{
  "schema_version": 1,
  "description": "Versioned original SXS horizon trajectories for an independent scattering extraction and 1PM/2PM comparison.",
  "sources": [
    {
      "title": "Highly accurate simulations of asymmetric black-hole scattering and cross validation of effective-one-body models",
      "authors": "Oliver Long et al.",
      "version": "arXiv:2507.08071v2",
      "url": "https://arxiv.org/html/2507.08071v2",
      "locators": "§II.D, Eqs. (8)–(12): extraction; Eqs. (1)–(6): initial inputs; Eq. (14): average angle; §III.2, Eqs. (26)–(27): relative angle and recoil; §V: released simulations"
    },
    {
      "title": "Classical and quantum scattering in post-Minkowskian gravity",
      "authors": "Thibault Damour",
      "year": 2020,
      "url": "https://arxiv.org/abs/1912.02139v3",
      "doi": "https://doi.org/10.1103/PhysRevD.102.024060",
      "locators": "Eqs. (1.4), (1.9)–(1.11), (2.45)–(2.46); the source expands HALF the angle"
    },
    {
      "title": "Radiative contribution to classical gravitational scattering at the third order in G",
      "authors": "Thibault Damour",
      "year": 2020,
      "url": "https://arxiv.org/abs/2010.01641",
      "locators": "§V, Eqs. (25)–(31): scattering-angle radiation reaction begins at 3PM"
    },
    {
      "title": "SXS waveform and horizon data documentation",
      "url": "https://data.black-holes.org/waveforms/documentation.html",
      "locators": "Horizons.h5: inertial coordinates and code units"
    }
  ],
  "rights": {
    "source": "https://data.black-holes.org/waveforms/",
    "statement": "The SXS catalog states that its data are free for anyone to use and requests acknowledgment of the original simulation publication.",
    "scope": "This package links to original versioned files and downloads them only on request. It does not redistribute the raw data or assign them a Creative Commons license.",
    "acknowledgment": "Cite the versioned SXS dataset DOIs and Long et al., arXiv:2507.08071, when using this calculation."
  },
  "dependencies": {
    "python": "3.12",
    "numpy": "2.5.3",
    "h5py": "3.16.0",
    "network": "Python standard-library HTTPS; optional system curl fallback for public repository redirects"
  },
  "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 2×7×16=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."
  ],
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