IMRPhenomHM second independent SXS holdout: frozen protocol

This second protocol is committed before downloading or decoding either 3631 waveform. Its file identities and gates were set after inspecting only the official record listing and small metadata/sidecar JSON files. The first 2265 holdout was already known to be red, and this case is not used to tune a correction. Its acceptance gates are not to be changed in response to the result. A red or infeasible run remains a red or infeasible result and needs a separately named future protocol. The test concerns the public, default-D-carrier, aligned-spin IMRPhenomHM six-mode Torch and JAX APIs. It uses no LAL code or coefficients.

Sources, case, and data identity

• Model source: London et al., First higher-multipole model of gravitational waves from spinning and coalescing black-hole binaries, especially the Results section. The paper reports typical full-polarization NR matches above 0.99 for nonspinning mass ratios through 8 using an aLIGO design PSD, 30 Hz lower bound, and optimized time, polarization and initial orbital phase. It reports individual (3,2)/(4,3) averages near 0.92 and typical subdominant-mode amplitude errors well below 15%. Our flat-band, one-22-alignment gates below are deliberately more permissive because those reported match values are not the identical statistic.
• Numerical source: SXS Collaboration, SXS:BBH:3631v3.0, CaltechDATA record fxz1a-agp58, SXS catalog paper, and SXS Catalog 3. The Lev3 metadata report reference_mass1=0.7998418582314967, reference_mass2=0.19997672921881424, reference_dimensionless_spin1_z=5.087564226443693e-05, reference_dimensionless_spin2_z=3.323760432983658e-05, reference_eccentricity=2.058e-04, reference_time=437.5 M, and 15.42360 orbits from the start. Lev2 has reference_time=176.5 M and 15.43583 orbits from the start. This is a near-nonspinning q=4 case inside the paper's stated domain. The official record was published in 2025, after the 2018 model paper, and is used only for validation, never fitting.
• Source files are the official record's Lev3 and Lev2 N2 strain and sidecar/metadata pairs. Verify both size and MD5 against this frozen list before decoding. The exact content URLs have the form https://data.caltech.edu/api/records/fxz1a-agp58/files/<key>/content.

key	bytes	MD5
Lev3:Strain_N2.h5	2545739	8def95de9bfdc95f6d811bc3abb9c447
Lev3:Strain_N2.json	2229	dc7ca3acef1807bb002a4cd2d621bbec
Lev3:metadata.json	3323	ff3041b7558bbe2c4b7affcbada315d9
Lev2:Strain_N2.h5	2720612	c02962c99dca27583fd784c2a965a8b6
Lev2:Strain_N2.json	2228	d43f61a21296d520a93b0bd96fc844e5
Lev2:metadata.json	3324	01971417a41e22fabd15d8165f4df99d

The raw SXS arrays stay outside Git. SXS asks users to acknowledge the first scientific publication describing a simulation. The record API does not declare a per-record SPDX license, so no such license is inferred.

Frozen conditioning and conventions

Use the official sxs decoder, requested version 2026.0.6 if available, with NumPy/SciPy, and record exact installed versions. Require strain type h, spin weight -2, the six positive-m modes (2,2),(2,1),(3,3),(3,2),(4,4),(4,3) and their negative-m partners in both resolutions. Reject absent/nonfinite modes. SXS uses h=h_+ - i h_× = Σ h_lm {}_{-2}Y_lm; the sidecar states mass and radius are scaled out. Require the two sidecars to agree on these conventions.

Set detector-frame total mass 80 M_sun, component masses 64,16 M_sun, aligned spins 0,0 (the metadata's residual spins are numerical), distance 500 Mpc, f_ref=35 Hz, and model phic=tc=phi0=0. Convert SXS code time to seconds with GM_sun/c^3 and strain to physical dimensionless amplitude with 80 GM_sun/(c^2 D). Use nominal IAU 2015 GM_sun=1.3271244e20 m^3 s^-2, exact c=299792458 m s^-1, and 1 pc=3.0856775814913673e16 m. These public unit definitions are not copied from LAL.

