By W.H.L., Claude Sonnet 5

Gradual AGI as Optimization

Formal Models and Empirical Tests

Companion to “Gradual AGI as Optimization: A Conceptual Framework” and “Ceiling, Floor, and Slope: A Falsifiable Dynamical Model of Synchronization for Gradual AGI”

W.H.L., Claude Sonnet 5

Gradual AGI Series #6

Abstract

This paper formalizes “Gradual AGI” — the rate of civilizational assimilation of advanced AI — as a multi-agent optimization problem over a nonconvex, possibly non-stationary landscape, with AGI-inclusive humanity as the governing long-term objective. Building on the discrete-time Ceiling/Floor/Slope (CFS) dynamical system, we introduce Cohesion and Dynamism as a two-axis extension of CFS’s constraint structure, formalize the scalar-to-tensor transition, and develop a Nash Bargaining Solution apparatus for negotiated outcomes, unified with the paper’s competitive-game and diffusion apparatus into a single master optimization statement (Section 4.6). We test this apparatus against six live case studies — AI-driven coding automation, an intra-organizational product regression, frontier-model export controls, AI content licensing and litigation, AI infrastructure buildout and local/environmental externality, and diffusion of alignment practices — deriving falsifiable predictions against current data, including one that fails outright and is revised rather than discarded. This paper offers a first, proof-of-concept attempt at three empirical operationalizations the companion theory paper explicitly deferred: a multi-indicator construction of C(t) and D(t) (Proposition 3), tested against additive, multiplicative, and minimum aggregation forms; a resolution of the lag-threshold question Propositions 3 and 4 pose but leave unspecified in Section 5.3, finding that pivot speed tracks a triggering event’s informational clarity rather than its position in a sequence; and a direct test of Proposition 3’s dynamical-transition (barrier-crossing) hypothesis, left open pending further data. Cases also test a general subject/actor decomposition, recurring from competing states down to uncoordinated engineering teams inside a single firm, and, in the infrastructure case, extending to conflict among governance tiers within one state. We treat strategic and technical diversity across frontier labs as a direct test of convergence under iterative local optimization, and establish catastrophic risk containment as a boundary condition external to the apparatus, not a term traded off within it. A recurring finding is that “optimal” is itself locally set by each agent’s objective, constraints, and metric — the deeper justification for treating this as a bargaining problem rather than a computable one.

1. Introduction and Founding Propositions

The “Gradual AGI” series has, across prior installments, framed AGI as a civilizational assimilation-rate problem: not a policy of restraint, but a description of how quickly a society absorbs a transformative capability. The CFS paper gave this framing a falsifiable dynamical form — fixed points, stability conditions, and empirical calibration across four domains. This companion paper asks a narrower and more mechanical question: if Gradual AGI is treated explicitly as an optimization process, what kind of optimization is it, who owns its objective, and what does “optimal” even mean when multiple agents pursue different local goals against a shared, evolving landscape?

Four founding propositions organize this paper — left unnumbered here specifically to avoid collision with the companion theory paper’s own five numbered Propositions, which this paper cites by number (Proposition 1 in Section 2.1, Proposition 2 in Section 5.4.3, Proposition 3 in Sections 2.3, 5.1.1, 5.4.3, and 4.6, Proposition 4 in Sections 2.4 and 5.4.3, and Proposition 5 in Section 4.6) where it draws on or resolves them directly:

• Optimization is goal-driven, but ownership of the goal differs by scope and time horizon — near-term and narrow-scope optimization can be single-agent and scalar; long-term, civilizational-scope optimization must be negotiated among stakeholders and is better represented as a tensor than a scalar.
• The optimization landscape is nonconvex, and whether it is stationary or non-stationary cannot be assumed — it is an empirical, case-by-case field question.
• The governing long-term objective is AGI-inclusive humanity, which is simultaneously cohesive and dynamic — two axes in tension, not one scalarized target.
• A time dimension is nearly always present: optimal solutions differ by horizon, and short-run local rationality can be dynamically inconsistent with long-run outcomes.

2. Foundational Propositions and Their Resolution

2.1 Ownership of the Objective: Scalar and Tensor Regimes

Near-term, narrow-scope optimization can be owned by a single agent or small coalition and represented as a scalar objective (the companion paper’s Proposition 1). Long-term, civilizational-scope optimization cannot: it must be reached through negotiation among stakeholders with divergent interests, and its natural representation is a vector or tensor of stakeholder values rather than a single number. Critically, scope (single-agent vs. multi-stakeholder) and time horizon (near-term vs. long-term) are not strictly coupled — a single state can hold a decades-long strategy that remains scalar-owned, and a near-term crisis can force multi-stakeholder tensor-valued coordination. Both variables should be tracked independently rather than collapsed into one axis. This paper does not fix the tensor’s dimensionality by assumption: where the tensor-valued regime is actually operationalized (Section 5.1.1’s C(t)/D(t) construction, and Section 4.6’s k in Jᵢ: Π → ℝᵏ), the case evidence examined supports treating it as two-dimensional — Cohesion and Dynamism — not because these are asserted to be the only possible axes, but because they are the two the evidence to date distinguishes as behaving differently rather than interchangeably (Section 4.3’s argument that summing them loses meaning). Additional axes remain an open empirical question this paper does not foreclose, not a completeness claim it makes.

Where a tensor-valued long-term objective must be resolved into a single outcome, three formal options exist: weighted scalarization (which re-imports the very who-decides-the-weights problem the tensor was meant to avoid), Pareto-optimality (identifying the solution set with no interior point dominating another, without selecting among them), and a bargaining solution concept that selects one point on the Pareto frontier via an axiomatic rule. This paper adopts the Nash Bargaining Solution (NBS) as the selection mechanism for the long-term regime, understood explicitly as sitting on top of, not instead of, the Pareto frontier.

2.2 Nonconvexity and the Stationarity Question

The optimization landscape for Gradual AGI is treated as nonconvex throughout — multiple local optima, no guarantee of a unique global solution reachable by simple gradient methods. Whether the landscape is additionally non-stationary (deforming under the actions of the agents searching it, rather than fixed) is left as an open, case-specific empirical question rather than assumed in either direction. Every case study in Section 5 reports its own stationarity finding rather than inheriting a global assumption.

2.3 Cohesion and Dynamism as Two Axes

AGI-inclusive humanity is not a single scalar target (the companion paper’s Proposition 3). Following the series’ first-principles framing, it is simultaneously cohesive (the social fabric holding together) and dynamic (continuous adaptation and change) — two axes in tension rather than one target to maximize. This choice is deliberately consistent with, and extends, the CFS system’s Ceiling and Floor as constraint-like axes: Cohesion and Dynamism form a second axis pair layered onto the same discrete-time system, with the interesting empirical work lying in whether the two axes move together or diverge in a given case. Case 1 (Section 5.1) provides the clearest instance of the axes moving in opposite directions rather than merely at different speeds, which is the strongest evidence available for treating them as genuinely separate dimensions rather than a single delayed scalar.

2.4 The Time Dimension: Discrete Time and Dynamic Inconsistency

This paper inherits the CFS system’s discrete-time formulation — validated by the companion paper’s own Proposition 4 (Section 4.2), which treats time as continuous at the level of the general civilizational process while noting that calibrated instantiations “sample this continuous process at discrete intervals matching each domain’s reporting cadence” — for consistency and reuse of calibrated domains, revisiting the choice only where a specific case demands finer time resolution. Two structural points follow from taking time seriously. First, short-run and long-run optimal trajectories can genuinely diverge — a classic dynamic-inconsistency (Strotz-style) problem, where the path that looks optimal from today’s vantage point is not the path an agent actually follows once tomorrow’s local incentives take over. Second, iteration across time periods does not automatically converge toward a global optimum merely because the process is repeated rather than single-shot; convergence must be earned by a specific structural property of the state-update rule (contraction mapping, simulated-annealing-style controlled exploration, or potential-game structure), or the more appropriate framing may be online learning / regret minimization against a possibly moving target rather than classical convergence. Section 6 treats this question empirically rather than assuming an answer.

3. The Locality of Optimality Criteria

A question that logically precedes the case studies, though it surfaced empirically only once concrete data forced it: what criteria determine that an action or practice is optimal at all? “Optimal” is never a free-standing property. It is well-defined only relative to three things that must be specified first: an objective function, a feasible set determined by the agent’s actual constraints, and a chosen metric for measuring success toward the objective. None of the three is fixed by nature — each is set locally, by the agent or by whoever is doing the evaluation.

3.1 Illustration: Hiring-Experience Heterogeneity Across Frontier Labs

Frontier AI labs differ substantially in the average years of experience stated in technical job postings, with U.S. labs (Anthropic, OpenAI, xAI, Google DeepMind) requiring materially more experience on average than Chinese labs (DeepSeek, Qwen, Moonshot, ByteDance Seed). If experience-years were a universal, causally reliable input to frontier capability, a roughly proportional relationship between average required experience and realized capability would be expected. The evidence does not support this. Chinese labs training at or near frontier scale on constrained compute, and DeepSeek’s own leadership stating explicitly that the firm hires on ability rather than experience, are both inconsistent with a strong proportional relationship. Part of the observed gap is plausibly not a difference in belief about optimal strategy at all but a difference in the feasible set: youth-weighted hiring practices common at Chinese labs would likely raise legal exposure if practiced identically under U.S. employment law.

3.2 Why This Necessitates a Bargaining Apparatus

This finding is not a minor empirical footnote; it is the deeper justification for the paper’s reliance on Nash Bargaining and Pareto apparatus rather than a single global objective function. If there were one universally correct criterion for optimality, no negotiation would be required — the answer could simply be calculated. Genuine disagreement among agents about what constitutes good practice for reaching even a broadly shared goal is precisely the condition under which bargaining, rather than computation, is the correct tool. This methodological point is treated as foundational and is intended to be read alongside Section 2.1 rather than as a late addition.

A reflexive caution follows: the metric used to rank “advancement” or “capability” across labs is itself a locally chosen construct — dependent on which benchmark or dimension (raw capability, efficiency, safety behavior, robustness) is weighted — so testing any proportionality claim requires first fixing what advancement means, which is its own contested, locally set criterion. The indeterminacy compounds on both sides of any such comparison.

3.3 A Live Instance: Contested Measurement of “AI Exposure”

A July 2026 episode supplies a sharper, more currently-dated illustration of this same point than the hiring case alone, and is worth reading alongside it. When over 200 economists and AI researchers, including sixteen Nobel laureates, signed a Stanford Digital Economy Lab statement warning that AI could drive an economic transformation unfolding faster than institutions can adapt, at least one prominent dissent focused not on whether the risk was real but on whether the field’s central measuring instrument means anything stable. Apollo Global Management’s chief economist documented that “AI exposure” — the concept underlying most labor-market research on this question — is measured by at least five competing frameworks: usage-based measures drawn from actual chat logs across different assistants, expert judgments of theoretical task-replaceability, and self-assessment by the models themselves. These frameworks do not converge. Theoretical exposure measures run systematically higher than usage-based ones, and the disagreement is worst precisely on the highest-stakes jobs — telemarketing, tax preparation, writing — the exact cases any policy response would most need to get right. This is the locality-of-criteria problem showing up one level upstream of where the hiring case placed it: not only do agents disagree about what constitutes optimal practice, they disagree about how to measure the very phenomenon a policy response would act on, and that disagreement is largest exactly where the stakes are highest rather than smallest, which is the more damaging pattern for any framework hoping measurement error averages out where it matters most. A minimal forward path, not attempted here: usage-based and theoretical measures disagree most where task content is genuinely ambiguous, so a hybrid that reports usage-based figures where available and flags theoretical estimates as lower-confidence rather than blending the two into one number would at least make the disagreement visible instead of averaging it away — a smaller claim than convergence, but a checkable one.

4. Formal Apparatus

4.1 Subject and Actors: A General Decomposition

Before specifying how agents interact (Sections 4.2–4.4), it is necessary to specify who counts as an agent at all, and this decomposition is stated here as general apparatus rather than case-specific, since it recurred as a needed correction across multiple cases once applied carefully. A first distinction: the artifact being optimized — a model, a product, a deployed system — is the optimization subject, not an actor. Conflating the subject with the agents acting on it obscures where responsibility and causal influence actually sit.

