{
 "run": "RUN-025",
 "subject": "Round 22: the symmetry-breaking Fourier witness oracle and the proof-cost Pareto search",
 "document": "main.zip!/AMRAL_LUC_FC_Round_22_Package_v0.1.zip!/AMRAL_Lebesgue_Finite_Closure_Round_22_Fourier_Pareto_v0.1.md",
 "checks": {
  "A0": {
   "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": {
  "budget_used": 0.033950744437483665,
  "budget_available": 0.036936283277021795,
  "candidate_least_radius": 0.005164704317787726,
  "radius_floor": 0.0029855388395381294,
  "width_error": 2.220446049250313e-16,
  "draws_least_radius": 8.837235110359387e-11,
  "harmonics": {
   "7": {
    "a": 0.009375,
    "reserve": 0.050000000000000044,
    "reserve_995": 0.0025000000000000022,
    "order": 7
   },
   "9": {
    "a": 0.005625,
    "reserve": 0.050000000000000044,
    "reserve_995": 0.0024999999999999467,
    "order": 9
   },
   "11": {
    "a": 0.0037500000000000003,
    "reserve": 0.04999999999999999,
    "reserve_995": 0.0025000000000000577,
    "order": 11
   },
   "13": {
    "a": 0.0026785714285714286,
    "reserve": 0.04999999999999999,
    "reserve_995": 0.0025000000000000577,
    "order": 13
   },
   "15": {
    "a": 0.0020089285714285717,
    "reserve": 0.04999999999999993,
    "reserve_995": 0.0024999999999999467,
    "order": 15
   },
   "17": {
    "a": 0.0015625,
    "reserve": 0.04999999999999999,
    "reserve_995": 0.0025000000000000022,
    "order": 17
   },
   "19": {
    "a": 0.00125,
    "reserve": 0.04999999999999999,
    "reserve_995": 0.0024999999999999467,
    "order": 19
   }
  },
  "orders": {
   "(5,)": 1,
   "(7,)": 7,
   "(21,)": 7,
   "(7, 21)": 7,
   "(3, 7)": 1
  }
 },
 "w2": {
  "cells": [
   {
    "package": 0.8370810228126362,
    "min": 0.8370777154320126,
    "basin": "A",
    "A": 0.8370777154320126,
    "B": 0.8370961318682906,
    "package_above_min": 3.3073806235961456e-06,
    "package_above_its_basin": 3.3073806235961456e-06
   },
   {
    "package": 0.837141974396681,
    "min": 0.837021098059539,
    "basin": "B",
    "A": 0.8371415884968616,
    "B": 0.837021098059539,
    "package_above_min": 0.00012087633714208401,
    "package_above_its_basin": 3.8589981943282226e-07
   },
   {
    "package": 0.836984864549911,
    "min": 0.8369847609370216,
    "basin": "A",
    "A": 0.8369847609370216,
    "B": 0.8369979154844477,
    "package_above_min": 1.0361288937943414e-07,
    "package_above_its_basin": 1.0361288937943414e-07
   },
   {
    "package": 0.8369262849724197,
    "min": 0.8369262830926686,
    "basin": "B",
    "A": 0.8370802310435198,
    "B": 0.8369262830926686,
    "package_above_min": 1.879751132527474e-09,
    "package_above_its_basin": 1.879751132527474e-09
   }
  ],
  "worst": 0.8369262830926686
 },
 "w3": {
  "support_error": 2.220446049250313e-16,
  "width_error": 2.220446049250313e-16,
  "symmetry_order": 1,
  "full": [
   0.8358390979709707,
   [
    -0.07687485778877513,
    0.008925386886043652,
    -0.004887336300471156
   ]
  ],
  "from_b7": [
   0.8374213466570328,
   [
    0.2911145276797098,
    -0.0032322815266895323,
    0.004930706771402914
   ]
  ],
  "reduced": [
   0.8368710230512737,
   [
    0.0,
    0.011793494530938205,
    -0.0005939174183575756
   ]
  ],
  "package_full_above": 4.375656503796677e-09,
  "package_optimistic_above": 1.1178217174112604e-07,
  "second_full": [
   0.8358390987429474,
   [
    2.1712699883002187,
    -0.008695241671230872,
    0.005285947893940506
   ]
  ]
 },
 "w4": {
  "conventions": {
   "vertex at pi": {
    "cells": [
     0.8368301984609509,
     0.8367753080685267,
     0.8367532964760147,
     0.8366861860647188
    ],
    "width": 1.6032140059962785e-09,
    "package_minus": [
     2.279285156059352e-06,
     -2.3844691944274743e-06,
     -3.6238868860172246e-06,
     -1.951802630628663e-08
    ],
    "worst_gap": 3.6238868860172246e-06
   },
   "vertex at 0": {
    "cells": [
     0.8368490074312661,
     0.8368121126711191,
     0.8367535758789355,
