{
  "schemaVersion": 1,
  "kind": "analytical-model-not-measurements",
  "assumptions": {
    "attemptHz": 1000000000,
    "seconds": 315576000,
    "years": 10,
    "secondsPerYear": 31557600,
    "stateCount": 2,
    "symmetricConstantRates": true,
    "initialState": "all in original state",
    "delta": "energy barrier / (Boltzmann constant * absolute temperature)",
    "population": "hypothetical isolated identical grains, except the explicit 50/70 mixture",
    "exclusions": "no grain coupling, field bias, time-dependent temperature, read channel or ECC"
  },
  "rows": [
    {
      "delta": 35,
      "attemptHz": 1000000000,
      "seconds": 315576000,
      "expectedTransitions": 198.97435267001367,
      "firstReversalProbability": 1,
      "oppositeStateProbability": 0.5,
      "normalizedMagnetization": 1.4896120961997719e-173
    },
    {
      "delta": 40,
      "attemptHz": 1000000000,
      "seconds": 315576000,
      "expectedTransitions": 1.3406786424678918,
      "firstReversalProbability": 0.7383319707267995,
      "oppositeStateProbability": 0.4657649212281397,
      "normalizedMagnetization": 0.0684701575437205
    },
    {
      "delta": 50,
      "attemptHz": 1000000000,
      "seconds": 315576000,
      "expectedTransitions": 0.00006086671620210584,
      "firstReversalProbability": 0.000060864863861117383,
      "oppositeStateProbability": 0.00006086301159529097,
      "normalizedMagnetization": 0.9998782739768094
    },
    {
      "delta": 60,
      "attemptHz": 1000000000,
      "seconds": 315576000,
      "expectedTransitions": 2.763344640448704e-9,
      "firstReversalProbability": 2.763344636630667e-9,
      "oppositeStateProbability": 2.7633446328126302e-9,
      "normalizedMagnetization": 0.9999999944733108
    },
    {
      "delta": 70,
      "attemptHz": 1000000000,
      "seconds": 315576000,
      "expectedTransitions": 1.254556525859101e-13,
      "firstReversalProbability": 1.2545565258590222e-13,
      "oppositeStateProbability": 1.2545565258589437e-13,
      "normalizedMagnetization": 0.9999999999997491
    }
  ],
  "dimensionlessExamples": [
    {
      "delta": 0,
      "attemptHz": 1,
      "seconds": 0,
      "expectedTransitions": 0,
      "firstReversalProbability": 0,
      "oppositeStateProbability": 0,
      "normalizedMagnetization": 1
    },
    {
      "delta": 0,
      "attemptHz": 1,
      "seconds": 0.1,
      "expectedTransitions": 0.10000000000000002,
      "firstReversalProbability": 0.09516258196404044,
      "oppositeStateProbability": 0.09063462346100909,
      "normalizedMagnetization": 0.8187307530779818
    },
    {
      "delta": 0,
      "attemptHz": 1,
      "seconds": 1,
      "expectedTransitions": 1,
      "firstReversalProbability": 0.6321205588285577,
      "oppositeStateProbability": 0.43233235838169365,
      "normalizedMagnetization": 0.1353352832366127
    },
    {
      "delta": 0,
      "attemptHz": 1,
      "seconds": 10,
      "expectedTransitions": 10.000000000000002,
      "firstReversalProbability": 0.9999546000702375,
      "oppositeStateProbability": 0.4999999989694232,
      "normalizedMagnetization": 2.0611536224385504e-9
    }
  ],
  "mixture": {
    "fractions": [
      0.5,
      0.5
    ],
    "barriers": [
      50,
      70
    ],
    "meanBarrier": 60,
    "firstReversalProbability": 0.00003043243199328652,
    "uniformMeanBarrierFirstReversalProbability": 2.763344636630667e-9,
    "riskRatio": 11012.897772459046
  },
  "barrierForOneInBillionFirstReversal": 61.01644177180982,
  "limitations": [
    "These are chosen parameters, not estimates from a drive population.",
    "First reversal, final opposite state and ensemble magnetization are different observables.",
    "A grain reversal probability is not a disk bit-error rate or a drive failure rate.",
    "No confidence interval exists without sampled data or a parameter uncertainty model."
  ],
  "generatedOn": "2026-10-17",
  "generator": "node scripts/build-magnetic-retention.mjs",
  "sourceSha256": "9379860072a39426086ec7f3d9385288103d9c38c771a5d347f0009d7880161d",
  "sources": [
    {
      "id": "rippard",
      "title": "Rippard et al. Thermal relaxation rates of magnetic nanoparticles in the presence of magnetic fields and spin-transfer effects. Physical Review B 84, 064439 (2011), doi:10.1103/PhysRevB.84.064439; arXiv:1107.5007v1, pp. 4-7, equation 1 and Figure 1.",
      "url": "https://arxiv.org/pdf/1107.5007v1",
      "accessed": "2026-10-17"
    },
    {
      "id": "weller",
      "title": "Weller and Moser. Thermal effect limits in ultrahigh-density magnetic recording. IEEE Transactions on Magnetics 35(6), 4423-4439 (1999), doi:10.1109/20.809134. IBM-hosted abstract only.",
      "url": "https://research.ibm.com/publications/thermal-effect-limits-in-ultrahigh-density-magnetic-recording",
      "accessed": "2026-10-17"
    },
    {
      "id": "zhou",
      "title": "Zhou et al. Plasmonic near-field transducer for heat-assisted magnetic recording. Nanophotonics 3(3), 141-155 (2014), doi:10.1515/nanoph-2014-0001; introduction and equation 1.",
      "url": "https://engineering.purdue.edu/NanoLab/publications/PDF/2014-Plasmonic-near-field-transducer-for-heat-assisted-magnetic-recording.pdf",
      "accessed": "2026-10-17"
    }
  ],
  "licenseScope": "Original explanatory arithmetic only; no third-party measured data or figures included."
}