metadata

These aggregates are retained only so that earlier analyses can be regenerated from versioned inputs. They are not substantive H-versus-G findings. Historical Mode is especially interpretation-sensitive because several distinct temporal forms collapse into M; historical Tempo reliability is non-evaluable from Pilot V1 because of rule leakage. For G, denominators refer to the nine stable G identities, while the numerator counts positive Direct Signature assignments only; Constraint and Explanandum coordinate locations are reported separately where relevant.

Instrument stress note. After rate-like overcoding is removed, several historically distinct temporal forms share Mode M. Historical Mode counts should therefore be treated as mechanically recoverable metadata rather than evidence that those forms are substantively equivalent.

Register	Coordinate	Descriptive value	Version note
Historical H register	S	9/25	H001,H003,H004,H006,H007,H009,H017,H022,H023 in the current first-coder view.
Historical H register	D	1/25	Post H-R5; Degree remains in the current first-coder H026 signature.
Historical H register	M	12/25	Mechanically recoverable first-coder count; substantive Mode-orientation interpretation withheld.
Historical H register	T	4/25	H013,H017,H027,H028 after H-R4; independent reliability non-evaluable under Pilot V1.
Historical H register	Δ	2/25	H010,H029 in the current first-coder view.
Historical H register	RS	5/25	H017,H022,H023,H025,H026 in current first-coder view; not independently reproduced as a complete set.
Historical H register	RT	3/25	H013,H014,H024.
Historical H register	RO	1/25	H016.
Endogenous G register	S	3/9	G002,G004,G007; G-R7 removes S from G008.
Endogenous G register	D	0/9	No current positive endogenous Direct Signature carries Degree.
Endogenous G register	M	2/9	PositiveFeature Direct Signatures only: G005,G009. Separately, CoordinateLocation(G001)=M; G001 is an Explanandum and is not included in this numerator.
Endogenous G register	T	1/9	G003 only under G-R5.
Endogenous G register	Δ	0/9	No current positive endogenous Direct Signature requires bounded or small increments.
Endogenous G register	RS	3/9	G002,G004,G007.
Endogenous G register	RT	1/9	G003.
Endogenous G register	RO	1/9	G008 after G-R7.

The former exact coincidence between failed DH1 cases and S-bearing endogenous signatures is no longer current. G002, G004 and G007 remain S-bearing, while G008 fails DH1 through observational partiality without State Structure. The dissolved correspondence is retained only as an example of a normalization-sensitive derived view.

A.10 Definienda and reduction links

ID	Object	Current definiens	Evidentiary basis	Reduction links
DFN001	Phenomenal gradualness	Given an individuation rule I fixing transformation X, GradP(X | I) iff realization is not exhausted by a single event; formally, ∃ t1<t2 in CX | I.	Direct textual point-event rejection plus endogenous reduction; transformation scope supplied source-relatively.	G001 is the phenomenal explanandum; G006 constrains smoothness; G002,G003,G004,G005,G007,G009 fail universal definitional necessity once I is fixed.
DFN002	Principled graduality	InformationResponsiveIteration(Π) ∧ PreservedRevisability(Π).	Directly anchored in Optimization’s definition and later governance distinction.	G005 supplies the principal constituent provenance; uncertainty, nonconvexity, heterogeneous objectives and evolving understanding justify the principle but are not constituents.

Grad_P(X | I) ⇔ ∃ t₁,t₂ ∈ C_{X | I} : t₁ < t₂

Grad_Pr(Π) = InformationResponsiveIteration(Π) ∧ PreservedRevisability(Π)

Grad_P(X | I) ⇏ Grad_Pr(Π)

A.11 Corpus-Deployment Test version record

CDT v2 uses exact source spans, routes G001 as the explanandum, treats G006 separately as a Compatibility/Boundary constraint, and permits a candidate to be load-bearing through source-level individuation as well as explanation. It remains FirstCoder.