     0.8367201606764901
    ],
    "width": 1.615717559744212e-09,
    "package_minus": [
     -1.6529685159194507e-05,
     -3.918907178679376e-05,
     -3.9032898068169786e-06,
     -3.399412979765426e-05
    ],
    "worst_gap": 3.918907178679376e-05
   },
   "vertex at pi, mirrored": {
    "cells": [
     0.836827294971596,
     0.8367849273540343,
     0.8367428043681626,
     0.8366961183117021
    ],
    "width": 1.6782342182608545e-09,
    "package_minus": [
     5.1827745108923295e-06,
     -1.2003754702005764e-05,
     6.868220966071981e-06,
     -9.951765009619251e-06
    ],
    "worst_gap": 1.2003754702005764e-05
   },
   "vertex at 0, mirrored": {
    "cells": [
     0.8368600370852852,
     0.83678966992611,
     0.8367667812991779,
     0.8366988507610706
    ],
    "width": 1.644451796956048e-09,
    "package_minus": [
     -2.7559339178306885e-05,
     -1.6746326777727916e-05,
     -1.7108710049229536e-05,
     -1.2684214378166914e-05
    ],
    "worst_gap": 2.7559339178306885e-05
   }
  },
  "fits": [
   "vertex at pi"
  ],
  "b7_above_candidate": [
   0.0002475169710617342,
   0.000245789991012213,
   0.00023146446100685836,
   0.0002400970279498038
  ]
 },
 "w5": {
  "7": {
   "cells": [
    0.8368048333650879,
    0.8367902741486034,
    0.8367775133223283,
    0.8367395218580933
   ],
   "worst": [
    0.8367395218580933,
    0.8367395230445541
   ],
   "worst_cell": 3,
   "width": 1.5033236877570744e-09,
   "margin": 0.0017395218580933403,
   "coarse": 0.836751605060185,
   "coarse_minus_worst": 1.2083202091672796e-05
  },
  "9": {
   "cells": [
    0.8355040249920362,
    0.8355138568353716,
    0.8354915864280088,
    0.8354944261958721
   ],
   "worst": [
    0.8354915864280088,
    0.8354915876516655
   ],
   "worst_cell": 2,
   "width": 1.7339205626853982e-09,
   "margin": 0.0004915864280088389,
   "coarse": 0.8354560816524321,
   "coarse_minus_worst": -3.550477557667797e-05
  },
  "11": {
   "cells": [
    0.8357762308074551,
    0.8357638060093449,
    0.8357852332974819,
    0.8357756973806472
   ],
   "worst": [
    0.8357638060093449,
    0.8357638074611825
   ],
   "worst_cell": 1,
   "width": 1.451837650101595e-09,
   "margin": 0.0007638060093448917,
   "coarse": 0.8357250193289757,
   "coarse_minus_worst": -3.8786680369162774e-05,
   "refined": 0.8357469845649449,
   "refined_minus_worst": -1.682144439996147e-05,
   "package_bracket": [
    0.8357861405290121,
    0.8358153891316992
   ],
   "package_bracket_minus_worst": 2.2333067829616304e-05
  },
  "13": {
   "cells": [
    0.8356711133020951,
    0.8356262746693099,
    0.8356457369820348,
    0.8356225717346687
   ],
   "worst": [
    0.8356225717346687,
    0.8356225726494421
   ],
   "worst_cell": 3,
   "width": 1.4502695711016145e-09,
   "margin": 0.000622571734668731,
   "coarse": 0.8356479929622119,
   "coarse_minus_worst": 2.542122754323195e-05,
   "refined": 0.8356380258124271,
   "refined_minus_worst": 1.5454077758381146e-05,
   "package_bracket": [
    0.8356777513565509,
    0.8356973102976427
   ],
   "package_bracket_minus_worst": 5.5178707108805014e-05
  },
  "15": {
   "cells": [
    0.835226192380788,
    0.8352442766152595,
    0.8352499070525552,
    0.8352607073449735
   ],
   "worst": [
    0.835226192380788,
    0.8352261934617305
   ],
   "worst_cell": 0,
   "width": 1.4274808002312511e-09,
   "margin": 0.00022619238078802617,
   "coarse": 0.8351768908141309,
   "coarse_minus_worst": -4.9301566657056206e-05
  },
  "17": {
   "cells": [
    0.8350877078399864,
    0.8350819468510804,
    0.8351097107661377,
    0.8350966911065253
   ],
   "worst": [
    0.8350819468510804,
    0.8350819485733523
   ],
   "worst_cell": 1,
   "width": 1.7222718806664261e-09,
   "margin": 8.194685108042776e-05,
   "coarse": 0.8350363259516909,
   "coarse_minus_worst": -4.562089938953129e-05,
   "refined": 0.8350783384890097,
   "refined_minus_worst": -3.608362070695037e-06
  },
  "19": {
   "cells": [
    0.8350481985637853,