Actors decompose further than a single organizational name usually suggests (Figure 1). Within any firm developing and shipping AI systems, at minimum two internal actor classes should be held distinct: the model maker (the research and training organization responsible for underlying model weights) and the product team (the organization building the surrounding product, harness, or deployment layer). These two can be, and in practice sometimes are, cleanly dissociated — a fault line worth checking explicitly in any case rather than assuming the firm behaves as one unified actor. Externally, at least four further classes recur: direct end users of a given product surface; API developers and other technical integrators, who may face materially different exposure than end users even when both depend on the same underlying organization; communities — the emergent, aggregating structures (forums, issue trackers, independent audits) through which individually scattered signals become a collective, actionable one; and governance bodies — government regulators and standards organizations, whose relevance to a given case does not depend on whether they actively intervened. A governance body’s absence from a case is itself informative and should be stated as a finding rather than an omission, particularly where an adjacent domain shows an active governance mechanism the case at hand lacks.

Governance bodies in particular should not be treated as a single present-or-absent class. Case 5 (Section 5.5) shows federal, state, and local tiers of government acting in open conflict with one another over the same underlying activity — one tier actively enabling what another tier is simultaneously restricting or litigating against. Where earlier cases treated a governance body’s absence as the relevant finding, Case 5 requires the finer-grained question of which tier, since the answer differs by tier within a single case.

Figure 1. Subject/Actor decomposition (Section 4.1): the optimization subject is not itself an actor; internal classes (model maker, product team) and external classes (end users, API developers, communities, governance bodies) are held distinct, with governance further split into potentially conflicting tiers.

This decomposition is applied fully in Case 2 (Section 5.2) and, with the governance-tier refinement above, in Case 5 (Section 5.5), and is available as a general tool for sharpening the coarser actor groupings used in earlier-drafted cases on later revision.

4.2 Nash Bargaining Solution over a Pareto Frontier

For any bilateral or multilateral relationship requiring a negotiated long-term outcome, we adopt the Nash Bargaining Solution: the point on the Pareto-efficient frontier maximizing the product of each party’s utility gain over a defined disagreement point. Two components require case-specific specification and are not free: the disagreement point (the outcome absent agreement — status quo, continued unilateral action, or a race-to-the-bottom trajectory) and the symmetry assumption (standard NBS assumes equal bargaining power, which is frequently false among frontier labs, states, and individual creators; the generalized/weighted NBS variant substitutes bargaining-power weights, which reintroduces a who-sets-the-weights problem one level down).

A separate axiomatic question, distinct from bargaining-power symmetry: standard NBS requires each uᵢ to be a von Neumann–Morgenstern cardinal utility, unique only up to positive affine transformation. This is what licenses combining heterogeneous stakeholder scales — a content creator’s revenue, a frontier lab’s capability metric, a state’s security posture — without first converting them to common units: the solution is invariant to each party’s own rescaling. What it does not relax is cardinality itself; an ordinal ranking of outcomes does not meet the bar, and no case in this paper independently verifies that its stakeholder utilities meet that standard rather than serving as convenient proxies for it. Where a disagreement point evolves through an external channel — Section 5.4’s dᵢ(t) = φᵢ(P(t)) + λΩᵢ(t) — the same cardinality assumption is inherited at every t, not just at a single evaluation point.

NBS: max (u₁ − d₁)(u₂ − d₂)   subject to (u₁,u₂) on the Pareto frontier     (1)

4.3 Security-Dilemma / Repeated-Game Apparatus

For cases structured as deliberate, adversarially-postured competition (export controls, offensive-cyber posture) rather than unintended externality, the relevant apparatus is game-theoretic rather than bargaining-theoretic. Under a single-shot Prisoner’s-Dilemma-type payoff structure, mutual restraint is Pareto-superior to mutual escalation but is not a Nash equilibrium — escalation is individually rational regardless of the other side’s move. Under a repeated game with sufficient patience and observability of defection, the Folk Theorem establishes that cooperative outcomes can be sustained via credible retaliation threats, without central enforcement. Three preconditions gate this outcome: repetition (generally satisfied for ongoing great-power AI competition), sufficient patience (uncertain, given political time horizons), and observability of defection — the weakest link for AI and chip competition relative to the nuclear-arms-control precedent it most resembles, given documented smuggling and concealment channels.

A further, largely ideology-independent obstacle: whether actors optimize absolute gains (am I better off than before) or relative gains (am I better off than my rival) determines whether a jointly superior outcome is reachable even when it exists in the solution space. Security competitions structurally favor relative-gains orientation, which can make a Pareto-improving deal rejected by whichever side loses relative position even when both sides are objectively better off.

This section formalizes competitive interaction as a distinct mode from bargaining and diffusion, which is worth noting explicitly given that the companion theory paper names competition as within its own stated scope (alongside cooperation and co-development) without formally treating it anywhere in its definitions, propositions, or mathematics. The apparatus here is offered as filling that specific, named gap.

4.4 Diffusion of Locally-Optimal-If-Universalized Practices

For practices that would move the system toward the global objective if universally adopted but are implemented unilaterally by one agent, we adapt the Bass diffusion model. Let m be the addressable population of potential adopters, N(t) the number of adopters, and f(t) = N(t)/m the adoption fraction:

ΔN(t+1) = [p + q·f(t)]·(m − N(t))     (2)

with p the innovation coefficient (independent adoption driven by the practice’s own visible merit) and q the imitation coefficient (adoption driven by observing other adopters). We parameterize both by properties of the practice itself rather than treating them as free-fit constants: p is bounded by codifiability κ (whether the practice exists as a transferable, evaluable artifact, such as a published technique, versus a bare unilateral stance with nothing to copy), and q is bounded by local incentive-compatibility γ (whether adopting the practice also serves the adopter’s own objective, or is purely costly with no compensating local benefit). A practice with κ ≈ 0 and γ ≈ 0 predicts near-total containment; a practice with κ, γ > 0 predicts partial, contested diffusion coexisting with deliberate holdouts. This paper does not commit to a specific functional form for p(κ) or q(γ) — no case here supplies enough calibration points to distinguish a linear from a sigmoidal or threshold mapping, and asserting one would manufacture false precision of exactly the kind flagged for C(t)/D(t) in Section 5.1.1. The commitment is to monotonicity alone: p′(κ) > 0 and q′(γ) > 0 — more codifiable practices diffuse more from visible merit, more locally-compatible practices diffuse more from imitation, holding the other factor fixed.

Because nominal adoption can mask cosmetic rather than binding implementation, we introduce a binding-power discount βᵢ(t) ∈ [0,1] per adopter, capturing whether the practice actually constrains outcomes (e.g., a pipeline into evaluation metrics or deployment gating) versus remaining advisory. Effective diffusion is then (Figure 3):

Φ(t) = (1/m) · Σᵢ βᵢ(t)·1[i has adopted]     (3)

Φ(t) is the quantity that actually predicts movement toward the global objective; raw adoption-fraction data alone can overstate a practice’s real effect. Equivalently, effective diffusion evolves by the same recursion as raw adoption, with β applied at the point of entry rather than after the fact: ΔΦ(t+1) = (1/m)·Σᵢ βᵢ(t+1)·ΔNᵢ(t+1), where ΔNᵢ(t+1) ∈ {0,1} indicates agent i adopting in period t+1 and ΔN(t+1) = [p + q·f(t)]·(m − N(t)) (Eq. 2) is its aggregate sum. This keeps β from functioning as a disconnected post-hoc discount on a separately-computed total — it is applied to each unit of adoption as it enters the process.

Figure 3. Bass diffusion with a binding-power discount (Section 4.4): raw adoption f(t) can overstate a practice’s real effect; effective diffusion Φ(t) discounts nominal adopters who have not made the practice binding.

The same apparatus generalizes to a direction not used elsewhere in this paper until Case 5: diffusion of resistance tactics among affected third parties, rather than diffusion of a practice among the agents doing the optimizing. Community opposition to a locally-optimizing agent’s activity can itself follow a Bass-type adoption curve — an early, visible instance of successful resistance functioning as the innovation term, subsequent adoption by observationally similar but previously unengaged communities functioning as the imitation term. Codifiability and incentive-compatibility apply on this side of the model too: a documented, replicable resistance playbook is more diffusible than an ad hoc, one-off objection, exactly as a published technique is more diffusible than a bare unilateral stance in the original formulation.

4.5 Existential Risk as a Boundary Condition, Not an Objective Term

Catastrophic and irreversible outcomes — the paradigm case being superintelligent capability directed toward mass-casualty ends — cannot be handled by the same apparatus as the rest of this paper for a specific structural reason: every mechanism above (the Folk Theorem, no-regret online learning, absorption-capacity arguments) presupposes that the system survives a bad round and can update from it. That assumption fails by construction for a genuinely existential outcome, since there is no next iteration to learn into. The standard response in decision theory for catastrophic, irreversible tail risk is to treat the outcome as a hard constraint the trajectory must never enter, rather than one more term traded off against benefit inside an expected-value objective. We therefore treat catastrophic-risk containment as a wall around the entire state space this paper’s optimization apparatus operates within, not as a point or case inside it.

This distinction is a general claim about the structure of this class of optimization problem, not something specific to the cases examined here. The companion theory paper’s own constraint treatment now carries the same distinction explicitly: catastrophic and irreversible outcomes bound the admissible state space directly, separated from ordinary constraints that may be traded off within the optimization process. The two papers’ treatments are stated independently but are mutually consistent.

Boundary condition, stated explicitly The optimization apparatus (Sections 4.2–4.4) governs ordinary cases: externalities, security dilemmas, and diffusion of practices. Catastrophic and irreversible risk is excluded from that apparatus by design and is instead a constraint the whole model must respect: near-zero admissible probability of entry, not a cost term. A related, checkable principle follows for governance choice: closed distribution preserves the option to contain a deployed system later (patch, suspend, revoke); open-weight release forfeits that option irreversibly once weights are distributed. This is a real-options argument independent of, and analytically separable from, commercial rationale for closed distribution.

A scope note, raised in review and worth stating rather than leaving implicit: none of the six case studies in Section 5 is a claim about this boundary. Each is chosen because it exercises the ordinary apparatus (Sections 4.1–4.4), not because it has been assessed against, or is asserted to approach, the catastrophic-risk wall. Where a case’s subject matter sits closer to frontier capability — Case 1’s coding automation, Case 5’s infrastructure buildout — this paper is silent on that case’s relationship to the boundary by design, not by oversight: evaluating a specific trajectory against the boundary is a distinct and harder problem this paper does not attempt, and the silence should not be read as an implicit “clear.”

4.6 A Master Statement: Unifying Sections 4.1–4.5

Sections 4.1–4.5 introduce a disagreement point and bargaining rule, competitive-game payoffs, diffusion dynamics, and a boundary condition, but never as one named optimization problem — the form reviewers of formal optimization work reasonably expect, and its absence is the strongest version of the recurring objection that “optimization” here is organizing metaphor rather than formal object. This section states one. Solving it is not the point: no case in Section 5 attempts a numerical solution, and none is claimed necessary for the paper’s empirical content, which rests on the case-by-case tests in Sections 5.1–5.7. The value of stating it is what collecting the separately-introduced pieces into a single object makes visible by construction. This mirrors, at the multi-actor level, what the companion paper’s own Section 4.4 already does for its single-Subject formulation — Γ* = argmax_Γ V(Γ; Ĝ(t)) subject to each stakeholder’s local goal and directional consistency with Ĝ(t), with catastrophic and irreversible outcomes bounding the admissible state space directly rather than being traded off within V. This paper’s max-π_i formulation below is the disaggregated analog: where the companion paper evaluates a single Subject’s trajectory against one holistic objective, this paper distributes that same structure across the Section 4.1 actor decomposition, with each actor solving its own local problem under the identical hard existential-risk boundary.

