{
  "status": "PASS",
  "checks": [
    "Initial conditions",
    "RK4 vs logistic closed form",
    "ODE derivative at six times",
    "Exact bilinear Taylor remainder"
  ],
  "rk4_error": 2.6645352591003757e-15,
  "empirical_benchmark": false,
  "source_proofs_verified": false,
  "figures": [
    {
      "id": "balanced-vs-frozen",
      "kind": "analytical_curve",
      "caption": "Author-constructed scalar model w0=.01: exact balanced gradient flow versus matched-initialization frozen tangent. Dimensionless; no empirical benchmark.",
      "x": {
        "name": "Dimensionless time",
        "values": [
          0,
          1,
          2,
          3,
          4,
          5
        ]
      },
      "series": [
        {
          "name": "Factorized dynamics",
          "values": [
            0.01,
            0.06945315965638048,
            0.3554609871366469,
            0.8029571527702831,
            0.9678567044042412,
            0.9955255179295147
          ]
        },
        {
          "name": "Frozen tangent",
          "values": [
            0.010000000000000009,
            0.029603313426312283,
            0.04881845523920003,
            0.06765311175159383,
            0.08611481707723057,
            0.10421095614440012
          ]
        }
      ]
    },
    {
      "id": "spectral-residual",
      "kind": "analytical_curve",
      "caption": "Author-constructed fixed-kernel residual modes with eigenvalues 1 and .01, both initialized at one. No trained-network measurement.",
      "x": {
        "name": "Dimensionless time",
        "values": [
          0,
          1,
          2,
          5,
          10
        ]
      },
      "series": [
        {
          "name": "Eigenvalue 1",
          "values": [
            1.0,
            0.36787944117144233,
            0.1353352832366127,
            0.006737946999085467,
            4.5399929762484854e-05
          ]
        },
        {
          "name": "Eigenvalue .01",
          "values": [
            1.0,
            0.9900498337491681,
            0.9801986733067553,
            0.951229424500714,
            0.9048374180359595
          ]
        }
      ]
    }
  ],
  "verification_code_sha256": "6e2c37bbfe6b2c1daacda8baf18441dcd1c899962d55629ed5910af9a1882d19",
  "execution_date": "2026-10-28",
  "standalone_no_filesystem_mutation_verified": true
}