Source	CDT v2 positive set	IMC v2 ScopeMotivation	IMC v2 ExtensionEmbedding
#1 Epistemic Extension (diagnostic only)	–	Unresolved	Embedded
#2 Abundant Resources	{G002,G003}	Independent	NotEmbedded
#3 Synchronization	{G002,G005}	Independent	NotEmbedded
#4 Ceiling, Floor, and Slope	{G002,G003}	Independent	Embedded
#7 Governance	{G007}	Independent	Embedded

IMC v2 is a FirstCoder analytical-test version. Current pairs are #2/#3 Independent/NotEmbedded, #4/#7 Independent/Embedded, and #1 Unresolved/Embedded. Accordingly, only routes #2 and #3 provide non-embedded source-level corroboration; Route₂ ∩ Route₃ = {G002}, so the four-passage empty-intersection result is not independently reproduced by that subset. IMC v1 assignments do not validate v2.

A.12 Antecedent classifications

Catalog object	Prior intellectual location	Classification	Implication for this paper
G007 partial order / incomparability	Hausdorff’s early order-theoretic treatment of partially ordered sets; later order theory, Pareto and multiobjective traditions.	Broader formal antecedent	No formal novelty claim for partial ordering itself. The application to this Gradual AGI architecture is a separate question not resolved by the targeted antecedent check.
DFN002 information-responsive iteration + preserved revisability	Walker, Rahman & Cave (2001), adaptive policymaking under uncertainty.	Exact conceptual antecedent	Conceptual priority for the abstract two-part decision structure is not claimed by this series.
DFN002 related recursive governance form	Sabel & Zeitlin (2008), experimentalist governance.	Closely related / recursive antecedent	Relevant to repeated revision under learning and provisional goals.
DFN002 operational adaptation pathway	Haasnoot et al. (2013), Dynamic Adaptive Policy Pathways.	Closely related / operational antecedent	Operationalizes adaptive pathways and future option preservation.
Information-responsive constituent	Walters & Holling (1990), adaptive management / learning-by-doing.	Constituent antecedent	Strong on learning and updating; does not by itself define the full two-part conjunction.
Revisability / option-value constituent	Arrow & Fisher (1974); McDonald & Siegel (1986), irreversibility and option value.	Constituent antecedent	Strong on preserving option value under uncertainty; does not by itself supply the full iterative-learning structure.
Incremental decision procedure	Lindblom (1959), successive limited comparisons.	Constituent antecedent	Repeated bounded adjustment is close to G005 but does not by itself guarantee information responsiveness plus preserved revisability.

The antecedent classifications are level-specific. A formal antecedent to one ingredient is not an historical graduality counterpart, and an exact conceptual antecedent to DFN002 does not determine whether the series’ application or larger configuration is useful or distinctive.

formal antecedent ≠ historical counterpart ≠ application identity

A.13 Status of appendix views

Object/view	Current status	Interpretive limit
H reference identities and normalized historical descriptions	Current reference register	Primary historical extraction is selective, not an exhaustive intellectual history.
H fine-grained Direct Signatures	Mixed	Raw Pilot V1 exact-set agreement 48%; no register-wide promotion.
H Tempo view	FirstCoder repair; reliability non-evaluable from Pilot V1	Validation rule leakage over-constrained the disputed boundary.
H modal crosswalk	Not independently reproduced as a whole	Pilot assigns Required to H002 and H026.
G identities and Standing	Current endogenous catalog	Seven PositiveFeatures, one Constraint, one Explanandum.
G004/G008 Direct Signatures	Adjudicated	Post-pilot G-R6/G-R7.
G002/G007 Locus separating case	IndependentlyCoded	Relation versus State reproduced under comparable targets.
G005 #3 and G003 #4 Roles	Adjudicated	Both retained as Phenomenal from exact source wording.
G005 split Optimization loci; G001 narrowed Process locus	FirstCoder repaired targets	Created after validation exposed target-grain defects.
CDT v2 route topology and NC counts	FirstCoder new analytical-test version	Candidate routing and exact source spans changed after Pilot V1.
DFN001 / DFN002 direct source distinction	DirectSource plus reduction	Phenomenal/principled distinction is textually explicit in the series.
IMC v2 source-level motivation check	FirstCoder new analytical-test version	IMC v2 pair assignments are FirstCoder: #2/#3 Independent-NotEmbedded; #4/#7 Independent-Embedded; #1 diagnostic Unresolved-Embedded. Not independently rerun.