For an actor i drawn from the Section 4.1 decomposition (model maker, product team, end user, community, governance body, …), let πᵢ denote its policy — a choice of action or trajectory over the relevant horizon — and π = (π₁, …, πₙ) the joint policy across all actors in a given case. The governing long-term objective (Section 2.1) is tensor-valued, Jᵢ: Π → ℝᵏ, where k = 1 recovers the scalar, single-agent, near-term regime and k > 1 the multi-stakeholder, long-term regime that cannot be collapsed to one number without a further, contested aggregation choice — the same choice tested against real data for C(t)/D(t) in Section 5.1.1, and the formal expression of the companion paper’s Proposition 5, that civilizational-scale optimization cannot be adequately evaluated by any single scalar metric. Each actor’s realized objective is itself a function of system-level Cohesion and Dynamism (Section 2.3), which depend on the joint policy π rather than on πᵢ alone:

Jᵢ(π) = Jᵢ(π; C(π,t), D(π,t))     (4)

This dependence on the joint policy, not the individual one, is the source of the interdependence Sections 4.2–4.4 exist to manage (shown schematically in Figure 5, below). Each actor’s local problem is then:

max over πᵢ:   Jᵢ(π; C(π,t), D(π,t))    subject to:     (5)

• Existential boundary (4.5): P(state ∈ catastrophic outcomes) ≈ 0 for all t — a hard constraint on the admissible trajectory, not a term inside Jᵢ, and the one constraint here that does not vary by case, actor, or bargaining outcome.
• Bargaining constraint (4.2): where πᵢ requires another actor j’s agreement, the realized pair (πᵢ, πⱼ) lies on the Pareto frontier of (Jᵢ, Jⱼ) and satisfies the Nash product condition of Section 4.2 (Eq. 1) given disagreement point dᵢ(t).
• Competitive constraint (4.3): where the relationship with actor j is adversarially rather than cooperatively postured, sustained cooperation — if it occurs — requires the Folk Theorem’s three preconditions (repetition, patience, observability of defection); absent them, the single-shot Nash equilibrium governs instead.
• Diffusion dynamics (4.4): where πᵢ is a practice rather than a one-off action, its uptake by other actors evolves according to ΔN(t+1) = [p + q·f(t)]·(m − N(t)) (Eq. 2), with effective (binding) uptake Φ(t) (Eq. 3) as defined there — a constraint on how fast πᵢ’s costs or benefits actually propagate, not a variable any single actor sets directly.

Figure 5. Section 4.6’s master statement (schematic): actors solve local problems under a shared existential boundary (a) and pairwise bargaining (b), competitive (c), and diffusion (d) constraints — no node solves the joint problem, by construction.

What this makes visible by omission is the paper’s central claim, now stated in the same notation as everything above it: there is no meta-actor solving a single joint problem maximizing Σᵢ Jᵢ(π) over π, and no aggregation rule anywhere in Sections 4.1–4.5 that would produce one without reintroducing the who-sets-the-weights problem already flagged in Section 4.2. That absence is not a gap to be closed in a future revision — it is the structural finding: Gradual AGI is a coupled system of local optimizations under constraints that are shared but only partly negotiable, of which existential-risk containment is the one member that is not negotiable at all. One question this statement does not resolve, raised in review: under what conditions does the coupled system converge to a stable configuration, as opposed to oscillating or diverging, as actors update against a landscape that itself moves with C(π,t) and D(π,t)? This paper does not attempt an answer, for a reason worth stating rather than leaving implicit: establishing contraction-mapping or bounded-oscillation conditions would require committing to a functional form linking Jᵢ to (C,D) that this paper declines to specify, for the same false-precision reason Section 4.4 gives for not specifying p(κ) and q(γ). What can be said without that commitment is only structural, not a stability result: Section 2.2 already treats landscape stationarity as a case-by-case empirical question rather than a global property, and the cases here are consistent with that — Case 2 reached a stable configuration within weeks, while Case 4’s central holdout pairs remain unresolved fifteen-plus months on — without this paper claiming in advance which regime a new case will fall into. A genuine stability analysis is left to future work building on this apparatus, alongside the calibration roadmap in Section 8.

5. Case Studies

Each case is built as an instance of the apparatus in Section 4, stated with explicit state variables, tested against available evidence, and revised where the evidence disagrees with the initial formulation. Cases are typed by structure (externality, intra-organizational aggregation failure, security dilemma, negotiated settlement, diffusion) rather than treated as an undifferentiated list, since the applicable formal apparatus differs by type.

5.1 Case 1 — AI-Driven Coding Automation (Externality Type)

Local optimization: AI-coding adoption pursued by firms for productivity and capital-reallocation objectives, evidenced by adoption-share figures ranging from roughly 27% to 75% of new production code depending on measurement methodology, with the most methodologically rigorous large-sample study finding 26.9%. Realized harm: entry-level pipeline compression rather than broad-based displacement is the best-evidenced mechanism — Stanford HAI’s 2026 AI Index found software-developer employment for the 22–25 age cohort fell nearly 20% from 2024 levels even as employment for developers over 26 continued to grow, consistent with senior engineers absorbing throughput that previously required a junior tier beneath them. Attribution of broader tech layoffs to AI specifically is genuinely contested in the evidence (“AI-washing”), which we treat as a modeling fact rather than resolve by assumption.

We formalize a leading/lagging indicator structure distinguishing realized harm L(t) (a backward-looking variable, explained by past adoption with lag k) from anticipated harm E(t) (a forward-looking, expectation-based variable, evidenced by commencement-speech backlash and survey sentiment data predating individual job loss):

ΔA(t+1) = h(ΔA(t), E(t), L(t), …)     with hypothesis  ∂h/∂E(t) < 0     (6)

This models a thermostatic, self-limiting mechanism: anticipated harm dampens future adoption slope through political and behavioral resistance, operating on a shorter lag than a purely reactive mechanism keyed to realized harm alone would allow, since expectations update on aggregate/structural signals rather than requiring personal realization of harm first. This case provides the clearest instance across the paper of Cohesion and Dynamism moving in opposite directions rather than merely at different speeds — Dynamism registers positive (adoption and throughput rising) while Cohesion registers negative on both a current-displacement axis and a structural pipeline-foreclosure axis. Calibration of the feedback coefficient was deliberately deferred pending longer time series and is flagged as open in Section 8.

A July 2026 development strengthens the E(t) side of this structure considerably. Over 200 economists and AI researchers, including sixteen Nobel laureates, signed a Stanford Digital Economy Lab statement warning that AI-driven economic transformation could unfold faster than institutions can adapt — a materially stronger anticipatory signal than the survey and commencement-speech data originally used to evidence E(t), since it is elite expert consensus rather than aggregate public sentiment. Most notably, two of the signatories, Daron Acemoglu and Simon Johnson, had spent preceding years publicly arguing against AI-displacement concern; their reversal is a documented instance of expert belief updating on accumulating evidence, rather than a static expression of pre-existing anxiety, and is a sharper data point for E(t)’s forward-looking character than anything available when this case was first drafted.

5.1.1 Operationalizing Cohesion and Dynamism

The companion theory paper (“Gradual AGI as Optimization: A Conceptual Framework,” Proposition 3, elaborated in its own Section 4.3) treats Cohesion and Dynamism as process-level properties — latent descriptors inferred from multiple indicators rather than measured directly — and explicitly defers their empirical operationalization to this paper. This subsection delivers a first instance, using Case 1 as the testbed, since it is the case where the two properties were already documented moving in opposite directions. The scores that follow throughout this subsection are proof-of-concept operationalizations, not validated estimators: the goal is demonstrating that C(t) and D(t) can be built from named, checkable indicators and that different aggregation rules produce meaningfully different readings of the same underlying situation — not a claim that 0.23 or 0.68 are correct to the precision stated. Sensitivity bounds are given alongside each point estimate below for exactly this reason.

Cohesion is constructed from two convergence indicators, each scored on a 0–1 scale and combined by mean rather than sum, for the same comparability reason used throughout this paper’s diffusion apparatus. The first is measurement-framework convergence: Apollo economist Torsten Slok’s finding that five competing frameworks for measuring “AI exposure” disagree systematically, with disagreement widening as the average exposure estimate rises — near-total agreement on low-exposure occupations (hairdressers, dancers), wide disagreement on high-exposure knowledge work (tax preparers, telemarketers, mathematicians). Software development sits structurally closer to the high-disagreement category than the low one, yielding an estimated score of approximately 0.25. The second is regulatory convergence specific to AI-labor policy: no federal framework exists (prior Department of Labor guidance was revoked rather than merely allowed to lapse), and state responses are explicitly characterized in trade coverage as reflecting “sharply different regulatory philosophies” producing compliance complexity described as a “multi-jurisdictional Sudoku,” yielding an estimated score of approximately 0.20. Combined, C(t) ≈ 0.23 — low, and notably convergent across two independent domains (labor-market measurement methodology and state regulatory philosophy), which is itself a validity check on the construction rather than a coincidence to be explained away. Varying each component by a plausible ±0.05 around its point estimate (framework convergence 0.20–0.30, regulatory convergence 0.15–0.25) gives C(t) ∈ [0.18, 0.28]: the point estimate could reasonably sit anywhere in this range without changing the qualitative reading of low, convergent Cohesion.

Dynamism is constructed from the same two components identified when this apparatus was first proposed — adoption pressure and containment pressure — computed two ways rather than one, since the theory paper leaves open whether Dynamism functions as a directional, gap-driven force (favoring a signed combination, where opposing pressures cancel) or as aggregate destabilizing energy against a stability barrier (favoring an unsigned combination, where opposing pressures add). Adoption pressure is reconstructed from a single consistent source: Stack Overflow’s annual Developer Survey, which has fielded the same question — “Do you currently use AI tools in your development process?” — every year since 2023. The affirmative share rose from 44% (2023) to 62% (2024) to 78.5% (2025) [16]. Read as year-over-year relative growth, the same lens applied to the containment series below, the rate fell from approximately 41% (2023–24) to approximately 27% (2024–25): a measured deceleration, consistent with a diffusion curve approaching its ceiling rather than accelerating growth. (Stack Overflow’s own respondent count fell over the same window, from roughly 90,000 to roughly 49,000 — a possible compositional confound, plausibly connected to the same AI adoption being measured, that this reconstruction flags rather than resolves; the question wording and administering organization, unlike the estimate this replaces, held constant throughout.) Adoption pressure is scored at approximately +0.55, preserving the previous draft’s magnitude but now traceable to one reproducible series rather than a synthesis of incompatible question wordings. Containment pressure is estimated at approximately −0.80 (signed) or 0.80 (unsigned magnitude), grounded in a genuine multi-year time series rather than a single snapshot: state AI-related bill introductions grew from fewer than 200 (2023) to roughly 600 (2024) to roughly 1,200 (2025) to over 2,000 year-to-date (2026), a sustained rather than merely episodic mobilization trend, using a single consistent tracking methodology throughout — an evidentiary basis that now matches, rather than exceeds, the adoption-side reconstruction above: both are single-source, multi-year, consistent-methodology series. The residual asymmetry is narrower than in earlier drafts — the containment series carries no comparable compositional risk, while the adoption series is drawn from a platform whose own respondent base shrank over the same window (Section 5.1.1, above) — and this narrower form is what Section 8 now carries forward.

Signed mean: (+0.55 + (−0.80)) / 2 ≈ −0.13 — near zero, reflecting substantial cancellation. Unsigned mean: (0.55 + 0.80) / 2 ≈ 0.68 — reflecting substantial pressure from both directions simultaneously, uncancelled. Varying each pressure component by a plausible ±0.05 (adoption 0.50–0.60, containment 0.75–0.85) gives an unsigned D(t) ∈ [0.63, 0.73]. The gap between these two readings is itself the test: Case 1’s observed trajectory — continued adoption growth alongside continued, escalating institutional pushback, with no visible settling — reads as more consistent with sustained high total pressure than with near-equilibrium, weakly favoring the unsigned, barrier-crossing interpretation over the signed, error-correcting one, though this remains a directional judgment rather than a statistically adjudicated result given the data quality asymmetry noted above.