For each resolution, retain the common SXS time interval beginning at the larger of 437.5 M and the two file start times and ending at the smaller file end time. Resample real and imaginary parts of each selected complex mode onto a uniform 1/8192 s grid by SciPy cubic spline; use the same physical grid for both resolutions. Set the time origin at the maximum of the Lev3 |h_22| on this grid. Apply a half-cosine amplitude ramp over the first 500 M and last 100 M of the common interval. Both windows must fit without overlap; otherwise the protocol is infeasible. This removes initial junk and endpoint leakage. The metadata initial orbital frequency 0.020310509286/M implies an initial (2,2) gravitational frequency of about 16.4 Hz at 80 M_sun. The 35 Hz lower edge lies above twice that value, reducing sensitivity to the short run's initial transient. If the decoded source cannot support the frozen interval and window, report infeasible. No per-mode cuts, rescalings or phase fits are allowed.

Evaluate the direct Riemann-sum Fourier transform at exactly f=35,36,...,350 Hz with kernel exp(-2πift) and dt=1/8192 s. The native positive-frequency mode target is H_lm(f)=dt Σ conj(h_lm(t)) exp(-2πift) times the physical amplitude scale. This is the conjugate of the negative-frequency SXS positive-m strain mode; it follows from the stated Fourier convention, not an empirical adapter. Project only the six selected ±m pairs to complex positive-frequency plus and cross with the independently specified spin-weighted harmonics in src/diffgw_reference/imrphenomhm_projection.py. Do not compare to the full SXS multipolar polarization, which contains modes absent from IMRPhenomHM. Use observer angles (inclination, azimuth)=(0.7,0.3) and (1.2,-0.2) radians.

Align once, using only the Lev3 (2,2) data and the native (2,2) mode over 35..85 Hz: search Δt on [-0.1,0.1] s at steps of 1/8192 s, maximizing |Σ H_NR,22 conj(H_model,22) exp(2πifΔt)|. Select the earliest grid point on an exact tie. Let φ=-arg(C)/2, for the complex sum C at the selected shift. Apply exp(-2πifΔt) exp(-imφ) to every native mode and its resulting plus/cross; the polarization projection must use these aligned modes. There is no per-mode time, phase, amplitude, polarization or orbital phase optimization. Use the identical rule on Lev2 versus Lev3 (2,2) solely to estimate numerical resolution error, applying that one Lev2 alignment to all Lev2 modes/projections. Record both shifts and phases.

Frozen statistics and gates

All statistics use the full 35..350 Hz grid, flat frequency weighting, with no pointwise masking or PSD. For complex vectors a (Lev3 NR) and b (aligned native), define phase-sensitive match=Re Σ conj(a)b/(||a||||b||) and amplitude_ratio=||b||/||a||. Norms must be finite and nonzero. Compute the same statistics for Lev3 versus aligned Lev2. Torch and JAX must each pass independently; their mutual parity is a separate gate elsewhere.

observable	minimum model–Lev3 match	model/Lev3 amplitude ratio	minimum Lev2–Lev3 match
(2,2), (3,3)	0.97	0.90–1.10	0.995
(2,1), (4,4)	0.94	0.80–1.20	0.99
(3,2), (4,3)	0.85	0.75–1.25	0.97
six-mode plus and cross at each angle	0.95	0.85–1.15	0.99

The resolution gate must pass before interpreting any model comparison. These bounds are conservative case-specific tests informed by London et al.'s reported NR behavior and by the explicit two-resolution screen. They do not prove the paper's PSD-weighted/population claims. Any passing claim is limited to this q=4 nearly nonspinning source, 80 M_sun, these two orientations, six-mode truncation, this conditioning and 35–350 Hz flat band. A gate failure is reported without weakening a bound. A decoder, data, or convention failure is reported as infeasible, not as a pass or an optional skip.