{
  "program": "spinor-algebra.py",
  "passed": true,
  "check_count": 7050,
  "script_sha256": "537852a60b8fc3d4177b8d37c0dd76a27bd90a7f7242f66476d102e00571ef74",
  "environment": {
    "python": "3.12.14",
    "numpy": "2.3.5",
    "platform": "Windows-11-10.0.26300-SP0",
    "rng": "PCG64"
  },
  "parameters": {
    "samples": 12,
    "seed": 20261002,
    "mass": 1.0,
    "max_ratio": 1000.0
  },
  "conventions": {
    "metric": "+---",
    "epsilon_0123_upper": 1,
    "units": "c=hbar=1",
    "u_v_norm": "ubar u=2m; vbar v=-2m; udag u=vdag v=2E; v future label has canonical -p",
    "T_phase": "U_T=-gamma1 gamma3 in Dirac basis; transform by congruence",
    "classical_CPT": "C P T=-gamma5 times spacetime inversion; linear commuting-column map only"
  },
  "tolerances": {
    "matrix_algebra_scaled": 5e-13,
    "kinematic_scaled": 3e-09
  },
  "summary": {
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      "count": 1,
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    },
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    },
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      "passed": true
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    "adjoint swaps chirality": {
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      "maximum_absolute_error": 2.7755575615628914e-17,
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      "passed": true
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      "passed": true
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      "passed": true
    },
    "polarization p dot s": {
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      "passed": true
    },
    "polarization norm": {
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      "passed": true
    },
    "polarized u outer product": {
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      "passed": true
    },
    "diagonal vector": {
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      "maximum_absolute_error": 1.5926304656797923e-12,
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      "passed": true
    },
    "diagonal axial": {
      "count": 384,
      "maximum_absolute_error": 1.5916157281026244e-12,
      "maximum_scaled_error": 1.1139069600692383e-15,
      "passed": true
    },
    "polarized tensor epsilon sign": {
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      "passed": true
    },
    "diagonal pseudoscalar": {
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      "maximum_absolute_error": 2.6203521364587025e-13,
      "maximum_scaled_error": 1.463400216788281e-16,
      "passed": true
    },
    "on-shell Ward identity": {
      "count": 51,
      "maximum_absolute_error": 1.1718571004216928e-13,
      "maximum_scaled_error": 6.90882945575049e-17,
      "passed": true
    },
    "massive Gordon identity": {
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      "maximum_absolute_error": 4.3177964999723874e-10,
      "maximum_scaled_error": 2.460237847682272e-16,
      "passed": true
    },
    "antilinear basis covariance": {
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      "maximum_absolute_error": 9.155133597044475e-16,
      "maximum_scaled_error": 2.710582496453158e-16,
      "passed": true
    },
    "antilinear inner product": {
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      "maximum_absolute_error": 5.4930801582266845e-15,
      "maximum_scaled_error": 5.445142501162894e-16,
      "passed": true
    },
    "classical CPT norm": {
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      "maximum_absolute_error": 2.842170943040401e-14,
      "maximum_scaled_error": 1.4332682516593047e-15,
      "passed": true
    },
    "classical CPT linearity": {
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      "maximum_scaled_error": 0.0,
      "passed": true
    },
    "Majorana real projection": {
      "count": 3,
      "maximum_absolute_error": 1.790180836524724e-15,
      "maximum_scaled_error": 3.6492529753416853e-16,
      "passed": true
    },
    "Majorana imaginary parity phase": {
      "count": 3,
      "maximum_absolute_error": 1.790180836524724e-15,
      "maximum_scaled_error": 3.8495260218548416e-16,
      "passed": true
    },
    "Majorana aligned time phase": {
      "count": 3,
