{
 "ok": true,
 "what": "EXACTLY-3: Krawczyk exhaustion census of the N=4 even Galerkin mfg-cap system",
 "statement": "The 4-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": 4,
 "box": [
  [
   -19.122716114804998,
   -9.5
  ],
  [
   -0.6920679698708527,
   0.6920679698708527
  ],
  [
   -0.35,
   0.35
  ],
  [
   -0.3530599761631459,
   0.3530599761631459
  ],
  [
   -0.35,
   0.35
  ],
  [
   -0.9126792568181784,
   0.9126792568181784
  ],
  [
   -0.35,
   0.5321438403880727
  ],
  [
   -0.39530113131052025,
   0.39530113131052025
  ],
  [
   -0.35,
   0.3603307106801617
  ]
 ],
 "count": 3,
 "solutions": [
  {
   "box": [
    [
     -12.126353555839735,
     -11.85907709271663
    ],
    [
     -0.016991556257395138,
     0.018441969107025002
    ],
    [
     -0.0023781252009977914,
     0.0020912327192875294
    ],
    [
     -0.0003008099524188734,
     0.0003106181364197899
    ],
    [
     -0.0000668072612141413,
     0.00006684402887742133
    ],
    [
     -0.018120283568772183,
     0.02997662761052802
    ],
    [
     -0.00801613258922915,
     0.00618237539338342
    ],
    [
     -0.0022324500468283307,
     0.0020532625016008352
    ],
    [
     -0.0007492026880594003,
     0.0007456144178427534
    ]
   ],
   "image": [
    [
     -12.026678837852328,
     -11.973272774429192
    ],
    [
     -0.004361997130068992,
     0.004354089512449954
    ],
    [
     -0.0004731080318718389,
     0.00047079075209939146
    ],
    [
     -0.00007009028872510445,
     0.00007044236717925129
    ],
    [
     -0.00001096731022612094,
     0.000010941922416615459
    ],
    [
     -0.0077059339088369535,
     0.0077175495178183895
    ],
    [
     -0.001941613823307562,
     0.0019551796563037184
    ],
    [
     -0.0004838176037993705,
     0.000479971247909681
    ],
    [
     -0.00011433905054190976,
     0.00011467276021012639
    ]
   ],
   "candidate": "constant"
  },
  {
   "box": [
    [
     -16.62323912417877,
     -16.6203347069929
    ],
    [
     0.3419920623293359,
     0.34214387745213426
    ],
    [
     -0.0000065019888242206985,
     0.00000650198882641639
    ],
    [
     0.003057166907886245,
     0.0030627854187593585
    ],
    [
     -4.730610824201179e-7,
     4.7306108210645323e-7
    ],
    [
     -0.5627997246248132,
     -0.5625587890769581
    ],
    [
     0.1820476302125955,
     0.1822400505916097
    ],
    [
     -0.04534943699692334,
     -0.04525282562939686
    ],
    [
     0.010312017293893843,
     0.010349404068115835
    ]
   ],
   "image": [
    [
     -16.622719427574143,
     -16.62271280203585
    ],
    [
     0.3420678650786482,
     0.34206807466305733
    ],
    [
     -9.422626864232503e-9,
     9.422626872548267e-9
    ],
    [
     0.003059972351019053,
     0.003059979975272789
    ],
    [
     -6.69884856033472e-10,
     6.698848560589372e-10
    ],
    [
     -0.5626794239310813,
     -0.5626790897052755
    ],
    [
     0.18214370534713478,
     0.18214397542901073
    ],
    [
     -0.04530119884250126,
     -0.04530106377853926
    ],
    [
     0.010330684547544622,
     0.01033073681277883
    ]
   ],
   "candidate": "mirror"
  },
  {
   "box": [
    [
     -16.62323912417877,
     -16.622031088727123
    ],
    [
     -0.34208975840934486,
     -0.34204618133237163
    ],
    [
     -0.0000018909964065539238,
     0.0000018909964065501334
    ],
    [
     -0.0030607789334375995,
     -0.0030591733928543425
    ],
    [
     -1.3686901976555467e-7,
     1.3686901976553397e-7
    ],
    [
     0.5626446462600645,
     0.5627138673763104
    ],
    [
     0.18211611358246588,
     0.18217156719368746
    ],
    [
     0.045287226127062805,
     0.04531503649397921
    ],
    [
     0.010325329451894677,
     0.010336091908429252
    ]
   ],
   "image": [
    [
     -16.622716389025804,
     -16.622715840584185
    ],
    [
     -0.3420679785509823,
     -0.3420679611907232
    ],
    [
     -7.775920618188723e-10,
     7.775920429131196e-10
    ],
    [
     -0.0030599764793748066,
     -0.003059975846917032
    ],
    [
     -5.533675876072579e-11,
     5.533675841953118e-11
    ],
    [
     0.5626792429792468,
     0.5626792706571099
    ],
    [
     0.18214382921484154,
     0.18214385156130392
    ],
    [
     0.04530112572106526,
     0.045301136899975246
    ],
    [
     0.010330708517183986,
     0.010330712843139465
    ]
   ],
   "candidate": "branch"
  }
 ],
 "matching": [
  {
   "name": "constant",
   "solutionBox": 0
  },
  {
   "name": "branch",
   "solutionBox": 2
  },
  {
   "name": "mirror",
   "solutionBox": 1
  }
 ],
 "oneToOne": true,
 "splitFrac": 0.537,
 "stats": {
  "processed": 335862,
  "dropRes": 157608,
  "dropK": 9399,
  "contracted": 1843,
  "bisected": 167009,
  "seconds": 17.692
 },
 "meta": {
  "date": "2026-09-01",
  "git": "c10d578"
 }
}