{
  "timestamp": "20260914T140629_150256Z",
  "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-3 kernel",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact full depth-3 generalized vector",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "physical orthogonality depth-3",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact physical secular coefficient depth-3",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega1,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega1,t0.1",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega1,t1.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega10,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega10,t0.1",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega10,t1.0",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega20,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega20,t0.1",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega20,t1.0",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega816,t0.01",
      "error": 1.1102230246251565e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega816,t0.1",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega816,t1.0",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega969,t0.01",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega969,t0.1",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-3,omega969,t1.0",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact full depth-4 kernel",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact full depth-4 generalized vector",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "physical orthogonality depth-4",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact physical secular coefficient depth-4",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega1,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega1,t0.1",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega1,t1.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega10,t0.01",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega10,t0.1",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega10,t1.0",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega15,t0.01",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega15,t0.1",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega15,t1.0",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega8855,t0.01",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega8855,t0.1",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega8855,t1.0",
      "error": 0.0,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega1215450,t0.01",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega1215450,t0.1",
      "error": 2.220446049250313e-16,
      "tolerance": 1e-12,
      "passed": true
    },
    {
      "name": "exact chain amplification depth-4,omega1215450,t1.0",
      "error": 1.1102230246251565e-16,
      "tolerance": 1e-12,
      "passed": true
    }
  ],
  "results": [
    {
      "depth": 3,
      "frequency": 1,
      "metric": "1/5",
      "spinor_rank": 4,
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 1.697056274847714,
      "one_time_unit_amplification_lower_bound": 1.969771560359221
    },
    {
      "depth": 3,
      "frequency": 10,
      "metric": "1/5",
      "spinor_rank": 4,
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 4.179156198881954,
      "one_time_unit_amplification_lower_bound": 4.297132361779593
    },
    {
      "depth": 3,
      "frequency": 20,
      "metric": "1/5",
      "spinor_rank": 4,
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 8.089893944910543,
      "one_time_unit_amplification_lower_bound": 8.15146514682485
    },
    {
      "depth": 3,
      "frequency": 816,
      "metric": "1/5",
      "spinor_rank": 4,
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 326.40220588078853,
      "one_time_unit_amplification_lower_bound": 326.40373772958645
    },
    {
      "depth": 3,
      "frequency": 969,
      "metric": "1/5",
      "spinor_rank": 4,
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 387.6018575842051,
      "one_time_unit_amplification_lower_bound": 387.6031475655563
    },
    {
      "depth": 4,
      "frequency": 1,
      "metric": "1/5",
      "spinor_rank": 4,
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 1.697056274847714,
      "one_time_unit_amplification_lower_bound": 1.969771560359221
    },
    {
      "depth": 4,
      "frequency": 10,
      "metric": "1/5",
      "spinor_rank": 4,
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 4.179156198881954,
      "one_time_unit_amplification_lower_bound": 4.297132361779593
    },
    {
      "depth": 4,
      "frequency": 15,
      "metric": "1/5",
      "spinor_rank": 4,
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 6.119748968187202,
      "one_time_unit_amplification_lower_bound": 6.20091343542452
    },
    {
      "depth": 4,
      "frequency": 8855,
      "metric": "1/5",
      "spinor_rank": 4,
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 3542.000203274985,
      "one_time_unit_amplification_lower_bound": 3542.0003444381587
    },
    {
      "depth": 4,
      "frequency": 1215450,
      "metric": "1/5",
      "spinor_rank": 4,
      "gap": 1,
      "binding": 2,
      "critical_transverse_wave_number": "sqrt(3)",
      "secular_rate": 486180.0000014809,
      "one_time_unit_amplification_lower_bound": 486180.00000250933
    }
  ],
  "sources": {
    "experiments/mass_operator_sectors.py": "c61bc3b54dd0807c6b457217038dc171756aca07b96f655f5ca7dfc1af50ffbe",
    "experiments/polarization_packet_response.py": "72873acfb045fe06818166a5664f8b44e2a36ba4c5b482e674a896f33825ec24",
    "experiments/polarization_bound_core.py": "b6428084852d678707e5dbc89ccbba03fb2415850a46d649694759890081e45c",
    "experiments/polarization_frozen_response.py": "b1ed0a704674e74a6ed8fa73ce0601965285a4ddda4167cff653c89264b1528d",
    "experiments/localized_current_model.py": "bea8db856f55959328e92d99c089ed26db3b35e717533c67a14c9444d5f1a2e4"
  },
  "raw_data": {
    "path": "polarization-packet-20260914T140629_150256Z.npz",
    "sha256": "5c1a773f745d2494449b1860e63dc54416f751b4c5dffda8f661eba642d94ab4"
  },
  "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."
}