{
 "what": "T8 \u2014 bracket instance (threshold pin, upper side: r = 0.14, two peaks expected)",
 "statement": "Bracket-table instance T8 (threshold pin, upper side: r = 0.14, two peaks expected) under the peak-splitting theorem: an exact equilibrium of the discounted congestion MFG (a = 1/2) enclosed at the certified radius, locally unique in the full l1_nu ball, m > 0 and w > 0 over the whole ball. Bracket instances are TABLE ROWS under one theorem, not separate theorems (honest counting, TERRA-PORT.md). The peak count is a separate certificate (instruments/critcount).",
 "verdict": "VERIFIED",
 "instance": {
  "sigma": 0.002,
  "gamma": 0.01,
  "A1": 0.003,
  "A2": 0.00042000000000000007,
  "A3": 0,
  "N": 96,
  "nu": 1.02,
  "G": 1536,
  "a": 0.5,
  "exactBinary64Hex": {
   "sigma": "0x1.0624dd2f1a9fcp-9",
   "gamma": "0x1.47ae147ae147bp-7",
   "A1": "0x1.89374bc6a7efap-9",
   "A2": "0x1.b866e43aa79bdp-12",
   "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)"
 },
 "bounds": {
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  "Z1": 0.8908966237682399,
  "Z1even": 0.8908966237682399,
  "Z1odd": 0.8908966237682399,
  "Z2": 1118.5054814255693,
  "r": 2.3234136035514796e-13,
  "rMin": 2.212774860525218e-13,
  "rMax": 0.0001950877808286724,
  "disc": 0.011903546651162816,
  "closureMargin": 5.321183893527983e-06,
  "worstCol": "p_97",
  "worstColEven": "p_97",
  "worstColOdd": "p_97",
  "Aopnorm": 93.9147119966114,
  "s0": 0.9996093938994938,
  "minWbar": 0.9733832785992952,
  "minW": 0.9733832785990627
 },
 "positivity": {
  "minMbar": 0.9029936770004368,
  "minM": 0.9029936770002043,
  "G": 1536
 },
 "witnesses": {
  "hjbMax": 1.5612511283791264e-17,
  "fpResMax": 1.4432899320127035e-15,
  "fpFluxConstDev": 3.642919299551295e-17,
  "reciprocalMaw": 1.5543122344752192e-15
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 "falsifiers": {
  "X1": true,
  "X2": true,
  "X3": true,
  "X4": true,
  "X5": true,
  "X6": true,
  "X7": true,
  "X8": true,
  "X9": true
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 "approxInverse": {
  "construction": "stdlib Gauss-Jordan (partial pivoting) on the midpoint finite Galerkin Jacobian at the candidate; recomputed deterministically by this runner \u2014 soundness never depends on A, a bad A fails Z1 < 1",
  "evenShaRepr": "e9b746e3b04383294e58c206442420e57fe06c5393a0e256522e72491bec59f8",
  "oddShaRepr": "6139418e4494571dd8883b256b2dceb2465c72927e38c797b24f6fdc6fe885a2"
 },
 "terraCrossCheck": {
  "recordedBounds": {
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   "Z1": 0.8908966237682399,
   "Z2": 1118.505481425569,
   "r": 2.323417642362896e-13,
   "rMin": 2.2127787070122816e-13,
   "rMax": 0.00019508778082867205,
   "closureMargin": 5.321183893527984e-06
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  "recordedMinM": 0.9031450464009549,
  "recordedMinW": 0.9733832785990627,
  "agreement": {
   "r_ratio": 0.9999982616937467,
   "Z1_diff": 0.0,
   "minM_diff": 0.00015136940075066718,
   "minW_diff": 0.0
  },
  "agree": true,
  "note": "two implementations (terra JS kernel / this stdlib Python), two independently computed approximate inverses"
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 "provenance": {
  "source": "/Users/carlostoledo/Documents/frontier-apps/experiments/terra/",
  "sourceNote": "frontier-apps has NO git and is NOT a lift source; only CANDIDATE data (coefficients + parameters) crossed \u2014 every proof-bearing quantity is recomputed here",
  "recordFile": "instruments/mfgcap/records/terra-t8-enclosure.json",
  "recordSha256": "7a10514f8fe3c97b3572d67245435db9305f6578ed0994eb03ef625d11d62c15",
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 },
 "meta": {
  "date": "2026-09-01",
  "git": "5c1b0c2",
  "ms": 424778
 }
}