Appendix B supplies the coding definitions, boundary rules, validation packet design, raw disagreement protocol, and adjudication rules used to generate these records.

Appendix B. Coding Definitions, Boundary Rules, and Validation Protocol

This appendix freezes the operational rules used to construct, code, reduce, and validate the catalog reported in §§2–6 and Appendix A. Its purpose is reproducibility rather than theoretical exposition. The rules are version-sensitive: where the main study records a revision, the later rule governs current objects while the earlier rule remains part of the revision history.

The protocol distinguishes extraction from coding, coding from reduction, and disagreement from target repair. A source passage can be correctly extracted while a normalized entry is badly coded; two coders can disagree on a sound target; and a disagreement can reveal that the target itself was malformed. Those cases receive different treatment.

source extraction ≠ normalized coding ≠ reduction ≠ validation

B.1 Units of analysis and versioned objects

Object type	Definition	Example
Entry	Stable normalized catalog identity with versioned label, definition, Standing, Sig/Mod and revision links.	G004, H017
Provenance	One source occurrence linking an entry version to evidence, Role, Locus and validation state.	P-B, P-D1
AnalyticalTest	A versioned test over pinned inputs with a defined rule and verdict.	DH1, CDT v2, IMC v2
Definiens	A versioned definition produced by reduction rather than stored as a feature field.	DFN001, DFN002
Revision	A logged change to an Entry, Provenance record, test, coding rule or instrument.	G-R7, REV-L1

Stable IDs are not reused. A change to label, definition, Standing, Direct Signature, source grain, test routing, or validation target creates a new version or revision record rather than silently overwriting the old state. Derived views must pin the exact versions they use.

Validation-Inheritance Rule. A derived view inherits the material validation limitations of its load-bearing inputs. Its evidentiary description must preserve any FirstCoder, IndependentlyCoded, Adjudicated, repaired-target, or non-evaluable state that bears on the claim. Validation states are categorical histories, not points on a single ordinal scale.

B.2 Admission, normalization, and source-role rules

Historical and endogenous records enter the catalog by different routes. Historical material is a reference register; endogenous material reconstructs what the Gradual AGI series itself treats as graduality-relevant. The two registers share a representational instrument but not an expectation of convergence.

Rule	Operational statement	Consequence
Historical admission	Retain a candidate when presence/absence discriminates between possible forms of transition or supplies a historically attested distinction needed for the representational scaffold or reception control.	Do not admit a mechanism merely because it can cause gradual change.
Endogenous admission	Retain a normalized structure when the source treats its presence/absence as constitutive, descriptive, explanatory, operational, epistemic, or boundary-setting for gradual / graduality / Gradual AGI.	Source role governs admission; later centrality is a separate question.
Source-Role Rule	Classify feature versus mechanism by the theoretical work performed in the source, not by the intrinsic nature of the object.	A threshold can be a mechanism in one source and a graduality-relevant feature in another.
No silent promotion	Admission does not imply centrality, necessity, universal explanatory use, or membership in the definiens.	G009 is admitted but has 0/4 CDT-v2 incidence and fails definitional necessity.

admission ≠ centrality ≠ necessity ≠ definiens

B.3 Direct Signature and Modulation

Direct Signature records the coordinates a normalized entry directly asserts, constrains, or makes applicable. Do not add a coordinate merely because it can be mathematically derived, because the source unfolds through time, or because one empirical application happens to instantiate it.

Sig(E_i) = coordinates directly asserted or constrained

Mod(E_i) = coordinates whose apparent value/classification/resolution is altered without directly specifying that coordinate