Applying these readings to the additive/multiplicative/minimum question (Figure 2) raised when Cohesion and Dynamism were first formalized: additive combination, C · w_C + D · w_D with equal weights, yields approximately 0.47 using the unsigned D(t) — a moderate, unremarkable figure that gives no indication anything is wrong, because high Dynamism is mathematically compensating for low Cohesion. Multiplicative combination, C × D, yields approximately 0.17 — correctly flagging a genuinely strained configuration: real disruptive pressure combined with fragmented, poorly-coordinated understanding of what is actually happening. Minimum combination yields 0.25, bottlenecked by the weak component, agreeing qualitatively with the multiplicative reading. This is the first instance in either paper where actual case data, rather than abstract argument alone, shows the additive form performing the specific masking that motivated rejecting it in the first place. This conclusion is robust to the sensitivity ranges above, not an artifact of the specific point estimates: across the full interval C(t) ∈ [0.18, 0.28] and unsigned D(t) ∈ [0.63, 0.73], multiplicative C(t) × D(t) ranges from roughly 0.11 to 0.20 — comfortably below the additive reading (≈0.47) everywhere in that range, so the qualitative finding does not depend on where within the stated intervals the true values actually sit.

Figure 2. Additive vs. multiplicative aggregation of Cohesion and Dynamism for Case 1 (Section 5.1.1): the same point (C≈0.23, D≈0.68) reads as moderate under an additive combination but low — correctly flagging strain — under a multiplicative one.

The theory paper’s other named candidate, drawn from the same Proposition 3 that motivates the dynamical-transition-models framing — barrier-crossing, metastable-transition dynamics — makes a sharper and more specific prediction than covariation: a genuine transition should show a discrete, threshold-like signature, not smooth joint movement. Legislative mobilization’s year-over-year growth rate (approximately 200% in 2023–24, 100% in 2024–25, and approximately 230%+ projected for 2025–26 on current pace) is accelerating rather than constant, which is a documented early-warning signature of approach to a genuine regime shift in the complex-systems literature on critical slowing down, distinguishable from steady drift with no transition pending — but this is consistent with an approaching, not-yet-completed transition, not confirmation that one has occurred. The July 13, 2026 economist statement is the best-positioned candidate marker for where a crossing might sit, given its scale and the documented reversal of previously skeptical signatories, but it is too recent — roughly ten days old as of this analysis — for downstream indicators to show whether it produced a visible kink or was simply one more point on the pre-existing trend. This is stated as a specific, dated, re-checkable open question rather than left as an unbounded one: re-running this series in the months following the letter would show a kink or would not.

5.2 Case 2 — Aggregation-Blind Product Regression (Intra-Organizational Type)

Every prior case in this section is cross-agent: one agent’s local optimization harms a different agent. This case is the paper’s only intra-organizational instance — a clean instantiation of Section 4.6’s basic πᵢ structure with no bargaining, competitive, or diffusion constraint active, only three uncoordinated local solvers sharing one Subject — and is included specifically as a structural counterpart to Case 1 — externality versus aggregation failure as two distinct ways local optimization generates damage, with no second agent required for the second.

Between March 4 and April 16, 2026, three engineering teams inside Anthropic independently shipped three locally-scoped optimizations to the Claude Code / Agent SDK / Cowork product layer: a default reasoning-effort reduction (high to medium, targeting UI latency), a session-idle caching change (targeting compute efficiency, which contained an implementation bug causing it to clear reasoning every turn rather than once per idle hour), and a system-prompt verbosity cap (targeting output token cost). Anthropic’s April 23 postmortem states that neither internal usage nor internal evals reproduced the resulting quality regression before external reports forced the investigation, and that the caching bug specifically passed human review, automated tests, and internal dogfooding — partly because an unrelated internal quirk suppressed the bug’s specific trigger condition in the exact sessions Anthropic’s own engineers used daily. The underlying model weights and the API were unaffected throughout; the failure is cleanly localized to the product-team layer, evidentially clearing the model-maker actor class rather than merely omitting it.

Applying the Section 4.1 decomposition directly:

• Subject: Claude Code, the Agent SDK, and Cowork — the product being acted upon, not an actor.
• Model maker: not implicated by the evidence — a cleared, not merely absent, actor class.
• Product team: the locus of all three changes, itself decomposable into the three sub-teams, none of which had visibility into the other two’s concurrent changes.
• Model users versus API developers: materially different exposure despite depending on the same organization — Claude Code/Agent SDK/Cowork users were directly exposed; API developers calling the raw API largely were not.
• Communities: GitHub issues, forum threads, and a systematic third-party audit (6,852 sessions, one engineering director) aggregated individually scattered complaints into a signal strong enough to force investigation — succeeding where a narrower, single-layer internal process did not.
• Governance bodies: no regulatory inquiry or formal governance action is evidenced. Public discourse explicitly raised the question in consumer-protection terms — whether a subscription buyer has any right to a disclosed change in served capability — and no disclosure mechanism comparable to the EU AI Act’s training-transparency mandate (Case 4) exists for serving-parameter changes. The gap itself, not an active intervention, is the relevant finding.

Formally: let m₁(t), m₂(t), m₃(t) be the three independently-optimized local metrics, each validated pre-deployment only against its own narrow proxy ∂Q/∂mᵢ in isolation, where Q(t) is the true, integrated quality metric as experienced in composite real-world use. No pre-deployment evaluation tested the joint, composite system. The interaction effect generated by simultaneous deployment across overlapping users and time windows is structurally invisible to any single team’s isolated validation process — a Goodhart’s Law failure at the level of engineering process rather than a single metric, resolved only once an external, high-volume, high-diversity signal (users, an independent auditor, and public benchmark reporting acting as three distinct correction roles rather than one undifferentiated “external reaction”) supplied the missing composite-system evaluation after the fact.

Whether the reasoning-effort and verbosity changes were purely well-intentioned or partly motivated by compute-cost pressure characterized elsewhere as deliberate is contested in the public record and is treated here as out of scope; it does not change the structural finding, which concerns detection and coordination rather than motive. Remediation itself inherited the same blind spot: at least one independent report found the verbosity-cap prompt text still present after Anthropic’s announced revert, confirmed only through an end user’s own testing rather than Anthropic’s verification process. No large-scale recurrence is evidenced through mid-2026, and Anthropic states the resulting governance changes — broader per-model ablation suites, staff dogfooding exact public builds — apply to all subsequent models running through the same harness, which gives this case a checkable forward prediction: detection lag on any future product-layer change should fall, independent of whether that future change is deliberate or accidental.

Whether this specific mechanism generalizes beyond Anthropic is a fair question, and the honest answer is partial. The surface-level symptom — user-perceived quality regression following product-layer changes, met with public acknowledgment and a coordination fix — recurred at OpenAI repeatedly across 2025–2026: a widely reported April 2025 episode in which Altman attributed an “annoying,” overly sycophantic ChatGPT personality shift to recent updates; a January 2026 developer town hall at which Altman said of GPT-5.2’s degraded writing quality, “I think we just screwed that up”; and a December 2025 “code red” memo, reported from an internal document, that explicitly instituted a coordination fix — a daily cross-team call among those responsible for ChatGPT’s quality — a response consistent with, though not confirmation of, a coordination failure across teams rather than one centralized decision. None of these carries a public postmortem as detailed as Anthropic’s April 23 document, so the specific mechanism this case establishes — three independently-validated local optimizations, each cleared on its own narrow proxy, with no pre-deployment test of the composite system — remains, at the mechanism level, an N=1 finding. What generalizes with more confidence is the higher-level pattern this case is best read as an instance of: product-layer Goodharting at multi-team frontier labs, where the recurring public fix, when one is reached for, is coordination — a shared call, a shared eval suite — rather than a change to any single team’s own process. That recurring choice of fix is indirect evidence for the coordination-failure mechanism, not direct confirmation of it for any case but this one.

5.3 Case 3 — Frontier-Model Export Controls and the Security Dilemma

This case is typed as security-dilemma rather than externality — the competitive constraint (c) of Section 4.6’s master statement, rather than its bargaining constraint (b): the restrictive intent is deliberate rather than an unintended byproduct. U.S. export controls on frontier chips and models cost the targeted firm commercial share unambiguously — Nvidia’s China AI-chip market share fell from over 90% to roughly 50% — while whether the controls narrow or widen the underlying capability gap is genuinely disputed in the evidence, with one credible analysis projecting the performance gap widening from roughly fivefold to seventeenfold by 2027 under current controls even as Huawei’s chairman has publicly credited the controls with forcing China’s domestic self-reliance push.

A second data point folded into this case rather than treated as independent: the Anthropic–NSA offensive-cyber-operations arrangement, and its subsequent expansion to CISA and allied signals-intelligence agencies, following the Pentagon’s rejection of Anthropic as a vendor over a refused “all lawful purposes” contract term covering autonomous weapons and mass surveillance. When Anthropic held that specific line, the Department of Defense simply contracted with OpenAI, Google, and xAI instead — reproducing the identical collective-action weakness the export-controls apparatus predicts: unilateral restraint by one actor does not remove the underlying demand, it only tests whether a competitor will fill the gap, and here one did within months. We treat this as a second empirical instance of the same security-dilemma structure rather than an independent fourth case.

A third data point, gathered live and reported with the same caution given to other unresolved disputes in this paper: Moonshot AI released Kimi K3, a 2.8-trillion-parameter open-weight model, on July 16, 2026, with full weights following July 27 — incomplete as of this writing. Independent trackers placed it third overall on Artificial Analysis’s Intelligence Index, behind only Claude Fable 5 and GPT-5.6 Sol Max, while running cheaper than either. On July 22, White House OSTP Director Michael Kratsios publicly accused Moonshot of covertly distilling Fable 5 specifically through “a sophisticated internal platform” built to evade detection; Treasury Secretary Bessent backed the claim, citing unspecified “watermarks” of U.S. models found in Chinese systems, and floated sanctions and Entity List designation. This escalates a claim Anthropic itself made in February against Moonshot, DeepSeek, and MiniMax jointly, based on 3.4 million traced exchanges [23]. Moonshot has not responded, and the claim is independently disputed rather than confirmed: several AI researchers argue that distillation at the scale and speed implied would be prohibitively expensive and slow relative to the capability gain observed, making it an implausible sole explanation even if it contributed in part — a tension reported here rather than resolved, consistent with this paper’s treatment of Case 5’s disputed Grok-benchmark claim.

The episode reproduces this case’s collective-action structure in a new channel: distillation, not export control, is the contested transmission mechanism, but the underlying logic is identical — restricting one channel does not remove the underlying capability pressure moving through others. It also surfaces a domestic-policy variant of the same dilemma this case otherwise treats as inter-state. Reporting describes the administration weighing targeted restrictions on domestic use of Chinese open-weight models rather than a blanket ban, while adoption already outpaces the policy debate: one venture-capital survey found 80% of developers worldwide building on open-source tools now use Chinese models, and Airbnb’s CEO has publicly credited Alibaba’s Qwen as a fast, cheap, production-grade choice. The proposed restriction itself divides the governance actors Section 4.1 already treats as internally split: a suggestion from a co-author of the administration’s own AI Action Plan that Kimi’s release could justify new “regulatory risk” around Chinese open models drew immediate pushback from within the same policy circle as a step toward “regulatory capture,” and Representative Ted Lieu separately noted the tension between the distillation accusation and the same administration’s continued clearance of high-performance chip sales to China. This is a fourth documented instance, after Cases 1, 2, and 5, of coordination failure among nominally aligned actors rather than only between competing firms or states — reinforcing, not merely repeating, the pattern named in Section 7.

This split escalated further within days: on July 24, 2026, Nvidia CEO Jensen Huang broke a long-standing silence on X — his first post ever on the platform — specifically to amplify a joint industry letter, “Open Weights and American AI Leadership,” signed by Nvidia and roughly twenty other organizations including Meta, Microsoft, and Palantir, sent to Congress arguing against restricting open-weight models and explicitly characterizing distillation as “a legitimate model-improvement technique” rather than the IP theft Bessent’s sanctions threat presumes. Huang had, the day before, called Chinese models “excellent” and dismissed the idea they threaten U.S. companies. This is no longer officials disagreeing with each other, as in the AI Action Plan exchange above: it is industry itself organizing a formal congressional intervention against the executive branch’s own stated position — the clearest evidence yet that the coordination failure this case documents runs through the government-industry boundary as well as within government [27].

