Recorded data and provenance for the associated calculation.

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experiment_keyinferred-shell-polarized-current-map
created_utc2026-10-12T06:54:24.314847+00:00
evaluations300
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{
  "experiment_key": "inferred-shell-polarized-current-map",
  "created_utc": "2026-10-12T06:54:24.314847+00:00",
  "sources": {
    "experiments/excited-shell-polarized-current.py": "af56f108736076d04add3985c4ebf50fdc4845e8f537dd7575506163cc150638",
    "experiments/inverse-current-radial.py": "52d9f1c981635192e06d96b11f0b1e4e5e2d1bf3d5ed420b59411fd45ef7be80",
    "experiments/excited-shell-orientation-current.py": "508484d445dbb86da9f88a31642268b5a1dba8264588e6f48ebb6cc00cf9c264"
  },
  "evaluations": 300,
  "conditions": {
    "transported right Clifford directions satisfy their exact pointwise algebra": 28,
    "the actual right-polarized shape current equals the exact closed two-form profile": 28,
    "both real orientation tangents remain in the complete polarized current kernel": 28,
    "every unitary right-polarized derivative has the exact horizontal canonical norm": 28,
    "complete complex polarized span has a nondegenerate canonical symplectic form": 26,
    "the higher-current shape witness has unit canonical norm": 26,
    "the shape witness has zero current in every first coexact harmonic": 26,
    "the shape witness is orthogonal to both orientation and conjugate directions": 26,
    "independent exact-degree angular and radial rules agree on gram": 14,
    "independent exact-degree angular and radial rules agree on symplectic": 14,
    "independent exact-degree angular and radial rules agree on current_gram": 14,
    "independent exact-degree angular and radial rules agree on first_harmonic_moments": 14,
    "independent cubature verifies the higher-current shape direction": 14,
    "exact rational shape harmonics verify the actual polarized current norm": 14
  },
  "maximum_errors": {
    "transported right Clifford directions satisfy their exact pointwise algebra": 2.4424906541753444e-15,
    "the actual right-polarized shape current equals the exact closed two-form profile": 5.071353049860596e-13,
    "both real orientation tangents remain in the complete polarized current kernel": 2.2289647144318516e-11,
    "every unitary right-polarized derivative has the exact horizontal canonical norm": 7.044843757595359e-13,
    "complete complex polarized span has a nondegenerate canonical symplectic form": 1.662042027826563e-15,
    "the higher-current shape witness has unit canonical norm": 1.9984014443252818e-15,
    "the shape witness has zero current in every first coexact harmonic": 2.074698555796728e-16,
    "the shape witness is orthogonal to both orientation and conjugate directions": 2.6156724140359902e-14,
    "independent exact-degree angular and radial rules agree on gram": 1.0372964367563178e-12,
    "independent exact-degree angular and radial rules agree on symplectic": 1.0372964367563178e-12,
    "independent exact-degree angular and radial rules agree on current_gram": 2.0548486038193295e-11,
    "independent exact-degree angular and radial rules agree on first_harmonic_moments": 1.6519008692956746e-12,
    "independent cubature verifies the higher-current shape direction": 4.121082548395651e-11,
    "exact rational shape harmonics verify the actual polarized current norm": 2.8282830450895822e-11
  },
  "cases": [
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      "particle": "W",
      "depth": 2,
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            -1.875928751350108e-33,
            4.88175325107883e-35
          ]
        ],
        "physical_real_rank": 16,
        "higher_current_shape_maximum": 100020.17738356256,
        "shape_witness": [
          -1.3010426069826053e-18,
          -5.421010862427522e-19,
          -0.03367972493569894,
          1.3877787807814457e-17,
          0.05080119197134175,
          -6.418476861114186e-17,
          3.252606517456513e-17,
          2.6020852139652106e-17,
          -8.673617379884035e-19,
          4.445228907190568e-18,
          0.050801191971341725,
          1.0061396160665481e-16,
          -0.0982275541774644,
          -5.551115123125783e-17,
          1.6479873021779667e-17,
          -1.0408340855860843e-17
        ],
        "current_rank": 8
      },
      "exact_shape": {
        "current_norm_squared_exact": "111294622986302498725671881481047616/17561895702893872449350206675",
        "static_response_form_exact": "-2832871801031715587715606637119873412/255964629869678190949279262288125",
        "harmonic_powers_exact": [
          {
            "harmonic": 3,
            "coefficient_exact": "15664/85595",
            "current_norm_squared_exact": "38276299776/36632520125"
          },
          {
            "harmonic": 5,
            "coefficient_exact": "18506224/195359325",
            "current_norm_squared_exact": "31570459210228224/2302031909284625"
          },
          {
            "harmonic": 7,
            "coefficient_exact": "1517057828/25039549437",
