{
 "ok": true,
 "what": "EXACTLY-3: Krawczyk exhaustion census of the N=2 even Galerkin mfg-cap system",
 "statement": "The 2-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": 2,
 "box": [
  [
   -18.760791197821284,
   -9.5
  ],
  [
   -0.6785226047839428,
   0.6785226047839428
  ],
  [
   -0.35,
   0.35
  ],
  [
   -0.8903980243388235,
   0.8903980243388235
  ],
  [
   -0.35,
   0.5275329665758868
  ]
 ],
 "count": 3,
 "solutions": [
  {
   "box": [
    [
     -12.058581375449272,
     -11.941418551238222
    ],
    [
     -0.007877038302916976,
     0.007880154385927204
    ],
    [
     -0.0008604800442866507,
     0.0008607151618232177
    ],
    [
     -0.00755646124683719,
     0.01396427671619916
    ],
    [
     -0.0033323963532351005,
     0.0033308469268348304
    ]
   ],
   "image": [
    [
     -12.005135037001823,
     -11.994864962803119
    ],
    [
     -0.0007585627682574026,
     0.000758571339912371
    ],
    [
     -0.00008214034061730755,
     0.0000821381649147679
    ],
    [
     -0.001337024779985659,
     0.0013370106826043845
    ],
    [
     -0.00033623399143792955,
     0.0003362482990446399
    ]
   ],
   "candidate": "constant"
  },
  {
   "box": [
    [
     -16.35532331975147,
     -16.09026610089676
    ],
    [
     0.31474678954692265,
     0.34229598747577816
    ],
    [
     -0.0013494590143633242,
     0.001349590492909264
    ],
    [
     -0.560561487107803,
     -0.5266405260870909
    ],
    [
     0.15919066162790907,
     0.184152099087653
    ]
   ],
   "image": [
    [
     -16.33309890304333,
     -16.188484614975753
    ],
    [
     0.3263347740977129,
     0.3307104787445595
    ],
    [
     -0.00022242593722613754,
     0.00022242443712840396
    ],
    [
     -0.5437128094113395,
     -0.5370833072083043
    ],
    [
     0.17452622996665565,
     0.18053975982111187
    ]
   ],
   "candidate": "mirror"
  },
  {
   "box": [
    [
     -16.35532331975147,
     -16.09026610089676
    ],
    [
     -0.34236546107105104,
     -0.3146445326694902
    ],
    [
     -0.0014786060262020186,
     0.0014798004704845336
    ],
    [
     0.5195709024946547,
     0.5611697036723519
    ],
    [
     0.1581854902790422,
     0.18106338806089656
    ]
   ],
   "image": [
    [
     -16.335145271473056,
     -16.186457924947128
    ],
    [
     -0.33077779534601687,
     -0.3262682171210452
    ],
    [
     -0.00024523426555263987,
     0.0002452342483018914
    ],
    [
     0.5369459455240808,
     0.5438514239740249
    ],
    [
     0.17433549745451832,
     0.18073130251452185
    ]
   ],
   "candidate": "branch"
  }
 ],
 "matching": [
  {
   "name": "constant",
   "solutionBox": 0
  },
  {
   "name": "branch",
   "solutionBox": 2
  },
  {
   "name": "mirror",
   "solutionBox": 1
  }
 ],
 "oneToOne": true,
 "splitFrac": 0.537,
 "stats": {
  "processed": 2077,
  "dropRes": 824,
  "dropK": 169,
  "contracted": 86,
  "bisected": 995,
  "seconds": 0.076
 },
 "meta": {
  "date": "2026-09-01",
  "git": "c10d578"
 }
}