{
  "experiment_key": "forward-discrete-spatial-count-action",
  "created_utc": "2026-10-12T07:58:35.807950+00:00",
  "sources": {
    "experiments/discrete-count-action.py": "35225ced6c2cc915645f780f1d61f86bb9d7fd4ff5d0eaf83aa604cc2846abcd",
    "experiments/forward-count-action.py": "5f1dd9a03cf8e6b07a56d507791fed8ff859f10abf22bb755c60c3bd1ed6d909",
    "experiments/inverse-current-radial.py": "52d9f1c981635192e06d96b11f0b1e4e5e2d1bf3d5ed420b59411fd45ef7be80",
    "experiments/excited-shell-orientation-current.py": "508484d445dbb86da9f88a31642268b5a1dba8264588e6f48ebb6cc00cf9c264"
  },
  "evaluations": 2929,
  "conditions": {
    "every reconstructed polarization lies strictly inside the corresponding integer-count selection interval": 14,
    "a forward search using only integer counts independently selects the inferred shell": 14,
    "an independent exhaustive finite comparison agrees with the all-label convex-difference theorem": 14,
    "exact adjacent count differences certify the minimum and its increasing tail": 1557,
    "three independent polarizations occupy the same geometric branch under the identical action": 42,
    "the selected integer-count action gives the exact same clock across the whole tested polarization family": 42,
    "the complete family energy retains spatial kinetics and the exact count frequency": 42,
    "the arbitrary full matrix source check remains in one smooth selected-label chart": 42,
    "independent variation of the actual minimum-over-counts potential verifies its full field source": 42,
    "the full Bloch-sphere energy deficit controls phase mismatch and distance to the stationary-family interval": 560,
    "the complete pair energy gives the quantitative transverse phase-persistence bound": 560
  },
  "maximum_errors": {
    "independent variation of the actual minimum-over-counts potential verifies its full field source": 1.2701628637756812e-10
  },
  "cases": [
    {
      "particle": "W",
      "depth": 2,
      "inferred_index": 76,
      "count_exact": "2926",
      "epsilon_exact": "3/955",
      "selected_c_interval_exact": [
        "228/955",
        "231/955"
      ],
      "original_polarization_exact": "459/1910",
      "original_polarization_margin_exact": "3/1910",
      "same_clock_test_polarizations_exact": [
        "183/764",
        "459/1910",
        "921/3820"
      ],
      "maximum_available_shell_at_c_one": 317,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "Z",
      "depth": 2,
      "inferred_index": 81,
      "count_exact": "3321",
      "epsilon_exact": "3/955",
      "selected_c_interval_exact": [
        "243/955",
        "246/955"
      ],
      "original_polarization_exact": "489/1910",
      "original_polarization_margin_exact": "3/1910",
      "same_clock_test_polarizations_exact": [
        "195/764",
        "489/1910",
        "981/3820"
      ],
      "maximum_available_shell_at_c_one": 317,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "Higgs",
      "depth": 2,
      "inferred_index": 95,
      "count_exact": "4560",
      "epsilon_exact": "3/955",
      "selected_c_interval_exact": [
        "57/191",
        "288/955"
      ],
      "original_polarization_exact": "3/10",
      "original_polarization_margin_exact": "3/1910",
      "same_clock_test_polarizations_exact": [
        "1143/3820",
        "3/10",
        "1149/3820"
      ],
      "maximum_available_shell_at_c_one": 317,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "down",
      "depth": 3,
      "inferred_index": 1,
      "count_exact": "1",
      "epsilon_exact": "9/370",
      "selected_c_interval_exact": [
        "0",
        "27/370"
      ],
      "original_polarization_exact": "33/740",
      "original_polarization_margin_exact": "21/740",
      "same_clock_test_polarizations_exact": [
        "27/1480",
        "27/740",
        "81/1480"
      ],
      "maximum_available_shell_at_c_one": 7,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "strange",
      "depth": 3,
      "inferred_index": 4,
      "count_exact": "20",
      "epsilon_exact": "9/370",
      "selected_c_interval_exact": [
        "9/37",
        "27/74"
      ],
      "original_polarization_exact": "3/10",
      "original_polarization_margin_exact": "21/370",
      "same_clock_test_polarizations_exact": [
        "81/296",
        "45/148",
        "99/296"
      ],
      "maximum_available_shell_at_c_one": 7,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "up",
      "depth": 4,
      "inferred_index": 3,
      "count_exact": "15",
      "epsilon_exact": "6/1323245",
      "selected_c_interval_exact": [
        "12/264649",
        "24/264649"
      ],
      "original_polarization_exact": "171/2646490",
      "original_polarization_margin_exact": "51/2646490",
      "same_clock_test_polarizations_exact": [
        "15/264649",
        "18/264649",
        "3/37807"
      ],
      "maximum_available_shell_at_c_one": 107,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "charm",
      "depth": 4,
      "inferred_index": 20,
      "count_exact": "8855",
      "epsilon_exact": "6/1323245",