    0.8350540450510605,
    0.8350682707283302,
    0.8350690095613188
   ],
   "worst": [
    0.8350481985637853,
    0.835048199661339
   ],
   "worst_cell": 0,
   "width": 1.4412955273712669e-09,
   "margin": 4.8198563785351034e-05,
   "coarse": 0.8349983400090083,
   "coarse_minus_worst": -4.985855477701584e-05,
   "refined": 0.8350496290305521,
   "refined_minus_worst": 1.4304667668163518e-06
  }
 },
 "w6": {
  "rebuilt": {
   "B7": {
    "20": [
     7037,
     1015
    ]
   },
   "H11": {
    "20": [
     9623,
     1929
    ]
   },
   "H13": {
    "20": [
     9211,
     1755
    ]
   },
   "H17": {
    "20": [
     7399,
     1533
    ],
    "22": [
     15581,
     4252
    ]
   },
   "H19": {
    "20": [
     7221,
     1504
    ],
    "22": [
     14973,
     4102
    ]
   }
  },
  "tail_rates_20_22": {
   "B7": 0.2576354679802956,
   "H17": 0.6934116112198304,
   "H19": 0.6818484042553191
  },
  "support_motion": {
   "11": [
    2893,
    772
   ],
   "13": [
    2737,
    749
   ],
   "17": [
    6225,
    2111
   ],
   "19": [
    5689,
    2010
   ]
  }
 },
 "w7": {
  "limits": {
   "B7": [
    0.8367313336140874,
    0.8367313336140874
   ],
   "H11": [
    0.8354118255019912,
    0.8354118266050189
   ],
   "H13": [
    0.8352941790983875,
    0.8352941803897895
   ],
   "H17": [
    0.8346707431123866,
    0.8346707442769364
   ],
   "H19": [
    0.834648042163717,
    0.834648043359368
   ]
  },
  "cores_alone": 0.8343637203965598,
  "closes": {
   "B7": [
    21,
    2509,
    0
   ],
   "H11-motion": [
    27,
    21029,
    0
   ],
   "H11-support": [
    24,
    1581,
    0
   ],
   "H13-motion": [
    30,
    43111,
    0
   ],
   "H13-support": [
    26,
    3257,
    0
   ],
   "H17-motion": [
    22,
    7291,
    1330
   ],
   "H17-support": [
    22,
    1677,
    357
   ],
   "H19-motion": [
    22,
    6883,
    1192
   ],
   "H19-support": [
    22,
    1515,
    348
   ]
  },
  "centre": {
   "H11": [
    0.8357992106364913,
    0.8357995406647679
   ],
   "H13": [
    0.835706148202997,
    0.8357064786905389
   ],
   "H17": [
    0.8350991908447588,
    0.8350995209457924
   ],
   "H19": [
    0.8350827261260736,
    0.8350830563617527
   ]
  },
  "loss_to_the_cores": {
   "H11": 0.0003873851345000956,
   "H13": 0.00041196910460949976,
   "H17": 0.0004284477323721614,
   "H19": 0.0004346839623565746
  },
  "volume20": {
   "B7": 4.8645825675117205e-06,
   "H11-motion": 7.072348696147298e-05,
   "H11-support": 1.0473994672283364e-05,
   "H13-motion": 5.219996497929789e-05,
   "H13-support": 1.1383169933180225e-05,
   "H17-motion": 3.8238841855368025e-05,
   "H17-support": 9.948316580258348e-06,
   "H19-motion": 3.31566919707821e-05,
   "H19-support": 8.734229260759714e-06
  },
  "B7_limit_placement": [
   0.8507426846554829,
   0.011213049227370648,
   -0.005827867190189012
  ]
 },
 "w8": {
  "lines": 18,
  "functions": [
   "legality_budget",
   "pure_harmonic"
  ],
  "searches_or_hulls": false,
  "lifts": false,
  "absolute_paths": false,
  "legality_formulas": true
 },
 "p1": {
  "values": 17,
  "volumes": {
   "7037": 0.00014107289445783973,
   "9623": 0.0001853608781911432,
   "9211": 0.00014269616594808068,
   "7399": 9.531730823460029e-05,
   "7221": 8.367057839606758e-05
  },
  "balanced_margins": [
   0.0006,
   0.0007
  ]
 },
 "p2": {
  "multi_mode_legality_budget_satisfied": true,
  "full_breaking_candidate_worse_than_B7_search": true,
  "H11_curvature_reserve_positive": true,
  "H19_orientation_domain_smaller_than_B7": true,
  "H19_depth20_unresolved_volume_smaller_than_B7": true,
  "no_global_theorem_claim": true
 },
 "drill": {
  "plants": 22,
  "plants_caught_by_named_checks": 22,
  "controls": 4,
  "controls_undisturbed": 4,
  "must_stay_green_assertions": 288,
  "must_stay_green_held": 288,
  "unplanted_checks": [],
  "cases": [
   {
    "case": "K0-unmodified",
    "kind": "control",
    "expected": [],
    "tripped": [],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "K1-doc-crlf",
