{
 "what": "T5 \u2014 bracket instance (replication at low viscosity: sigma = 0.001, r = 0.15, N = 176)",
 "statement": "Bracket-table instance T5 (replication at low viscosity: sigma = 0.001, r = 0.15, N = 176) 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": 0.001,
  "gamma": 0.01,
  "A1": 0.001,
  "A2": 0.00015,
  "A3": 0.0,
  "N": 176,
  "nu": 1.015,
  "G": 2816,
  "a": 0.5,
  "exactBinary64Hex": {
   "sigma": "0x1.0624dd2f1a9fcp-10",
   "gamma": "0x1.47ae147ae147bp-7",
   "A1": "0x1.0624dd2f1a9fcp-10",
   "A2": "0x1.3a92a30553261p-13",
   "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": 3.7458647085607927e-14,
  "Z1": 0.9259760724291124,
  "Z1even": 0.9259760724291124,
  "Z1odd": 0.9259760724291124,
  "Z2": 1300.9322092635077,
  "r": 5.313360274907975e-13,
  "rMin": 5.060343118959975e-13,
  "rMax": 0.0001138013598473918,
  "disc": 0.005479541755557693,
  "closureMargin": 2.106005914067624e-06,
  "worstCol": "p_177",
  "worstColEven": "p_177",
  "worstColOdd": "p_177",
  "Aopnorm": 114.44702804068682,
  "s0": 0.999950834652252,
  "minWbar": 0.9905805264970179,
  "minW": 0.9905805264964864
 },
 "positivity": {
  "minMbar": 0.9649428198002614,
  "minM": 0.96494281979973,
  "G": 2816
 },
 "witnesses": {
  "hjbMax": 2.2551405187698492e-17,
  "fpResMax": 3.774758283725532e-15,
  "fpFluxConstDev": 1.1275702593849246e-16,
  "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": "502ffbe5fa32249b07185fa05c76918892b0cd6c5705ef23035744ad2a40603f",
  "oddShaRepr": "93fb56b8d828abd5f054ccfc10780270c57389bd6e20e84595663736380b0286"
 },
 "terraCrossCheck": {
  "recordedBounds": {
   "Y0": 3.745864708560798e-14,
   "Z1": 0.9259760724291124,
   "Z2": 1300.932209263507,
   "r": 5.313360274907982e-13,
   "rMin": 5.060343118959982e-13,
   "rMax": 0.00011380135984739185,
   "closureMargin": 2.106005914067625e-06
  },
  "recordedMinM": 0.9649579341920714,
  "recordedMinW": 0.9905805264964864,
  "agreement": {
   "r_ratio": 0.9999999999999987,
   "Z1_diff": 0.0,
   "minM_diff": 1.511439234147538e-05,
   "minW_diff": 0.0
  },
  "agree": true,
  "note": "two implementations (terra JS kernel / this stdlib Python), two independently computed approximate inverses"
 },
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