{
 "what": "T4 \u2014 bracket instance (replication: r = 0.15 above threshold, two peaks expected)",
 "statement": "Bracket-table instance T4 (replication: r = 0.15 above threshold, 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": 0.00045,
  "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.d7dbf487fcb92p-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": 2.4370838183199653e-14,
  "Z1": 0.891904814365038,
  "Z1even": 0.891904814365038,
  "Z1odd": 0.891904814365038,
  "Z2": 1120.7119477802207,
  "r": 2.367300631563991e-13,
  "rMin": 2.2545720300609433e-13,
  "rMax": 0.00019290449383131572,
  "disc": 0.011684569102831518,
  "closureMargin": 5.213011773721324e-06,
  "worstCol": "p_97",
  "worstColEven": "p_97",
  "worstColOdd": "p_97",
  "Aopnorm": 93.99997984191309,
  "s0": 0.9996053348688636,
  "minWbar": 0.9737982587830535,
  "minW": 0.9737982587828167
 },
 "positivity": {
  "minMbar": 0.9015595874337102,
  "minM": 0.9015595874334734,
  "G": 1536
 },
 "witnesses": {
  "hjbMax": 1.734723475976807e-17,
  "fpResMax": 1.4432899320127035e-15,
  "fpFluxConstDev": 3.8163916471489756e-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": "3f10e171fec830038bb793cff8938e5ee04dc190a29c351b53439834c675363d",
  "oddShaRepr": "6095e4575e5d6dfdd2d24fe4d0e288ceb1102453f92198e927e6042516845b26"
 },
 "terraCrossCheck": {
  "recordedBounds": {
   "Y0": 2.4370838183199656e-14,
   "Z1": 0.891904814365038,
   "Z2": 1120.7119477802216,
   "r": 2.3673006315639915e-13,
   "rMin": 2.2545720300609436e-13,
   "rMax": 0.00019290449383131556,
   "closureMargin": 5.21301177372132e-06
  },
  "recordedMinM": 0.9017146703342643,
  "recordedMinW": 0.9737982587828167,
  "agreement": {
   "r_ratio": 0.9999999999999998,
   "Z1_diff": 0.0,
   "minM_diff": 0.0001550829007909149,
   "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-t4-enclosure.json",
  "recordSha256": "d90e12f50175e31ddf2e2c0f1c75880d59d099ddaa3aef89424d5925985055f3",
  "frozenVerifierSha256": "7c5356222d6289be31e948a192d6f06ff4c0e557cc8c474306aa19cb3cd3927b"
 },
 "meta": {
  "date": "2026-09-01",
  "git": "5c1b0c2",
  "ms": 442628
 }
}