{
 "what": "certified critical-point count for the T3 equilibrium and its potential",
 "statement": "EVERY function in the certified enclosure ball (radius 2.966e-14, l1_nu with nu=1.05) around the T3 candidate density has EXACTLY 1 strict local maxima and 1 strict local minima on the torus; the potential has exactly 1 well(s). The ceiling holds at this instance (peaks <= wells).",
 "verdict": "VERIFIED",
 "source": {
  "cert": "certs/terra-recert-t3.json",
  "verdict": "VERIFIED",
  "r": 2.9664112988846404e-14,
  "nu": 1.05,
  "N": 64
 },
 "instance": {
  "sigma": 0.02,
  "gamma": 0.01,
  "A1": 0.003,
  "A2": 0.0006000000000000001,
  "A3": 0,
  "N": 64,
  "nu": 1.05,
  "G": 1024,
  "a": 0.5,
  "exactBinary64Hex": {
   "sigma": "0x1.47ae147ae147bp-6",
   "gamma": "0x1.47ae147ae147bp-7",
   "A1": "0x1.89374bc6a7efap-9",
   "A2": "0x1.3a92a30553262p-11",
   "A3": "0x0.0p+0"
  },
  "note": "the theorem is about these exact binary64 values, not the decimal strings that name them (TERRA-PORT.md coefficient condition)"
 },
 "ballPads": {
  "d1": 1.4049318214134685e-12,
  "d2": 2.6631618136159007e-10,
  "d3": 8.515560396303704e-8
 },
 "m": {
  "label": "density m*",
  "maxima": 1,
  "minima": 1,
  "chain": [
   0,
   0.5
  ],
  "curv": [
   "+",
   "-"
  ],
  "regions": [
   {
    "kind": "curv",
    "lo": 0,
    "hi": 0.12857764506323974,
    "sign": "+",
    "margin": 0.864350277870962,
    "grid": 256
   },
   {
    "kind": "slope",
    "lo": 0.12857764506323974,
    "hi": 0.2785776450632398,
    "sign": "+",
    "margin": 0.1807843618784358,
    "grid": 256
   },
   {
    "kind": "curv",
    "lo": 0.2785776450632398,
    "hi": 0.5,
    "sign": "-",
    "margin": 0.4953921068131227,
    "grid": 256
   }
  ],
  "minMargin": 0.1807843618784358,
  "assertions": {
   "contiguous": true,
   "curvatureAlternates": true,
   "slopeMatchesChain": true,
   "countFrom": "certified region signs only"
  }
 },
 "V": {
  "label": "potential V",
  "maxima": 1,
  "minima": 1,
  "chain": [
   0,
   0.5
  ],
  "curv": [
   "-",
   "+"
  ],
  "regions": [
   {
    "kind": "curv",
    "lo": 0,
    "hi": 0.12167421592694123,
    "sign": "-",
    "margin": 0.08938183204534694,
    "grid": 256
   },
   {
    "kind": "slope",
    "lo": 0.12167421592694123,
    "hi": 0.2716742159269413,
    "sign": "-",
    "margin": 0.0166157104890301,
    "grid": 256
   },
   {
    "kind": "curv",
    "lo": 0.2716742159269413,
    "hi": 0.5,
    "sign": "+",
    "margin": 0.022825255373484215,
    "grid": 256
   }
  ],
  "minMargin": 0.0166157104890301,
  "assertions": {
   "contiguous": true,
   "curvatureAlternates": true,
   "slopeMatchesChain": true,
   "countFrom": "certified region signs only"
  }
 },
 "peaks": 1,
 "wells": 1,
 "peaksExceedWells": false,
 "rigor": {
  "countFrom": "certified region signs only (float is the proposer, never the authority)",
  "coefficientProducts": "outward interval arithmetic, 2pi enclosed, trig argument rounding chain bounded",
  "cellPad": "(L + ballPadNextDeriv) * h/2 + ballPad — the ball Lipschitz is folded in"
 },
 "meta": {
  "date": "2026-09-01",
  "git": "5c1b0c2"
 }
}