lin-0134

10.3 Constructive epistemic status

Chapter 0 explained why internal excluded middle is not generally available in the smooth and sheaf semantics used by lincs. CoLT turns that logical fact into an operational discipline. A system must not collapse lack of a witness into a witness of negation.

CoLT is therefore not a symbolic checker placed after a neural rationale. In the terminology of Section 0.13, its maintained sketch is a revisable declaration, a language or neural model may propose a realization or repair, and the public trace records the typed obstruction and the evidence that licenses a transition. Constructive status is what prevents the proposer from silently converting fluency into proof.

Status	Available evidence	Licensed action
Unobserved	No registered observer resolves the obligation	Acquire a probe or preserve uncertainty
Locally supported	A witness exists on one or more contexts	Retain with its scope; do not promote globally
Locally refuted	A typed counter-witness exists on a context	Localize the failure and block incompatible promotion
Compatible	Local witnesses agree on declared overlaps	Test effectivity in the admitted global model class
Globally effective	Compatible witnesses glue to an admitted realization	Submit the realization to independent admission
Repaired but untested	A registered edit removes the generating obstruction	Run preservation and held-out tests
Admitted	The admission contract accepts a certified successor	Update the maintained state
Abstained	Evidence, observability, power, or identifiability is insufficient	Keep the state and record the unresolved obligation

Table 10.1 CoLT preserves epistemic distinctions that a Boolean pass/fail label would collapse.

Holmes’s elimination principle from Chapter 0 is valid when the alternatives are positively certified as exhaustive and the refutations are constructive. CoLT stores precisely those missing certificates. Without them, the last surviving hypothesis is a repair candidate rather than an admitted truth.

Design principle

A CoLT trace records the strongest judgment supported by the evidence. It never upgrades not observed to false, locally coherent to globally effective, or repaired to admitted without the corresponding witness.