      "selected_c_interval_exact": [
        "24/3437",
        "138/17185"
      ],
      "original_polarization_exact": "19823/2646490",
      "original_polarization_margin_exact": "1343/2646490",
      "same_clock_test_polarizations_exact": [
        "249/34370",
        "129/17185",
        "267/34370"
      ],
      "maximum_available_shell_at_c_one": 107,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "top",
      "depth": 4,
      "inferred_index": 72,
      "count_exact": "1215450",
      "epsilon_exact": "6/1323245",
      "selected_c_interval_exact": [
        "388944/1323245",
        "81030/264649"
      ],
      "original_polarization_exact": "3/10",
      "original_polarization_margin_exact": "16059/2646490",
      "same_clock_test_polarizations_exact": [
        "785991/2646490",
        "8103/27005",
        "72927/240590"
      ],
      "maximum_available_shell_at_c_one": 107,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "nu1",
      "depth": 5,
      "inferred_index": 10,
      "count_exact": "2002",
      "epsilon_exact": "9/412561",
      "selected_c_interval_exact": [
        "6435/412561",
        "9009/412561"
      ],
      "original_polarization_exact": "76143/4125610",
      "original_polarization_margin_exact": "11793/4125610",
      "same_clock_test_polarizations_exact": [
        "14157/825122",
        "7722/412561",
        "16731/825122"
      ],
      "maximum_available_shell_at_c_one": 29,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "nu2",
      "depth": 5,
      "inferred_index": 15,
      "count_exact": "11628",
      "epsilon_exact": "9/412561",
      "selected_c_interval_exact": [
        "27540/412561",
        "34884/412561"
      ],
      "original_polarization_exact": "619911/8251220",
      "original_polarization_margin_exact": "69111/8251220",
      "same_clock_test_polarizations_exact": [
        "29376/412561",
        "31212/412561",
        "33048/412561"
      ],
      "maximum_available_shell_at_c_one": 29,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "nu3",
      "depth": 5,
      "inferred_index": 22,
      "count_exact": "65780",
      "epsilon_exact": "9/412561",
      "selected_c_interval_exact": [
        "113850/412561",
        "134550/412561"
      ],
      "original_polarization_exact": "3/10",
      "original_polarization_margin_exact": "99183/4125610",
      "same_clock_test_polarizations_exact": [
        "119025/412561",
        "124200/412561",
        "129375/412561"
      ],
      "maximum_available_shell_at_c_one": 29,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "electron",
      "depth": 6,
      "inferred_index": 13,
      "count_exact": "18564",
      "epsilon_exact": "9/18462575",
      "selected_c_interval_exact": [
        "55692/18462575",
        "77112/18462575"
      ],
      "original_polarization_exact": "1309533/369251500",
      "original_polarization_margin_exact": "195693/369251500",
      "same_clock_test_polarizations_exact": [
        "61047/18462575",
        "66402/18462575",
        "71757/18462575"
      ],
      "maximum_available_shell_at_c_one": 44,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "muon",
      "depth": 6,
      "inferred_index": 35,
      "count_exact": "3838380",
      "epsilon_exact": "9/18462575",
      "selected_c_interval_exact": [
        "5181813/18462575",
        "5922072/18462575"
      ],
      "original_polarization_exact": "3/10",
      "original_polarization_margin_exact": "713919/36925150",
      "same_clock_test_polarizations_exact": [
        "21467511/73850300",
        "2220777/7385030",
        "22948029/73850300"
      ],
      "maximum_available_shell_at_c_one": 44,
      "classification": "conditional integer-count action with a geometric local label selector"
    },
    {
      "particle": "tau",
      "depth": 10,
      "inferred_index": 23,
      "count_exact": "64512240",
      "epsilon_exact": "189/14943591113",
      "selected_c_interval_exact": [
        "3810254175/14943591113",
        "5301223200/14943591113"
      ],
      "original_polarization_exact": "3/10",
      "original_polarization_margin_exact": "6728231589/149435911130",
      "same_clock_test_polarizations_exact": [
        "16731985725/59774364452",
        "828316125/2717016566",
        "19713923775/59774364452"
      ],
      "maximum_available_shell_at_c_one": 26,
      "classification": "conditional integer-count action with a geometric local label selector"
    }
  ],
  "limits": [
    "the minimum of count-contact cost minus spatial support is an explicit new constitutive premise",
    "the discrete geometric rule does not select the sparse list of observed particles",
    "the proof uses smooth open winner charts; action derivatives at ties and vacuum need a specified global evolution",
    "the polarization family has a zero reduced shape curvature and potential secular drift",
    "proper-current full spatial persistence is not inherited from other actions",
    "no spatial localization, complete boost inertia or assigned-depth preference is established"
  ]
}