Coordinate	Definition	Primary boundary test
S — State Structure	Structure, ordering, dimensionality, admissible state space, or representation structure.	Ask whether the feature constrains the space/order itself independently of which value is occupied.
D — Degree	Occupied level or position inside an already specified state space.	Ask whether changing occupied level while holding the state-space structure fixed changes whether the feature is instantiated.
M — Mode	Transition or path form: how a process moves through its state space.	Iteration, succession, continuity, punctuation, accumulation and stasis can be Mode claims without being Tempo claims.
T — Tempo	Rate or rate-like temporal quantity.	Requires a rate, rate comparison, or explicit clock quantity; mere duration or temporal extension is insufficient.
Δ — Magnitude	Size of an individual change or increment.	Do not infer Δ from accumulation unless step size itself is asserted.
RS	Structural relation among levels, dimensions, units, or states.	Remove the relation while holding participating objects fixed; code only if the feature collapses.
RT	Temporal relation among rates, clocks, lags, or trajectories.	Use where the relation itself is temporal rather than structural.
RO	Observational relation between an underlying object and its measurement or representation.	Use where the normalized property concerns what an observation preserves, loses, or identifies.

B.3.1 State Structure versus Degree

S and D must not be inferred from each other. S concerns the structure of possible states; D concerns the occupied position inside that structure.

S : structure/order of 𝒳

D : X_t ∈ 𝒳

D-test. Change the occupied level while holding the state-space structure fixed. If the normalized feature remains fully instantiated, D is not direct.

change occupied value; feature survives ⇒ D ∉ Sig(E)

S-test. Hold occupied values constant and alter the admissible ordering, dimensionality, representation, or category structure. If the normalized feature changes because that structure changes, S is direct.

Case	Current coding	Boundary rationale
G004 Heterogeneous realization	{S, D, RS} → {S, RS}	Units can remain heterogeneous at different occupied values. Heterogeneity requires structured cross-unit difference, not any particular degree. G-R6.
G007 Multidimensionality / partial order	{S, RS}	Removing dimensional or order structure destroys the normalized feature; occupied degree is not sufficient.
G008 Observational partiality	{S, RO} → {RO}	The normalized minimum is failure of identification/information preservation in the observation relation. A particular state-space structure is not required. G-R7.

B.3.2 Tempo rule

Tempo is reserved for rate or rate-like temporal quantity. The positive criterion should be applied without enumerating the disputed negative cases in a blinded packet.

T = rate or rate-like temporal quantity

Examples of direct T include an assimilation rate, relative timescale, selected pace, or variable rate. Temporal extension, repeated iteration, synchronic heterogeneity, and the mere fact that two events occur at different times do not by themselves satisfy the positive criterion.

Pilot warning. Validation Packet v0.1 spelled out several nearby negatives in the instruction itself. That made the disputed boundary unusually determinate and renders Tempo reliability non-evaluable from that pilot. A fresh test requires a new blinded coder receiving only the positive rule.

B.3.3 Relation typing

Rule	Operational test
RS test	Holding states/units fixed, remove their structural relation. If the normalized feature survives, do not code RS merely because multiple objects are mentioned.
RT test	Ask whether the relation is specifically among rates, clocks, lags or trajectories. A relation across units is not temporal merely because the source is dynamic.
RO test	Ask whether the claim is about mapping, measurement, resolution, observability, information loss, or identification between object and representation.
Typed relation vs dependency edge	Coordinate relation is part of Sig/Mod. Analytical dependence belongs in LIT/CDT or another test and must not be inferred from RS/RT/RO.

typed coordinate relation ≠ analytical dependency edge

B.4 Analytical Role

Role is provenance-indexed. It asks what theoretical work a particular source occurrence performs, not what kind of object the normalized feature is in the abstract.

Role	Definition	Typical evidence
Phenomenal	Describes what the gradual phenomenon or transition is like.	Direct predicates such as ‘Gradual AGI should be understood as…’ or ‘gradual as used of the phenomenon means…’
Structural/Generative	Supplies structure that generates, conditions, or makes gradual realization possible.	A potential-realization mapping, partial-order structure, or adoption mechanism used as an antecedent explanation.
Principled	Specifies how an actor or system should proceed.	Iterative refinement, learning, feedback, revisability, sequencing of action.
Epistemic	Specifies how graduality is observed, represented, measured, or identified.	Observable/latent distinction, measurement resolution, non-identification.
Compatibility/Boundary	States what graduality permits, does not require, or where the account ceases to apply.	Local jumps permitted; smoothness not required.

B.4.1 Phenomenal versus Structural/Generative

This is the highest-priority Role boundary because the paper distinguishes semantic membership/characterization from explanatory structure. Use the grammatical and theoretical work of the exact occurrence.

