{
 "what": "T3 \u2014 bracket instance (one-peak negative: sigma = 0.02 above sigma*, gain ratio kills the split)",
 "statement": "Bracket-table instance T3 (one-peak negative: sigma = 0.02 above sigma*, gain ratio kills the split) 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": 0.02,
  "gamma": 0.01,
  "A1": 0.003,
  "A2": 0.0006000000000000001,
  "A3": 0.0,
  "N": 64,
  "nu": 1.05,
  "G": 1024,
  "a": 0.5,
  "exactBinary64Hex": {
   "sigma": "0x1.47ae147ae147bp-6",
   "gamma": "0x1.47ae147ae147bp-7",
   "A1": "0x1.89374bc6a7efap-9",
   "A2": "0x1.3a92a30553262p-11",
   "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": 1.3462524127173243e-14,
  "Z1": 0.5234763857951094,
  "Z1even": 0.5234763857951094,
  "Z1odd": 0.5234763857951094,
  "Z2": 227.71267296134204,
  "r": 2.9664112988846404e-14,
  "rMin": 2.825153617985371e-14,
  "rMax": 0.004185306052619843,
  "disc": 0.22707475488876028,
  "closureMargin": 0.0004985992916903688,
  "worstCol": "tail(analytic)",
  "worstColEven": "tail(analytic)",
  "worstColOdd": "tail(analytic)",
  "Aopnorm": 19.929575876325835,
  "s0": 0.9999308391759583,
  "minWbar": 0.9863569628230591,
  "minW": 0.9863569628230293
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 "positivity": {
  "minMbar": 0.9620729027916697,
  "minM": 0.9620729027916399,
  "G": 1024
 },
 "witnesses": {
  "hjbMax": 2.0816681711721685e-17,
  "fpResMax": 1.4432899320127035e-15,
  "fpFluxConstDev": 4.163336342344337e-17,
  "reciprocalMaw": 8.881784197001252e-16
 },
 "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": "0fb6ac253f9d9938f9e1efb28b44ee46efb140b33391a7248ad1eb7066670d3b",
  "oddShaRepr": "e882abe2897acf0b156d04c059cf11f754a1e99573dac933e9a02f76408b0ed4"
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 "terraCrossCheck": {
  "recordedBounds": {
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   "Z1": 0.5234763857951094,
   "Z2": 227.71267296134204,
   "r": 2.966411298884642e-14,
   "rMin": 2.8251536179853727e-14,
   "rMax": 0.004185306052619843,
   "closureMargin": 0.0004985992916903688
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  "recordedMinM": 0.9621715069595649,
  "recordedMinW": 0.9863569628230292,
  "agreement": {
   "r_ratio": 0.9999999999999993,
   "Z1_diff": 0.0,
   "minM_diff": 9.860416792495386e-05,
   "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-t3-enclosure.json",
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 "meta": {
  "date": "2026-09-01",
  "git": "5c1b0c2",
  "ms": 153520
 }
}