{
 "ok": true,
 "what": "EXACTLY-3: Krawczyk exhaustion census of the N=3 even Galerkin mfg-cap system",
 "statement": "The 3-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": 3,
 "box": [
  [
   -19.155332961128277,
   -9.5
  ],
  [
   -0.6932564014521403,
   0.6932564014521403
  ],
  [
   -0.35,
   0.35
  ],
  [
   -0.35326605997433486,
   0.35326605997433486
  ],
  [
   -0.9146341484123568,
   0.9146341484123568
  ],
  [
   -0.35,
   0.5327495119673857
  ],
  [
   -0.39835207984537624,
   0.39835207984537624
  ]
 ],
 "count": 3,
 "solutions": [
  {
   "box": [
    [
     -12.127721170879287,
     -11.8575957336527
    ],
    [
     -0.017792999897579386,
     0.019189527150927237
    ],
    [
     -0.0024071361170830514,
     0.0021379867476551137
    ],
    [
     -0.0002762139690169442,
     0.00028591184432121897
    ],
    [
     -0.024675280827310644,
     0.031314861752274666
    ],
    [
     -0.00830264175141893,
     0.0075753770252088015
    ],
    [
     -0.002081345125845703,
     0.0019055836563690864
    ]
   ],
   "image": [
    [
     -12.028953715073113,
     -11.971001897440539
    ],
    [
     -0.004881961644611367,
     0.00487807813400838
    ],
    [
     -0.0005259707885977175,
     0.0005245713656021562
    ],
    [
     -0.00007220991099329194,
     0.00007242553104852183
    ],
    [
     -0.00859602819189209,
     0.008601157669555631
    ],
    [
     -0.0022144457194719193,
     0.002222106118266471
    ],
    [
     -0.0005119156352525914,
     0.0005099570948124175
    ]
   ],
   "candidate": "constant"
  },
  {
   "box": [
    [
     -16.67224931290237,
     -16.647383824392865
    ],
    [
     0.3427276358044654,
     0.34378503243862085
    ],
    [
     -0.000048330709869599754,
     0.00004833070992170849
    ],
    [
     0.003246514665406473,
     0.00328560400172806
    ],
    [
     -0.5654688252208089,
     -0.5637992500900387
    ],
    [
     0.1820736357649797,
     0.183425243701866
    ],
    [
     -0.04869874037742167,
     -0.04800540034590064
    ]
   ],
   "image": [
    [
     -16.655495397865767,
     -16.655170524391515
    ],
    [
     0.3432512758087205,
     0.34326152709560037
    ],
    [
     -4.401563907003693e-7,
     4.40156390708989e-7
    ],
    [
     0.003265870400163537,
     0.0032662495485066448
    ],
    [
     -0.564642296519413,
     -0.5646260003053665
    ],
    [
     0.18274303969982864,
     0.18275598423497139
    ],
    [
     -0.04835544776080921,
     -0.04834871192994901
    ]
   ],
   "candidate": "mirror"
  },
  {
   "box": [
    [
     -16.713205918952962,
     -16.647383824392865
    ],
    [
     -0.34504889890560436,
     -0.3414642995234353
    ],
    [
     -0.00017357584524516043,
     0.00017357584526376323
    ],
    [
     -0.003331820471965138,
     -0.0032003032402722078
    ],
    [
     0.5618192905361228,
     0.5674496568994494
    ],
    [
     0.18042761917473488,
     0.18507182517919826
    ],
    [
     0.047182398227632406,
     0.04952181718176009
    ]
   ],
   "image": [
    [
     -16.657236310543187,
     -16.653429611719545
    ],
    [
     -0.3433166144977195,
     -0.34319618840690314
    ],
    [
     -0.000005068598526428725,
     0.0000050685985264066995
    ],
    [
     -0.0032683021063604997,
     -0.0032638178423125557
    ],
    [
     0.5645386309034424,
     0.5647296659218334
    ],
    [
     0.18267401585922177,
     0.18282500807579238
    ],
    [
     0.04831270635598759,
     0.04839145333481321
    ]
   ],
   "candidate": "branch"
  }
 ],
 "matching": [
  {
   "name": "constant",
   "solutionBox": 0
  },
  {
   "name": "branch",
   "solutionBox": 2
  },
  {
   "name": "mirror",
   "solutionBox": 1
  }
 ],
 "oneToOne": true,
 "splitFrac": 0.537,
 "stats": {
  "processed": 21642,
  "dropRes": 9742,
  "dropK": 945,
  "contracted": 263,
  "bisected": 10689,
  "seconds": 0.759
 },
 "meta": {
  "date": "2026-09-01",
  "git": "c10d578"
 }
}