Definition
A10: for a state s, a corrective objective J, remaining time H, budget B, the description or cue q under which correction is sought, and the institutional arrangement G,
α_J(s, q, H, B; G) = sup over π in Π(G, q, B) of Pr_s^π(T_J ≤ H),
where Π is the set of search-and-action policies available to the arrangement and T_J the time J is achieved. “The search and implementation procedures belong to the same policy. Planning is not free.” The correctability set at reliability 1 − δ is the set of objectives J with α_J ≥ 1 − δ, and its boundary is A9’s “correctability frontier”, relative to the declared time, resources, information, arrangement and reliability.
It is TERM-055 carried over, item for item: the resource becomes a plan for J, the agent–environment system becomes an arrangement of institutions, the cue becomes the description under which the problem reaches them. A10 decomposed the time as discovery, verification, coordination and execution, which overlap and compete, so “A sufficiently long search can make an otherwise available remedy unusable”, and further search can have negative value.
TERM-055’s two notes carry over too. Hutchins’s cockpit (LIT-1066): preparation moves the cost of search ahead of the deadline, and A10’s “precomputed search infrastructure” is custody records, standing channels for executing orders and clear escalation, maintained beforehand. And the supremum is the best available policy, not the one used; A10’s three levels are oracle feasibility, bounded-optimal capability and realized organizational competence.
Whose correctability. G is the arrangement through which correction is sought: the institutions that would find, authorize and carry out the plan, and the one whose act or state J would correct. The correctability of an arrangement is its capacity to correct a state of itself through its parts. When a claim speaks of one institution’s being correctable by others (CLAIM-462), G is the arrangement that holds both, and J a correction of the first.
What it is not
- A remedy’s existence, or its legality. A10’s four propositions, existence, knowability, findability and deployability, of which this is the last; QUESTION-279 asks what would certify that it is zero.
- Contestability. A9 separated formal contestability (one is entitled to challenge), practical contestability (one can start and sustain a challenge) and effective answerability (the challenge can constrain or correct the exercise of authority), after Pettit (LIT-1614). Correctability is about the last, and says nothing about the first two.
- A score. A9: “The relevant object is a structured attainable set, not a single accountability score.” Costs of time, money, risk and lost capability are kept apart.
- Exogenous. A10: “the budget is itself partly an outcome of political and organizational decisions”, so (B, G) evolve with the arrangement’s own acts. The term measures what can be corrected now; how the arrangement came to have that capacity is a separate, historical question (CLAIM-464).
- A unified agent’s property. The arrangement may span courts, agencies, enforcers and foreign governments with no one of them in charge, and coalitions can do what no member can (CLAIM-457).
A10 itself advised against “an entirely new TERM called resource-bounded availability”, since TERM-055 “already covers the underlying concept”, and proposed questions instead. The term is filed anyway because the object recurred under four names in A7 to A10 and the claims filed from them need one; whether it should instead be a note widening TERM-055 is the owner’s call.
Note of 2026-10-31: correctability is bounded by legibility
At U25 of the exchange “Analyze nucleation concepts” the owner suggested connecting corrigibility with the record’s treatment of legibility. A25 gave the bound that ties this term’s “starting from the description of the problem it actually has” to legibility (TERM-064). Suppose two equally likely failures need remedies that exclude each other, and the description the arrangement corrects from has laws P₀ and P₁ under them. Then no remedy, actuator or decision rule acting on that description picks the right remedy with probability above (1 + TV(P₀, P₁))/2. It is ½ when the description is the same under both. This is the two-point Bayes-risk identity of Le Cam, the record’s CLAIM-199 and CLAIM-503 applied to correction, and it is not filed as a new claim. Its use: “no improvement in the downstream corrective mechanism can recover that lost distinction from those observations alone”. A25’s reading of CASE-154 is corrected. That case restricts the observer to one coordinate, not the representation to one bit. A25’s table of correction stages extends CLAIM-403’s rungs for a contributor; CLAIM-349’s split of access, authority and action is the version for an organization’s own signals. A corrected judgment need not be a corrected organization. In CASE-124’s model, resetting the interpretation’s state while its residue r₀ ≠ 0 remains regrows it at the next step (m₁ = ν·r₀), which then decays at the slow rate (CLAIM-400).