Datasets:
claim_id stringclasses 6
values | evidence stringclasses 6
values | limitation stringclasses 6
values | next_step stringclasses 6
values | stage stringclasses 4
values | statement stringclasses 6
values | status stringclasses 4
values |
|---|---|---|---|---|---|---|
base-v13 | cjc0013/laplacian-matching-theorem-frontier-v13@6286998de432d8e623324ca546d29d9c38755e72 | v13 does not prove effective-core positivity dimension-free. | Control the complete Schur image. | prior_dataset | v13 proves the canonical block reduction and Hall-residual M-matrix positivity. | proved |
m-matrix-harmonic-comparison | data/certificates/block_schur_dirichlet_to_neumann_certificate.json | This comparison does not alone prove the graph-local lower envelope is nonnegative. | Prove the remaining core/interface inequality. | v14 | For lambda=max_j b_j/(D1)_j, the residual harmonic extension satisfies D^(-1)b <= lambda 1. | proved |
bounded-monotone-envelope | 14832 applicable sign partitions; zero failures; minimum 17/9. | Finite exact verification is not a dimension-free proof. | Extract a graph-local symbolic proof. | v14 | The monotone lower envelope is nonnegative on every applicable order-eight frontier coordinate. | verified |
harmonic-unit-cap | 84 exact failures; maximum 20/17. | This refutes a shortcut, not the surviving comparison. | Use lambda rather than a unit cap. | v13 | The residual harmonic extension is always coordinatewise at most one. | refuted |
rank-one-interface | data/certificates/core_residual_rank_one_compression_obstruction.json | The arbitrary-rank Schur route survives. | Preserve full coupling topology. | v13 | Every core-residual interface has rank one. | refuted |
graph-local-envelope | Exact frontier support only; no dimension-free certificate yet. | This is the remaining obligation for the current branch. | Prove or falsify the attachment-local inequality. | next | Every admissible core coordinate satisfies A1_i >= lambda(-B1)_i. | open |
Laplacian Matching Theorem Frontier v14
Produced by the Ouroboros AI Research System, under human direction.
This private-review dataset advances
cjc0013/laplacian-matching-theorem-frontier-v13, pinned at
revision 6286998de432d8e623324ca546d29d9c38755e72. It does not claim the unrestricted Laplacian
matching theorem and does not claim that the current unmatched-vertex branch
is closed.
What changed in v14
- Exact replay rows now expose the attachment-local Schur decomposition instead of only scalar summaries.
- For the Hall residual block, with
b=-B^T 1,r=D 1,h=D^(-1)b, andlambda=max_j b_j/r_j, the dimension-free M-matrix comparisonh <= lambda 1is proved. - This reduces effective-core positivity to the graph-local inequality
A 1_i >= lambda (-B 1)_i. - The complete order-eight frontier evaluates that lower envelope on 14,832
applicable sign partitions: zero comparison failures, zero nonnegative-envelope
failures, and sharp minimum
17/9. - The earlier false shortcut
h <= 1remains retired: 84 exact cases exceed one, with maximum20/17.
Current claim boundary
- Proved dimension-free: canonical Hall-core reduction, rank-agnostic block
Schur algebra, Hall-residual M-matrix positivity, and the new harmonic comparison
h <= lambda 1. - Verified exactly: the graph-local monotone lower envelope is nonnegative over the complete order-eight frontier.
- Open: prove
A 1_i >= lambda (-B 1)_ifor every admissible canonical Hall-core coordinate, or find a genuine counterexample. - Not proved: the unrestricted theorem and the full unmatched-vertex branch.
Verification surfaces
Exact rational replay is the primary mathematical evidence. CrossHair supplied a bounded symbolic falsifier for the two-residual-coordinate attachment inequality. Temporal-model checking guarded proof-state transitions; fixed-point provenance analysis checked claim propagation; answer-set checking validated the research obligation ordering. Probabilistic model checking was intentionally not applied because no calibrated theorem-workflow probabilities exist.
See FRONTIER.md for the derivation, CHANGELOG.md for the v13-to-v14 delta,
data/claim_ledger.jsonl for machine-readable claim status, and REPRODUCE.md
for exact regeneration instructions.
Review status
The bundle is prepared for private human review. Public visibility, mathematical endorsement, authorship, licensing, and any stronger claim remain human decisions. No priority or novelty claim is made.
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