https://github.com/inaciovasquez2020/cycle-local-rigidity
Cycle-Local Rigidity — locality-based rigidity from cycle structure; executable witnesses and proofs of local-to-global obstruction.
https://github.com/inaciovasquez2020/cycle-local-rigidity
cycle-local-rigidity cycles formal-methods formal-verification graph-theory invariants lean4 locality mathlib reproducible-research rigidity-theory unified-rigidity-framework
Last synced: 2 days ago
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Cycle-Local Rigidity — locality-based rigidity from cycle structure; executable witnesses and proofs of local-to-global obstruction.
- Host: GitHub
- URL: https://github.com/inaciovasquez2020/cycle-local-rigidity
- Owner: inaciovasquez2020
- License: mit
- Created: 2026-01-23T01:06:34.000Z (3 months ago)
- Default Branch: main
- Last Pushed: 2026-04-13T10:41:53.000Z (15 days ago)
- Last Synced: 2026-04-13T12:29:27.887Z (15 days ago)
- Topics: cycle-local-rigidity, cycles, formal-methods, formal-verification, graph-theory, invariants, lean4, locality, mathlib, reproducible-research, rigidity-theory, unified-rigidity-framework
- Language: TeX
- Homepage: https://inaciovasquez2020.github.io
- Size: 846 KB
- Stars: 1
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE
- Citation: CITATION.cff
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README
# Cycle Local Rigidity
# Cycle–Local Rigidity (bounded verification)
Bounded, exhaustive verification of a cycle–local rigidity implication for finite graphs.
## Result (bounded)
Fix parameters ρ₀ = 1 and C₀ = 1. For all graphs G with at most 7 vertices satisfying:
- maximum degree Δ(G) ≤ 4
- Ihara–Bass / nonbacktracking spectral condition IB_{ρ₀}
- FO^4 radius-2 homogeneity
no counterexample exists to:
IB_{ρ₀} ⇒ CLR(4,4,2; ρ₀, C₀)
## Method
All graphs up to n ≤ 7 are exhaustively enumerated and filtered by:
- nonbacktracking / Ihara–Bass spectral verifier
- FO^4 radius-2 homogeneity checker
- local F₂ cycle-rank checker
Verification is deterministic and enforced by CI.
## Status / Scope
- Verified: n ≤ 7 (bounded exhaustive)
- Not claimed: any unbounded-n theorem
- n ≥ 8: infeasible without additional structure
## Quickstart
```bash
./verify.sh
Artifacts
certificate.json
certificate.sha256
Citation
See CITATION.cff.