Compact Certificate-Bearing Strictifier Persistence

Statement

Fix . Suppose every space of certificate-bearing pairs with distortion at most is nonempty compact Hausdorff, pair restrictions are continuous and satisfy the inverse-system identities, and every finite subdiagram has a compatible pair-valued section. Then .

Meaning and scope

The compatible family preserves both the relational choices and their graph equivalences. Compactness of these spaces is a hypothesis; a norm bound alone does not prove it.

Source

Paper 3, Theorem 9.4. Frozen manuscript — research note, not peer reviewed.