{
 "what": "certified critical-point count for the T6 equilibrium and its potential",
 "statement": "EVERY function in the certified enclosure ball (radius 2.731e-13, l1_nu with nu=1.02) around the T6 candidate density has EXACTLY 3 strict local maxima and 3 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-t6.json",
  "verdict": "VERIFIED",
  "r": 2.7311095673162594e-13,
  "nu": 1.02,
  "N": 96
 },
 "instance": {
  "sigma": 0.002,
  "gamma": 0.01,
  "A1": 0.003,
  "A2": 0,
  "A3": 0.00075,
  "N": 96,
  "nu": 1.02,
  "G": 1536,
  "a": 0.5,
  "exactBinary64Hex": {
   "sigma": "0x1.0624dd2f1a9fcp-9",
   "gamma": "0x1.47ae147ae147bp-7",
   "A1": "0x1.89374bc6a7efap-9",
   "A2": "0x0.0p+0",
   "A3": "0x1.89374bc6a7efap-11"
  },
  "note": "the theorem is about these exact binary64 values, not the decimal strings that name them (TERRA-PORT.md coefficient condition)"
 },
 "ballPads": {
  "d1": 3.187721768766678e-11,
  "d2": 1.4884157602531557e-8,
  "d3": 0.000011726911145460797
 },
 "m": {
  "label": "density m*",
  "maxima": 3,
  "minima": 3,
  "chain": [
   0,
   0.19910862716778266,
   0.2992715841197512,
   0.5
  ],
  "curv": [
   "+",
   "-",
   "+",
   "-"
  ],
  "regions": [
   {
    "kind": "curv",
    "lo": 0,
    "hi": 0.06424289481514664,
    "sign": "+",
    "margin": 7.8091607670437915,
    "grid": 256
   },
   {
    "kind": "slope",
    "lo": 0.06424289481514664,
    "hi": 0.12397548296548144,
    "sign": "+",
    "margin": 0.8893438474066447,
    "grid": 256
   },
   {
    "kind": "curv",
    "lo": 0.12397548296548144,
    "hi": 0.2340722696479579,
    "sign": "-",
    "margin": 3.773107972032359,
    "grid": 256
   },
   {
    "kind": "slope",
    "lo": 0.2340722696479579,
    "hi": 0.26412115673354847,
    "sign": "-",
    "margin": 0.26622861524876085,
    "grid": 256
   },
   {
    "kind": "curv",
    "lo": 0.26412115673354847,
    "hi": 0.3749606759028014,
    "sign": "+",
    "margin": 3.773895188449654,
    "grid": 256
   },
   {
    "kind": "slope",
    "lo": 0.3749606759028014,
    "hi": 0.43517920066687604,
    "sign": "+",
    "margin": 0.8807406568538954,
    "grid": 256
   },
   {
    "kind": "curv",
    "lo": 0.43517920066687604,
    "hi": 0.5,
    "sign": "-",
    "margin": 7.66730120654855,
    "grid": 256
   }
  ],
  "minMargin": 0.26622861524876085,
  "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": 0.0718203692372048,
    "sign": "-",
    "margin": 0.1638809810158558,
    "grid": 256
   },
   {
    "kind": "slope",
    "lo": 0.0718203692372048,
    "hi": 0.42817963076279525,
    "sign": "-",
    "margin": 0.004445519380100062,
    "grid": 256
   },
   {
    "kind": "curv",
    "lo": 0.42817963076279525,
    "hi": 0.5,
    "sign": "+",
    "margin": 0.1638809810158537,
    "grid": 256
   }
  ],
  "minMargin": 0.004445519380100062,
  "assertions": {
   "contiguous": true,
   "curvatureAlternates": true,
   "slopeMatchesChain": true,
   "countFrom": "certified region signs only"
  }
 },
 "peaks": 3,
 "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": "2026-09-01",
  "git": "5c1b0c2"
 }
}