{
  "schema": "AN02-L148-independent-examples/v1",
  "status": "PASS",
  "checks": 53,
  "scope": "Physical complex transforms, shifted physical squared norms, actual truncated Fourier planes with analytic tails, complex-atom physical pairing, reflected nonsymmetric dual, weak-data tails, divergence bounds and finite lattice shells.",
  "numeric_checks_do_not_replace_proofs": true,
  "maximum_equality_error": 3.387333806789408e-16,
  "rows": [
    {
      "name": "physical interval transform xi=0.0 eta=0.0",
      "actual": [
        2.0,
        0.0
      ],
      "expected": 2.0,
      "relative_or_absolute_error": 0.0,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=0.7 eta=0.0",
      "actual": [
        1.8406219635362604,
        0.0
      ],
      "expected": [
        1.8406219635362602,
        0.0
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      "relative_or_absolute_error": 1.2063563802011376e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=2.3 eta=0.0",
      "actual": [
        0.6484393149362786,
        0.0
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      "expected": [
        0.6484393149362785,
        0.0
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      "relative_or_absolute_error": 1.1102230246251565e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=6.2 eta=0.0",
      "actual": [
        -0.026803033166934248,
        0.0
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      "expected": [
        -0.02680303316693432,
        0.0
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      "relative_or_absolute_error": 7.28583859910259e-17,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical shifted squared norm eta=0.0",
      "actual": 12.566370614359172,
      "expected": 12.566370614359172,
      "relative_or_absolute_error": 0.0,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=0.0 eta=0.5",
      "actual": [
        2.0843812219749895,
        0.0
      ],
      "expected": [
        2.0843812219749895,
        0.0
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      "relative_or_absolute_error": 0.0,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=0.7 eta=0.5",
      "actual": [
        1.912928244813121,
        -0.22764682275932527
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      "expected": [
        1.912928244813121,
        -0.227646822759325
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      "relative_or_absolute_error": 1.440780703439918e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=2.3 eta=0.5",
      "actual": [
        0.6355304814969254,
        -0.4400660236749564
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      "expected": [
        0.6355304814969253,
        -0.4400660236749564
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      "relative_or_absolute_error": 1.1102230246251565e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=6.2 eta=0.5",
      "actual": [
        -0.01660659900078887,
        0.16885324459222267
      ],
      "expected": [
        -0.01660659900078886,
        0.1688532445922227
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      "relative_or_absolute_error": 2.8609792490763984e-17,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical shifted squared norm eta=0.5",
      "actual": 5.432848644004313,
      "expected": 5.432848644004314,
      "relative_or_absolute_error": 1.6348300457078223e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "Fourier plane truncation rigorous tail eta=0.5",
      "actual": 0.011337726384593516,
      "upper_bound": 0.04,
      "pass": true
    },
    {
      "name": "physical interval transform xi=0.0 eta=1.0",
      "actual": [
        2.3504023872876028,
        0.0
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      "expected": [
        2.3504023872876028,
        0.0
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      "relative_or_absolute_error": 0.0,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=0.7 eta=1.0",
      "actual": [
        2.1405360240177553,
        -0.48978445875146004
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      "expected": [
        2.140536024017756,
        -0.48978445875146004
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      "relative_or_absolute_error": 2.0223968377131038e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=2.3 eta=1.0",
      "actual": [
        0.5925479016007295,
        -0.9385063706997018
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      "expected": [
        0.5925479016007293,
        -0.9385063706997014
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      "relative_or_absolute_error": 3.163160501173845e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=6.2 eta=1.0",
      "actual": [
        0.019077730302866358,
        0.37470922476985447
      ],
      "expected": [
        0.019077730302866268,
        0.3747092247698546
      ],
      "relative_or_absolute_error": 1.4304896245381993e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical shifted squared norm eta=1.0",
      "actual": 3.0840523770111425,
      "expected": 3.084052377011142,
      "relative_or_absolute_error": 1.439953527249898e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "Fourier plane truncation rigorous tail eta=1.0",
      "actual": 0.01017733169028201,
      "upper_bound": 0.04,
      "pass": true
    },
    {
      "name": "physical interval transform xi=0.0 eta=2.0",
      "actual": [
        3.6268604078470186,
        0.0
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      "expected": [
        3.6268604078470186,
        0.0
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      "relative_or_absolute_error": 0.0,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=0.7 eta=2.0",
      "actual": [
        3.2269589307609365,
        -1.2942373812791759
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      "expected": [
        3.226958930760937,
        -1.2942373812791756
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      "relative_or_absolute_error": 1.4280465201761723e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=2.3 eta=2.0",
      "actual": [
        0.34868553464056384,
        -2.4045005712332133
      ],
      "expected": [
        0.3486855346405642,
        -2.4045005712332137
      ],
      "relative_or_absolute_error": 2.2847375334448995e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical interval transform xi=6.2 eta=2.0",
