Item 25: Bound the near-indifference leakage, or show it cannot be bounded

The controlling competence question after Stage II, and the one item that decides whether the surviving competence candidate has any finite consequence at all.

Margin-gated calibration — the principal's grades are calibrated where the principal is decisive — is the only non-circular candidate found. It supports

Δ_𝒞  ≤  2η  +  2B · P(γ_n < γ̄)

and asserts nothing on {γ_n < γ̄} by construction. The second term is not a competence claim: it is the agent's credence mass on the principal's near-indifference region, a fact about a different object. Unbounded, it makes the bound 2η + 2B, which is vacuous.

Decide the question in the sharp negative shape, which is the cheaper direction: exhibit a family in which margin-gated calibration holds at η = 0, the decision-time margin estimate γ̂_n ≥ γ̄ + 2s on the certified event, the trust tolerance holds at ε_n → 0, and Δ_{𝒞_fix} → 2B anyway — or prove no such family exists.

The one partial lead is a relocation, not a bound. Under the trust tolerance the gate is estimable at decision time — |γ_n − γ̂_n| ≤ 2η_n pointwise and attained — so P(γ_n < γ̄) ≤ P(γ̂_n < γ̄ + 2s) + ε_n/s for every rational s > 0, the first term computable at t(n) from the model's grades alone. Nothing bounds that first term, and whether relocating the leakage into a decision-time observable suffices is the question.

Deliverable shape: the refuting family as a witness-checked instance with exact rationals; or a lean-proved bound on the leakage under a stated non-circular hypothesis, with an inhabitation witness. Acceptance check: the house witness checker accepts the instance; or the lean gate builds and audits clean with a typechecking witness. Context: prompts/2026-08-11-phase-ii-competence/REPORT.md §1.6, §4.3 and §10; prompts/2026-08-11-corrigibility-phase-ii/REPORT.md §9. A solution ships: the verdict, plus an explicit statement of whether the competence candidate survives it, plus — if the bound exists — whether the bounding hypothesis is itself credence-free or is a joint competence–credence hypothesis under skeleton v2 §2a.