{
 "what": "T7 \u2014 bracket instance (threshold pin, lower side: r = 0.13, one peak expected)",
 "statement": "Bracket-table instance T7 (threshold pin, lower side: r = 0.13, one peak 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": 0.00039000000000000005,
  "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": "0x1.98f1d3ed527e6p-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": 2.4125685435680546e-14,
  "Z1": 0.889889492858591,
  "Z1even": 0.889889492858591,
  "Z1odd": 0.889889492858591,
  "Z2": 1116.3042913666666,
  "r": 2.300595137852456e-13,
  "rMin": 2.19104298843091e-13,
  "rMax": 0.00019727686773345575,
  "disc": 0.012124323729075074,
  "closureMargin": 5.4305639943812925e-06,
  "worstCol": "p_97",
  "worstColEven": "p_97",
  "worstColOdd": "p_97",
  "Aopnorm": 93.82958902750708,
  "s0": 0.9996131983493484,
  "minWbar": 0.9728067612385105,
  "minW": 0.9728067612382804
 },
 "positivity": {
  "minMbar": 0.9044277944316867,
  "minM": 0.9044277944314566,
  "G": 1536
 },
 "witnesses": {
  "hjbMax": 1.734723475976807e-17,
  "fpResMax": 1.4432899320127035e-15,
  "fpFluxConstDev": 3.2959746043559335e-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": "95e1351c4710ad256579f0c8748f24bdf5f7560501173b43885c61a80faacc7b",
  "oddShaRepr": "fad590a5a9ccdd096e7741fd7496aab7a2dcf9a949971d22b54a7c2324edd7f8"
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 "terraCrossCheck": {
  "recordedBounds": {
   "Y0": 2.41257273646083e-14,
   "Z1": 0.889889492858591,
   "Z2": 1116.3042913666663,
   "r": 2.3005991361424816e-13,
   "rMin": 2.1910467963261726e-13,
   "rMax": 0.0001972768677334554,
   "closureMargin": 5.430563994381294e-06
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  "recordedMinM": 0.90457545089693,
  "recordedMinW": 0.9728067612382802,
  "agreement": {
   "r_ratio": 0.9999982620657538,
   "Z1_diff": 0.0,
   "minM_diff": 0.00014765646547343358,
   "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-t7-enclosure.json",
  "recordSha256": "c6584f350ab55cca2f0fb04d4eb9ecd5d13de0868ca4b0087ae5e100b4e2bc79",
  "frozenVerifierSha256": "7c5356222d6289be31e948a192d6f06ff4c0e557cc8c474306aa19cb3cd3927b"
 },
 "meta": {
  "date": "2026-09-01",
  "git": "5c1b0c2",
  "ms": 428817
 }
}