Defect Flow, Incidence Rank, and Boundary Descent for Seymour's Second-Neighborhood Conjecture
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.
Authors
- Hainan Zhao
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-08-23
- DOI
- https://doi.org/10.5281/zenodo.22068837
- Citations
- 2
- Primary Topic
- Complexity and Algorithms in Graphs
- Type
- article
- Field-Weighted Citation Impact
- 12.34