{
 "what": "certified critical-point count for the T5 equilibrium and its potential",
 "statement": "EVERY function in the certified enclosure ball (radius 5.313e-13, l1_nu with nu=1.015) around the T5 candidate density has EXACTLY 2 strict local maxima and 2 strict local minima on the torus; the potential has exactly 1 well(s). Peaks exceed wells: gain-weighted well-counting beats flat well-counting — the equilibrium re-weights a harmonic the potential already contains (it does not \"invent structure\").",
 "verdict": "VERIFIED",
 "source": {
  "cert": "certs/terra-recert-t5.json",
  "verdict": "VERIFIED",
  "r": 5.313360274907975e-13,
  "nu": 1.015,
  "N": 176
 },
 "instance": {
  "sigma": 0.001,
  "gamma": 0.01,
  "A1": 0.001,
  "A2": 0.00015,
  "A3": 0,
  "N": 176,
  "nu": 1.015,
  "G": 2816,
  "a": 0.5,
  "exactBinary64Hex": {
   "sigma": "0x1.0624dd2f1a9fcp-10",
   "gamma": "0x1.47ae147ae147bp-7",
   "A1": "0x1.0624dd2f1a9fcp-10",
   "A2": "0x1.3a92a30553261p-13",
   "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": 8.248958236188461e-11,
  "d2": 5.122582204991543e-8,
  "d3": 0.000053681241298898685
 },
 "m": {
  "label": "density m*",
  "maxima": 2,
  "minima": 2,
  "chain": [
   0,
   0.40269056026689865,
   0.5
  ],
  "curv": [
   "+",
   "-",
   "+"
  ],
  "regions": [
   {
    "kind": "curv",
    "lo": 0,
    "hi": 0.1117663489478319,
    "sign": "+",
    "margin": 1.0064663511864325,
    "grid": 256
   },
   {
    "kind": "slope",
    "lo": 0.1117663489478319,
    "hi": 0.2325735170279015,
    "sign": "+",
    "margin": 0.18819863003069176,
    "grid": 256
   },
   {
    "kind": "curv",
    "lo": 0.2325735170279015,
    "hi": 0.4322877303715086,
    "sign": "-",
    "margin": 0.10440357726533116,
    "grid": 256
   },
   {
    "kind": "slope",
    "lo": 0.4322877303715086,
    "hi": 0.461480562291439,
    "sign": "-",
    "margin": 0.007240988644406301,
    "grid": 256
   },
   {
    "kind": "curv",
    "lo": 0.461480562291439,
    "hi": 0.5,
    "sign": "+",
    "margin": 0.11332215264676371,
    "grid": 256
   }
  ],
  "minMargin": 0.007240988644406301,
  "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": 0.1286581438374038,
    "sign": "-",
    "margin": 0.026160645260112386,
    "grid": 256
   },
   {
    "kind": "slope",
    "lo": 0.1286581438374038,
    "hi": 0.27865814383740384,
    "sign": "-",
    "margin": 0.005507405434632312,
    "grid": 256
   },
   {
    "kind": "curv",
    "lo": 0.27865814383740384,
    "hi": 0.5,
    "sign": "+",
    "margin": 0.015555655762697445,
    "grid": 256
   }
  ],
  "minMargin": 0.005507405434632312,
  "assertions": {
   "contiguous": true,
   "curvatureAlternates": true,
   "slopeMatchesChain": true,
   "countFrom": "certified region signs only"
  }
 },
 "peaks": 2,
 "wells": 1,
 "peaksExceedWells": true,
 "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": "2026-09-02",
  "git": "5b6a608"
 }
}