RFP-05: Witness Persistence, Finite Branching, Survivor Recursion, and Infinite Ancestry Path Extraction

Witness Persistence, Finite Branching, Survivor Recursion, and Infinite Ancestry Path Extraction

RFP-02 builds the first-passage level and nonlinear source debt; RFP-03 builds the exact signed parent-output ledger; RFP-04 further builds the adjoint spacetime tube refinement and quantitative parent tightness. This round proves: for a thresholded RFP witness graph, a finite-branching path-extraction theorem holds; gives an exact backward survivor recursion and a finite-horizon obstruction certificate; separates persistent infinite ancestry from bottleneck-collapse escape. The graph-theoretic theorem is exact once nodes and compatibility certificates are supplied, but the PDE-bridge fraction required for full ancestry compatibility remains open.