A Chapter-Structured Framework for Fixed-Order Graph Reconstruction Audits: Group-Flow Certificates and Central-Corridor Compression

This paper presents a chapter-structured auditing framework for fixed-order graph reconstruction. Instead of claiming an unconditional proof of the reconstruction conjecture, it organizes every assertion into deck-determined identities, finite upper bounds, conditional certificate theorems, or open obligations. Two main advances are introduced. First, a group-flow screening layer converts multi-card overlap constraints into decidable linear systems over finite abelian groups, providing a new class of compatibility certificates. Second, a sharp compression is established for the even-order central degree window: for any deck whose realizations lie in the corridor {m-1,m}, the realization fiber is bounded by the central binomial coefficient. In the order-32 case this reduces the upper bound from 300 million to 12,870. The paper does not claim a complete order-32 proof; it supplies a rigorous, audit-ready framework with explicit certificate interfaces and open archive obligations. Keywords graph reconstruction conjecture, fixed-order audit, packet-cover coordinates, group-flow certificates, central corridor compression, finite certificates, order 32