{
  "schema": "sensor-overview-paired-v1",
  "master_seed": 2026102901,
  "racks_per_count": 1000,
  "model": "X=y a^T+sqrt(v) Z; iid standard Gaussian y,Z; normalized Gaussian a with norm\u00b2=p",
  "seed_policy": "First 8 SHA256 bytes, little-endian: sensor-overview-paired-v1:master:preset:rack[:p]:component",
  "pairing": "Both rules use exactly the same X,y,a at every rack/count; Gaussian y is shared across counts, a/noise refresh by count",
  "selection_policy": "All indices 0..999 retained, without conditioning label energy, filtering, replacement, clipping, winsorizing, or seed search; invalid arithmetic aborts",
  "quantile_policy": "NumPy quantile(method='linear'), q25/q50/q75, full float64 output; intervals describe racks, not confidence intervals",
  "score": "Population fresh MSE=(a\u00b7w\u22121)\u00b2+v||w||\u00b2; min-norm least squares and correlator w=X^T y/(p y^T y)",
  "computation": "Direct SVD at p<=n; equivalent Gram solve at p>n; 12 independent direct square-solve checks versus SVD at p=n, and 24 full-vector SVD checks versus Gram solve at n+1,last count for first three racks",
  "runtime": {
    "python": "3.14.7",
    "numpy": "2.5.2"
  },
  "generator_sha256": "c603ae49788ce13894d08560e10227eeb1de28a497383ca5a8245e4bdae8a1ac",
  "data_sha256": "d2124e4d0d133d60bdf37a945b8ee50d6c767f276d54554a9871dcd2e74f5b3b",
  "presets": {
    "n5s4": {
      "n": 5,
      "variance": 4,
      "p": [
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        18,
        24,
        31,
        42,
        55,
        74,
        98,
        130,
        173,
        231,
        307,
        408,
        543,
        722,
        961,
        1278,
        1700,
        2261,
        3007,
        4000
      ],
      "racks": 1000,
      "paired_draws": 32000
    },
    "n20s1": {
      "n": 20,
      "variance": 1,
      "p": [
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        40,
        42,
        55,
        74,
        98,
        130,
        173,
        231,
        307,
        408,
        543,
        722,
        961,
        1278,
        1700,
        2261,
        3007,
        4000
      ],
      "racks": 1000,
      "paired_draws": 44000
    },
    "n5s25": {
      "n": 5,
      "variance": 25,
      "p": [
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        18,
        24,
        31,
        42,
        55,
        74,
        98,
        130,
        173,
        231,
        307,
        408,
        543,
        722,
        961,
        1278,
        1700,
        2261,
        3007,
        4000
      ],
      "racks": 1000,
      "paired_draws": 32000
    },
    "n20s40": {
      "n": 20,
      "variance": 40,
      "p": [
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        40,
        42,
        55,
        74,
        98,
        130,
        173,
        231,
        307,
        408,
        543,
        722,
        961,
        1000,
        1278,
        1700,
        2261,
        3007,
        4000
      ],
      "racks": 1000,
      "paired_draws": 45000
    }
  },
  "validation": [
    {
      "preset": "n5s4",
      "p": 5,
      "rack": 0,
      "method": "direct square solve versus SVD",
      "relative_error": 4.172723924398678e-15
    },
    {
      "preset": "n5s4",
      "p": 5,
      "rack": 1,
      "method": "direct square solve versus SVD",
      "relative_error": 5.613082769891242e-14
    },
    {
      "preset": "n5s4",
      "p": 5,
      "rack": 2,
      "method": "direct square solve versus SVD",
      "relative_error": 2.1094237467877974e-15
    },
    {
      "preset": "n5s4",
      "p": 6,
      "rack": 0,
      "method": "SVD versus Gram solve",
      "relative_error": 8.881784197001252e-16
    },
    {
      "preset": "n5s4",
      "p": 6,
      "rack": 1,
      "method": "SVD versus Gram solve",
      "relative_error": 2.5168164796176068e-15
    },
    {
      "preset": "n5s4",
      "p": 6,
      "rack": 2,
      "method": "SVD versus Gram solve",
      "relative_error": 3.1512351458623504e-15
    },
    {
      "preset": "n5s4",
      "p": 4000,
      "rack": 0,
      "method": "SVD versus Gram solve",
      "relative_error": 1.942890293094024e-16
    },
    {
      "preset": "n5s4",
      "p": 4000,
      "rack": 1,
      "method": "SVD versus Gram solve",
      "relative_error": 1.249000902703301e-16
    },
    {
      "preset": "n5s4",
      "p": 4000,
      "rack": 2,
      "method": "SVD versus Gram solve",
