Manuscript · frozen
The theory is frozen at the audited 51-page candidate. It will be reopened only for a demonstrated error, a dated factual refresh, a mandatory journal rule, or actual editor/referee feedback.
In Brief (no math)
AI tasks differ on two economically distinct margins: the length of the action chain they require and how much they forgive errors through retries, monitoring, or rollback. Serial tasks with retries generate a two-dimensional task frontier rather than a single quality ladder. Imitation is also directional. A successful trajectory can reveal a plan, while certifying a rare failure rate requires many independent trials. In the paper's certification-and-entry equilibrium, an entrant with less transferable and deployment evidence can test harder yet certify later. Competition prices each capability lead through that imitation window. A longer reliability annuity and complementarity between the two task boundaries then make an optimizing research program invest in horizon first and rotate toward reliability. Repeated racing can make laboratories herd on that margin. Liability and public verification both affect reliability, but their effects on frontier incentives, entry, and market structure differ.
Current Assessment
The latest internal top-five desk screen recommends sending the manuscript to external referees. That is a screening judgment, not a journal decision or an acceptance claim. The paper has survived a proof-level rebuild: the task environment now retains primitive heterogeneity; the certification lag comes from an entry and verification problem; rotation is solved as an optimizing research program; state-dependent lags and total program size are allowed; racing is a renewal game; and welfare and market structure use exact accounting.
The main remaining publication risks are explicit. The paper composes conditional equilibrium modules rather than one global Markov-perfect equilibrium; the direction-specific certification lag is not directly measured; the mapping from program scale to observed training expenditure is qualitative; and the paper is broad. The manuscript treats these as scope and falsification limits rather than disguising them. Read the latest desk screen, its response, and the submission-readiness memorandum.
Current Publication State
Technical package · ready
The executable preflight passes all 7 technical and package gates: complete hashes, 132/0 mathematics, an independent three-pass build, and clean PDF structure.
External decision · pending
No journal submission or decision exists. The recommended first target is JPE; submission awaits author metadata, disclosures, exclusivity, fee authorization, and final human approval.
See the submission-candidate freeze and the public preflight status. Private author-controlled fields and portal materials are not published.
Theorem 1 · Representation
An O-ring task with retries yields a horizon and a fragility requirement. A scalar quality ladder exists exactly when task requirements form a chain; heterogeneous forgiveness supplies a robust route to nonnested tasks.
Lemma 2 · Profits are gaps
Task-by-task Bertrand competition makes frontier profit the boundary-value integral over the capability gap to the best alternative. A task can be valuable and widely served while generating no frontier rent.
Theorems 2–3 · Certification and entry
Behavior-only certification at failure rate ε needs Ω(1/ε) observations. Firms choose verification and entry; incomplete transfer and deployment evidence create an endogenous entrant lag, while public evidence lowers costs and can induce entry.
Theorems 4–5 + Proposition 3 · Rotation
A capability increment earns a lag-window boundary value plus a post-absorption remainder. A solved research program is horizon-first and then reliability; a signed curl preserves the ordering with state-dependent annuities and endogenous program size.
Corollary 1 + Theorem 6 · Scale and racing
Faster horizon imitation alone reduces research scale; an expanding reliability annuity raises it. Repeated direction choice yields moat herding, horizon herding, differentiation, or coordination under explicit renewal-game inequalities.
Theorem 7 + Corollary 2 · Welfare and policy
Private value differs from social value because imitation transfers the post-absorption stream. Liability raises reliability investment and leader task share; public verification accelerates diffusion and entry while weakening frontier incentives.
Evidence, Scope, and Verification
What the public measurements establish
- Measured task horizons are rising, but high-reliability horizon estimates are method-sensitive.
- Open models have recently lagged the closed frontier by roughly four months on a composite capability index; that aggregate is not either directional lag in the model.
- Estimated fixed-performance inference prices have fallen rapidly while frontier training compute and estimated training cost have risen.
- The paper does not calibrate the certification lag, annuity wedge, switch point, herding cutoff, or research scale from those aggregates.
- The evidence ledger records dates, sources, interpretation, and explicit non-mappings.
What has been verified
- 132 symbolic, numerical, comparative-static, and counterexample checks pass; none fail.
- All 93 labels are unique and all 73 referenced keys resolve.
- All 53 citation keys match the 53 bibliography entries.
- The 51-page PDF builds without warnings or bad boxes and passes structural validation.
- The current source and PDF are exact copies of the audited canonical artifacts.
- Earlier draft archived: June 2026 version (19 pp).
Open full learning log (through the current website release)
The public files include the full revision log, protected-message charter, staged revision plan, derivation audits, evidence ledger, source manifest, machine checker, and internal referee reports. Internal authorship, conflict, funding, and portal-submission materials are intentionally not published.
Research Files
Architecture and evidence
Task Regions
Forgiving (retries, rollback)
Unforgiving (one-shot, costly errors)
Short horizon
Recommendation, ad copy, search help. Saturated interior: served, commoditizing, rentless.
Payments control, medication dosing, driving maneuvers. Reliability margin: slow to imitate, self-protecting rents.
Long horizon
Coding, debugging, research assistance. Horizon margin: plans and scaffolds copy fast, rents are transient.
Autonomous science, critical infrastructure, agentic organizations. Corner where both bind: the direction the race rotates toward.
Paper
The PDF, LaTeX source, research architecture, evidence files, derivations, and math checker are synchronized with the current July 2026 audited manuscript. The checker reports 132 passes and 0 failures.