5.4 Case 4 — AI Content Licensing and Litigation (Negotiated-Settlement Type)

This is the paper’s principal test of the Nash Bargaining apparatus — Section 4.6’s constraint (b) — since it is the first case offering an observable disagreement point running in parallel with observable negotiated settlements for the same underlying dispute type, across many independent stakeholder pairs. New York Times v. OpenAI and Microsoft (filed December 2023, still active, escalating as of a July 9, 2026 sanctions motion alleging OpenAI misrepresented its ability to search its own systems for evidence — telling the court it could not search its models for the plaintiffs’ copyrighted material while, per the plaintiffs’ filing, having already done so before the first suit was even filed) is the flagship disagreement point. Dozens of structurally similar pairs converged to settlement over the same period — News Corp–Meta (up to $50M/year, 3+ years), NYT–Amazon ($20–25M), Anthropic–authors ($1.5B, the Bartz settlement), among others.

State variables and formal structure:

dᵢ(t) = φᵢ(P(t)) + λ·Ωᵢ(t)     [disagreement point: direct legal-state channel plus vicarious peer-observation channel]     (7)

P(t) is a shared legal/regulatory-certainty variable moved by binding rulings rather than private settlements (which resolve one pair without setting precedent for others). Two independent rulings — the Bartz settlement and the UK Getty v. Stability judgment — both rejected the broad claim that training itself is categorically infringing while finding narrower liability tied to specific conduct (pirated acquisition; reproduced trademarks), giving P(t) a specific, evidenced doctrinal direction rather than merely an acknowledged capacity to move. Ωᵢ(t) captures a vicarious-learning channel independent of P(t): OpenAI’s proactive licensing approach to Getty, explicitly motivated by observing Stability’s litigation exposure, is a documented instance of a pair adjusting strategy based on a different pair’s outcome rather than its own bilateral history or a ruling directly binding it.

Section 4.2’s cardinal-utility requirement is not free here: dᵢ(t) mixes a directly monetary channel (φᵢ(P(t)), settlement dollar amounts) with a non-monetary, strategic one (Ωᵢ(t), precedent-observation effects). Treating their sum as one cardinal quantity implicitly commits to a proxy — the natural one being each party’s own estimate of the expected present value of future licensing-market position, converting precedent stakes into a dollar-equivalent via that estimate. This paper does not measure that conversion rate for any pair; it is assumed rather than estimated. The qualitative findings in Sections 5.4.1–5.4.3 do not depend on its specific value, only on the ordinal claim that holdout pairs value precedent more than settlement — a claim the pattern of who settles and who doesn’t already supports without requiring the dollar-equivalent figure.

Bargaining weight αᵢⱼ is driven by litigation-sustaining capacity and, independently, by precedent stakes: a case explicitly framed as the industry’s defining test is worth more unsettled than settled to both sides, since a binding ruling outvalues a private deal for whichever party believes it can win outright. Two independent, high-profile pairs — NYT–OpenAI and Getty–Stability — confirm this pattern: both remain unresolved fifteen-plus months after the ruling that pulled a broad wave of other pairs into settlement, and both are the pairs most explicitly described in coverage as precedent-defining.

A three-way strategy typology, rather than a settle/litigate binary, is required by the evidence: settle, hold-to-precedent (litigate specifically because a ruling would move P(t) favorably — the Times, Getty), and hold-by-delay (decline both paths, exemplified by Midjourney’s continued shipping with no settlement and no visible behavioral change, rational specifically when litigation-visibility cost is low relative to the value of continued unconstrained operation). Repeat-player AI companies exhibit portfolio-level rather than case-by-case selection: Anthropic settled with book authors while simultaneously escalating against music-rights holders on a larger claim, and this is best read as coherent portfolio selection between two different precedent-value calculations for two content types, not inconsistency.

5.4.1 Tested prediction — P(t)-shift triggers reorganization then a settlement wave

The naive form of this prediction (settlement frequency accelerates immediately following a P(t)-shifting ruling) is falsified by the data: bilateral deal announcements were notably sparse in the September–October 2025 window immediately following the Bartz settlement. The revised and better-supported form is that a P(t)-shifting ruling first triggers reorganization of the bargaining mechanism itself — Microsoft’s Publisher Content Marketplace launched within days of the settlement — with a genuine settlement wave following on a two-to-three-month lag, concentrated disproportionately among prior holdouts: Meta, previously absent from bilateral licensing, signed seven multi-year deals in a single December 2025 announcement, explicitly framed by industry analysis as risk-management-driven.

5.4.2 Tested prediction — standardization of settlement mechanism

The Really Simple Licensing (RSL) standard shows sharply asymmetric adoption rather than the predicted absence of standardization altogether: over 1,500 publisher-side endorsers by mid-2026, against zero committed adopters on the AI-company side as of the most recent reporting, with RSL’s own leadership stating the explicit strategy is to build supply-side scale before approaching AI companies at all. This is consistent with, and sharpens, the αᵢⱼ framework: standardization is a rational coalition-formation response specifically for the side with weaker individual bargaining power (many small publishers pooling leverage, explicitly modeled on ASCAP/BMI-style collective licensing), while the side with stronger individual power has no incentive to cede it by joining a shared framework. This asymmetry is the specific finding the companion theory paper’s own Section 5.3 reports as mixed evidence for Proposition 3 — bilateral settlements proliferating alongside a standardization attempt that secured supply-side endorsement but no demand-side adoption — before connecting it to Proposition 4 and deferring the lag-threshold question resolved in Section 5.4.3 below.

5.4.3 Delivering paper 1’s deferred lag/threshold question — clarity, not sequence, drives pivot speed

The companion theory paper’s Proposition 2 (its own Section 3.3, distinct from this paper’s own Section 3.3) distinguishes gradual drift from punctuated shift as structurally different forms of landscape non-stationarity, citing this case’s ruling-driven jumps as an instance of the latter. The specific deferred question resolved below comes from elsewhere in the companion paper: its Section 5.3, testing Propositions 3 and 4 together, reports mixed evidence for Proposition 3 in this very case (bilateral settlements proliferating alongside the RSL standard’s supply-side-only adoption — Section 5.4.2 below), connects that finding to Proposition 4’s temporal claim, and explicitly declines to specify — leaving to this paper — a lag or threshold level of landscape non-stationarity past which incentives shift from bilateral settlement toward persistent coordination. Given the punctuated-shift framing, the naive version of that question — is there a single threshold of accumulated non-stationarity — is not quite the right one to ask; a discrete-jump landscape does not accumulate smoothly toward a crossing point the way continuous drift would. The better-posed and testable question is whether successive punctuating events produce progressively faster pivots, and if not, what does predict pivot speed instead.

The data does not support progressively faster pivots (Figure 4). Section 5.4.1 established the Bartz-to-Meta lag at two to three months; Getty’s UK ruling (November 4, 2025) to Getty’s own licensing deal with OpenAI shows a longer lag of roughly seven months (June 2026) — longer, not shorter, than the first gap, directly against the naive hypothesis.

The better-supported explanation is that pivot speed tracks the triggering event’s informational clarity rather than its position in a sequence. Bartz was a clean settlement with an explicit, quotable price ($1.5 billion, approximately $3,000 per work) — an unambiguous signal other parties could act on directly. Getty’s ruling was structurally murkier: Getty lost its central copyright claim, won only a narrow trademark finding, and the court’s final order states explicitly that Getty’s core copyright claims were never adjudicated, since Getty withdrew them before judgment rather than losing them outright. A weaker, more ambiguous precedent took longer to move behavior. This reframes the deferred question from “when does the threshold trigger” to “does the triggering event supply a clear price or precedent” — a claim checkable against any future ruling in this space by assessing its clarity independent of how many prior rulings preceded it.

Figure 4. Case 4 timeline (Section 5.4.3): the Bartz-to-Meta lag (~2–3 months, clear price) is shorter than the Getty-ruling-to-Getty–OpenAI-deal lag (~7 months, murky precedent) — pivot speed tracks informational clarity, not sequence position.

One genuine confound is reported rather than absorbed into the landscape story: Getty’s OpenAI deal closed three weeks before a regulatory deadline on an unrelated Getty corporate merger, meaning some or most of the seven-month gap may reflect Getty’s own transactional calendar rather than anything about the shared landscape’s non-stationarity. This is stated as an open limitation on the finding, not resolved in either direction.

The companion question — whether supply-side and demand-side coordination are converging or diverging — returns an unambiguous result. RSL’s supply-side endorsement grew roughly thirtyfold (from approximately 50 partner organizations in November 2025 to over 1,500 by mid-2026) while demand-side adoption remained at exactly zero throughout the same window: not slow convergence, but literal non-movement on one side against thirtyfold growth on the other. A third, independent confirmation of the precedent-suppression pattern from Section 5.4.1 also emerged during this check: Getty was granted leave to appeal its loss against Stability AI in December 2025, meaning the same rights-holder is simultaneously escalating litigation against its original, highest-stakes precedent-setting opponent while settling quickly with a different, lower-stakes counterparty — the identical within-agent divergence pattern already documented independently for Anthropic and for the Times.

5.5 Case 5 — AI Infrastructure Buildout and Local/Environmental Externality

Type: externality, in the mold of Case 1 — Section 4.6’s diffusion constraint (d), exercised here on the resistance-tactics side of Section 4.4’s apparatus rather than the practice-adoption side — but geographically concentrated rather than diffuse, with a sharper distributional dimension and a distinct illegitimate-means sub-instance that is the strongest current candidate for the taxonomy’s still-empty fourth cell (Section 8). The local optimization here — frontier labs and hyperscalers building compute capacity to train and serve frontier models — is straightforwardly legitimate; the externality falls on residents living near the physical sites rather than on the optimizing firms’ own workforce or customers.

Scale, as of mid-2026: local opposition blocked or delayed 75 data center projects worth $130 billion in Q1 2026 alone, matching the full-year 2025 total in a single quarter. Active opposition groups more than doubled in the same quarter, from 396 to 833, across 49 states. A May 2026 Gallup poll found 71% of Americans oppose data center construction in their own area, exceeding opposition to a nearby nuclear plant. More than 300 state bills were introduced in the first six weeks of 2026, and at least 14 states have considered outright moratoriums.

State variables: B(t), buildout capacity (capital deployed, megawatts online — this case’s Dynamism-registering quantity, the direct analog of Case 1’s A(t)); H_r(t), realized local harm (documented emissions, aquifer drawdown, litigated health impact, and realized electricity-cost pass-through — wholesale costs more than doubled in some residential areas adjacent to data centers per Bloomberg reporting); and H_a(t), anticipated/mobilized opposition (petition counts, active-group formation, state bill introduction rate), reproducing Case 1’s E(t)/L(t) leading/lagging structure with a sharper instance — opposition has in some documented cases mobilized before a project was formally filed, meaning H_a(t) can lead not just the realization of harm but the triggering event itself.

Applying the Section 4.1 actor decomposition, with the governance-tier refinement it now carries: federal government is actively enabling (an executive order fast-tracking construction; Department of Justice intervention on a company’s behalf in the xAI instance below); state legislatures are increasingly restrictive (New York’s one-year permit pause; Maine’s near-miss statewide moratorium; Florida blocking cost pass-through; Idaho restricting water use; Washington withdrawing a tax break); state regulators are mixed, in at least one documented instance enabling evasion through a permitting classification; and county/local government is the site of the public hearings that generate H_a(t) in the first place. Community actors are similarly differentiated — hyperlocal groups alongside large national organizations (Greenpeace, Friends of the Earth, and a NAACP-backed 500-group coalition) — and resistance tactics are documented as diffusing across communities via the extension to Section 4.4’s apparatus described there, with reporting explicitly describing an internalized “opposition playbook” spreading between affected areas.

