{
 "run": "RUN-012",
 "subject": "Round 09: adaptive atlas refinement and certificate-cost minimization",
 "document": "main.zip!/AMRAL_LUC_FC_Round_09_Package_v0.1.zip!/AMRAL_Lebesgue_Finite_Closure_Round_09_Adaptive_Atlas_v0.1.md",
 "snapshot_retrieved": "2026-09-24",
 "checks": {
  "A0": {
   "pass": true,
   "failures": []
  },
  "X1": {
   "pass": true,
   "failures": []
  },
  "W1": {
   "pass": true,
   "failures": []
  },
  "W2": {
   "pass": true,
   "failures": []
  },
  "W3": {
   "pass": true,
   "failures": []
  },
  "W4": {
   "pass": true,
   "failures": []
  },
  "W5": {
   "pass": true,
   "failures": []
  },
  "W6": {
   "pass": true,
   "failures": []
  },
  "W7": {
   "pass": true,
   "failures": []
  },
  "W8": {
   "pass": true,
   "failures": []
  },
  "P1": {
   "pass": true,
   "failures": []
  },
  "P2": {
   "pass": true,
   "failures": []
  },
  "R1": {
   "pass": true,
   "failures": []
  }
 },
 "w1": {
  "largest_dH_over_radius": 0.7657135767279685
 },
 "w2": {
  "least_4area_over_per": 1.053470796499898,
  "least_transfer_slack_over_tau": 1.79625286749339
 },
 "w3": {
  "tau_star": 0.000447386884564525,
  "tau_star_old": 0.00014246151852747717,
  "ratio": 3.14040513669125
 },
 "w4": {
  "taus": {
   "root": 0.6046803712311051,
   "d3": 0.2755682537535419,
   "x3": 0.6046803712311051,
   "y3": 0.6046803712311051,
   "phi5": 0.44424560555692344,
   "x5": 0.5460899294180139,
   "y5": 0.5460899294180139
  },
  "first_cut": "phi5",
  "radius_rule": [
   [
    "phi5",
    0.44424560555692344
   ],
   [
    "phi5",
    0.3622574503039218
   ],
   [
    "x5",
    0.3036670084908306
   ],
   [
    "phi5",
    0.2755682537535419
   ],
   [
    "x3",
    0.26245044638632253
   ],
   [
    "y5",
    0.21785583317410917
   ],
   [
    "y3",
    0.18116055070031428
   ],
   [
    "x5",
    0.15186532979376868
   ],
   [
    "phi5",
    0.13778412687677094
   ],
   [
    "x3",
    0.13122920253721618
   ],
   [
    "y5",
    0.10892791658705459
   ],
   [
    "y3",
    0.09058425469421204
   ],
   [
    "x5",
    0.07593664424093925
   ],
   [
    "phi5",
    0.06889206343838547
   ],
   [
    "x3",
    0.06561509872257361
   ],
   [
    "y5",
    0.05446395829352729
   ]
  ],
  "mishra_rule": [
   [
    "phi5",
    0.44424560555692344
   ],
   [
    "x5",
    0.38565516374383224
   ],
   [
    "y5",
    0.30436526805782405
   ],
   [
    "x3",
    0.30436526805782405
   ],
   [
    "y3",
    0.30436526805782405
   ],
   [
    "phi5",
    0.2223771128048224
   ],
   [
    "x5",
    0.1930818918982768
   ],
   [
    "y5",
    0.1524369440552727
   ],
   [
    "x3",
    0.1524369440552727
   ],
   [
    "y3",
    0.1524369440552727
   ],
   [
    "phi5",
    0.11122038195076456
   ],
   [
    "x5",
    0.09657277149749177
   ],
   [
    "y5",
    0.07625029757598971
   ],
   [
    "x3",
    0.07625029757598971
   ],
   [
    "y3",
    0.07625029757598971
   ],
   [
    "phi5",
    0.05561417031943719
   ]
  ],
  "rules_first_differ_at_step": 1
 },
 "w5": {
  "rows": {
   "seed + best B7 @ 0.0001": {
    "center_area": 0.8371345412488154,
    "rep": 0.8364864814973708,
    "core_exact": 0.836835202666911,
    "core_inner_run011": 0.8368147577246808,
    "exact_minus_run011_inner": 2.044494223019111e-05,
    "exact_minus_points_and_corners": 1.2278545613586545e-07
   },
   "seed + best B7 @ 0.001": {
    "center_area": 0.8371345412488154,
    "rep": 0.8306433030857056,
    "core_exact": 0.834239706732341,
    "core_inner_run011": 0.8342258382820734,
    "exact_minus_run011_inner": 1.3868450267628951e-05,
    "exact_minus_points_and_corners": 9.761140407071878e-08
   },
   "four-body optimum @ 0.0001": {
    "center_area": 0.8364914415826941,
    "rep": 0.8358433818312495,
    "core_exact": 0.8361915654187968,
    "core_inner_run011": 0.836155023525527,
    "exact_minus_run011_inner": 3.6541893269848025e-05,
    "exact_minus_points_and_corners": 1.2746134914198848e-07
   },
   "four-body optimum @ 0.001": {
    "center_area": 0.8364914415826941,
    "rep": 0.8300002034195842,
    "core_exact": 0.8337264823915235,
    "core_inner_run011": 0.8337169823009518,
    "exact_minus_run011_inner": 9.500090571656905e-06,
    "exact_minus_points_and_corners": 8.161815290286256e-08
   }
  },
  "rep_closes": {
   "seed + best B7 @ 0.0001": 1.0,
   "seed + best B7 @ 0.001": 0.0,
   "four-body optimum @ 0.0001": 1.0,
   "four-body optimum @ 0.001": 0.0
  },
  "widest_closing_half_width": {
   "seed + best B7": {
    "rep": 0.0003292364519479575,
    "core": 0.0007295511057172972
   },
   "four-body optimum": {
