{
 "what": "T2 \u2014 bracket instance (one-peak negative: r = 0.12 below the predicted threshold 0.1327)",
 "statement": "Bracket-table instance T2 (one-peak negative: r = 0.12 below the predicted threshold 0.1327) 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": 0.00035999999999999997,
  "A3": 0.0,
  "N": 96,
  "nu": 1.02,
  "G": 1536,
  "a": 0.5,
  "exactBinary64Hex": {
   "sigma": "0x1.0624dd2f1a9fcp-9",
   "gamma": "0x1.47ae147ae147bp-7",
   "A1": "0x1.89374bc6a7efap-9",
   "A2": "0x1.797cc39ffd60ep-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": {
  "Y0": 2.377083846716454e-14,
  "Z1": 0.8888834157058526,
  "Z1even": 0.8888834157058526,
  "Z1odd": 0.8888834157058526,
  "Z2": 1114.1083556900792,
  "r": 2.2462335911279024e-13,
  "rMin": 2.1392700867884781e-13,
  "rMax": 0.00019947177239533904,
  "disc": 0.012346895252231784,
  "closureMargin": 5.5411555088601285e-06,
  "worstCol": "p_97",
  "worstColEven": "p_97",
  "worstColOdd": "p_97",
  "Aopnorm": 93.74461019678797,
  "s0": 0.999616748213066,
  "minWbar": 0.9721495173893584,
  "minW": 0.9721495173891337
 },
 "positivity": {
  "minMbar": 0.9058619375966687,
  "minM": 0.905861937596444,
  "G": 1536
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 "witnesses": {
  "hjbMax": 1.5612511283791264e-17,
  "fpResMax": 1.4432899320127035e-15,
  "fpFluxConstDev": 4.163336342344337e-17,
  "reciprocalMaw": 9.992007221626409e-16
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 "falsifiers": {
  "X1": true,
  "X2": true,
  "X3": true,
  "X4": true,
  "X5": true,
  "X6": true,
  "X7": true,
  "X8": true,
  "X9": true
 },
 "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": "8643a1027b833e29d8c8c6a01f7c9a41904d0fd4fba6af8211fa740d4ea3217b",
  "oddShaRepr": "47c39f7d395ac2bb2cc6cafac6197d09c36c8ec09f55157c4757930fb41616fb"
 },
 "terraCrossCheck": {
  "recordedBounds": {
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   "Z1": 0.8888834157058526,
   "Z2": 1114.1083556900792,
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   "rMin": 2.139270086788479e-13,
   "rMax": 0.00019947177239533904,
   "closureMargin": 5.5411555088601285e-06
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  "recordedMinM": 0.9060058816915085,
  "recordedMinW": 0.9721495173891336,
  "agreement": {
   "r_ratio": 0.9999999999999997,
   "Z1_diff": 0.0,
   "minM_diff": 0.00014394409506457428,
   "minW_diff": 1.1102230246251565e-16
  },
  "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-t2-enclosure.json",
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  "frozenVerifierSha256": "7c5356222d6289be31e948a192d6f06ff4c0e557cc8c474306aa19cb3cd3927b"
 },
 "meta": {
  "date": "2026-09-01",
  "git": "5c1b0c2",
  "ms": 623515
 }
}