lin-0193

15.6 Localization over Bellman covers

The Bellman computation can be covered by local subdiagrams for representation, transition, reward, successor value, and action contrast. Shared bootstrap branches form overlaps.

Proposition 15.3 Tangent stability of Bellman localization

For every cover inclusion \(i_a:J_a\to J\),

\[ T(D\circ i_a)=(TD)\circ i_a. \]

If the cover is complete and tangent lift preserves its overlap descent data, compatible local tangent factorizations glue to a global tangent factorization.

Proof ▼

The restriction identity is functoriality of \(T\). Under the stated descent hypotheses, the overlap equalities that glue the base family also glue its tangent lift.

Localization of obstruction data does not imply localization of parameter repair. Cotangent transport and parameter sharing can couple distant modules.