Defect Flow, Incidence Rank, and Boundary Descent for Seymour's Second-Neighborhood Conjecture

Abstract

We develop a degree-independent structural toolkit for Seymour's second-neighborhood conjecture. The main contributions are block and trap defect factorizations, arbitrary-baseline total-defect balance, protected-parent and Hall-deficiency separator geometry, Boolean defect flow and incidence-rank decomposition, minimum-degree-free host compression, tight-root shell and portal descent, per-arc curvature with repeated-two-path localization, and exact affine certificate interfaces. Known external-boundary descent, triangular finite-witness, and dense-boundary results are used as calibrated prior inputs. The paper does not prove Seymour's conjecture or the minimum-out-degree-eight case. Its exact unresolved endpoint is bounded-capacity routing of repeated-two-path overlap. This record contains version 1.0.0 of the paper, source, bibliography, selected reusable proof records, licenses, deterministic archive manifest, replay script, and checksums.