{
  "experiment_key": "balanced-beam-nodeless-persistence",
  "created_utc": "2026-10-12T10:09:54.612716+00:00",
  "sources": {
    "experiments/balanced-beam-persistence.py": "72bb09151c5578d1a5931e6d5cdeeae7c7b81918678c97890444fa6478dea16e",
    "experiments/balanced-count-beams.py": "5dc135a2da86d32000c4e73836526f2bfb01360da075cb0cb1985fe6914304c5",
    "experiments/minimal-count-carrier.py": "c32f6a998a844bbccd3bc46483a551addf224b2b254f7b6d218a8fd0ca87ad2b",
    "experiments/forward-count-action.py": "5f1dd9a03cf8e6b07a56d507791fed8ff859f10abf22bb755c60c3bd1ed6d909",
    "experiments/inverse-current-radial.py": "52d9f1c981635192e06d96b11f0b1e4e5e2d1bf3d5ed420b59411fd45ef7be80",
    "experiments/excited-shell-orientation-current.py": "508484d445dbb86da9f88a31642268b5a1dba8264588e6f48ebb6cc00cf9c264"
  },
  "evaluations": 2420,
  "conditions": {
    "the actual global zonal map is invertible with a scalar positive norm": 112,
    "the zonal background is nonzero at every evaluated position": 112,
    "the concrete nodeless direct sum retains the exact positive shell": 112,
    "the direct-sum density has its rigorous zonal floor": 112,
    "nodeless direct sums preserve scalar balance": 112,
    "nodeless direct sums preserve current balance": 600,
    "the Clifford entries are exactly Gaussian integers before symbolic conversion": 13,
    "the balanced real structure is an exact involution": 2,
    "every Hermitian vector has odd antiunitary parity and zero expectation on real spinors": 13,
    "every Hermitian bivector also has odd antiunitary parity": 36,
    "the invariant real balanced seed space has exactly eight real dimensions": 2,
    "the beam seed has a real-structure phase choice": 2,
    "independent real seeds remain in the balanced space": 40,
    "a coherent beam plus zonal mode remains a real balanced section": 40,
    "coherent real beam additions retain the full spatial eigenvalue": 40,
    "arbitrary coherent real sections annihilate all local low Clifford moments": 952,
    "the exact bad-seed map identifies every possible coherent zero": 40,
    "distance from the compact bad-seed image gives an exact density bound": 40,
    "the entire bad-seed map belongs to the same real eight-dimensional space": 40
  },
  "maximum_errors": {
    "the actual global zonal map is invertible with a scalar positive norm": 1.0818123649861556e-15,
    "the concrete nodeless direct sum retains the exact positive shell": 1.8631875668925802e-14,
    "the direct-sum density has its rigorous zonal floor": 1.0458386542075513e-15,
    "nodeless direct sums preserve scalar balance": 1.2504102800994295e-16,
    "nodeless direct sums preserve current balance": 1.151144234273257e-16,
    "the beam seed has a real-structure phase choice": 2.220446049250313e-16,
    "independent real seeds remain in the balanced space": 0.0,
    "a coherent beam plus zonal mode remains a real balanced section": 3.3769845779833775e-16,
    "coherent real beam additions retain the full spatial eigenvalue": 1.5522155008251984e-15,
    "arbitrary coherent real sections annihilate all local low Clifford moments": 2.522906204474857e-16,
    "the exact bad-seed map identifies every possible coherent zero": 5.893194484411744e-16,
    "distance from the compact bad-seed image gives an exact density bound": 1.171848506058429e-15,
    "the entire bad-seed map belongs to the same real eight-dimensional space": 2.7972111965477463e-16
  },
  "cases": [
    {
      "particle": "W",
      "depth": 2,
      "inferred_index": 76,
      "direct_sum_columns": 4,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": false,
      "bad_seed_image_dimension_bound": null,
      "unit_real_seed_sphere_dimension": null,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "Z",
      "depth": 2,
      "inferred_index": 81,
      "direct_sum_columns": 4,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": false,
      "bad_seed_image_dimension_bound": null,
      "unit_real_seed_sphere_dimension": null,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "Higgs",
      "depth": 2,
      "inferred_index": 95,
      "direct_sum_columns": 4,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": false,
      "bad_seed_image_dimension_bound": null,
      "unit_real_seed_sphere_dimension": null,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "down",
      "depth": 3,
      "inferred_index": 1,
      "direct_sum_columns": 4,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": false,
      "bad_seed_image_dimension_bound": null,
      "unit_real_seed_sphere_dimension": null,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "strange",
      "depth": 3,
      "inferred_index": 4,
      "direct_sum_columns": 4,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": false,
      "bad_seed_image_dimension_bound": null,
      "unit_real_seed_sphere_dimension": null,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "up",
      "depth": 4,
      "inferred_index": 3,
      "direct_sum_columns": 8,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": false,
      "bad_seed_image_dimension_bound": null,
      "unit_real_seed_sphere_dimension": null,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "charm",
      "depth": 4,
      "inferred_index": 20,
      "direct_sum_columns": 8,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": false,
      "bad_seed_image_dimension_bound": null,
      "unit_real_seed_sphere_dimension": null,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "top",
      "depth": 4,
      "inferred_index": 72,
      "direct_sum_columns": 8,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": false,
      "bad_seed_image_dimension_bound": null,
      "unit_real_seed_sphere_dimension": null,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "nu1",
      "depth": 5,
      "inferred_index": 10,
      "direct_sum_columns": 2,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": true,
      "bad_seed_image_dimension_bound": 5,
      "unit_real_seed_sphere_dimension": 7,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "nu2",
      "depth": 5,
      "inferred_index": 15,
      "direct_sum_columns": 2,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": true,
      "bad_seed_image_dimension_bound": 5,
      "unit_real_seed_sphere_dimension": 7,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "nu3",
      "depth": 5,
      "inferred_index": 22,
      "direct_sum_columns": 2,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": true,
      "bad_seed_image_dimension_bound": 5,
      "unit_real_seed_sphere_dimension": 7,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "electron",
      "depth": 6,
      "inferred_index": 13,
      "direct_sum_columns": 2,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": true,
      "bad_seed_image_dimension_bound": 6,
      "unit_real_seed_sphere_dimension": 7,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "muon",
      "depth": 6,
      "inferred_index": 35,
      "direct_sum_columns": 2,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": true,
      "bad_seed_image_dimension_bound": 6,
      "unit_real_seed_sphere_dimension": 7,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    },
    {
      "particle": "tau",
      "depth": 10,
      "inferred_index": 23,
      "direct_sum_columns": 2,
      "zonal_energy_fraction_exact": "1/100",
      "coherent_pure_nodeless_existence_by_dimension": false,
      "bad_seed_image_dimension_bound": null,
      "unit_real_seed_sphere_dimension": null,
      "classification": "constructive direct-sum persistence; generic pure existence at five and six"
    }
  ],
  "proof_dependencies": [
    "nonzero Gegenbauer polynomial and derivative cannot share a root",
    "a smooth image of a compact d-manifold has Hausdorff dimension at most d",
    "for d five or six this image cannot cover the unit seven-sphere of real seeds",
    "the preferred-time convex-envelope graph-norm proof applies to a positive density floor"
  ],
  "limits": [
    "generic pure existence is analytic, not certified by finite spatial samples",
    "no specific random seed is asserted globally nodeless by the checker",
    "the direct sum is globally nodeless by its exact positive density sum",
    "no covariant proper-current or responding-clock stability theorem is transferred",
    "no full containing-space localization or translational inertia theorem follows"
  ]
}