[
  {
    "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"
  }
]