IMRPhenomT dominant ringdown amplitude supplied-input gate, 2026-09-27

The component specification pins Estellés et al., arXiv:2012.11923v1, Eqs. (26), (27c)–(27e). This is an equation-level test of the dominant (2,2) ringdown ansatz on supplied QNM damping rates, peak amplitude, and shape input. It does not validate those inputs or the full waveform.

The test used a private snapshot of the isolated worktree based on integration commit bbccb1d at /home/xangma/tmp/diffgw-phenomt-ringdown-amplitude-20260927 on len. The scalar reference and test file in the snapshot had SHA-256 values 4baa86838c6792df0aadb5a75fb4b70b6dc70d4c40a6290c535e5603a5ec7530 and 0a343219193014728eec83e3f3eebefcff6403e5c4efcd2fdd2f62e8fa413212, respectively, matching the committed files. The existing environment used Python 3.12.3, NumPy 2.5.3, PyTorch 2.14.0+cpu, JAX 0.11.2, mpmath 1.3.0, and pytest 9.1.1. No packages or native source were changed.

cd /home/xangma/tmp/diffgw-phenomt-ringdown-amplitude-20260927
JAX_ENABLE_X64=1 JAX_PLATFORMS=cpu PYTHONPATH=src:tests /home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python -m pytest -q tests/test_phenomt_ringdown_amplitude_math_reference.py --reference-device=cpu -ra

The len CPU run returned 8 passed in 60.48 s, with no skips. The equation identities H(0)=H_peak and H'(0)=0 passed at 100-digit precision on two independent scalar inputs. A high-precision central difference checked the analytic derivative at u=2,25.

The public IMRPhenomT.time_domain Torch and JAX polarizations were converted to the intrinsic face-on amplitude for (30,30,0,0), (35,25,0.7,-0.5), and (60,6,0.9,0.1), with masses in solar masses. At seven ringdown times u=0,0.5,2,8,25,80,160, amplitudes agreed with the scalar reference to rtol=3e-11, atol=2e-13. Automatic derivatives of the public amplitude at u=0,2,25,80 agreed to rtol=5e-10, atol=2e-12; the zero-time peak derivative also met atol=2e-12. Both frontends used FP64 CPU.

The first two binaries take the printed d2=(alpha2-alpha1)/2 branch. The high mass-ratio case instead activates the carriers' existing bounded-d2 convention: actual d2≈0.0469122, versus printed d2≈0.0622423. Its match is a carrier-ansatz check with supplied actual d2, not Eq. (27d) fidelity. The bound and all native defaults were left unchanged. This evidence does not cover the QNM/remnant, peak and shape fits, inspiral or merger, other modes, calibration against NR, physical accuracy, or whole IMRPhenomT qualification.