      "relative_error": 3.7470027081099033e-16
    },
    {
      "preset": "n20s1",
      "p": 20,
      "rack": 0,
      "method": "direct square solve versus SVD",
      "relative_error": 3.0531133177191805e-16
    },
    {
      "preset": "n20s1",
      "p": 20,
      "rack": 1,
      "method": "direct square solve versus SVD",
      "relative_error": 2.220446049250313e-15
    },
    {
      "preset": "n20s1",
      "p": 20,
      "rack": 2,
      "method": "direct square solve versus SVD",
      "relative_error": 9.479328986255436e-14
    },
    {
      "preset": "n20s1",
      "p": 21,
      "rack": 0,
      "method": "SVD versus Gram solve",
      "relative_error": 6.490758532936934e-14
    },
    {
      "preset": "n20s1",
      "p": 21,
      "rack": 1,
      "method": "SVD versus Gram solve",
      "relative_error": 6.661338147750939e-16
    },
    {
      "preset": "n20s1",
      "p": 21,
      "rack": 2,
      "method": "SVD versus Gram solve",
      "relative_error": 1.2921728819446778e-14
    },
    {
      "preset": "n20s1",
      "p": 4000,
      "rack": 0,
      "method": "SVD versus Gram solve",
      "relative_error": 2.0383000842727483e-17
    },
    {
      "preset": "n20s1",
      "p": 4000,
      "rack": 1,
      "method": "SVD versus Gram solve",
      "relative_error": 4.336808689942018e-17
    },
    {
      "preset": "n20s1",
      "p": 4000,
      "rack": 2,
      "method": "SVD versus Gram solve",
      "relative_error": 7.546047120499111e-17
    },
    {
      "preset": "n5s25",
      "p": 5,
      "rack": 0,
      "method": "direct square solve versus SVD",
      "relative_error": 2.989221764023815e-14
    },
    {
      "preset": "n5s25",
      "p": 5,
      "rack": 1,
      "method": "direct square solve versus SVD",
      "relative_error": 1.2399105077911236e-15
    },
    {
      "preset": "n5s25",
      "p": 5,
      "rack": 2,
      "method": "direct square solve versus SVD",
      "relative_error": 3.565521496658286e-16
    },
    {
      "preset": "n5s25",
      "p": 6,
      "rack": 0,
      "method": "SVD versus Gram solve",
      "relative_error": 1.324256311947987e-14
    },
    {
      "preset": "n5s25",
      "p": 6,
      "rack": 1,
      "method": "SVD versus Gram solve",
      "relative_error": 4.095063483514758e-16
    },
    {
      "preset": "n5s25",
      "p": 6,
      "rack": 2,
      "method": "SVD versus Gram solve",
      "relative_error": 2.8884270701347087e-15
    },
    {
      "preset": "n5s25",
      "p": 4000,
      "rack": 0,
      "method": "SVD versus Gram solve",
      "relative_error": 2.220446049250313e-16
    },
    {
      "preset": "n5s25",
      "p": 4000,
      "rack": 1,
      "method": "SVD versus Gram solve",
      "relative_error": 0.0
    },
    {
      "preset": "n5s25",
      "p": 4000,
      "rack": 2,
      "method": "SVD versus Gram solve",
      "relative_error": 2.220446049250313e-16
    },
    {
      "preset": "n20s40",
      "p": 20,
      "rack": 0,
      "method": "direct square solve versus SVD",
      "relative_error": 1.1291054668256824e-15
    },
    {
      "preset": "n20s40",
      "p": 20,
      "rack": 1,
      "method": "direct square solve versus SVD",
      "relative_error": 1.960664735170396e-15
    },
    {
      "preset": "n20s40",
      "p": 20,
      "rack": 2,
      "method": "direct square solve versus SVD",
      "relative_error": 6.7422293291402166e-15
    },
    {
      "preset": "n20s40",
      "p": 21,
      "rack": 0,
      "method": "SVD versus Gram solve",
      "relative_error": 2.61529573111907e-15
    },
    {
      "preset": "n20s40",
      "p": 21,
      "rack": 1,
      "method": "SVD versus Gram solve",
      "relative_error": 1.150066537067649e-13
    },
    {
      "preset": "n20s40",
      "p": 21,
      "rack": 2,
      "method": "SVD versus Gram solve",
      "relative_error": 8.695816873339326e-15
    },
    {
      "preset": "n20s40",
      "p": 4000,
      "rack": 0,
      "method": "SVD versus Gram solve",
      "relative_error": 7.771561172376096e-16
    },
    {
      "preset": "n20s40",
      "p": 4000,
      "rack": 1,
      "method": "SVD versus Gram solve",
      "relative_error": 1.1102230246251565e-16
    },
    {
      "preset": "n20s40",
      "p": 4000,
      "rack": 2,
      "method": "SVD versus Gram solve",
      "relative_error": 0.0
    }
  ],
  "elapsed_seconds": 10.770971500081941,
  "raw_archive_sha256": "4cd0041a665df46c5c62bc106048be458fbeb4b9f5b9bb5eba0f106eea14eddd"
}