Occurrence	Current Role	Decision rationale
Paper #3 / G005	Phenomenal	The source directly says Gradual AGI should be understood as an iterative process of mutual learning. The occurrence characterizes the phenomenon, even though surrounding theory explains synchronization.
Paper #4 / G003	Phenomenal	The source explicitly reframes Gradual AGI as a civilizational assimilation-rate problem. The rate characterizes the phenomenon in this occurrence; it may be structural elsewhere.
Paper #7 / G007	Structural/Generative	The source derives gradualness through multidimensional partial-order structure. The state-space structure supplies the reason for the conclusion.

Do not create a separate Characterizing Role solely because a feature is theoretically important but non-constitutive. Membership versus characterization is handled by Standing, reduction, and the distinction between the definiens and the wider apparatus; Role remains source-occurrence work.

B.5 Locus and provenance grain

Locus is the immediate object or site whose configuration is directly specified, transformed, observed, classified, institutionally assigned, decided, or acted upon. Code the smallest directly asserted site and do not propagate to downstream effects.

Locus	Definition
State	Configuration, representation, or admissible structure at a point, without requiring change.
Process	Trajectory, succession, or transition of one object.
Relation	Direct relation among two or more states, levels, processes, or clocks.
Distribution	Allocation, spread, or heterogeneity across units, populations, domains, or locations.
Observation	Acquisition, resolution, measurement, or representation of evidence.
Classification	Assignment to categories, boundaries, ranks, or orderings.
Institution	Formal arrangement of standing, authority, qualification, roles, or status.
Decision	Selection or revision of an action, policy, or decision rule.
Intervention	Actor-imposed staging, pacing, sequencing, or implementation directed at another object or process.

B.5.1 Provenance-grain rule

One source span should support one immediate Role/Locus operation. If a passage combines a definition with a later consequence operating at another site, split the provenance record before coding.

Narrow occurrence	Immediate operation	Role	Locus
G005 Optimization definition	‘Graduality’ as iterative refinement through observation, learning and feedback.	Principled	Process
G005 Optimization consequence	Successive observations inform future decisions while premature irreversible commitment is avoided.	Principled	Decision
G001 Governance phenomenal definition	Extended, non-instantaneous, piecewise unfolding.	Phenomenal	Process
G007 Governance derivation	Multidimensional partial-order state space and expanding region.	Structural/Generative	State

If a pilot item combined two of these operations, its raw disagreement remains part of the validation record, but the repaired targets begin at FirstCoder unless independently recoded at the new grain.

B.6 Standing and applicability routing

Standing	Meaning	Coding consequence	Example
PositiveFeature	A normalized feature admitted as a positive catalog property.	Code Direct Signature normally.	G002–G005, G007–G009
Constraint	A compatibility or boundary condition rather than a sibling generator.	Positive Direct Signature may be inapplicable; route separately in CDT.	G006
Explanandum	The phenomenal outcome that explanatory routes terminate in.	Do not treat CoordinateLocation as positive Signature and do not include the explanandum in candidate-generator CDT lists.	G001

Standing is an entry-version property. Role is provenance-indexed. The same PositiveFeature can therefore be Phenomenal in one source and Principled in another without changing Standing.

B.7 Modal relation to DFN001

The historical modal crosswalk is a contextual derived view, not a validation benchmark for the endogenous definition. It is conditional on a fixed individuation rule I. Modal coding asks whether a historical structure is necessary or compatible once the transformation to which DFN001 applies has been fixed; coders must not alter I while testing a candidate’s modal relation.

Required(H_i, DFN001 | I) ⇔ (DFN001 | I) ⇒ H_i

Modal code	Definition
Required	Every competent instance of phenomenal gradualness, holding I fixed, requires the historical structure.
Permitted	Compatible with DFN001 under fixed I but not required.
LocallyPermitted	Can occur inside an individuated gradual transformation but cannot by itself constitute the global transformation.
Orthogonal	Primarily concerns observation, classification, institution, decision, or another question rather than phenomenal membership.
Incompatible	Requires a structure that contradicts DFN001 under fixed I.

