lin-0261
22.2 What is fixed, and what may be learned?
A present LINCS instance can be summarized by a declaration
where \(\mathbb S\) is a learning sketch, \(\mathcal T\) a tangent site, \(\chi \) a decision or presentation quotient, \(\mathcal U\) a cover, \(\mathcal R\) a typed repair language, and \(\mathcal A\) an admission rule. The candidate model \(D\) varies while much of \(\mathfrak L\) remains fixed.
Future systems may instead move in a category of declarations. A morphism
would have to state how objects, paths, designated cones, probes, null directions, covers, repairs, and admission blocks are transported. It should also say which previously visible failures remain visible after transport.
A change \(\Phi :\mathfrak L\to \mathfrak L'\) is conservative on an audit family \(\mathcal Q\) when every obstruction witnessed by a registered probe in \(\mathcal Q\) has a transported witness in \(\mathfrak L'\). It may expose new obstructions, but it may not erase an old one merely by changing the declaration.
This is only a first safeguard. A useful declaration change must also preserve the intended decision semantics, expose its new blind spots, and be evaluated on held-out audit families. The idea is analogous to conservative extension in logic: a richer language may prove new statements without invalidating the meaning of the old fragment.
A learned declaration is not admitted because it makes the current model look more compositional. It is admitted only through evidence independent of the repair that proposed it.