Item 86: Bounded competence against legitimate continuation policies under endogenous admissibility

*Refined by the continuation-BRIA round and its four later passes (2026-09-08); the canonical statement is wiki/Continuation-BRIA.md.* The static gate is sound and Lipschitz at one occasion. When an admissible action changes the next admissible set, test_dynamic of the decision-theory-bill round shows legitimate continuation policies induce different admissibility histories, so fixed action-sequence regret is ill-typed. Two of the item's original premises are corrected: the "myopic gated learner" that loses linearly there is an argmax that never tests a hypothesis outpromising it forever, hence not a bounded inductive learner; and on that exact fixture — which keeps expanded under work, so the amendment is absorbing — every BRIA is competent, because a single forced test of the outpromising claim is irrevocable and the sound stay claim then forces adoption. That competence is an accident of absorption: on the variant where work revokes the amendment, the criterion permits an asymptotically myopic BRIA (auction on base rounds, sparse losing tests, return to base), while the published auction happens to keep the benefit. The one-step criterion forces testing, not adoption; what forces adoption is a sound claim about the whole investment, i.e. temporal credit assignment at the testing granularity.

What the round supplies (projects/deference/rounds/2026-09-08-continuation-bria/, unregistered): continuation hypotheses (continuation, accountable claim) at the system's block contract — the claim may be wrong — tested by the realized execution of the selected continuation through the gate with the exterior live; for a fixed horizon the published criterion verbatim and its guaranteed-option theorem; for unbounded horizons the duration-weighted criterion, the auction in total-reward units with the round's subsidy credited at its opening (the paper's auction, modified so the subsidy that funds a block may read that block's length), capital adequacy A_i(K) − m_K → ∞ with the subsidy through the round inclusive, and subsidies satisfying it with negligible total existing iff the schedule is non-dominant (m_K / Σ_{k≤K} m_k → 0), with the prefix rule s(k) = ⌊√(S_k/M_k)⌋, A(k,i) = ΔM_k + 1/k as a uniform online witness needing no modulus of convergence — and no prefix-online rule under the paper's own settlement timing; continuation-promise competence — the learner's observed m-weighted average is asymptotically at least the m-weighted average of the claims of every covered hypothesis whose tested record is bounded below (BR) — which with vanishing promise slack is competence against the controller's actual-history value and learns every fixed finite investment delay; and the irreversible-branch witness that this does not yield regret against Π_leg on its own trajectories. The exact identity, with the learner's observed return G^obs and an external rollout evaluator Ĝ typed separately, is Regret_T(α, π) = SHIFT_T + SLACK_T + LEARN_T (SHIFT = Σ m_k (Ĝ(π;H^π) − Ĝ(π;H^α)), SLACK = Σ m_k (Ĝ(π;H^α) − L), LEARN = Σ m_k (L − G^obs(α))), and low external regret holds exactly for Π_rec,prom = {legitimate π : covered claim with record bounded below, SLACK ≤ o(T), SHIFT ≤ o(T)}. The item's "bounded task regret against Π_leg" is false for the unrestricted class.

Legitimacy certifies admissibility, authorization, protected correction and legitimate transition — hence which continuations are allowed comparators — and does not certify task reward or future-principal value. The item therefore asks for three things, and task-value recognition is not a duty of legitimacy:

1. Recoverability of legitimate slow-lane continuations — the condition under which SHIFT_T(π) ≤ o(T) for π ∈ Π_leg, one-sided along the learner's actual block starts. The candidate theorem shape is bounded catch-up (joinability): from every block start the learner reaches, some legitimate continuation reaches within d steps a state value-equivalent for π to π's own — an amendment π requested earlier can still be requested from the learner's history at cost d, so the per-block shift is at most d and SHIFT_T ≤ dK = o(T) with growing average blocks (exact on the round's fixture, and on its sticky variant, where the amendment cannot be undone). Wanted: this as a property of the slow-lane relation — which authorized transitions are joinable from a lagging history — and whether any form is certifiable by the constitution or checkable by the learner from realized data. The excluded case is foreclosure, not irreversibility: a choice after which the comparator's state can be neither reached nor matched in value at any cost; the policies that make a foreclosing choice the learner did not fall outside the class, which is a statement about the class and not a defect.
2. A promise-recognizability interface for performance — which legitimate continuation policies carry an efficiently computable contextual claim with SLACK_T ≤ o(T) on the learner's histories, and where such claims come from (a learning hypothesis after finitely many refutations; a certified lower bound supplied with the value; an averaged claim of the published Theorem 4's kind, whose weighted form is a side question). This is an interface on the value's settlement and the hypothesis class, separate from the legitimacy certificate.
3. Composition — with (1) and (2), the corollary Regret_T(α, π) ≤ o(T) for π ∈ Π_rec,prom on the round's two-state process with a joinable amendment, stated with the three bridges explicit.

Deliverable shape: the recoverability condition on the slow lane with its witness; the recognizability interface with one realization; the composed corollary — or the negative for any of the three. Acceptance check: python3 tests/run.py green; any Lean audits clean.

Context: PRESSURE_PASS.md, CORRIGIBILITY_COMPOSITION.md §6 and POLICY_REGRET_FRONTIER.md §3–4 of projects/deference/rounds/2026-09-08-continuation-bria/; NORMATIVE_CHOICE_THEOREM.md §5 and CANDIDATE_DECISION_THEORIES.md §2.8 of projects/deference/rounds/2026-09-06-decision-theory-bill/. Consumed by: the task-competence half of the gated architecture; the corrigibility specialization's investing-in-amendment case. A solution ships: the three objects with the composed corollary, or the negative.