      "maximum_absolute_error": 1.790180836524724e-15,
      "maximum_scaled_error": 3.649252975341686e-16,
      "passed": true
    },
    "norm is basis invariant": {
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      "maximum_absolute_error": 3.552713678800501e-15,
      "maximum_scaled_error": 1.7915853145741303e-16,
      "passed": true
    },
    "bilinear basis invariance": {
      "count": 2176,
      "maximum_absolute_error": 1.5916157281026244e-12,
      "maximum_scaled_error": 9.666301294665828e-16,
      "passed": true
    },
    "explicit chiral table": {
      "count": 4,
      "maximum_absolute_error": 2.220446049250313e-16,
      "maximum_scaled_error": 2.220446049250313e-16,
      "passed": true
    },
    "explicit chiral gamma5": {
      "count": 1,
      "maximum_absolute_error": 2.220446049250313e-16,
      "maximum_scaled_error": 2.220446049250313e-16,
      "passed": true
    },
    "Dirac C matrix square distinct from full map": {
      "count": 1,
      "maximum_absolute_error": 0.0,
      "maximum_scaled_error": 0.0,
      "passed": true
    },
    "aligned T ordinary matrix square": {
      "count": 1,
      "maximum_absolute_error": 0.0,
      "maximum_scaled_error": 0.0,
      "passed": true
    },
    "aligned T=i times common T": {
      "count": 1,
      "maximum_absolute_error": 0.0,
      "maximum_scaled_error": 0.0,
      "passed": true
    },
    "common T matrix square only": {
      "count": 1,
      "maximum_absolute_error": 0.0,
      "maximum_scaled_error": 0.0,
      "passed": true
    },
    "common T antiunitary square": {
      "count": 1,
      "maximum_absolute_error": 0.0,
      "maximum_scaled_error": 0.0,
      "passed": true
    },
    "alternative classical CPT phase": {
      "count": 1,
      "maximum_absolute_error": 0.0,
      "maximum_scaled_error": 0.0,
      "passed": true
    },
    "negative control: similarity is wrong for B": {
      "count": 1,
      "maximum_absolute_error": 0.0,
      "maximum_scaled_error": 0.0,
      "passed": true
    },
    "negative control: i gamma2 cannot be blindly rebuilt": {
      "count": 1,
      "maximum_absolute_error": 0.0,
      "maximum_scaled_error": 0.0,
      "passed": true
    },
    "negative control: wrong v momentum label is not Hilbert orthogonal": {
      "count": 1,
      "maximum_absolute_error": 0.0,
      "maximum_scaled_error": 0.0,
      "passed": true
    },
    "massless zero-energy apex is rejected": {
      "count": 1,
      "maximum_absolute_error": 0.0,
      "maximum_scaled_error": 0.0,
      "passed": true
    }
  },
  "failed_checks": [],
  "negative_controls": {
    "wrong_similarity_B_gap": 0.8673226162795822,
    "blind_rebuild_B_gap": 0.8673226162795822,
    "wrong_v_label_overlap": 1.649242250247064
  },
  "limitations": [
    "Finite exact and floating fixtures do not prove identities for all representations or momenta.",
    "Absolute errors and scales are exported; high-momentum cancellation can lose digits in small invariants.",
    "Massless nonzero modes skip massive rest-polarization and Gordon formulas; E=0 is excluded.",
    "C/P/T are commuting solution maps with declared phases, not quantum Fock-space operators or a CPT theorem test.",
    "Only constant unitary component-basis changes are tested; Lorentz boosts are a different, generally nonunitary representation."
  ],
  "output_files": {
    "matrices": "/data/relativistic-qm/spinor-algebra/matrices.csv",
    "spinors": "/data/relativistic-qm/spinor-algebra/spinors.csv",
    "bilinears": "/data/relativistic-qm/spinor-algebra/bilinears.csv",
    "checks": "/data/relativistic-qm/spinor-algebra/checks.csv",
    "summary": "/data/relativistic-qm/spinor-algebra/summary.json"
  },
  "output_sha256": {
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    "spinors": "451d54ce6c8a8d6b6626cd5e9ce7e0b01b6083fec8ef3475ce549c793917e341",
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  },
  "publication": {
    "normalization": "Absolute output locations replaced by site download paths; numerical results and CSV bytes unchanged.",
    "source_run_report_sha256": "c1351a5fb82a8a7475d8e48d4fcb0176a0b7930b79080530b4256142fd1859be",
    "public_program_sha256": "537852a60b8fc3d4177b8d37c0dd76a27bd90a7f7242f66476d102e00571ef74"
  }
}