      "actual": [
        0.249317948855494,
        1.0854842347067277
      ],
      "expected": [
        0.24931794885549374,
        1.0854842347067277
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      "relative_or_absolute_error": 2.2428780510329477e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical shifted squared norm eta=2.0",
      "actual": 1.5702693833312102,
      "expected": 1.5702693833312102,
      "relative_or_absolute_error": 0.0,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "Fourier plane truncation rigorous tail eta=2.0",
      "actual": 0.01000224445629505,
      "upper_bound": 0.04,
      "pass": true
    },
    {
      "name": "physical shifted triangle transform z=0j",
      "actual": [
        0.5,
        0.0
      ],
      "expected": 0.5,
      "relative_or_absolute_error": 0.0,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical shifted triangle transform z=(1+1j)",
      "actual": [
        0.6150049253468813,
        -0.18464125172482934
      ],
      "expected": [
        0.6150049253468812,
        -0.18464125172482942
      ],
      "relative_or_absolute_error": 1.3877787807814457e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical shifted triangle transform z=(-2-0.5j)",
      "actual": [
        0.36592939966242216,
        0.18023808186841095
      ],
      "expected": [
        0.3659293996624221,
        0.18023808186841098
      ],
      "relative_or_absolute_error": 6.206335383118183e-17,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical shifted triangle transform z=(0.8-1.4j)",
      "actual": [
        0.35795441673897366,
        -0.055414606516243164
      ],
      "expected": [
        0.3579544167389737,
        -0.05541460651624319
      ],
      "relative_or_absolute_error": 6.206335383118183e-17,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "two complex atoms physical bilinear pairing",
      "actual": [
        0.5162131518767158,
        0.30485888780856735
      ],
      "expected": [
        0.5162131518767157,
        0.3048588878085673
      ],
      "relative_or_absolute_error": 1.2412670766236366e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical triangle squared norm",
      "actual": 0.33333333333333337,
      "expected": 0.3333333333333333,
      "relative_or_absolute_error": 5.551115123125783e-17,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "negative-frequency reflected dual norm squared",
      "actual": 0.07957747154594767,
      "expected": 0.07957747154594767,
      "relative_or_absolute_error": 0.0,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "positive-frequency bilinear dual pairing",
      "actual": 0.07957747154594767,
      "expected": 0.07957747154594767,
      "relative_or_absolute_error": 0.0,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "physical squared-data integral versus beta reference",
      "actual": 5.244115108584242,
      "expected": 5.24411510858424,
      "relative_or_absolute_error": 3.387333806789408e-16,
      "tolerance": 2e-09,
      "pass": true
    },
    {
      "name": "squared-data tail T=1.0",
      "actual": 3.582322676222367,
      "upper_bound": 4.0,
      "pass": true
    },
    {
      "name": "squared-data tail T=4.0",
      "actual": 1.9817980327813165,
      "upper_bound": 2.0,
      "pass": true
    },
    {
      "name": "squared-data tail T=16.0",
      "actual": 0.9994151723695947,
      "upper_bound": 1.0,
      "pass": true
    },
    {
      "name": "squared-data tail T=64.0",
      "actual": 0.4999816916258758,
      "upper_bound": 0.5,
      "pass": true
    },
    {
      "name": "divergent absolute integral lower bound T=1.0",
      "actual": 0.0,
      "upper_bound": 1.8173640429015498,
      "pass": true
    },
    {
      "name": "divergent absolute integral lower bound T=2.0",
      "actual": 1.1671890440056063,
      "upper_bound": 3.1138411890687525,
      "pass": true
    },
    {
      "name": "divergent absolute integral lower bound T=10.0",
      "actual": 4.801083725416529,
      "upper_bound": 7.715678135320327,
      "pass": true
    },
    {
      "name": "divergent absolute integral lower bound T=100.0",
      "actual": 13.33875206019771,
      "upper_bound": 18.780202786605297,
      "pass": true
    },
    {
      "name": "divergent absolute integral lower bound T=1000.0",
      "actual": 28.52111186968038,
      "upper_bound": 38.46915440868213,
      "pass": true
    },
    {
      "name": "lattice square-shell count j=1",
      "actual": 8.0,
      "expected": 8.0,
      "relative_or_absolute_error": 0.0,
      "tolerance": 0,
      "pass": true
    },
    {
      "name": "lattice data shell bound j=1",
      "actual": 0.20938271604938272,
      "upper_bound": 0.5,
      "pass": true
    },
    {
      "name": "lattice square-shell count j=2",
      "actual": 16.0,
      "expected": 16.0,
      "relative_or_absolute_error": 0.0,
      "tolerance": 0,
      "pass": true
    },
    {
      "name": "lattice data shell bound j=2",
      "actual": 0.03565451460117348,
      "upper_bound": 0.0625,
      "pass": true
    },
    {
      "name": "lattice square-shell count j=3",
      "actual": 24.0,
      "expected": 24.0,
      "relative_or_absolute_error": 0.0,
      "tolerance": 0,
      "pass": true
    },
    {
      "name": "lattice data shell bound j=3",
      "actual": 0.011279511219207675,
      "upper_bound": 0.018518518518518517,
      "pass": true
    },
    {
      "name": "lattice square-shell count j=4",
      "actual": 32.0,
      "expected": 32.0,
      "relative_or_absolute_error": 0.0,
      "tolerance": 0,
      "pass": true
    },
    {
      "name": "lattice data shell bound j=4",
      "actual": 0.004870998154584115,
      "upper_bound": 0.0078125,
      "pass": true
    },
    {
      "name": "lattice square-shell count j=5",
      "actual": 40.0,
      "expected": 40.0,
      "relative_or_absolute_error": 0.0,
      "tolerance": 0,
      "pass": true
    },
    {
      "name": "lattice data shell bound j=5",
      "actual": 0.0025212426090236756,
      "upper_bound": 0.004,
      "pass": true
    },
    {
      "name": "lattice square-shell count j=6",
      "actual": 48.0,
      "expected": 48.0,
      "relative_or_absolute_error": 0.0,
      "tolerance": 0,
      "pass": true
    },
    {
      "name": "lattice data shell bound j=6",
      "actual": 0.0014677326279189404,
      "upper_bound": 0.0023148148148148147,
      "pass": true
    }
  ]
}