Certification within a Declared Class: Four Corrections to the Acceptance Criterion of Note 13

Note 13 of this series specified a construction attaining state IV₂ together with a machine-checkable acceptance criterion for the run intended to test it. Four defects in that specification were established after deposit. The deposited text is not amendable; this note corrects it, and corrects it in one direction only. The corrections are four. The class of admissible rules must be declared by enumeration and not by a property: under a class declared by a property the uniqueness condition is decidable and identically false on every run that does not exhaust the admissible domain (Proposition 1). The acceptance parameter p_min — an assigned quantity inside a certifying procedure, by the note's own account — is replaced by a separating-set requirement computed from the class and the domain before the run (Propositions 2 and 3); and the fork by which failure to attain p_min was made both a refutation of the construction and a licence to repeat with an enlarged corpus is closed by fixing the number of permitted extensions at zero. Condition 5 is restated for a fold that returns a verdict and no confidence, the budget it places on consensus confidence having lost its referent. A small run is defined, with a lower bound on its corpus derived from the separating structure of the declared class, and with the notion of a partial certificate indexed to the conditions it actually discharges. No correction enlarges the set of runs that would count as certified. Three of the four defects are instances of one failure — an outcome settled by the specification rather than by the world — and the corrections are directed at restoring the run's capacity to fail.