CLAIMS.json

{
  "release": "SERAPH-5 / SAELYRA v6.0.0",
  "date": "2026-10-03",
  "original_target": "Every unconditional convex body K in R^5 has illumination number at most 32",
  "original_target_status": "NOT PROVED",
  "proved_in_manuscript": [
    "Blocking-slack positivity is equivalent to illumination by the fixed family",
    "Fixed and optimized blocking-slack functionals are 2-Lipschitz in infinity-Hausdorff distance",
    "Explicit rational facet collars certify full neighborhoods and common-step core landings",
    "An exact finite arrangement test verifies a general rational collar",
    "Verified rational neighborhoods form a complete certificate atlas for the m-illuminable normalized class",
    "The universal n-dimensional m-direction statement is equivalent to existence of one whole finite-integer level",
    "A local common-direction margin failure has a witness using at most n+1 normals"
  ],
  "computer_assisted_results": {
    "finite_templates": 361,
    "legacy_templates": 360,
    "legacy_uniform_closed_radius": "1/6156",
    "irregular_model_direction_count_upper_bound": 10,
    "irregular_model_closed_radius": "1/63072",
    "irregular_model_open_radius": "1/42048",
    "irregular_model_minimality_proved": false,
    "nearby_bodies_need_symmetry": false,
    "two_geometric_implementations": true,
    "separate_orbit_enumeration": true
  },
  "unproved": [
    "A universal five-dimensional integer level Phi(5,32,N)",
    "Coverage of every normalized five-dimensional unconditional body by the supplied finite atlas",
    "Strict inequality for every five-dimensional unconditional nonparallelotope",
    "Global minimality of the ten-direction irregular-model family"
  ],
  "legacy_policy": "All earlier manuscripts preserved as research records; the finite catalogue upper directions are rechecked, other earlier analytic claims are not all re-audited",
  "finite_net_antecedent": "Chuanming Zong, arXiv:0911.4580",
  "publication_priority_established": false,
  "externally_peer_reviewed": false,
  "proof_assistant_verified": false
}