    "rep": 0.0002300849127238233,
    "core": 0.0005078849722361918
   }
  }
 },
 "w6": {
  "exact_minus_points_and_corners_worst": 6.238932126478858e-07,
  "exact_minus_points_alone_worst": 9.523237984798705e-05,
  "pairs_checked_and_containing": {
   "nested": {
    "checked": 12,
    "containing": 12
   },
   "shifted": {
    "checked": 12,
    "containing": 11
   },
   "parent-in-child": {
    "checked": 12,
    "containing": 5
   }
  },
  "theorem_19_1_trials": 56,
  "least_area_gain": 0.0
 },
 "w7": {
  "least_area_gain": 0.0,
  "largest_area_gain": 0.09058607370607974,
  "constant_width_deviation": {
   "7": 2.220446049250313e-16,
   "9": 1.1102230246251565e-16,
   "11": 1.1102230246251565e-16,
   "13": 1.1102230246251565e-16
  }
 },
 "w8": {
  "S0_root": 0.6100872749176112,
  "tau_star": 0.000447386884564525,
  "cycles_bound": 11,
  "cycles_actually_needed": 11,
  "splits_on_one_path": 55
 },
 "p1": {
  "largest_relative_difference": 4.5336507387049184e-13,
  "spec_modes_missing": [
   "OTHER-VERIFIED"
  ],
  "spec_modes_unmetered": [
   "SUPPORT-CORE"
  ]
 },
 "drill": {
  "plants": 17,
  "plants_caught_by_named_checks": 17,
  "controls": 4,
  "controls_undisturbed": 4,
  "must_stay_green_assertions": 256,
  "must_stay_green_held": 256,
  "unplanted_checks": [],
  "cases": [
   {
    "case": "K0-unmodified",
    "kind": "control",
    "expected": [],
    "tripped": [],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "K1-radius-by-double-angle",
    "kind": "control",
    "expected": [],
    "tripped": [],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "K2-doc-crlf",
    "kind": "control",
    "expected": [],
    "tripped": [],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "K3-rep-cost-factored",
    "kind": "control",
    "expected": [],
    "tripped": [],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M1-doc-root-radius-digit",
    "kind": "mutation",
    "expected": [
     "A0"
    ],
    "tripped": [
     "A0"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M2-split-weight-misread",
    "kind": "mutation",
    "expected": [
     "X1"
    ],
    "tripped": [
     "X1"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M3-radius-without-rotation",
    "kind": "mutation",
    "expected": [
     "W1"
    ],
    "tripped": [
     "W1"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M4-perimeter-factor-2",
    "kind": "mutation",
    "expected": [
     "W2"
    ],
    "tripped": [
     "W2"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M5-tau-star-digit",
    "kind": "mutation",
    "expected": [
     "W3"
    ],
    "tripped": [
     "W3"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M6-ratio-as-pi-squared",
    "kind": "mutation",
    "expected": [
     "W3"
    ],
    "tripped": [
     "W3"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M7-x5-radius-digit",
    "kind": "mutation",
    "expected": [
     "W4"
    ],
    "tripped": [
     "W4"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M8-first-cut-x5",
    "kind": "mutation",
    "expected": [
     "W4"
    ],
    "tripped": [
     "W4"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M9-rep-cost-without-4",
    "kind": "mutation",
    "expected": [
     "W5"
    ],
    "tripped": [
     "W5"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M10-rep-claimed-wider",
    "kind": "mutation",
    "expected": [
     "W5"
    ],
    "tripped": [
     "W5"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M11-containment-ends-only",
    "kind": "mutation",
    "expected": [
     "W6"
    ],
    "tripped": [
     "W6"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M12-dominance-reversed",
    "kind": "mutation",
    "expected": [
     "W7"
    ],
    "tripped": [
     "W7"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M13-S0-without-rotation",
    "kind": "mutation",
    "expected": [
     "W8"
    ],
    "tripped": [
     "W8"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M14-validation-child-tau",
    "kind": "mutation",
    "expected": [
     "P1"
    ],
    "tripped": [
     "P1"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M15-spec-mode-assumed",
    "kind": "mutation",
    "expected": [
     "P1"
    ],
    "tripped": [
     "P1"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M16-crystal-digest",
    "kind": "mutation",
    "expected": [
     "P2"
    ],
    "tripped": [
     "P2"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M17-review-dropped",
    "kind": "mutation",
    "expected": [
     "R1"
    ],
    "tripped": [
     "R1"
    ],
    "vacuous": false,
    "ok": true
   }
  ]
 }
}
