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IMRPhenomHM leading (4,4) amplitude-ratio gate — 27 September 2026

The source-first v1 specification was frozen in commit 87d1898 before the independent reference and tests. London et al., arXiv:1708.00404v4, Eqs. (3)–(4) and Mishra et al., arXiv:1601.05588v1, Eqs. (11), (12a), (12f) fix the restricted leading (4,4) amplitude ratio. The scalar source reduces the full SPA-amplitude quotient symbolically, evaluates it with mpmath, and composes the independent Eq. (5) map. The public gate removes the public PhenomD carrier magnitude from the public HM unprojected (4,4) magnitude.

Host len, cwd /home/xangma/tmp/diffgw-hm44-source-gate-20260927; source copied from isolated branch codex/hm-leading-44-amplitude based on b111a76, with reference/test changes recorded in d4021cf. Python: /home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python. Packages: Python 3.12, mpmath 1.3.0, SymPy 1.14.0, NumPy 2.5.3, Torch 2.14.0+cpu, JAX 0.11.2, pytest 9.1.1, and PyCBC 2.11.0 from a separate compatible package directory. The exact final command was:

JAX_ENABLE_X64=1 JAX_PLATFORMS=cpu OMP_NUM_THREADS=1 \
PYTHONPATH=/home/xangma/tmp/diffgw-pycbc-2.11.0-full/packages:src:tests \
/home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python -m pytest -q \
tests/test_imrphenomhm_amplitude_ratio_math_reference.py \
--reference-device=cpu -ra

Result: 15 passed in 14.23 s, no skips or warnings. Log: /home/xangma/tmp/diffgw-hm44-source-gate-20260927/hm44-pytest-rerun.log. The initial run had 14 passes and one test-fixture failure: synthetic f_{22}^{RD}=0.05 made the map's middle and upper slopes identical for m=4, contradicting the test's asserted kink. Correcting only that synthetic fixture to 0.045 produced the passing result. The frozen equation, tolerance, and test grid were unchanged.

This qualifies the sampled leading (4,4) rescaling component through the public D-carrier assembly. It does not independently qualify the D carrier, QNM inputs, (4,4) phase or projection, higher PN amplitude terms, other modes, physical accuracy, or the complete HM waveform.