IMRPhenomHM leading (3,3) amplitude-ratio gate — 27 September 2026

The source-first v1 specification was frozen in commit 7249360 before the independent reference and tests. London et al. Eqs. (3)–(4) and Mishra et al. Eqs. (11), (12a), (12c) fix the leading restricted stationary-phase (3,3) amplitude ratio. The scalar reference reduces their full leading SPA amplitudes with SymPy, then uses mpmath to evaluate the positive-mass-ordering ratio and its one-sided frequency slopes. The test divides the public unprojected HM (3,3) mode magnitude by the public PhenomD (2,2) carrier magnitude at the mapped frequency. It exercises both the historical and opt-in London map cutoffs.

On len, from the integrated checkout archived at /home/xangma/tmp/diffgw-integration-gate-20260927h (local commit 1a49502), CPU FP64 Torch/JAX tests passed 94/94 in 31.39 s. The command used JAX_ENABLE_X64=1 JAX_PLATFORMS=cpu OMP_NUM_THREADS=1, PYTHONPATH=/home/xangma/tmp/diffgw-pycbc-2.11.0-full/packages:src:tests, and the existing len venv's Python to run pytest -q over test_imrphenomhm_amplitude_ratio_math_reference.py, test_imrphenomhm_frequency_map_math_reference.py, test_imrphenomhm_phase_offsets_math_reference.py, test_imrphenom_hm.py, and test_phenomhm_reconstruction.py with --reference-device=cpu -ra. PyCBC 2.11.0 came from a separate compatible package directory. There were no skips or failures; one pre-existing Torch JIT deprecation warning remains.

This qualifies the leading positive-delta (3,3) rescaling component at the sampled D-carrier boundary. Other mode ratios, complex spin terms, equal-mass zeros and sign conventions, the carrier and QNM fits, phase, projection, and complete HM waveform are separate gates.