{
 "what": "Tables 1 and 2 of Ashrafyan–Gomes (arXiv:2403.02785v2, §8) re-decided: the two analytic solutions the paper tests against are enclosed in interval arithmetic (every π, e, sin, cos, tanh, cube root and integral with its rounding), the semi-Lagrangian scheme is written from the paper and run on the paper's four meshes at the paper's tolerance and at a tight one, and every printed relative error is met by an interval and given a verdict",
 "statement": "The exact price of test 1, ϖ = −Q + (1 − t)/4 − ∫ₜ¹∫₀ˢQ, satisfies the clearing identity ϖ + a₁ + 2a₂K = −Q at 21 times as an interval fact; the value function's constant a₀(0) is enclosed to 6.9e-8. Of the 24 printed cells, 13 are REPRODUCED within their two printed digits by an independent implementation of the scheme, 5 are within 15 % and 6 differ — the value function and density columns of test 1 at the fine meshes, where the port's errors are up to 2.4 times the printed ones, and the price of test 2 at the finest mesh, where the port does better than printed (×0.85). The price column of test 1 is reproduced at every mesh to its two digits. At the finest mesh of test 1 the paper's tolerance ε = 0.004 changes the price error by 39 % against ε = 1e−8: the printed number there is part tolerance. The density printed for both tests, read literally, has a mass above 3.9e+95 on a sliver of width 0.001 just outside |x| = 1/λ and is not a probability density; the integrable reading (support |x| < 1/λ) is the one enclosed.",
 "verdict": "MEASURED",
 "pins": {
  "tables": "9cebdd7efed3fb24f6ea3b87e8faa67f3ca4b6c41072b73917382f96922bbea1"
 },
 "meshes": [
  [
   100,
   25
  ],
  [
   200,
   50
  ],
  [
   400,
   100
  ],
  [
   800,
   200
  ]
 ],
 "tight": 1e-8,
 "printed": {
  "source": "Y. Ashrafyan, D. A. Gomes, A fully-discrete semi-Lagrangian scheme for a price formation MFG model, arXiv:2403.02785v2 (30 Jan 2025), §8, Tables 1 (p. 24) and 2 (p. 27); read from the PDF on 2026-09-07",
  "definition": "relative errors in l∞ norms: ϖ over the time grid, u at t = 0 over the space grid, m at t = T over the space grid; ρ = 2h; all cases converging within 4 (test 1) or 3 (test 2) iterations of steps 1–4",
  "test1": {
   "eps": 0.004,
   "setup": "l0 = α²/2, V = (x − 1/4)²/2 (η = 1, τ = 1/4), ū ≡ 0, m̄ ∝ exp(−1/(1 − (1.1x)²)), Q̇ = 5 sin(3πt) − 4Q, Q(0) = −0.5, T = 1, [a, b] = [−1, 1]",
   "rows": [
    {
     "rho": 0.02,
     "h": 0.04,
     "w": 0.012,
     "u": 0.025,
     "m": 0.088
    },
    {
     "rho": 0.01,
     "h": 0.02,
     "w": 0.006,
     "u": 0.011,
     "m": 0.042
    },
    {
     "rho": 0.005,
     "h": 0.01,
     "w": 0.0033,
     "u": 0.0047,
     "m": 0.018
    },
    {
     "rho": 0.0025,
     "h": 0.005,
     "w": 0.0021,
     "u": 0.0012,
     "m": 0.0067
    }
   ]
  },
  "test2": {
   "eps": 0.0002,
   "setup": "l0 = 3|α|^{4/3}/4, V = x (η = 1, τ = 0), ū ≡ 0, m̄ ∝ exp(−1/(1 − (1.2x)²)), the same Q",
   "rows": [
    {
     "rho": 0.02,
     "h": 0.04,
     "w": 0.026,
     "u": 0.0085,
     "m": 0.053
    },
    {
     "rho": 0.01,
     "h": 0.02,
     "w": 0.013,
     "u": 0.0074,
     "m": 0.026
    },
    {
     "rho": 0.005,
     "h": 0.01,
     "w": 0.0067,
     "u": 0.0068,
     "m": 0.013
    },
    {
     "rho": 0.0025,
     "h": 0.005,
     "w": 0.0039,
     "u": 0.0065,
     "m": 0.0066
    }
   ]
  },
  "printedPrice": {
   "test1": "ϖ(t) = η(τ − ∫x m̄)(T − t) − η∫ₜᵀ∫₀ˢQ(r) dr ds − cQ(t)",
   "test2": "ϖ(t) = −Q(t)^{1/3} − (T − t)η − ā₁"
  },
  "printedDensity": "m̂(x) = exp(−1/(1 − (λx)²)) for |x| < 1, 0 otherwise — as printed the exponent is positive and unbounded on 1/λ < |x| < 1 and the integral diverges; the integrable reading is support |x| < 1/λ"
 },
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  "Q1": [
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  "K1": [
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  "J0": [
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  "a0": {
   "value": [
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    -0.02912305538639233
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   "remainder": 6.89790816440545e-8,
   "K": 4096
  },
  "a1_0": [
   -0.24939682452402276,
   -0.24939682452402176
  ],
  "a2_0": [
   0.3807970779778791,
   0.38079707797788576
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  "sigmaT": [
   0.6480542736638821,
   0.6480542736638887
  ],
  "Z1": {
   "value": [
    0.40363062160136853,
    0.4036308623405955
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   "remainder": 2.4073909341169943e-7
  },
  "Z2": {
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   "remainder": 2.2063235917796098e-7
  },
  "int2": {
   "value": [
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   "remainder": 3.76159354085279e-7
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