Absorption capacity reproduces the Section 7 synthesis theme with a clean new instance: communities with existing hyperscaler presence (Northern Virginia, Northern California) show greater capacity to absorb new proposals without escalation, while opposition intensifies fastest in rural communities encountering large-scale development for the first time — absorption capacity determined by prior institutional and civic exposure rather than headcount, as in the DeepMind talent case’s counterpart in Section 5.6. The political-accountability feedback channel that Case 1 evidenced only anecdotally gets a realized instance here: Utah’s state senate leader lost his position over a data center deal, an actual electoral consequence rather than an anxiety signal. And Section 3’s locality-of-criteria point gets a current illustration at the state level — different states reaching opposite conclusions from the same underlying tradeoff using entirely different locally-set criteria, with no shared standard across them.

The xAI Memphis/Southaven instance is a sub-case in illegitimate-means territory, distinct in kind from the broader buildout pattern, and it has escalated substantially since first documented here. One actor-level change is worth noting under this paper’s own Section 4.1 apparatus: xAI was acquired by SpaceX in the first quarter of 2026, consolidating what this decomposition would previously have treated as two separate actors under common ownership — a fact that does not change the turbine record below but is relevant to how “the company” should be read in what follows. xAI’s unpermitted turbine count at Colossus 2 grew from 27 at the time of formal notice (February 2026) to 33 at filing (April) to 46 (May) to 59 as of mid-July — nearly double the count previously reported — in a majority-Black area already failing federal ozone standards. This is now documented as a repeated pattern rather than a one-off: an xAI senior manager described the Colossus 2 approach internally as “copy and paste what we did at the Colossus 1 site,” and Colossus 1 shows the identical sequence — 30-plus unpermitted turbines discovered by aerial imagery in April 2025, resolved only after the Southern Environmental Law Center threatened suit, with just 15 of them ever actually permitted. The NAACP, Southern Environmental Law Center, and Earthjustice sued under the Clean Air Act in April 2026; rather than complying after notice, the company added more turbines through the litigation. The Department of Justice intervened in June 2026 to seek dismissal, on a legal theory broader than this case specifically: the motion argues the government’s right to intervene in a citizen suit includes the right to unilaterally dismiss it in its entirety, which watchdog groups characterize as effectively claiming veto power over citizen suits as an enforcement category, not just this dispute. The national-security justification is specific and worth reporting precisely: a Department of Defense declaration states Grok is one of four AI models cleared for “mission-critical operations,” crediting a Grok variant with enabling deployment of over 2,000 munitions to 2,000 targets within 96 hours during a recent conflict — alongside independent reporting noting Grok trails competing frontier models on most 2026 benchmarks, a tension in the claim worth flagging as reported rather than resolved. A further governance-tier actor has since emerged: the Senate Environment and Public Works Committee’s ranking member sent a formal oversight letter to the EPA in April 2026 documenting the cross-site pattern, adding legislative oversight to the federal-executive/state/local conflict already present in this case. This remains the strongest candidate the paper has found for the empty fourth taxonomy cell (illegitimate means, contained damage), provided the litigation ultimately produces a shutdown and remediation; as of the most recent reporting, no ruling has issued on either the DOJ’s motion to dismiss or the NAACP’s pending preliminary-injunction request, turbines are still operating and still increasing, and cell membership remains undetermined rather than confirmed — if anything, the trajectory since this case was first documented has moved toward continued escalation rather than toward resolution.

Testable claims: opposition intensity should continue correlating inversely with prior hyperscaler exposure as buildout pushes into new rural markets, checkable against ongoing tracker data; state legislative activity should continue to outpace realized-harm documentation in raw volume if H_a(t) genuinely leads H_r(t) as hypothesized; and the xAI sub-case’s fourth-cell status resolves in one of two directions depending on whether the DOJ succeeds in dismissing the suit (cell stays empty) or the litigation proceeds to shutdown and remediation (cell fills) — a near-term-trackable fork rather than a settled outcome.

5.6 Contained and Null-Damage Instances

The damage taxonomy requires a control set, not only escalating cases, both because escalation-only sampling is a real selection-bias risk (visible, reportable cases oversample escalation) and because local optimization does not necessarily generate global, or even local, damage at all. Meta’s July 2026 X-platform product announcement and xAI’s reciprocal publicity response is treated as a genuine null/contained case at the level of the specific interaction, while flagging that Meta’s broader AI strategy (funded partly by roughly 8,000 job cuts in 2026) is not null-damage at the company-strategy level — illustrating that containment classifications must specify their scope (single event vs. broader strategy) rather than being applied at the company level uniformly.

Google DeepMind’s response to a wave of senior-researcher departures to OpenAI, Anthropic, and Meta is the paper’s clearest test case for absorption capacity as a distinct containment mechanism, separate from reciprocal tit-for-tat symmetry — a candidate instance, not a confirmed one, for reasons the rest of this paragraph complicates rather than resolves: DeepMind’s public position rested on bench depth (roughly 3,000 researchers against — by the fuller count assembled since — six departures since February 2026) rather than a claim of reciprocal poaching — CEO Demis Hassabis has maintained publicly that DeepMind has “by far the biggest and broadest research bench of any of the labs out there.” A real market-perceived reaction (up to a 7% intraday share-price decline, closing nearer 5%, on the day both Noam Shazeer’s move to OpenAI and John Jumper’s to Anthropic became public) coexists with genuine, if incomplete, evidence of operational response: Google had already formed a dedicated internal “AI Coding Strike Team” in April 2026, before the highest-profile departures, targeting a perceived coding-capability gap against Anthropic and OpenAI — evidence of organizational concern predating the visible exodus, not only a reaction to it, which complicates a pure bench-depth-absorbs-it reading without confirming the alternative. A separate, later complication is worth reporting rather than folding into the same causal story: subsequent reporting attributes some departures specifically to opposition to an April 2026 Pentagon technology-use agreement, a values-driven exit distinct from competitive poaching, meaning this instance likely now contains two different departure mechanisms rather than one. The claim this subsection originally left open — whether departures show up in output pace — remains open: independent commentary published since is explicit that no established link between researcher turnover and model-quality decline exists, which this paper reports as continued absence of confirmation rather than resolution in either direction.

5.7 Diffusion Instance — Constitutional AI and Philosophy-Integrated Alignment

Constitutional AI and the practice of integrating philosophers into alignment teams are structurally identical to the weapons-restraint instance in Case 3 — a unilateral practice with no binding power over competitors — but positively valenced, and the diffusion apparatus in Section 4.4 predicts, and the evidence confirms, a materially different outcome. At least three leading labs (Anthropic, Google DeepMind, and one further lab per industry coverage) show substantive philosophy integration, including a highly-cited (1,700+ citations) foundational paper from a DeepMind researcher — real multi-agent adoption, unlike the weapons-restraint case, where restraint was circumvented rather than copied. OpenAI is an explicit, named holdout, treating safety as an engineering problem rather than integrating philosophical inquiry, reproducing the partial-diffusion-with-holdout pattern found independently in Sections 5.6 and 6.1.

We attribute the diffusion/containment asymmetry between this case and the weapons-restraint case to codifiability κ and incentive-compatibility γ: Constitutional AI and its published successor, the Claude Constitution, are transferable, independently evaluable artifacts, whereas a refusal is not something a competitor can adopt; and the practice is plausibly compatible with adopting labs’ own commercial and reputational objectives, unlike the weapons restraint, which was purely costly.

A nested binding-power gap is separately evidenced: hiring philosophers does not guarantee influence over shipped model behavior absent a pipeline into evaluation metrics or deployment gating, and industry coverage explicitly raises the possibility that some hiring is more optics than substance — precisely the βᵢ(t) discount formalized in Section 4.4.

A related but distinct extension of this pattern surfaced this week, reported here for its topicality rather than claimed as confirming the same mechanism: at the Fields Medal award ceremony on July 23, 2026, laureate Jacob Tsimerman announced he is leaving pure mathematics to join OpenAI’s AI safety research, explicitly citing AI-risk concern and the value of mathematical rigor and proof-based methods for safety work. This is not philosopher hiring, but it plausibly is the same underlying phenomenon in a different discipline — elite outside-field talent recruited into safety-adjacent work at a frontier lab — and is reported here as a second, separate data point rather than folded into the philosopher-specific evidence above. A non-parallel development from the same week is worth distinguishing rather than conflating, despite the coincidence that made both newsworthy together: Tsimerman’s former undergraduate advisee, Levent Alpöge, already an Anthropic researcher, used Claude Fable 5 three days earlier to find a counterexample disproving the 87-year-old Jacobian conjecture for dimensions three and higher. That is a demonstration of AI capability in mathematical research, not an instance of talent recruitment into alignment work, and this paper does not treat it as evidence for the claim above — the mentor/student, same-week pairing is a coincidence of timing, not a second confirming case [26].

6. Diversity as Search: Parallel Local Optimization and the Convergence Question

This section is a direct empirical test of the iterative-convergence question from Section 2.4, using strategic and technical diversity across frontier labs as the observable rather than damage. Parallel local search across a nonconvex landscape (Section 2.2) only converges toward a global optimum if a recombination mechanism moves information between independently searching agents; without one, diversity produces permanently separate local optima rather than synthesis. We treat governance/distribution strategy and technical/architectural paradigm as at minimum two independent axes of this search space, not one spectrum, and find that the two behave differently with respect to convergence.

6.1 Architecture Axis: Transformer versus World-Model Approaches

A well-capitalized, explicit rejection of the mainstream transformer paradigm exists (a dedicated world-models startup founded on the claim that large language models are a dead end for general intelligence, raising roughly $1B at a $3B valuation, alongside broader embodied-world-model investment near $6B in Q1 2026), coexisting with active technical hybridization in the mainstream literature: architecture surveys describe monolithic transformers fragmenting into hybrid designs, and recent papers formally frame standard transformer language models as a special case of world models, building an explicit technical bridge between the paradigms. We treat this hybridization, carried through ordinary publication, as the recombination mechanism predicted necessary in Section 2.4, actively operating rather than absent. A genuine, documented counter-argument survives unresolved: the scaling-law analogy underlying the world-model bet may not transfer outside language, since the physical world lacks a natural discrete unit equivalent to a token.

6.2 Distribution Axis: Closed versus Open Release — A Three-Factor Model

An initial two-factor account (export-control exposure Xᵢ versus stated safety philosophy) was tested against Mistral AI as a disconfirming case and falsified in its original form: Mistral has full, unexcluded access to closed Western alternatives yet ships its flagship 675-billion-parameter model fully open-weight, explicitly framed around European sovereignty rather than any access constraint. The revised, evidence-consistent model requires three independent factors:

oᵢ(t) = g(Xᵢ, Sovᵢ, Mᵢ)     (8)

Xᵢ — export-control exclusion (the mechanism behind Chinese-lab openness); Sovᵢ — sovereignty/independence positioning as a goal in itself, evidenced cleanly by Mistral, where Sovᵢ is high and Xᵢ is zero; and Mᵢ — ecosystem/commoditization strategy (“commoditize the complement”), a freestanding commercial logic evidenced in both early Meta and Mistral’s own open-core product structure (small tiers open, flagship tiers closed and metered). None of the three reduces to another, and safety philosophy — the variable originally proposed as the alternative explanation — does not appear as an explanatory factor anywhere in the evidence reviewed. (Note: this factor was originally labeled Dᵢ; it is relabeled Sovᵢ here to avoid collision with the Dynamism variable D(t) introduced in Section 5.1.1, following the companion theory paper’s C(t)/D(t) convention.)

The revised, more immediately checkable prediction: since Xᵢ is approximately constant across Chinese labs (similar exclusion), any variation in openness observed among them cannot be explained by Xᵢ and should trace instead to differences in Sovᵢ or Mᵢ — a within-group test that holds the confounding factor fixed rather than attempting to control for it after the fact. We treat the falsification-then-revision itself as a finding: the distribution axis is not merely failing to converge, it is fragmenting for more independent reasons than a first pass suggested, which is a stronger, not weaker, version of the core claim that this axis behaves as portfolio allocation rather than convergent search.

