Recorded data and provenance for the associated calculation.

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version20261022-scoped-correction
scopeSupplied projected-force law, fixed nuclear geometry and specified preparations; no directional-force derivation, nuclear alignment dynamics or polarization selection.
statuspass
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{
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  "parameters": {
    "beta": 1.0,
    "k": 3.0,
    "separation": 2.0,
    "dt": 0.004,
    "duration": 400.0,
    "seed": 1
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  "counterexamples": {
    "roundness_fourth_moments_exact": [
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      "11/64",
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      "7/64"
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    "rank_one_identity": "q1*q4-q2*q3=0",
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    "shared_plane_projection_shares": [
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  "propagator": {
    "method": "NumPy Hermitian diagonalization in energy coordinates; aligned reduced invariant block plus analytical free drift",
    "max_semigroup_error": 2.183659604071949e-15,
    "analytic_aligned_error": 1.4220500840710913e-15
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  "scope": "Supplied projected-force law, fixed nuclear geometry and specified preparations; no directional-force derivation, nuclear alignment dynamics or polarization selection.",
  "sources": {
    "experiments/nuclear_depth_orbit_dimension_checks.py": "b8b2b19e78b6031c8cd420068e8ef6012ad6c90c30d5717c9f120a2df04d1e55"
  },
  "checks": [
    {
      "name": "C1 stated single-center preparations keep unit radius",
      "ok": true
    },
    {
      "name": "C2 stated L=2,3,4 and long irrational run have diagonal second moments near 1/4",
      "ok": true
    },
    {
      "name": "C3 L=1 diagonal second moments are 3/8,1/8,1/8,3/8",
      "ok": true
    },
    {
      "name": "C4 symmetric two-center static minima equal k d^2/4",
      "ok": true
    },
    {
      "name": "C5 sampled spectra have no exponential rate; this does not test free drift",
      "ok": true
    },
    {
      "name": "C6 aligned restricted frequencies match doubled single-center law",
      "ok": true
    },
    {
      "name": "C7 sqrt(k) mode is mixed private-axis difference with canceling gyro terms",
      "ok": true
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    {
      "name": "C8 seeded finite trajectories respect their conserved-energy radius bounds",
      "ok": true
    },
    {
      "name": "C9 spread is preparation-dependent: shared plane sees 1; private difference sees 1/2 each",
      "ok": true
    },
    {
      "name": "C10 exact rank-one constraint retained by every sampled trajectory",
      "ok": true
    },
    {
      "name": "C11 L=2 fourth moments 11/64,11/64,7/64,7/64 refute rotational roundness",
      "ok": true
    },
    {
      "name": "C12 full potential depends on orientation although its minimum does not",
      "ok": true
    },
    {
      "name": "C13 analytical spare block retains aligned linear drift",
      "ok": true
    },
    {
      "name": "C14 energy-coordinate propagator agrees with two half steps",
      "ok": true
    },
    {
      "name": "C15 aligned propagation agrees with analytical gyro solution",
      "ok": true
    },
    {
      "name": "C16 finite runs conserve the complete quadratic energy",
      "ok": true
    },
    {
      "name": "C17 sampled stiffness matches analytic 2k,2k,2k,k(1-cos phi),k(1+cos phi)",
      "ok": true
    },
    {
      "name": "C18 independent uniform axes in R7 have E|cos|=5/16 and E cos^2=1/7",
      "ok": true
    }
  ],
  "status": "pass"
}