{ "schema_version": 1, "script_sha256": "db01f43a3781242c5bd0ae535007ce7eb94a2b34b827c61c660d3f9617fff7f3", "inputs_manifest_sha256": "b814b712029111a67a5c9a7dce35d6f77728a4e48c911c78c15a936b9d503dc3", "environment": { "python": "3.12.9", "numpy": "2.5.3", "h5py": "3.16.0" }, "method": { "units": "G=c=1. D is the distance between the two supplied inertial horizon centers, divided by the sum M of INITIAL Christodoulou masses from metadata. Time remains in source code units.", "coordinates": "Use supplied inertial x,y coordinates in the nominal initial center-of-mass frame; unwrap atan2(y,x) separately for each black hole. Small initial ADM momentum and out-of-plane coordinate variation are reported.", "observable": "theta_i=phi_i,out(infinity)-phi_i,in(infinity)-pi; theta_avg=(theta_A+theta_B)/2. This is not the relative final-CoM scattering angle.", "incoming_lower_D_over_M": [ 50, 55, 60, 65, 70, 75, 80 ], "incoming_upper_D_over_M": 200, "outgoing_lower_D_over_M": [ 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230 ], "outgoing_upper_D_over_M": 350, "models": { "cubic": "phi=phi_infinity+a1/D+a2/D^2+a3/D^3, with design columns scaled by z=100/D.", "kepler": "1/D=A cos(phi)+B sin(phi)+C. Solve for zero inverse distance with phase atan2(B,A), choosing the root nearest the unwrapped largest-D end of the leg. This avoids the incompatible arctan(A/B) printed in Eq. (12c)." }, "sampling": "Ordinary unweighted least squares on stored time samples within each window; repeat with every second and fourth sample. Data are not interpolated.", "averaging": "Use the same model on both legs. Give equal weight to all 2\u00d77\u00d716=224 model/window pairs. The reported range is the minimum and maximum of these paired mean angles, not the combination of unrelated endpoints.", "window_refinement": "Also average over the subset incoming lower=50,60,70,80 and outgoing lower=80,110,140,170,200,230. Compare this coarser grid with the full fixed grid.", "PM_inputs": "nu=m1*m2/M^2, Gamma=E_ADM/M, gamma=1+(Gamma^2-1)/(2nu), j=(J_ADM,z-m1^2*chi1,z-m2^2*chi2,z)/(m1*m2). Tiny residual spins enter the orbital angular-momentum conversion only.", "PM_full_angle_radians": "chi_1PM=2(2gamma^2-1)/(j sqrt(gamma^2-1)); chi_through_2PM=chi_1PM+3pi(5gamma^2-1)/(4Gamma j^2).", "PM_interpretation": "Leading analytic truncations at the actual release inputs; no fitting, resummation, or nearest ancillary-table substitution." }, "scope": [ "The model/window envelope is a finite-separation coordinate-extraction sensitivity estimate. It is neither a rigorous error bound nor a Gaussian confidence interval.", "Lev1/2/3 are distinct adaptive-resolution runs with a shared prefix; no uniform mesh spacing or Richardson convergence order is inferred.", "These released initial inputs do not coincide exactly with rows of ScatteringAngles.dat. This is an independent extraction, not a claimed reproduction of a particular tabulated angle.", "Strong deflection can invalidate a low-order PM approximation. No 3PM-or-higher truncation-error bound is asserted.", "Radiation affects the full scattering angle from 3PM. The mean individual and relative-CoM angles differ from 4PM for unequal masses; the present cases are nominally equal mass and nonspinning.", "Radiated energy/angular momentum at infinity are not recomputed. The retained horizon trajectories and initial metadata do not supply those fluxes.", "No numerical-relativity spacetime evolution is rerun; the calculation refines the analysis of the released trajectories." ], "analytic_checks": { "cubic_intercept_error_rad": 6.661338147750939e-16, "rotated_kepler_angle_error_rad": 6.661338147750939e-16, "pm_impact_parameter_identity_error_rad": 1.1102230246251565e-16 }, "cases": [ { "id": "SXS:BBH:4292v3.0", "doi": "https://doi.org/10.26138/SXS:BBH:4292v3.0", "resolutions": [ { "lev": 1, "initial_inputs_and_PM": { "M_initial_code_units": 0.9999987970987416, "mass_ratio_m1_over_m2": 1.0000000003104113, "nu": 0.25, "Gamma_ADM_over_M": 1.022642049125655, "gamma": 1.0915935212798367, "J_ADM_z_over_M2": 1.2000195575983867, "spin_z_over_M2": -2.9603335743482567e-09, "j_orbital": 4.800078242234881, "initial_ADM_momentum_norm_over_M": 8.865719694647747e-08, "maximum_initial_dimensionless_spin_component": 1.01198947e-08, "chi_1PM_deg": 75.44030922491335, 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