T1 · Representation
O-ring with retries: fragility requirement f = φ + (h + ln(1/ε))/(1+ℓ), success converges to a Gumbel kernel, and the scalar quality ladder is exactly the case of homogeneous forgiveness.
What Changed in v3
An independent three-referee round judged the June draft's propositions to be identities on top of assumed payoffs. The v3 rebuild keeps the same main contribution — the two-dimensional task frontier — but derives everything that was previously posited: the two dimensions now come from one O-ring-with-retries primitive, market profits come from Bertrand competition task by task, appropriability comes from the statistics of imitation, and the dynamic results are theorems rather than a relabeled 2×2. The format is Facts → five theorems → aggregate quantification, with every formal claim machine-verified.
L2 · Profits are gaps
Bertrand in tasks: frontier profit equals the boundary-value integral over the capability gap to the best imitator. Saturation is an equilibrium state — served, valuable, and rentless.
T2 · The tail cannot be distilled
Certifying failure rate ε needs Ω(1/ε) observations; the tolerated ε at the fragility frontier is exponentially small. A plan is copied from one observation; a failure rate must be estimated from many.
T3 · Rotation
Shadow value of direction i is B_i/(r+λ_i). Along a horizon push B_F/B_H rises, so investment rotates to the reliability boundary in finite time — and faster imitation brings the rotation earlier. Imitation steers.
T4 · Herding on the moat
When imitation asymmetry is strong enough, racing on the unforgiving boundary is a dominant strategy: rival labs crowd onto the same reliability-heavy direction despite splitting its rents.
T5 · Wedge & policy reversal
The direction wedge equals (r+λ_F)/(r+λ_H), signed by observable imitation lags. Liability raises reliability investment and concentration; public verification raises reliability diffusion and lowers concentration.
Revision Log & Verification
Aggregate discipline (public data only)
- Fact 1: 50% time-horizons double every ~7 months; 80% horizons are ~5× shorter (METR).
- Fact 2: open-weight lag is 3–4 months on capability indices but 6–12+ months on autonomy/reliability margins.
- Fact 3: price at fixed capability falls 9–900× per year (median ~50×) while frontier spend rises.
- Specification test: a constant-hazard scalar model predicts a parameter-free 50/80 horizon ratio of 3.11; the data say ~5. The excess is the second dimension.
- Calibrated direction wedge ≈ 0.3: the market prices a horizon lead at about a third of a reliability lead.
Round 95: 2026-07-04
- Independent three-referee assessment of the June draft: no R&R at top-5 or strong field journals — identities, a static 2×2 labeled dynamic, assumed payoffs.
- Full rebuild in
paper_v3/: five theorems replace four propositions; payoffs, appropriability, and dynamics all derived. - All 58 machine checks pass; pre-writing verification caught two errors before they entered the text.
- Compile is fully clean: 0 errors, 0 warnings, 0 overfull/underfull boxes, no undefined references.
- Earlier draft archived: June 2026 version (19 pp).
Open full learning log (Rounds 1–95)
Synced from the project-level learning.md; Round 95 documents the referee round, the rebuild, and its verification.
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 compiled PDF, LaTeX source, design spec, and math checker on this page are synchronized with the v3 rebuild. Every numbered claim in the paper has a corresponding check in math_check_v3.py (58 pass, 0 fail).