{
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    "constant_coefficient_positive": true,
    "scope": "Local algebraic reduction with induced quadratic AND cubic terms; not a trajectory-error guarantee."
  },
  "mechanism": {
    "static_characteristic": [
      "1",
      "1074850767739/145194851031",
      "290975881448/145194851031",
      "3248745856/48398283677"
    ],
    "static_independence": "Exact at two distinct family values; row-factor cancellation proves the full static field independence.",
    "resonance_constants": {
      "S3": [
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        "1051106141690074951088529580229432708687851960207/730750818665451459101842416358141509827966271488"
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    "rank_one_identity": {
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      "im": [
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        "818139/1461501637330902918203684832716283019655932542976"
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    },
    "amplitude_prefactors": {
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        "1964931743981688088755800401031425062884522890515/730750818665451459101842416358141509827966271488"
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      "S3+D3": [
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        "730490220115048221481750167596284738520359645801/91343852333181432387730302044767688728495783936"
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    "radial_recovery_prefactor": [
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      "74998286596003528452098971488239078570613656961/730750818665451459101842416358141509827966271488"
    ],
    "all_n_scope": "The positive-load site-addition theorem is imported; this run freshly certifies the configured finite extension. n<=2 means no Hopf, not no periodic orbit.",
    "finite_amplitude_scope": "Manuscript interval orbit proofs and validated pulse proof are not rerun here. Simulations, shooting, Floquet spectra and pulse trajectories below are numerical only."
  }
}