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 |
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