{
 "ok": true,
 "what": "EXACTLY-3: Krawczyk exhaustion census of the N=5 even Galerkin mfg-cap system",
 "statement": "The 5-mode even Galerkin truncation of the mfg-cap system (sigma=0.5, c=-12, V=0, 2pi enclosed) has EXACTLY 3 solutions in the printed box B: every subbox was eliminated by an interval-residual or Krawczyk exclusion, and each solution box is isolated by Moore-Krawczyk K(X) in int(X) (existence and uniqueness per box). The claim is about the TRUNCATION on B — the PDE-level count is an open problem, not an implication.",
 "verdict": "VERIFIED",
 "sigma": 0.5,
 "c": -12,
 "N": 5,
 "box": [
  [
   -19.12428488864971,
   -9.5
  ],
  [
   -0.6921252878329249,
   0.6921252878329249
  ],
  [
   -0.35,
   0.35
  ],
  [
   -0.35306817917758543,
   0.35306817917758543
  ],
  [
   -0.35,
   0.35
  ],
  [
   -0.35005235203438256,
   0.35005235203438256
  ],
  [
   -0.9127735410866331,
   0.9127735410866331
  ],
  [
   -0.35,
   0.5321709928194212
  ],
  [
   -0.3954225720716419,
   0.3954225720716419
  ],
  [
   -0.35,
   0.3600655169650224
  ],
  [
   -0.35215289112061765,
   0.35215289112061765
  ]
 ],
 "count": 3,
 "solutions": [
  {
   "box": [
    [
     -12.150693995214219,
     -11.834274665423765
    ],
    [
     -0.02256159399053606,
     0.032988174176464595
    ],
    [
     -0.002971716807347944,
     0.00271539817407354
    ],
    [
     -0.0005123124975969295,
     0.0005192244292772111
    ],
    [
     -0.00014357554282662263,
     0.0001435625738499995
    ],
    [
     -0.00004137438392591999,
     0.000041374689688450706
    ],
    [
     -0.029754188152523744,
     0.05576441820539885
    ],
    [
     -0.01069248613952122,
     0.011756094684338286
    ],
    [
     -0.004020390571453715,
     0.0038890170956348154
    ],
    [
     -0.0016876728321052058,
     0.0016845829664713977
    ],
    [
     -0.0006645385571963018,
     0.0006642804997396888
    ]
   ],
   "image": [
    [
     -12.066791135718795,
     -11.931045483695101
    ],
    [
     -0.010080570920447809,
     0.010045910376121271
    ],
    [
     -0.0012942367419424077,
     0.001244802888069912
    ],
    [
     -0.00015914716953258185,
     0.0001597566936142843
    ],
    [
     -0.000028916366149235527,
     0.00002890965784030135
    ],
    [
     -0.000006489342767160458,
     0.000006489477952873878
    ],
    [
     -0.01758362106900303,
     0.01763349700247117
    ],
    [
     -0.005233695957520512,
     0.005469275356817017
    ],
    [
     -0.0011762246126819293,
     0.001174326342058248
    ],
    [
     -0.0003294054039497275,
     0.00032912374236321117
    ],
    [
     -0.00010289938464249741,
     0.0001029068291388863
    ]
   ],
   "candidate": "constant"
  },
  {
   "box": [
    [
     -16.624400412851777,
     -16.623967742090592
    ],
    [
     0.3421152526560125,
     0.3421353230099001
    ],
    [
     -8.964228070859424e-7,
     8.964228053400403e-7
    ],
    [
     0.0030678075183640957,
     0.003068550836807446
    ],
    [
     -6.652477214273378e-8,
     6.652477224304592e-8
    ],
    [
     0.00005233131932389852,
     0.00005237274944124663
    ],
    [
     -0.5627894929350091,
     -0.5627575892383646
    ],
    [
     0.18215813864281544,
     0.1821838469960838
    ],
    [
     -0.0454290713926201,
     -0.04541607275067043
    ],
    [
     0.010063023303065006,
     0.01006801062697855
    ],
    [
     -0.002153745435898785,
     -0.002152036805335445
    ]
   ],
   "image": [
    [
     -16.624284947780996,
     -16.624284829518423
    ],
    [
     0.34212528595717245,
     0.3421252897086772
    ],
    [
     -1.6692789250889212e-10,
     1.669278763299949e-10
    ],
    [
     0.0030681791082131375,
     0.003068179246957733
    ],
    [
     -1.2365202117905414e-11,
     1.2365201775068979e-11
    ],
    [
     0.00005235203056024836,
     0.000052352038204901824
    ],
    [
     -0.5627735440763462,
     -0.56277353809692
    ],
    [
     0.18217099041121362,
     0.18217099522762853
    ],
    [
     -0.04542257328887792,
     -0.04542257085440592
    ],
    [
     0.010065516497693845,
     0.010065517432351094
    ],
    [
     -0.0021528912802858766,
     -0.0021528909609494972
    ]
   ],
   "candidate": "mirror"
  },
  {
   "box": [
    [
     -16.624400412851777,
     -16.623896021794142
    ],
    [
     -0.3421376586688095,
     -0.3421129169970406
    ],
    [
     -0.0000010805603838546025,
     0.0000010805603838445275
    ],
    [
     -0.003068639754131131,
     -0.003067718601039752
    ],
    [
     -8.112208754086876e-8,
     8.112208754055561e-8
    ],
    [
     -0.00005237755303716987,
     -0.00005232651572798064
    ],
    [
     0.5627538687952878,
     0.562793213377979
    ],
    [
     0.18215522097261136,
     0.1821867646662312
    ],
    [
     0.04541458606957888,
     0.04543055807370514
    ],
    [
     0.010062449993712813,
     0.010068583936332174
    ],
    [
     0.002151839592728396,
     0.0021539426485069914
    ]
   ],
   "image": [
    [
     -16.624284977874716,
     -16.62428479942471
    ],
    [
     -0.34212529066060504,
     -0.34212528500524486
    ],
    [
     -2.531427428191472e-10,
     2.5314274037726143e-10
    ],
    [
     -0.003068179281927665,
     -0.0030681790732432113
    ],
    [
     -1.870766214241398e-11,
     1.8707661990595173e-11
    ],
    [
     -0.000052352040138222345,
     -0.000052352028626928034
    ],
    [
     0.5627735365769678,
     0.5627735455962987
    ],
    [
     0.18217098918176045,
     0.1821709964570819
    ],
    [
     0.04542257023381921,
     0.04542257390946471
    ],
    [
     0.01006551625948926,
     0.010065517670555699
    ],
    [
     0.0021528908796046215,
     0.002152891361630758
    ]
   ],
   "candidate": "branch"
  }
 ],
 "matching": [
  {
   "name": "constant",
   "solutionBox": 0
  },
  {
   "name": "branch",
   "solutionBox": 2
  },
  {
   "name": "mirror",
   "solutionBox": 1
  }
 ],
 "oneToOne": true,
 "splitFrac": 0.537,
 "stats": {
  "processed": 6954073,
  "dropRes": 3322545,
  "dropK": 143471,
  "contracted": 22036,
  "bisected": 3466018,
  "seconds": 586.742
 },
 "meta": {
  "date": "2026-09-01",
  "git": "c10d578"
 }
}