{
 "what": "T6 \u2014 three-peak equilibrium over a one-well potential (3rd harmonic re-weighted)",
 "statement": "At the exact binary64 instance below (V = A1 cos 2pi x + A3 cos 6pi x, one well), an exact equilibrium of the discounted congestion MFG (a = 1/2) lies within the certified radius of the candidate, locally unique in the full l1_nu ball (even AND odd blocks), with m > 0 and w > 0 certified over the whole ball. The three-peak count is a separate certificate (instruments/critcount).",
 "verdict": "VERIFIED",
 "instance": {
  "sigma": 0.002,
  "gamma": 0.01,
  "A1": 0.003,
  "A2": 0,
  "A3": 0.00075,
  "N": 96,
  "nu": 1.02,
  "G": 1536,
  "a": 0.5,
  "exactBinary64Hex": {
   "sigma": "0x1.0624dd2f1a9fcp-9",
   "gamma": "0x1.47ae147ae147bp-7",
   "A1": "0x1.89374bc6a7efap-9",
   "A2": "0x0.0p+0",
   "A3": "0x1.89374bc6a7efap-11"
  },
  "note": "the theorem is about these exact binary64 values, not the decimal strings that name them (TERRA-PORT.md coefficient condition)"
 },
 "bounds": {
  "Y0": 2.480364500748514e-14,
  "Z1": 0.9046401227896799,
  "Z1even": 0.9046401227896799,
  "Z1odd": 0.9046401227896799,
  "Z2": 1150.4172265828386,
  "r": 2.7311095673162594e-13,
  "rMin": 2.6010567307773895e-13,
  "rMax": 0.00016578311738943432,
  "disc": 0.009093506124498253,
  "closureMargin": 3.952264435651048e-06,
  "worstCol": "p_97",
  "worstColEven": "p_97",
  "worstColOdd": "p_97",
  "Aopnorm": 95.08806258702882,
  "s0": 0.9995333894752755,
  "minWbar": 0.9461912143230282,
  "minW": 0.946191214322755
 },
 "positivity": {
  "minMbar": 0.8823424150534742,
  "minM": 0.882342415053201,
  "G": 1536
 },
 "witnesses": {
  "hjbMax": 2.0816681711721685e-17,
  "fpResMax": 1.3322676295501878e-15,
  "fpFluxConstDev": 4.163336342344337e-17,
  "reciprocalMaw": 1.1102230246251565e-15
 },
 "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": "9197325d03de49a1a2163a55071ddbf745cb08d90d91fbff6ffe0deb9061d8b3",
  "oddShaRepr": "d81efeb055b4d63e17009714c74eb624e7607335bf5dd4fc7ec2a8bdc2ea3b9f"
 },
 "terraCrossCheck": {
  "recordedBounds": {
   "Y0": 2.4803654157664187e-14,
   "Z1": 0.9046401227896799,
   "Z2": 1150.4172265828388,
   "r": 2.731110574835178e-13,
   "rMin": 2.6010576903192164e-13,
   "rMax": 0.00016578311738943421,
   "closureMargin": 3.952264435651047e-06
  },
  "recordedMinM": 0.8825993974607177,
  "recordedMinW": 0.9461912143227549,
  "agreement": {
   "r_ratio": 0.9999996310955229,
   "Z1_diff": 0.0,
   "minM_diff": 0.00025698240751670376,
   "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-t6-enclosure.json",
  "recordSha256": "1434a24be5780c4bd323d00fb28726357ba1b3739d3fdf34e3c4f434545182ba",
  "frozenVerifierSha256": "7c5356222d6289be31e948a192d6f06ff4c0e557cc8c474306aa19cb3cd3927b"
 },
 "meta": {
  "date": "2026-09-01",
  "git": "5c1b0c2",
  "ms": 535473
 }
}