{
  "slug": "2026-09-09-geodynamo-polarity",
  "mode_model": {
    "equations": "Qdot=mu Q-VD; Ddot=-nu D+VQ; Vdot=Gamma-V+QD (Gissinger2012 Eqs1-3)",
    "initial_Q_D_V": [
      1.0,
      -1.0,
      0.1
    ],
    "nu": 0.1,
    "Gamma": 0.9,
    "observation_window": [
      1000.0,
      6000.0
    ],
    "baseline_rtol": 1e-10,
    "refined_rtol": 1e-11,
    "atol_factor": 0.01,
    "max_step": 0.5,
    "method": "DOP853",
    "runs": {
      "0.119": [
        {
          "run": "baseline",
          "crossings": 15,
          "D_range": [
            -2.8587883426208602,
            2.6224543168998133
          ],
          "max_abs_amplitude": 2.8587883426208602,
          "min_abs_Q_at_D_zero": 2.2900816793828143,
          "crossing_times": [
            1220.6991475832097,
            1507.0042433529065,
            1725.4100294034602,
            1806.9323040904699,
            2356.6319177446676,
            2823.7562978886313,
            3026.192779362952,
            3364.4450934286497,
            4011.4580637024546,
            4173.325979347714,
            4397.309623581548,
            4641.227384855362,
            5262.01316437667,
            5583.864242768086,
            5682.719700035155
          ]
        },
        {
          "run": "refined",
          "crossings": 32,
          "D_range": [
            -2.7761526631569318,
            2.56839680744569
          ],
          "max_abs_amplitude": 2.7761526631569318,
          "min_abs_Q_at_D_zero": 2.289477468021317,
          "crossing_times": [
            1064.5691710210533,
            1162.881109404475,
            1283.5811814454012,
            1422.938777414222,
            1576.5255059532144,
            1785.1496861536095,
            1948.2735305176918,
            2175.1292275872374,
            2600.556416584181,
            2698.591267351582,
            2786.3175349315366,
            2999.3497830553006,
            3303.7084520964395,
            3396.986874019219,
            3474.842499046693,
            3631.0736188204596,
            3824.538266653361,
            4110.801106482433,
            4388.789472318656,
            4492.635115246219,
            4728.761531167506,
            4780.39711955669,
            4931.168818932369,
            4998.873554530513,
            5030.604123073798,
            5273.950027500348,
            5305.089347136652,
            5409.030734959469,
            5543.9290660557535,
            5793.889151585044,
            5825.031604507448,
            5984.5299379231155
          ]
        }
      ],
      "0.12": [
        {
          "run": "baseline",
          "crossings": 0,
          "D_range": [
            -2.1199760550045297,
            -0.5683252575602367
          ],
          "max_abs_amplitude": 2.1199760550045297,
          "min_abs_Q_at_D_zero": null,
          "crossing_times": []
        },
        {
          "run": "refined",
          "crossings": 0,
          "D_range": [
            -2.118369243029452,
            -0.5668301726382903
          ],
          "max_abs_amplitude": 2.118369243029452,
          "min_abs_Q_at_D_zero": null,
          "crossing_times": []
        }
      ]
    },
    "checks": {
      "symmetry_error": 0.0,
      "quadratic_identity_error": 3.552713678800501e-15,
      "fixed_point_Q_D_V": [
        0.9617840960035626,
        -1.0491825819738023,
        -0.10908712114635714
      ],
      "fixed_point_residual": 1.3877787807814457e-17,
      "origin_eigenvalues": [
        [
          0.009500000000000012,
          0.8933139145899386
        ],
        [
          0.009500000000000012,
          -0.8933139145899386
        ],
        [
          -1.0,
          0.0
        ]
      ],
      "divergence": -0.981,
      "short_DOP853_Radau_max_error": 6.18635420668312e-10,
      "short_opposite_polarity_max_error": 0.0
    },
    "limits": [
      "Finite-window mode dynamics, not a 3D Earth geodynamo or forecast.",
      "Long chaotic trajectories need not agree pointwise; crossing counts are solver-sensitive finite-run descriptions.",
      "H=Q^2+D^2/2+V^2/2 is a mathematical diagnostic, not calibrated terrestrial energy.",
      "Growth coefficient mu already assumes inductive amplification; these equations do not derive its fluid mechanism."
    ]
  },
  "paleomagnetic_data": {
    "source": "Biggin2026 SourceDataFig1 sheets c,d, MOESM3",
    "sha256": "9f0237cfaaa0982b87f63fc146ebd745463186d9c1a5e1ed5edebc001396d5d2",
    "summaries": [
      {
        "period": "0-5 Ma",
        "sheet": "c",
        "localities": 40,
        "within_30_degrees": 19,
        "raw_low_latitude_S_median_deg": 11.860366826338,
        "low_latitude_S_IQR_MATLAB_midpoint_deg": 4.323832155920714,
        "quartiles_MATLAB_midpoint_deg": [
          9.90715010661931,
          14.230982262540024
        ]
      },
      {
        "period": "5-23 Ma",
        "sheet": "d",
        "localities": 27,
        "within_30_degrees": 12,
        "raw_low_latitude_S_median_deg": 15.372642966815249,
        "low_latitude_S_IQR_MATLAB_midpoint_deg": 6.178947022840948,
        "quartiles_MATLAB_midpoint_deg": [
          14.097292115078101,
          20.27623913791905
        ]
      }
    ],
    "quantile_method": "MATLAB midpoint (formerly exact): ranks (k-.5)/n, linearly interpolated; NumPy hazen. Verified independently by rank interpolation and published summary values.",
    "limits": "Published derived S and 95% error lengths redrawn. No raw specimen processing, VGP cutoff rerun, or original 10000-bootstrap uncertainty reproduction."
  }
}