Do not infer Required from the converse implication. A structure can be sufficient for or strongly associated with gradualness while remaining unnecessary to other competent instances.

H_i ⇒ DFN001 does not establish (DFN001 | I) ⇒ H_i

Operational control: hold individuation fixed during modal and definitional-necessity coding.

B.8 Logical Independence and definitional reduction

The Logical Independence Test asks whether a normalized candidate can be instantiated while the phenomenal explanandum is absent. A single coherent counterexample defeats entailment. It tests identity, minimal entailment and irreducibility, not how often the source uses a feature in an argument.

G_i ⇏ G001 if ∃ coherent case in which G_i is instantiated and G001 is absent

The first DH1 run showed that G002, G004, G007 and G008 can be instantiated synchronically. After G-R7 only the first three remain S-bearing. The former exact S/DH1 correspondence is therefore a version-sensitive artifact, not independent coordinate validation.

Two reduction criteria are kept separate. GUNI_E concerns explanatory candidates: Generality, Upstreamness, Irreducibility and Necessity. GINS_D concerns definitional candidates: Generality, Irreducibility, Necessity and Sufficiency. GINS_D was introduced after G001 exposed the category difference between explanandum and generator.

Individuation control. LIT and N_D counterexamples hold the target transformation’s individuation fixed. A candidate does not fail semantic necessity merely because its removal is accompanied by redefining what counts as the transformation.

membership ≠ characterization

constitution ≠ justification

B.9 Corpus-Deployment Test v2

CDT v2 is source-relative. A passage enters only if it explicitly defines or derives gradualness, states why AGI is gradual, or narrows the concept by contrast with a candidate interpretation. Code a structure load-bearing only where removing it causes the source argument, in the form actually stated, to lose its gradualness conclusion.

Routing rules: exclude G001 from the candidate-generator set because it is the phenomenal explanandum; assess G006 separately as a Compatibility/Boundary constraint; use exact published source spans; and use the transformation scope fixed by that source rather than imposing one individuation across passages. Where a premise fixes the source’s transformation scope, its removal may be load-bearing through loss of individuation.

IMC v2 operates on the same frozen source scope but asks two counterfactual questions. ScopeMotivation: if the source expected point-exhaustion rather than gradual realization, would its substantive problem still require the same I_p? Codes: Independent / NotIndependent / Unresolved. ExtensionEmbedding: does I_p itself entail or substantially encode realization across more than one temporal location? Codes: Embedded / NotEmbedded / Unresolved.

Any change to source span, candidate set, transformation scope or IMC rule creates a new test version. Superseded coding does not validate the repaired target.

Source	Current positive LB set	IMC v2 pair
#2 Abundant Resources	{G002,G003}	Independent / NotEmbedded
#3 Synchronization	{G002,G005}	Independent / NotEmbedded
#4 Ceiling, Floor, and Slope	{G002,G003}	Independent / Embedded
#7 Governance	{G007}	Independent / Embedded
#1 Epistemic Extension (diagnostic)	–	Unresolved / Embedded

CDT v2 and IMC v2 are FirstCoder current test versions. A clean rerun requires a new coder who receives frozen inputs and rules without the current assignments or downstream conclusions.

B.10 Validation states and blinding protocol

State	Operational meaning
FirstCoder	Only the initial assignment exists for the current target version.
IndependentlyCoded	A second coder coded the same frozen target without access to the first assignment or aggregate findings.
Adjudicated	Comparable independent assignments were compared and a post-comparison disposition recorded.
DirectSource	Used descriptively for claims anchored directly in published wording rather than a coder judgment; not part of the three-state coding enum.

Blinding requirement. The independent coder receives frozen definitions, coding rules, and source passages needed for the target, but not the first-coder assignments, prior agreement figures, or downstream findings that would reveal the expected answer. The first-coder record remains hidden until the independent return is frozen.

Pilot V1 return fields were: blinding confirmation, coder type, coding date, unresolved count, rule-ambiguity note, normalized-definition ambiguity note, and scope limitation. The returned coder identified itself as model-based and confirmed that no first-coder assignment or aggregate finding had been consulted.