A third, later data point is consistent with the revised model rather than prompting a further revision: Thinking Machines Lab’s July 2026 release of Inkling, a 975-billion-parameter model under a fully open Apache 2.0 license. Thinking Machines is a well-capitalized U.S. lab (reported $10–12B valuation) with Xᵢ = 0, the same position as Mistral — full, unexcluded access to closed Western alternatives. Sovᵢ is again the explanatory factor a two-factor account would miss: the company frames Inkling explicitly around resistance to “censorship” and reversing “the trend of commercial AI models becoming increasingly closed,” an independence-positioning claim structurally identical to Mistral’s European-sovereignty framing though aimed at a different audience. Mᵢ is also cleanly present, and unusually, named by the company itself rather than inferred after the fact: Inkling’s weights are free, but Thinking Machines monetizes a companion fine-tuning platform, Tinker — a textbook commoditize-the-complement structure stated as the business model, not reconstructed from indirect evidence [24]. One further, unplanned confirmation ties this case back to this paper’s own apparatus: Thinking Machines states Inkling’s architecture “largely follows” DeepSeek’s V3 design, making the model itself a live instance of Section 4.4’s diffusion apparatus — a high-codifiability practice (a published architecture) diffusing across the same geopolitical line Case 3’s export-control regime was built to police, independent of and faster than any policy response to it.

7. Synthesis: Recurring Structures Across Cases

Six structural patterns recur independently across cases developed under different prompts and different data, which we take as the paper’s principal intellectual payoff rather than a coincidence of case selection:

• Absorption capacity as a containment mechanism distinct from reciprocal restraint — first identified in the DeepMind talent case (Section 5.6), structurally identical to the collective-action weakness of unilateral restraint documented in Case 3 (Section 5.3), and reproduced a third time in Case 5 as prior institutional and civic exposure to hyperscaler development predicting lower-escalation outcomes: all three concern whether a system’s buffering capacity exceeds a local shock, just with different valence and different units (headcount, market confidence, civic experience).
• Within-agent and within-organization portfolio splitting rather than uniform strategy — documented independently in Anthropic’s simultaneous settlement (authors) and escalation (music rights) in Case 4, in Getty’s simultaneous litigation against Stability AI and settlement with OpenAI (now reinforced by Getty’s December 2025 appeal grant against Stability specifically, a third confirming instance of precedent-value suppressing convergence for an agent’s highest-stakes counterparty while it settles freely elsewhere), in Mistral’s own open-core product tiering in Section 6.2, and — at a finer grain, among sub-units of a single firm rather than across counterparties — in the three uncoordinated engineering teams of Case 2. No case examined settled into one uniform strategy across all counterparties, product lines, or internal sub-units.
• Leading versus lagging indicator structure — formalized first for anticipatory labor-market anxiety versus realized layoffs in Case 1, reproduced independently in DeepMind’s market-perceived share-price reaction versus claimed operational impact in Section 5.6, reproduced a third time in Case 2 as the asymmetry between a narrow internal eval process and a slower but eventually more sensitive external correction network, and reproduced a fourth time in Case 5, where opposition has in documented instances mobilized before a project was even formally filed — the most extreme anticipatory signal found in the paper.
• Partial diffusion with a persistent, named holdout, rather than either full convergence or total containment — found independently in the philosopher-hiring diffusion case (OpenAI as holdout), the architecture-hybridization finding (the world-models dissent), and Midjourney’s delay strategy in Case 4.
• Coordination failure between independently-optimizing local agents lacking a shared integration mechanism recurs at whatever granularity such agents are found — among competing firms and states (Case 3), among rights-holder pairs settling or litigating independently (Case 4), among engineering teams inside a single firm (Case 2), and among governance tiers within a single state apparatus (Case 5, where federal, state, and local government act at cross purposes over the same underlying activity). The failure mode appears to be scale-independent rather than specific to inter-firm or interstate competition, and Case 5 extends it one level further than previously observed — into conflict within a single governance hierarchy rather than only between separate agents. Case 3’s Kimi K3 aftermath reproduces this within a single federal administration’s own policy circle — a proposed restriction on domestic use of Chinese open-weight models drawing “regulatory capture” pushback from within the same coalition that proposed it — confirming the pattern is not specific to formal governance tiers acting at cross purposes, but recurs even within one nominally unified actor once its internal factions are examined.
• Measurement or coordination fragmentation functioning as a direct symptom of low Cohesion, not merely a nuisance obscuring an otherwise-clear picture — first made explicit when operationalizing C(t) for Case 1 (Section 5.1.1), where competing AI-exposure measurement frameworks and fragmented state labor-AI policy both scored low on convergence, but visible independently elsewhere once named: Case 4’s RSL asymmetry (Section 5.4.2) and Section 6.2’s distribution-axis fragmentation are both, in retrospect, instances of the same underlying pattern — stakeholders failing to converge on a shared framework for understanding or responding to the same phenomenon, read as evidence of low Cohesion in the companion theory paper’s specific sense, not just as loosely related cases of disagreement.

7.1 Case Comparison Summary

The following summarizes type, status, and tested predictions across all five numbered cases, for reference against the fuller treatment in Section 5.

• Case 1 — AI coding automation. Type: externality. Status: escalating, feedback coefficient uncalibrated. Key evidence: entry-level pipeline compression (Stanford HAI); E(t)/L(t) structure reinforced by the July 2026 economist letter and the Acemoglu/Johnson reversal.
• Case 2 — Aggregation-blind product regression. Type: intra-organizational. Status: disclosed and remediated, no large-scale recurrence through mid-2026. Key evidence: Anthropic’s own April 2026 postmortem; forward prediction on detection lag not yet independently checkable.
• Case 3 — Export controls / security dilemma. Type: security-dilemma. Status: ongoing, unresolved by design (Folk Theorem preconditions only partially satisfied). Key evidence: Nvidia China market-share decline; NSA/DoD vendor-switching finding as a second data point; Kimi K3 distillation dispute and the domestic ban-versus-adopt debate as a third and fourth, now escalated to industry’s own congressional intervention (Nvidia’s Huang, July 24, 2026), still-live as of this writing.
• Case 4 — AI content licensing and litigation. Type: negotiated-settlement. Status: two tested predictions, one falsified-then-revised (reorganization-then-wave), one confirmed with sharpening (asymmetric RSL adoption). Key evidence: Bartz and Getty rulings; NYT and Getty/Stability as matched precedent-suppression instances.
• Case 5 — AI infrastructure buildout. Type: externality, with an illegitimate-means sub-instance. Status: escalating at the level of the general phenomenon; the xAI sub-case’s fourth-taxonomy-cell status is an open, near-term-trackable fork pending litigation outcome. Key evidence: Q1 2026 opposition data; multi-tier governance conflict; Utah’s realized electoral-consequence data point.

8. Limitations

• Rigor is unevenly applied across cases, though less so than in earlier drafts: Case 4 now carries three numbered, falsifiable predictions tested against real tracker data (the third, Section 5.4.3, delivering the companion theory paper’s deferred lag/threshold question), and Case 1 now carries an operationalized C(t)/D(t) construction (Section 5.1.1) tested against three candidate aggregation forms. Cases 2, 3, and 5 remain more conceptually elaborated than empirically tested against comparably explicit predictions (Case 2’s forward prediction on detection lag, and Case 5’s three testable claims, are stated but not yet checkable against future data), and full calibration of Case 1’s feedback coefficient, beyond the illustrative construction in 5.1.1, remains open. A concrete calibration strategy, not attempted here: pair quarterly developer-sentiment and policy indices (e.g., the AI-exposure measures discussed in Section 3.3, state bill-introduction rates) with enterprise software-deployment metrics in a structural equation or vector-autoregression model, using E(t) and L(t) as the two latent or observed series and testing the hypothesized sign ∂h/∂E(t) < 0 directly rather than inferring it qualitatively as this paper does.
• Case visibility is a real selection-bias risk: reportable, escalating cases are structurally overrepresented relative to null or well-contained ones, since containment that works quietly generates no coverage. Section 5.6 is a deliberate but partial correction, not a full solution. Case 2 is a partial exception — its damage was disclosed voluntarily by the implicated organization rather than surfaced entirely by outside pressure, which may make it a less representative instance of intra-organizational failure than cases where no comparable disclosure norm exists.
• Attribution uncertainty in Case 1 (AI-washing) is treated as a modeling fact rather than resolved, consistent with the evidence available.
• The two components of D(t) in Case 1 (Section 5.1.1) previously rested on data of unequal quality; the adoption-side component has since been reconstructed from a single consistent source (Stack Overflow’s Developer Survey, fielding the same question every year since 2023), closing the original asymmetry with the mobilization-side time series. A smaller residual risk remains: Stack Overflow’s own respondent count fell over the same window (roughly 90,000 to roughly 49,000), a possible compositional confound a same-instrument series doesn’t fully escape — a different and more inspectable kind of uncertainty than the original cross-survey incompatibility, but not a resolved one.
• Several empirical anchors are live and unresolved as of this writing — the NYT v. OpenAI sanctions motion, Getty’s pending UK appeal, RSL’s stalled demand-side adoption, the DOJ’s intervention in the xAI Memphis litigation, now further escalated (Section 5.5), and the Kimi K3 distillation dispute (Section 5.3), the freshest of these: Kimi K3’s own weights are not fully public until July 27, 2026, Moonshot has not yet responded to the distillation accusation, and the domestic ban-versus-adopt policy debate it triggered is, as of this writing, days old — findings tied to any of these should be understood as current only as of that date, not as settled.
• The fourth cell of the damage taxonomy (illegitimate means, contained damage) now has a live candidate (Case 5’s xAI sub-instance) rather than remaining wholly empty, but its status is presently undetermined pending litigation outcome rather than confirmed — a distinct and more precise state than either “empty” or “filled,” worth tracking explicitly in future revisions rather than collapsing into either. As of this writing, the trajectory has moved toward further escalation rather than toward resolution.
• A further live illegitimate-means instance was tracked but is deliberately excluded from the main taxonomy rather than treated as a sixth case: Apple’s July 10, 2026 trade-secret lawsuit against OpenAI, alleging former Apple employees — including OpenAI’s hardware chief, a former Apple vice president — fed confidential unreleased-hardware IP into OpenAI’s consumer-device development [7]. This is corporate espionage in a product-development race, not an instance of the AI-capability, distribution, or infrastructure-externality dynamics this paper’s apparatus is built to analyze; it is noted here for completeness rather than integrated, since forcing it into the existing taxonomy would stretch the framework past what it is designed to explain.
• Section 3’s own finding — that optimality criteria are locally set — applies reflexively to this paper’s own case classifications, which should be read as one defensible local framing rather than an objectively correct partition of the evidence.
• A further limitation, raised in review: Case 5’s xAI sub-instance (Section 5.5) receives detailed, unfavorable scrutiny, which risks looking asymmetric given this paper’s own Anthropic-adjacent authorship context (Author Contributions, above), even with that context anonymized for review. Two things partially offset this without resolving it. First, Case 2 turns the identical critical lens on Anthropic itself — the paper’s one intra-organizational case is a self-critical postmortem, not a comparison chosen to flatter the author’s own affiliation. Second, Case 3’s Anthropic–NSA/DoD vendor-switching finding (Section 5.3) is reported as a demonstration of collective-action failure, not of Anthropic’s restraint being rewarded — the point of including it is that the restraint did not hold competitors back, which is not a flattering framing read carefully. Neither offset is a substitute for the actual gap: this paper does not systematically survey comparable infrastructure-buildout permitting or environmental incidents at other frontier labs’ data center sites to confirm xAI’s treatment is proportionate rather than singled out. That survey is identified here as a specific, checkable item for the next revision rather than deferred silently.

