cjc0013/vc3-laplacian-delta-plus-3-schur-lemma

VC3 Laplacian Delta+3 Schur Lemma

This dataset-style release packet contains generated evidence artifacts for a bounded finite-graph-theory certificate run.

Candidate inequality:

For every connected simple graph G:
lambda_max(L(G)) <= Delta(G) + matching_number(G)

What We Found

Within the specific bounded VC3 residue universe represented by this packet, the certificate coverage is complete:

Quantity	Value
Support-offset source rows	3870
Support rows covered by certified families	3870
Support rows remaining	0
Prior bounded rows already covered before support-offset stage	286
Overall bounded residue rows	4156
Overall bounded coverage fraction	1.000000000000
Deduplicated certified support-offset families	1266

The short version: the bounded residue coverage fraction reached 1.0 for this enumerated VC3 residue set.

Update: Frontier Quotient-Lemma Route Candidates (2026-05-30)

This repository has been updated with a second-stage proof-shape discovery packet derived from the original bounded VC3 certificate release.

What changed:

• The old bounded certificate packet is now used as seed material for a structured proof-shape update.
• The main support-size-6 frontier pressure rows were exact-rechecked with integer Laplacian characteristic-polynomial root counts.
• The apparent failures were classified as certificate-compression pressure, not Delta + matching counterexamples.
• Two piecewise frontier proof-template route candidates were materialized with finite low-c branches and symbolic c >= 3 suffix branches.
• A quotient-lemma route packet now records weighted quotient symmetry checks, real-spectrum bridge candidates, suffix no-root route candidates, and an obligation DAG.

Current machine-backed result:

Candidate	Piecewise RHS	Suffix branch	Finite branch	Status
0d80da1b64db	max(3*c + 10, 4*c + 7)	c >= 3: 4*c + 7	c in [1, 2]	piecewise_frontier_proof_route_candidate
d016ecacc169	max(3*c + 8, 4*c + 5)	c >= 3: 4*c + 5	c in [1, 2]	piecewise_frontier_proof_route_candidate

Key counts from the latest route packet:

Check	Value
Weighted quotient symmetry rows	25
Weighted symmetry failures	0
Real-spectrum bridge candidates	2
Suffix no-root route candidates	2
Piecewise proof-template route candidates	2

Claim boundary for this update:

These are machine-checked proof-template route candidates and finite exact checks.
They do not prove the global theorem.
They do not claim a counterexample.
Human/math review gates remain for the quotient-to-full lift, real-spectrum bridge, and determinant no-root implication.

New artifacts are under:

updates/2026-05-30-frontier-quotient-route/
code/frontier_quotient_route/

Update: VC3 Schur Delta+3 Lemma (2026-07-08-schur-delta-plus-3)

This update adds a direct Schur-complement proof object for the VC3 quotient setting.

What is now proved:

For every VC3 quotient graph G:
lambda_max(L(G)) <= Delta(G) + 3

Machine audit for the current frontier:

Check	Value
Frontier rows audited	9223
Schur/radius mismatches	0
Schur PSD failures	0

Claim boundary:

The Delta+3 VC3 Schur lemma is proved.
The full Delta+matching theorem is not claimed as proved.
No counterexample is claimed.

New public-safe files are under:

updates/2026-07-08-schur-delta-plus-3/

What This Is Not

This is not a theorem proof for all connected simple graphs. It is not a peer-reviewed result. It is not a formal proof checked by a proof assistant. It is a reproducible, hash-backed computational certificate packet for one bounded VC3 residue pipeline.

Public claim boundary:

Complete coverage of the enumerated bounded VC3 residue set included here.
No claim of a full graph-theoretic theorem beyond that bounded set.

Contents

• data/coverage_summary.json: compact machine-readable summary of counts, hashes, and source paths.
• data/final_aggregate_manifest.json: final aggregate manifest reporting 100% bounded support coverage.
• data/final_driver_manifest.json: final frontier-driver receipt that reached target coverage.
• data/source_vc3_bounded_residue_rows.json: source bounded residue rows used as the support-offset coverage target.
• data/aggregate_family_certificates.json: deduplicated support-offset family certificate records.
• data/aggregate_coverage_rows.json: row-level coverage map.
• data/aggregate_covered_rows.json: covered source rows.
• data/aggregate_still_uncovered_rows.json: should contain zero rows.
• code/: exact Python scripts used by the packet generator and certificate pipeline.
• METHODOLOGY.md: full method description.
• LIMITATIONS.md: scope, caveats, and interpretation limits.
• EVIDENCE.md: hash and provenance map.
• REPRODUCE.md: reproduction outline.
• updates/: release notes, validation summaries, and claim-boundary artifacts.

Intended Hugging Face Use

Intended repository type: dataset.

Suggested repo id:

cjc0013/vc3-laplacian-delta-plus-3-schur-lemma

This README follows the Hugging Face dataset card pattern: a repository README.md is rendered as the dataset card, with metadata in a YAML block at the top. See the official Hugging Face docs for dataset cards and upload workflows:

• https://huggingface.co/docs/hub/main/datasets-cards
• https://huggingface.co/docs/hub/datasets-adding
• https://huggingface.co/docs/huggingface_hub/en/guides/upload

Responsible Use

Use this packet as computational evidence, regression-test material, or a starting point for independent verification. Do not cite it as a proof of the global conjecture without additional proof work.