Cofinal Extension of Certificate Equivalences

Statement

For compatible directed effective graph systems with their specified completed direct limits, let . Uniform bounds on both and give a boundedly invertible total map with the same bounds.

Meaning and scope

Compatibility makes the algebraic limit map well defined; two-sided uniform control lets it extend with an inverse. The Hilbert direct-limit setting uses isometric transition maps.

Source

Paper 3, Theorem 6.3. Frozen manuscript — research note, not peer reviewed.