{
  "timestamp": "20260914T131301_562773Z",
  "scope": "Exact full-multiplet Jordan chain for the localized core's tail operator.\n\nTranslated broad packets promote this chain to unbounded amplification of\nthe formal full-space linearized evolution. Nonlinear stability is separate.\n",
  "passed": true,
  "checks": [
    {
      "name": "exact full depth-5 kernel",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact full depth-5 generalized vector",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "physical orthogonality depth-5",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact physical secular coefficient depth-5",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega1,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega1,t0.1",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega1,t1.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega10,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega10,t0.1",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega10,t1.0",
      "error": 3.3306690738754696e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega18564,t0.01",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega18564,t0.1",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega18564,t1.0",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega3838380,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega3838380,t0.1",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-5,omega3838380,t1.0",
      "error": 4.440892098500626e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact full depth-6 kernel",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact full depth-6 generalized vector",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "physical orthogonality depth-6",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact physical secular coefficient depth-6",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega1,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega1,t0.1",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega1,t1.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega10,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega10,t0.1",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega10,t1.0",
      "error": 3.3306690738754696e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega18564,t0.01",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega18564,t0.1",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega18564,t1.0",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega3838380,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega3838380,t0.1",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-6,omega3838380,t1.0",
      "error": 4.440892098500626e-16,
      "tolerance": 1e-12,
      "passed": true
    }
  ],
  "results": [
    {
      "depth": 5,
      "frequency": 1,
      "metric": "1/9",
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 1.5713484026367723,
      "one_time_unit_amplification_lower_bound": 1.8625616238044678
    },
    {
      "depth": 5,
      "frequency": 10,
      "metric": "1/9",
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 2.410201194064196,
      "one_time_unit_amplification_lower_bound": 2.609419436554514
    },
    {
      "depth": 5,
      "frequency": 18564,
      "metric": "1/9",
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 4125.333435083435,
      "one_time_unit_amplification_lower_bound": 4125.333556285757
    },
    {
      "depth": 5,
      "frequency": 3838380,
      "metric": "1/9",
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 852973.3333338255,
      "one_time_unit_amplification_lower_bound": 852973.3333344116
    },
    {
      "depth": 6,
      "frequency": 1,
      "metric": "1/9",
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 1.5713484026367723,
      "one_time_unit_amplification_lower_bound": 1.8625616238044678
    },
    {
      "depth": 6,
      "frequency": 10,
      "metric": "1/9",
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 2.410201194064196,
      "one_time_unit_amplification_lower_bound": 2.609419436554514
    },
    {
      "depth": 6,
      "frequency": 18564,
      "metric": "1/9",
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 4125.333435083435,
      "one_time_unit_amplification_lower_bound": 4125.333556285757
    },
    {
      "depth": 6,
      "frequency": 3838380,
      "metric": "1/9",
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 852973.3333338255,
      "one_time_unit_amplification_lower_bound": 852973.3333344116
    }
  ],
  "sources": {
    "experiments/polarization_packet_response.py": "a0c126970e4a511f058e970676d999b27988b278a4aaea9f606f75ddc9305a12",
    "experiments/polarization_bound_core.py": "b6428084852d678707e5dbc89ccbba03fb2415850a46d649694759890081e45c",
    "experiments/polarization_frozen_response.py": "b1ed0a704674e74a6ed8fa73ce0601965285a4ddda4167cff653c89264b1528d",
    "experiments/localized_current_model.py": "bea8db856f55959328e92d99c089ed26db3b35e717533c67a14c9444d5f1a2e4"
  },
  "raw_data": {
    "path": "polarization-packet-20260914T131301_562773Z.npz",
    "sha256": "7aabd94ae65330c9dbb63482e03aa2b40201880dcac3d4fbe5900ec48b4fee40"
  },
  "domain": "Canonical L2 norm of the formal linearized real field, before quotienting global symmetries.",
  "limitation": "The packet argument is analytic. This report verifies its full-multiplet Jordan chain; it is not a nonlinear core time simulation."
}