    "kind": "control",
    "expected": [],
    "tripped": [],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "K2-pareto-keys-sorted",
    "kind": "control",
    "expected": [],
    "tripped": [],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "K3-candidates-reversed",
    "kind": "control",
    "expected": [],
    "tripped": [],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M1-doc-ratio",
    "kind": "mutation",
    "expected": [
     "A0"
    ],
    "tripped": [
     "A0"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M2-budget-used",
    "kind": "mutation",
    "expected": [
     "W1"
    ],
    "tripped": [
     "W1"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M3-harmonic-amplitude",
    "kind": "mutation",
    "expected": [
     "W1"
    ],
    "tripped": [
     "W1"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M4-b7-cell01-true-min",
    "kind": "mutation",
    "expected": [
     "W2"
    ],
    "tripped": [
     "W2"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M5-b7-claim",
    "kind": "mutation",
    "expected": [
     "W2"
    ],
    "tripped": [
     "W2"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M6-mixture-claim",
    "kind": "mutation",
    "expected": [
     "W3"
    ],
    "tripped": [
     "W3"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M7-mixture-full-below",
    "kind": "mutation",
    "expected": [
     "P1",
     "W3"
    ],
    "tripped": [
     "P1",
     "W3"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M8-multimode-convention",
    "kind": "mutation",
    "expected": [
     "W4"
    ],
    "tripped": [
     "W4"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M9-multimode-cell",
    "kind": "mutation",
    "expected": [
     "P1",
     "W4"
    ],
    "tripped": [
     "P1",
     "W4"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M10-harmonic-claim",
    "kind": "mutation",
    "expected": [
     "W5"
    ],
    "tripped": [
     "W5"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M11-coarse-scan",
    "kind": "mutation",
    "expected": [
     "W5"
    ],
    "tripped": [
     "W5"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M12-pilot-pending",
    "kind": "mutation",
    "expected": [
     "W6"
    ],
    "tripped": [
     "W6"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M13-support-motion-claim",
    "kind": "mutation",
    "expected": [
     "W6"
    ],
    "tripped": [
     "W6"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M14-tail-rate-claim",
    "kind": "mutation",
    "expected": [
     "W6"
    ],
    "tripped": [
     "W6"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M15-cannot-close",
    "kind": "mutation",
    "expected": [
     "W7"
    ],
    "tripped": [
     "W7"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M16-dense-claim",
    "kind": "mutation",
    "expected": [
     "W7"
    ],
    "tripped": [
     "W7"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M16b-centre-claim",
    "kind": "mutation",
    "expected": [
     "W7"
    ],
    "tripped": [
     "W7"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M17-repro-computes",
    "kind": "mutation",
    "expected": [
     "W8"
    ],
    "tripped": [
     "W8"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M18-crystal-value",
    "kind": "mutation",
    "expected": [
     "P1"
    ],
    "tripped": [
     "P1"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M19-validation-digest",
    "kind": "mutation",
    "expected": [
     "P2"
    ],
    "tripped": [
     "P2"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M20-validation-check",
    "kind": "mutation",
    "expected": [
     "P2"
    ],
    "tripped": [
     "P2"
    ],
    "vacuous": false,
    "ok": true
   },
   {
    "case": "M21-review-dropped",
    "kind": "mutation",
    "expected": [
     "R1"
    ],
    "tripped": [
     "R1"
    ],
    "vacuous": false,
    "ok": true
   }
  ]
 }
}
