{
 "what": "T1 \u2014 two-peak equilibrium over a one-well potential (2nd harmonic re-weighted)",
 "statement": "At the exact binary64 instance below (V = A1 cos 2pi x + A2 cos 4pi x, A1 > 4 A2: exactly 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 the physical branch w = +m^{-1/2} certified over the whole ball. HONEST FRAMING: the potential already contains the second harmonic; the crowd RE-WEIGHTS it across the 1/4 critical-point threshold \u2014 gain-weighted well-counting beats flat well-counting. The peak COUNT itself is a separate certificate (instruments/critcount).",
 "verdict": "VERIFIED",
 "instance": {
  "sigma": 0.002,
  "gamma": 0.01,
  "A1": 0.003,
  "A2": 0.0006000000000000001,
  "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": "0x1.3a92a30553262p-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": 2.4724699375651686e-14,
  "Z1": 0.8969618723747638,
  "Z1even": 0.8969618723747638,
  "Z1odd": 0.8969618723747638,
  "Z2": 1131.8243174043334,
  "r": 2.519546402577481e-13,
  "rMin": 2.399568002454743e-13,
  "rMax": 0.00018207441898004804,
  "disc": 0.010616855688546438,
  "closureMargin": 4.690151811220407e-06,
  "worstCol": "p_97",
  "worstColEven": "p_97",
  "worstColOdd": "p_97",
  "Aopnorm": 94.42852810209328,
  "s0": 0.9995812212170507,
  "minWbar": 0.9742798234770113,
  "minW": 0.9742798234767592
 },
 "positivity": {
  "minMbar": 0.8943896325415887,
  "minM": 0.8943896325413366,
  "G": 1536
 },
 "witnesses": {
  "hjbMax": 1.734723475976807e-17,
  "fpResMax": 1.3322676295501878e-15,
  "fpFluxConstDev": 3.8163916471489756e-17,
  "reciprocalMaw": 9.992007221626409e-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": "c49c3cdb8c20a0858c00a9b53ff0c8b4cefa3b96575c6a64a93fe0de8fb5396d",
  "oddShaRepr": "b62d7d59933f4c046be68a97ab84f043a765852f8388558b2bd6499130987f98"
 },
 "terraCrossCheck": {
  "recordedBounds": {
   "Y0": 2.472469937565169e-14,
   "Z1": 0.8969618723747638,
   "Z2": 1131.824317404334,
   "r": 2.519546402577481e-13,
   "rMin": 2.399568002454743e-13,
   "rMax": 0.00018207441898004795,
   "closureMargin": 4.690151811220405e-06
  },
  "recordedMinM": 0.8945632914094146,
  "recordedMinW": 0.9742798234767592,
  "agreement": {
   "r_ratio": 1.0,
   "Z1_diff": 0.0,
   "minM_diff": 0.00017365886807796382,
   "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-t1-enclosure.json",
  "recordSha256": "88838d5a57f6e48f54226c33161e67d09c58c45774083926aec6f2437f80d214",
  "frozenVerifierSha256": "7c5356222d6289be31e948a192d6f06ff4c0e557cc8c474306aa19cb3cd3927b"
 },
 "meta": {
  "date": "2026-09-01",
  "git": "5c1b0c2",
  "ms": 572973
 }
}