Paper 20 characterized world-fixed truth for embedded observers, and Paper 21 characterized a framework-relative anti-luck knowledge standing. Both evaluated truth and knowledge at a declared stage of inquiry while leaving open the dynamic question of how that stage changes. This paper supplies the missing dynamics. It denies a global editor: no physically realized subsystem jointly possesses complete access to all relevant records, an exhaustive candidate generator, infallible diagnosis of every challenge, unrestricted revision authority, complete foresight of the consequences of every possible revision, and a guaranteed rule for selecting the globally correct next inquiry state. It nevertheless affirms local and distributed epistemic corrigibility. An Inquiry State types the retained record domain, candidate family, candidate weights, executed and admissible protocols, challenge architecture, specifications, attributed standings, provenance graph, revision repertoire, agenda, and resource budget. The formal core separates representational reach from discriminatory resolution by distinguishing world candidates, model candidates, and a typed adequacy relation between them. Accumulating protocols can refine the world-side transcript partition only at the idealized forward-law level and cannot recover a structure omitted from the candidate family. Conversely, a nested family expansion that preserves the predictive semantics of old candidates can restore representational reach but cannot, under fixed evidence, shrink the model-side compatible set. No finite-stage admissible inquiry history can reach a target-adequate representation outside the revision closure generated by its transition architecture. These results yield a Conditional Joint-Corrigibility Proposition: when misspecification is present and model-side predictive equivalence persists after candidate-family revision, correction requires both family revision for reach and protocol refinement for resolution. This is a necessity result; it does not guarantee that a discriminating protocol exists, is feasible within available resources, or will lead to selection of the adequate candidate. A separate realized-transcript readout allows rare but highly diagnostic evidence to provide token-level support under a declared epistemic prior while preserving the protocol-kernel limit: observationally equivalent worlds have likelihood ratio one and cannot be separated by the realized transcript. Inquiry progress is profile-valued, path-dependent, and potentially non-monotone. Inquiry requires neither a global editor nor guaranteed convergence, but it requires challenge uptake, protocol extensibility, candidate-family revisability, and provenance-preserving requalification of prior standings.
Tomoyuki Uchida (Fri,) studied this question.