Version 2.0 — Unbounded Signature of Line Graphs

Version 2.0 release notes

• DOI: 10.5281/zenodo.21534809
• Release date: 2026-07-24
• License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Version 2 substantially expands and supersedes the Version 1 research version
while preserving the Version 1 chronology and finite-counterexample record. It
proves that the failure of the line-graph inertia inequality is unbounded even
within connected simple planar subcubic cactus graphs, supplies rooted-module
and four-subdivision transfer principles, and gives an exact computer-assisted
classification of all 256 three-cycle-chain residue classes.

This manuscript is a preprint and has not undergone peer review. No claim of
absolute historical priority or of being the first such result is made.

Reproducibility

• authoritative 11-page PDF and LaTeX source;
• pinned Python dependencies and reproducible-environment recipe;
• exact seed, amplifier, and four-subdivision checks;
• two independently generated 256-class outputs;
• genuine rowwise comparison with 256 matches and zero mismatches;
• clean-room manuscript audit;
• SHA-256 checksums and machine-readable release manifest.

Verification summary

• PDF: 11 pages, 264738 bytes;
• PDF SHA-256:
  357970ffce7493e3c7f97b0176188bee4ee82215f3cd56c8a67c558c353b8658;
• canonical 256-class SHA-256:
  f674e3d39241774d1c89101337cbc938927af7167ce2aee964bf36cc5a13b1a4;
• rowwise comparison SHA-256:
  ac8756eac191036fbd27921e8eb6e2bdd80aec6656a3c069e57a077cb3ab50a2;
• rowwise mismatches: 0.