            "current_norm_squared_exact": "964977664928315850240/9952048190602651063"
          },
          {
            "harmonic": 9,
            "coefficient_exact": "2699268/62755763",
            "current_norm_squared_exact": "1891272529186634880/3938285789712169"
          },
          {
            "harmonic": 11,
            "coefficient_exact": "937119832/28912476525",
            "current_norm_squared_exact": "34517921438927903488512/18576251084637246125"
          },
          {
            "harmonic": 13,
            "coefficient_exact": "2814482203016/111191602219845",
            "current_norm_squared_exact": "834563304802937016057414453504/140176557870932420994465125"
          },
          {
            "harmonic": 15,
            "coefficient_exact": "534340587352/26474191004725",
            "current_norm_squared_exact": "458519439262545654270774841344/28035311574186484198893025"
          },
          {
            "harmonic": 17,
            "coefficient_exact": "1791873944696/110157261734079",
            "current_norm_squared_exact": "253710501620851918556755478208000/6441836536398352814404062523"
          },
          {
            "harmonic": 19,
            "coefficient_exact": "677223926947040/51499691746445061",
            "current_norm_squared_exact": "18546350096984168490292175606714880000/219848779098776882266717744780961"
          },
          {
            "harmonic": 21,
            "coefficient_exact": "1738025053825632/163989533338951075",
            "current_norm_squared_exact": "24932425316018898800665089685795497984/153671811684153977789050178535175"
          },
          {
            "harmonic": 23,
            "coefficient_exact": "558986852996/65991763919095",
            "current_norm_squared_exact": "1227066413316340692864772026676224/4354912905153568673705619025"
          },
          {
            "harmonic": 25,
            "coefficient_exact": "696095190164/104214146016725",
            "current_norm_squared_exact": "11353653216423089547354688372487424/25630988222788858874192152475"
          },
          {
            "harmonic": 27,
            "coefficient_exact": "26700365939720/5164853076588891",
            "current_norm_squared_exact": "38114078007853467695965722042496000/60489132205781706943093479841"
          },
          {
            "harmonic": 29,
            "coefficient_exact": "10705696965304/2742107496952311",
            "current_norm_squared_exact": "15076629170303797514766441713990289920/18658640228311799065565864893641"
          },
          {
            "harmonic": 31,
            "coefficient_exact": "1293783027364234/452833949320645725",
            "current_norm_squared_exact": "100001538305076325387942958130120476109824/107845626530893725937064673320111625"
          },
          {
            "harmonic": 33,
            "coefficient_exact": "128203375680094/63846375265917993",
            "current_norm_squared_exact": "4564139478032801893717548125542112669888/4852809088805267704003725001366725"
          },
          {
            "harmonic": 35,
            "coefficient_exact": "21671105914311568/16183843856962124175",
            "current_norm_squared_exact": "2011397111574979248305361077891675341939712/2432854480533324397684399097204166375"
          },
          {
            "harmonic": 37,
            "coefficient_exact": "177983266731248/213768402261127443",
            "current_norm_squared_exact": "9530066839701688139681106916791904606720/15608416353242145301494963866175369"
          },
          {
            "harmonic": 39,
            "coefficient_exact": "13042470091420/27766474785091671",
            "current_norm_squared_exact": "92494923182947749385683722843891008000/256992373997043852415013291190747"
          },
          {
            "harmonic": 41,
            "coefficient_exact": "37913355479474332/165251358022449989025",
            "current_norm_squared_exact": "6255434528416467807649931707935919908655744/40456313078909550144350657640329808075"
          },
          {
            "harmonic": 43,
            "coefficient_exact": "14900644074543304/168730333980817357215",
            "current_norm_squared_exact": "15199576714919912754683353984885223543762432/378007397973644446184901030524193807525"
          },
          {
            "harmonic": 45,
            "coefficient_exact": "2094283948950424/100813721560865716575",
            "current_norm_squared_exact": "172319337975281463310221717160875738119936/45170695355341160235931569685281021025"
          }
        ]
      },
      "classification": "finite polarized selected-shell current map, with no dynamics or stability conclusion"
    }
  ],
  "limits": [
    "a finite complex current span is not the full degenerate zero shell",
    "the finite-span ranks and optimal witnesses are numerical; the explicit right-polarized shape profile and its signed response are exact",
    "the full reciprocal frequency-dependent background and off-shell modes remain retained",
    "a nonzero higher current with zero first harmonic has negative leading static response, not automatically growing dynamics",
    "the massive current factor c_l and physical amplitudes remain explicit"
  ]
}