| [ |
| { |
| "id": "main-one-sided-classification", |
| "claim": "High-index lower equality iff phase-locked lasso tree, common-parity theta, or even figure-eight; forces maximal degeneracy and upper equality.", |
| "status": "full proof supplied; candidate novelty; independent review pending", |
| "location": "MANUSCRIPT.tex Sections 2-8" |
| }, |
| { |
| "id": "direct-nodal-inertia", |
| "claim": "For fully supported positive tree eigenfunction: below=s, multiplicity=r-s, at-or-below=r.", |
| "status": "proof supplied; relation to prior nodal theory credited", |
| "location": "Section 3" |
| }, |
| { |
| "id": "residue-only", |
| "claim": "For admissible saturated-tree opening: lower equality iff R=0, and then K=0.", |
| "status": "proof supplied; not valid for generic finite-rank problems", |
| "location": "Section 9" |
| }, |
| { |
| "id": "quantitative-inheritance", |
| "claim": "delta >= g*rho/(lambda+g+rho) for energy-contractive constraints.", |
| "status": "proof supplied; no claim to originate all spectral-subspace gap methods", |
| "location": "Section 10" |
| }, |
| { |
| "id": "exact-checks", |
| "claim": "604 exact cases and 604 independent ODE-nullity checks passed.", |
| "status": "verified finite-instance computation, not general theorem proof", |
| "location": "data/exact_cases.json" |
| } |
| ] |
