{ "experiment": "Mott scattering from a fixed Coulomb source at leading Born order", "passed": true, "check_count": 9458, "failed_checks": [], "maximum_absolute_check_error": 3.7427885096752433e-10, "maximum_scaled_check_error": 1.0328109029870628e-08, "parameters": { "mass": 1.0, "momentum": 1.3333333333333333, "coupling": -0.001, "theta_min_deg": 1.0, "theta_max_deg": 180.0, "azimuth_deg": 37.0, "samples": 181 }, "units": { "hbar": 1, "c": 1, "metric": "+---", "mass_and_momentum": "energy", "cross_section": "energy^-2", "angles_input": "degrees" }, "methods": [ "explicit 4-component positive-energy spinors", "independent 4x4 gamma-matrix trace", "exact rational massive/massless fixtures", "rotated spin bases and spatial directions", "composite Simpson quadrature in log(sin(theta/2)^2)", "independent 60-digit Decimal closed acceptance integral" ], "assumptions": [ "infinitely heavy spinless fixed point Coulomb source", "elastic one-body external-potential Born approximation", "unpolarized initial spin average and final spin sum", "no recoil, screening, finite-size structure, exact Coulomb phases, radiative corrections or pair calculation", "finite angular acceptance only; unscreened total cross section diverges" ], "born_parameter_abs_g_over_beta": 0.00125, "born_parameter_note": "A small |g|/beta is a sufficient perturbative regime away from the forward singularity; this diagnostic does not bound physical truncation error.", "precision_note": "Near massive ultrarelativistic backscatter the trace subtracts O(E^2) terms. Small absolute error divided by 4E^2 does not imply small relative error in the suppressed signal. Use the stable scalar expression; raw residuals remain available.", "spin_transition_basis": "Seed index 0 is (1,0), index 1 is (0,1). These are canonical rest-z spin labels for m>0, not momentum-helicity labels; m=0 has no rest frame. A zero exact spin sum leaves conditional fractions undefined.", "runtime": { "python": "3.12.14", "numpy": "2.3.5" }, "randomness": "none; deterministic fixtures (only default temporary path has a unique identifier)", "script_sha256": "71fbd5f7cf0918681760a02aff80c9e0e52c8c9f0be6f9cea14237a51dbe0847", "output_files": { "angular": "/data/relativistic-qm/mott-scattering/angular.csv", "spin_transitions": "/data/relativistic-qm/mott-scattering/spin-transitions.csv", "limits": "/data/relativistic-qm/mott-scattering/limits.csv", "convergence": "/data/relativistic-qm/mott-scattering/angular-convergence.csv", "forward_cutoffs": "/data/relativistic-qm/mott-scattering/forward-cutoffs.csv", "summary": "/data/relativistic-qm/mott-scattering/summary.json" }, "output_sha256": { "angular": "e842d6bc4c78fbcc126576c9769242489874aaf5aca766f92ca8b8e9207efad7", "spin_transitions": "e649adc6285e5dcd96a6977420b107207a91d1999ab36cbf6e60245d453fa36a", "limits": 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