B.10.1 Agreement metrics

Target	Metric	Rule
Direct Signature primary	Per-coordinate binary agreement	For each entry, code presence/absence of S,D,M,T,Δ,RS,RT,RO; report coordinate-level and pooled micro agreement.
Direct Signature secondary	Exact-set agreement	Whole signature set must match exactly.
Modal	Exact category agreement	Required / Permitted / LocallyPermitted / Orthogonal / Incompatible.
Role	Exact Role agreement	One primary Role unless the source irreducibly performs more than one operation.
Locus	Exact primary Locus or exact set	Use narrow provenance grain.
CDT	Exact LB/NLB/U agreement by candidate	Report rationale separately.
IMC v2 primary	Per-dimension exact category agreement	Score ScopeMotivation and ExtensionEmbedding separately on the frozen source scope.
IMC v2 secondary	Exact-pair agreement	Both dimensions must match exactly; report rationales separately.

The metric set was selected before the returned pilot assignments were inspected but was formally documented only afterward in the leakage-repaired packet. It is therefore pre-specified in the workflow sense, not preregistered.

Do not recompute a post-adjudication agreement statistic as if adjudicated convergence were independent reproduction. For example, G-R6 and G-R7 now match the independent Signature assignments, but Pilot V1 remains 7/9 exact-set on endogenous records rather than becoming 9/9.

B.11 Target repair versus adjudication

Disagreement is not always an adjudication problem. First determine whether both coders actually coded the same sound target.

Diagnostic	Required response	Example
Same target, same rule, different value	Adjudicate after both assignments are frozen.	G004 Signature; G008 Signature; G005 #3 Role; G003 #4 Role.
Target combines distinct source operations	Split/version the provenance target; do not choose one coder for the old compound item.	G005 Optimization Process vs Decision.
Candidate routing is logically wrong	Create a new test version.	G001 removed from CDT candidate generators.
Rule leaks expected boundary	Mark reliability non-evaluable for that facet and require a fresh coder for clean retest.	Tempo in Pilot V1.
Derived view depends on superseded input	Mark stale and recompute.	Exact S/DH1 correspondence after G-R7.

same target + disagreement → adjudication

changed target/rule → new version, not retroactive validation

B.12 Adjudication protocol and recorded dispositions

Adjudication in the present study is author-led rather than performed by a third adjudicator. The adjudicator re-reads the frozen normalized definition and the exact published source span, applies the explicit boundary rule, records the disposition and rationale, and preserves both original assignments.

Target	Frozen disagreement	Disposition	Rule-based rationale
G004 Direct Signature	First {S,D,RS}; Independent {S,RS}	{S,RS}	Independent assignment adopted under D-test. G-R6.
G008 Direct Signature	First {S,RO}; Independent {RO}	{RO}	Independent assignment adopted under normalized-minimum RO/S test. G-R7.
G005 Role, paper #3	First Phenomenal; Independent Structural/Generative	Phenomenal	First-coder assignment retained because the exact sentence directly predicates what Gradual AGI is.
G003 Role, paper #4	First Phenomenal; Independent Structural/Generative	Phenomenal	First-coder assignment retained because the exact framing directly characterizes Gradual AGI as an assimilation-rate problem.

The directly comparable adjudications divide evenly by facet: both Signature disagreements adopt the independent value; both Role disagreements retain the first-coder value. This pattern is reported rather than normalized away. The decisions are justified by different frozen rules, not by a balancing criterion.

B.13 Leakage diagnosis for Pilot V1

Defect	What happened	Risk	Repair
Tempo instruction	Listed disputed negative cases such as duration, succession, iteration, lag or non-coincidence.	Could manufacture agreement by supplying the intended boundary in the rule.	Tempo reliability non-evaluable from Pilot V1; future packet uses positive-only rule.
Heading leakage	A heading named the REV-L1 / G005 variation target.	Could cue the expected contrast.	Use neutral task headings.
Stable H identifiers	Retired gaps revealed revision history.	Could leak instrument genealogy.	Use neutral historical IDs in a clean packet.
Provenance paraphrases	Some packet occurrences were coder-generated paraphrases rather than cold source text.	Could encode first-coder interpretation and blur Locus grain.	Use exact source excerpts and narrow source spans.
CDT candidate set	Included G001 after it had become the explanandum.	Confounded outcome with generator.	Exclude G001; route G006 separately; create CDT v2.
Metric documentation	Metrics were not printed in the packet actually returned.	Makes documentation weaker than preregistration.	State them as pre-specified in workflow, documented post hoc.

