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    "scope": "Four rational matrices and two shell points; finite exact fixtures, not a universal proof",
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        "energy_ratio": "157/144",
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  "scalar_product_max_absolute_error": 4.991888680194734e-09,
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  "measure_scope": "Massive and nonzero massless shell; finite-difference rapidities |xi|<=3, plus noncollinear rotation/boost composition.",
  "limitations": [
    "Finite deterministic cases and optional seeded samples do not prove group identities globally.",
    "Scaled errors test floating-point consistency relative to product magnitudes; they do not certify relative accuracy of a small norm, determinant, or Doppler-shifted energy.",
    "At high rapidity a tiny invariant is a difference of large terms. Inspect absolute errors and the Decimal comparison before interpreting digits.",
    "Three finite-difference steps separate step sensitivity from matrix stress. Refinement need not be monotone after roundoff dominates and is not a rigorous error bound.",
    "The massless cone apex p=0 is excluded; no derivative or measure density is asserted there.",
    "The positive-shell measure also survives parity; time-reversing components do not preserve the selected positive-energy sheet.",
    "No continuum integration, spacetime microcausality, Wigner-angle extraction, or quantum time-reversal implementation is tested."
  ],
  "schema_version": 1,
  "program": "lorentz-transformations",
  "script_sha256": "c6ec269a2a48835ad279ea13b378695c0dbce708d6291c5103c3696bb46ed729",
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    "platform": "Windows-11-10.0.26300-SP0",
    "float": "IEEE-754 binary64",
    "rng": "numpy.random.default_rng / PCG64"
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  "git": {
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    "tracked_worktree_dirty": true,
    "qualification": "HEAD alone does not identify the script or a dirty checkout; use script_sha256."
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  "parameters": {
    "samples": 16,
    "seed": 20261002,
    "max_rapidity": 8.0,
    "decimal_rapidity": 40.0,
    "fd_step": 0.0001
  },
  "units": "c=hbar=1; momenta and masses in any one consistent energy unit",
  "conventions": "eta=(+---); passive boosts with -sinh(xi) mixed entries; column vectors; rightmost matrix acts first; Rodrigues positive component rotation",
  "method": "Exact Fraction fixtures; float64 Lorentz matrices and vector products; independent five-point on-shell spatial Jacobian at three steps; 100-digit Decimal exponential Doppler reference.",
  "outputs": {
    "vectors": "/data/relativistic-qm/lorentz-transformations/lorentz-transformations-vectors.csv",
    "matrices": "/data/relativistic-qm/lorentz-transformations/lorentz-transformations-matrices.csv",
    "rapidity": "/data/relativistic-qm/lorentz-transformations/lorentz-transformations-rapidity.csv",
    "composition": "/data/relativistic-qm/lorentz-transformations/lorentz-transformations-composition.csv",
    "measure": "/data/relativistic-qm/lorentz-transformations/lorentz-transformations-measure.csv",
    "components": "/data/relativistic-qm/lorentz-transformations/lorentz-transformations-components.csv",
    "report": "/data/relativistic-qm/lorentz-transformations/lorentz-transformations-report.json"
  },
  "output_sha256": {
    "vectors": "0230b0d839819c3a98e01307a9e1f37a38da84cb9671032d6379bb28bcf68ad1",
    "matrices": "dabaf8e5fe3be2d57136ac4cceb35074129b4dd7cde7dd9a2f62573fbd65bd06",
    "rapidity": "69ccab1bc032420ddc50fc0655ee973ec6f04858ea7e6ff55d2db29539cdeb52",
    "composition": "094f09ad7cf270c936436a1aa371d236f320e9e7a1fdcb152054bad874eb33fc",
    "measure": "c447af13874ae4b4bbc09e01c6e78c86bea67eb70e5a337e25e38dcb7bba1e81",
    "components": "0d6d33df4dd9a1b1c3ac3134b62c27bb7383912a750ba089129ed59432182d85"
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  "publication": {
    "normalization": "Absolute output locations replaced by site download paths; numerical results and CSV bytes unchanged.",
    "source_run_report_sha256": "fc7d219d581f399cc610f102af1343d991703ab12a04f59bde722963a78cff43",
    "public_program_sha256": "c6ec269a2a48835ad279ea13b378695c0dbce708d6291c5103c3696bb46ed729"
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}