lin-0280

Repair and admission

Notation	Meaning	Role in lincs
\(\mathcal U=\{ U_i\to U\} \)	cover	Contexts over which an obstruction is localized or evidence is assembled.
\(D/{\sim }\)	quotient realization	Removes declared gauge, presentation, or decision-irrelevant variation.
\(\operatorname {Loc}(\mathcal O)\)	localization of an obstruction	Assigns surviving failure to modules, overlaps, agents, or contexts.
\(\mathcal R\)	repair language	Registered class of typed changes that may be proposed.
\(r:D\rightsquigarrow D'\)	repair proposal	A controlled structural change, not yet an admitted update.
\(\mathcal A\)	admission rule or contract	Independent criteria for accepting, rejecting, quarantining, or deferring a repair.
\(\operatorname {Cert}(r)\)	repair certificate	Provenance, invariants, uncertainty, tests, and evidence associated with a proposal.
\(\mathfrak C_k\)	CoLT reasoning state	Packages the maintained sketch and realization with its probes, quotient, cover, repair language, admission rule, and evidence registry.
\(\tau _k\)	CoLT transition record	Records a probe, typed obstruction, localization, repair proposal, certificate, and admission decision.
\(\mathrm{SCoLT}\)	Sheaf-theoretic Chain of LINCS Thought	Specializes CoLT to the Toulmin argument sheaf supplied by SCoTT.
\(\operatorname {ESS}\)	effective sample size	Statistical admission diagnostic in weighted or off-policy settings.
\(\operatorname {Lan}_J F\)	left Kan extension	Universal extension by colimit-like aggregation.
\(\operatorname {Ran}_J F\)	right Kan extension	Universal extension by limit-like consistency.