9. Conclusion and Directions for Further Formalization

Treating Gradual AGI explicitly as a multi-agent optimization problem, rather than a metaphor, produces concrete, falsifiable structure: a tensor-valued long-term objective requiring genuine bargaining rather than calculation; a nonconvex landscape whose stationarity must be checked case by case rather than assumed; two axes (Cohesion, Dynamism) in genuine tension rather than one target; and a family of borrowed but precisely-adapted formal tools — Nash Bargaining, the Folk Theorem, real-options reasoning, Bass diffusion — unified into the single master optimization statement of Section 4.6 and each earning its place by being tested against current, checkable evidence rather than asserted. The clearest open items for the next round of work are calibrating Case 1’s feedback coefficient against a longer time series, confirming or ruling out the xAI candidate already identified for the taxonomy’s fourth cell (Section 5.5) once its litigation resolves, and extending the Section 6 diversity apparatus to the further strategic axes (compute-scaling philosophy in particular) flagged but not yet examined in depth. One further direction worth naming rather than developing here: Section 4.6’s finding that no meta-actor solves a single joint problem is a structural fact about this apparatus, not a design recommendation, and it leaves open what institutions could make Shared Stewardship of a tensor-valued objective more effective without collapsing it into a scalar. Case 4’s RSL standardization attempt and Section 4.2’s own weighted-NBS discussion both gesture at this without resolving it: coalitions that pool bargaining power still need someone to set the weights, and this paper does not propose a governance design that avoids that regress.

Appendix A. Symbol Table

Consolidated for reference across Sections 4–6. First-defined section given for each; case-local symbols reused across multiple cases (t as a discrete time index; generic h, g update functions) are omitted where their meaning is stated locally at each use.

• A(t) — adoption share, Case 1 (5.1).
• E(t), L(t) — anticipated / realized harm, Case 1 (5.1). Distinct from the companion theory paper’s use of E(t)/L(t) for exogenous influence and the optimization landscape respectively; see the cross-paper notes accompanying this paper.
• C(t), D(t) — Cohesion and Dynamism, defined by the companion theory paper’s Proposition 3 and instantiated as process-level definitions in its own Section 4.3 (distinct from this paper’s Section 4.3, the Nash Bargaining apparatus), operationalized for Case 1 in Section 5.1.1. D(t) is computed both signed and unsigned (Section 5.1.1); which form better fits the data remains an open, case-by-case question.
• Q(t) — integrated composite-system quality metric, Case 2 (5.2).
• βᵢ(t) — binding-power discount per adopter, Section 4.4, reused in Case 2 (5.2) and Section 5.7.
• Φ(t) — effective (β-weighted) diffusion, Section 4.4. Originally labeled E(t); renamed to avoid collision with Case 1’s E(t) (anticipated harm, Section 5.1) and the companion theory paper’s own E(t) (exogenous influence) — the same class of collision the Sovᵢ rename below addresses, caught on the same review pass.
• P(t) — shared legal/regulatory-certainty variable, Case 4 (5.4).
• Ωᵢ(t) — vicarious-learning / peer-observation term, Case 4 (5.4).
• αᵢⱼ — bargaining weight, Section 4.2, applied in Case 4 (5.4).
• m, N(t), f(t) — addressable population, adopter count, adoption fraction, Section 4.4 (Bass diffusion apparatus).
• h(·) — acceleration-response function in Case 1’s ΔA(t+1) = h(ΔA(t), E(t), L(t)) (Eq. 6, Section 5.1); left functionally unspecified beyond the hypothesized sign ∂h/∂E(t) < 0, for the same reason p(κ) and q(γ) are left unspecified in Section 4.4 — no case here supplies calibration points to justify a specific form.
• g(·) — distribution-strategy function in oᵢ(t) = g(Xᵢ, Sovᵢ, Mᵢ) (Eq. 8, Section 6.2); likewise not given a specific functional form, only the claim that all three arguments are independently necessary (Section 6.2’s within-group test).
• p, q — innovation and imitation coefficients, Section 4.4.
• κ, γ — codifiability and local incentive-compatibility, Section 4.4, bounding p and q respectively.
• oᵢ(t) — openness (distribution-strategy) variable, Section 6.2.
• Xᵢ, Sovᵢ, Mᵢ — export-exclusion, sovereignty-positioning, and ecosystem-strategy factors composing oᵢ(t), Section 6.2. Sovᵢ was originally labeled Dᵢ; renamed to avoid collision with Dynamism once D(t) was operationalized in Section 5.1.1 — a collision this table exists specifically to catch.
• B(t), H_r(t), H_a(t) — buildout capacity, realized local harm, anticipated/mobilized opposition, Case 5 (5.5).
• πᵢ, π, Jᵢ, k — actor policy, joint policy, actor objective, and objective dimensionality, Section 4.6 (the master statement unifying 4.1–4.5). Notation only; no case in Section 5 evaluates these directly, and none of the case-level operationalizations (C(t), D(t), Φ(t), etc.) require them.

New symbols introduced in future revisions should be checked against this table and against the companion theory paper’s own notation before adoption, given the L(t)/E(t) collision documented earlier in this project’s history.

Author Contributions and Methodological Disclosure

This paper is produced through a human-directed, multi-model collaborative workflow, disclosed here in the spirit of CRediT-style contributor statements. The human author, W.H.L., originated the project, initiated with core concepts and propositions, selected its case studies, made all final editorial judgments on claims, framing, and inclusion or exclusion of material, and is responsible for the paper’s conclusions. Large language model, Claude Sonnet 5 (Anthropic), contributed to drafting, formal notation, fact verification via web search against primary and news sources, and internal consistency review across sections and against the companion papers in this series, in all cases under the human author’s direction and subject to the human author’s revision or rejection of any AI-drafted content. A breakdown of specific contributions, including peer reviews, is provided as the byline at the end of this paper.

References

Companion Series Papers

W.H.L., Claude Sonnet 4. (2026). First Principles of AGI-Inclusive Humanity. Champaign Magazine.

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

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

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

Primary Sources

[1] Stanford Institute for Human-Centered AI (HAI). “2026 AI Index Report” — software-developer employment by age cohort.

[2] Federal Reserve Bank of New York. Entry-level unemployment data, recent college graduates, March 2026.

[3] Pew Research Center. Survey on public sentiment toward everyday AI use, 2026.

[4] Gallup. Longitudinal tracking of public excitement/concern toward AI, 2025–2026.

[5] Bartz et al. v. Anthropic PBC — settlement announcement and terms, September 2025; final-approval proceedings through mid-2026.

[6] New York Times Co. v. Microsoft Corp. and OpenAI, Inc. et al., S.D.N.Y., filed December 27, 2023; amended complaint June 2026; sanctions motion filed July 9, 2026.

[7] Getty Images (US), Inc. v. Stability AI, Inc., UK High Court judgment, November 2025; and parallel U.S. proceedings.

[8] Really Simple Licensing (RSL) Collective. RSL 1.0 specification and adoption announcements, September 2025–July 2026.

[9] Columbia Journalism Review, Tow Center for Digital Journalism. AI deals-and-lawsuits tracker.

[10] White House. National AI Policy Framework, March 2026.

[11] EU AI Act, Article 53 (training-data transparency), enforcement effective August 2026.

[12] Anthropic. Public statements regarding Department of Defense contract terms and vendor status, and NSA/CISA deployment reporting, 2026.

[13] Mistral AI. “Introducing Mistral 3” product announcement, December 2025.

[14] Anthropic. Claude Code / Agent SDK / Cowork quality-regression postmortem, published April 23, 2026.

[15] NAACP, Southern Environmental Law Center, and Earthjustice v. xAI Corp. — Clean Air Act suit filed April 2026, Memphis/Southaven, TN/MS.

[16] Gallup. Poll on public opposition to local data center construction, May 2026.

[17] Data Center Watch. Tracker of blocked/delayed data center projects and active opposition groups, Q1 2026 update.

[18] Stanford Digital Economy Lab. “We Must Act Now: A Statement on AI’s Transformation of the Economy,” July 13, 2026.

[19] Getty Images. UK High Court ruling, November 4, 2025; appeal granted December 16, 2025; Getty-OpenAI licensing agreement, June 2026.

[20] NAACP, Southern Environmental Law Center, and Earthjustice v. xAI Corp. and MZX Tech — amended filings and DOJ motion to intervene and dismiss, N.D. Mississippi, through July 2026.

[21] MultiState.ai and National Conference of State Legislatures. State AI-related bill tracking, 2023–2026.

[22] Reporting on OpenAI product-quality regression episodes and internal responses: Altman’s April 2025 statement on ChatGPT personality/sycophancy; a January 2026 developer town hall on GPT-5.2 writing quality; and a December 2025 internal “code red” memo reported via the Wall Street Journal.

[23] Reporting on Moonshot AI’s Kimi K3 release (July 16, 2026) and the ensuing distillation dispute: White House OSTP Director Michael Kratsios’s July 22, 2026 accusation regarding Anthropic’s Fable 5; Treasury Secretary Bessent’s supporting statement; independent technical assessments disputing the claim; and coverage of the domestic ban-versus-adopt policy debate over Chinese open-weight models.

[24] Reporting on Thinking Machines Lab’s release of Inkling (July 15, 2026), a 975-billion-parameter open-weight model, including the company’s own disclosure regarding its architecture’s relationship to DeepSeek V3 and its Tinker fine-tuning platform.

[25] Reporting on the Google DeepMind researcher-departure wave (Noam Shazeer, John Jumper, Denny Zhou, David Silver, and others, February–July 2026), Alphabet’s market reaction, the internal AI Coding Strike Team formed April 2026, and subsequent reporting linking some departures to opposition to an April 2026 Pentagon technology-use agreement.

[26] Reporting on the 2026 Fields Medal ceremony (July 23, 2026, Philadelphia) and laureate Jacob Tsimerman’s announced move to OpenAI for AI safety research; and on Levent Alpöge’s July 20, 2026 counterexample to the Jacobian conjecture using Anthropic’s Claude Fable 5.

[27] Reporting on Nvidia CEO Jensen Huang’s July 24, 2026 debut X post and the “Open Weights and American AI Leadership” letter to Congress, signed by Nvidia and approximately twenty organizations including Meta, Microsoft, and Palantir.

Secondary Sources and Analysis

[1] Epoch AI. Analysis of Chinese frontier-lab job postings (n≈1,604), 2026.

[2] Reporting on frontier-lab philosopher hiring and alignment-team composition, multiple outlets, 2026.

[3] Reporting on Nvidia China market-share decline and Huawei domestic chip self-sufficiency, 2026.

[4] Trensee. “The Open Source AI Paradox: Why Meta and Mistral Give Away Models Worth Billions,” March 2026.

[5] Industry coverage of the Meta–xAI product-announcement exchange on X, July 2026.

[6] Industry coverage of Google DeepMind researcher departures and market reaction, June 2026.

[7] Apple Inc. v. OpenAI, Inc. et al. — filed July 10, 2026 (referenced as an excluded/illegitimate-means instance, set aside from the main taxonomy per Section 8).

[8] Coverage of Yann LeCun’s departure from Meta and founding of a world-models venture, late 2025–early 2026.

[9] Architecture-survey and technical literature on hybrid transformer/world-model designs, 2026.

[10] Independent third-party audit of Claude Code session quality (n=6,852), and related community and trade-press coverage of the March–April 2026 regression, including post-postmortem developments through June 2026.

[11] Bloomberg. Reporting on wholesale electricity cost increases in residential areas adjacent to data centers, 2026.

[12] Reporting on state-level data center legislation and moratorium proposals (New York, Maine, Florida, Idaho, Washington), and on the Utah state senate leadership contest, 2026.

[13] Apollo Global Management. Chief economist commentary on competing “AI exposure” measurement frameworks, July 2026.

[14] “Why I Didn’t Sign the AI Open Letter,” The Geek Way (Substack), July 2026.

[15] Apollo Global Management, The Daily Spark. “How Exposed Is Your Job to AI? The Experts Can’t Agree,” July 14, 2026, citing Massenkoff and McCrory (2026), Felten et al. (2021), Eisfeldt et al. (2023), Eloundou et al. (2024), and Tomlinson et al. (2025).

[16] Stack Overflow. Annual Developer Survey, “AI” section, 2023–2025 (single organization, consistent question wording: “Do you currently use AI tools in your development process?”).

[17] Trade and legal press coverage of the DOJ’s June 2026 intervention in the xAI Memphis/Southaven litigation and the April 2026 Senate EPW Committee oversight letter.

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Byline
Authors: W.H.L., Claude Sonnet 5
Peer reviews: GPT-5.5, Gemini 3.5, Grok 4, DeepSeek-V4

Publication history:
Current version and date: v0.8, 07.24.2026