B.14 Interpreting model-based independent coding

The independent coder was model-based. Prompt-level blinding establishes separation from the first assignment within the coding exercise, but it does not establish independence of model training provenance, model family, latent priors, or error-generating processes.

prompt-level independence ≠ independence of training provenance or error

Agreement also partly measures instrument tightness. Where a rule sharply constrains a boundary, two model-based coders may converge because the instruction largely determines the answer; where the rule is thin, divergence may reflect greater interpretive latitude. Observed agreement is therefore a mixture of coder reproducibility and rule specificity.

observed agreement = f(coder reproducibility, rule tightness, target quality)

Zero Unresolved responses do not establish reliability. Pilot V1 produced no unresolved items while still yielding systematic disagreements. A rule can feel determinate to both coders without determining the same assignment.

subjective determinacy ⇏ inter-coder determinacy

B.15 Reproducibility checklist for a future coder

A clean future run should archive the model/coder identifier, complete task instructions and source packet, coding date, explicit blinding confirmation, and decoding settings such as temperature or sampling mode when the platform exposes them. Settings that are not exposed should be recorded as unavailable rather than inferred. The coder return must be frozen before any comparison with first-coder assignments or downstream findings.

Step	Requirement
1	Freeze exact Entry/provenance/test versions, source spans, and rule versions.
2	Hide first-coder assignments, prior agreement figures, revision outcomes, and downstream findings.
3	For Signature, Role and Locus, apply the frozen positive definitions at the narrowest source grain; split compound targets before coding.
4	For historical modal coding, hold I fixed and enforce (DFN001 | I) ⇒ Hi for Required.
5	For CDT v2, exclude G001, route G006 separately, and use the exact source-relative transformation scope.
6	For IMC v2, code ScopeMotivation and ExtensionEmbedding independently. For motivation, use the point-exhaustion counterfactual; for embedding, inspect the scope definition itself.
7	Mark Unresolved whenever the frozen source does not support a determinate value.
8	Freeze and return all assignments before comparison; report raw agreement on the same target versions only.
9	If disagreement exposes a target or rule defect, create a new version and reset ValidationState rather than retroactively promoting agreement.

B.16 Current validation map and remaining clean-retest targets

The table reports load-bearing and retest-relevant targets, not every independently matched provenance assignment. Appendix A carries the fuller assignment-level record.

Target	Current state	Retest priority / implication
G004 Direct Signature	Adjudicated	No clean rerun required for current paper; a third coder would strengthen rule-level reliability.
G008 Direct Signature	Adjudicated	Same.
G002 Relation / G007 State separating case	IndependentlyCoded	Supports Locus as non-redundant under current targets.
G005 #3 Role; G003 #4 Role	Adjudicated	Author-led adjudication; third-party human coding would strengthen external reliability.
G005 split Optimization Loci	FirstCoder	Priority retest: new Process and Decision targets created after Pilot V1.
G001 narrowed Process locus	FirstCoder	Priority retest: exact phenomenal-definition span.
CDT v2	FirstCoder	Priority retest: repaired candidate routing and exact source spans.
Historical S/D and RS boundaries	Mixed	Retest only where historical interpretation is load-bearing; not required to validate the endogenous reconstruction.
Historical Tempo	Non-evaluable from Pilot V1	Requires a new coder and positive-only Tempo rule.
IMC v2	FirstCoder	Priority retest: revised two-dimensional test (ScopeMotivation / ExtensionEmbedding) supersedes v1; rerun on frozen source scopes and contexts.

No additional validation run is required merely to make the present manuscript look cleaner. The current evidentiary map is itself a result: some targets reproduce, some adjudicate cleanly, some require version repair, and some remain FirstCoder. Future replication should target the objects whose current status is load-bearing rather than exhaustively recoding the historical reference register.