{"generated":"2026-08-28",
"config":{"model":"stationary quadratic MFG on the 1-torus, F(m) = c m, V(x) = A cos 2 pi x","sigma":0.5,"N":16,"nu":1.02,"cRange":[-18,2],"aRange":[0,1.2],"baseCell":{"c":0.125,"A":0.05},"maxDepth":2,"atlas":{"dc":0.125,"dA":0.05},"cellCap":40000,"collapseTol":0.05},
"cStar":-9.869604401089358,
"statement":"Each cell is decided UNIFORMLY over its own rectangle by labs/mfg/box.js: a MULTIPLE cell carries two disjoint certified balls valid for every parameter in the cell, so at least two exact solutions exist there; a UNIQUE cell lies in the monotone half-plane where Lasry-Lions gives global uniqueness (cited) and carries our enclosure of that solution; an UNDECIDED cell states its reason.",
"tally":{"counts":{"MULTIPLE":11330,"UNIQUE":384,"UNDECIDED":8086},"area":{"MULTIPLE":7.371874999996794,"UNIQUE":2.4000000000000172,"UNDECIDED":14.228124999998462},"total":24,"enclosedOnly":6470,"enclosedArea":13.596874999999036,"covered":23.999999999995275},
"seconds":2037,
"reasons":["only one solution found at the cell midpoint — a second branch is not excluded, it is not exhibited","herding branch: discriminant <= 0 — no radius closes the contraction over the box","aligned branch: discriminant <= 0 — no radius closes the contraction over the box","aligned branch: Z1 >= 1 over the box — the midpoint inverse does not control the whole cell","herding branch: contraction factor Z1 + Z2 r >= 1 at the smallest admissible radius — T is a self-map but not a contraction"],
"reasonsNote":"cell.why is an index into reasons[]",
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