NSBH explicit-gauge phase composition — 27 September 2026

The v1 specification was frozen in commit 2f68cff before scalar/native comparison. Thompson et al. Sec. II.2 prescribe a PhenomD phase plus the updated NRTidal phase. The scalar expression composes the independent PhenomD and NRTidalv2 references; it does not import the Torch/JAX NSBH implementations or LAL code.

On len, Linux x86-64 CPU FP64, in /home/xangma/tmp/diffgw-nsbh-explicit-phase-20260927, the command PYTHONPATH=src OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 /home/xangma/repos/diffgw-worktrees/xas-whole-waveform-gate/.venv/bin/python -m pytest -q tests/test_nsbh_explicit_phase_math_reference.py passed 10/10 in 13.83 s with no skips or expected failures. Log: nsbh-phase-pytest.log. The frozen sample has mass ratios 5 and 9, zero and nonzero NS deformability, four frequency points spanning the PhenomD phase regions, and both explicit phase gauges. The scalar 70/90 digit check passed the 1e-30 absolute phase limit; both native backends passed the 3e-7 maximum unit-phasor error limit. No numerical alignment or binary-derived fit was applied.

The neighboring command using the same environment, python -m pytest -q tests/test_imrphenomd_waveform_math_reference.py tests/test_nrtidalv2_phase_math_reference.py tests/test_nsbh_clean_phase.py, passed 189/189 in 386.81 s, with no skips or expected failures. Log: nsbh-phase-neighbors.log. Environment: Python 3.12.3, Torch 2.14.0+cpu, JAX 0.11.2, SymPy 1.14.0, mpmath 1.3.0, pytest 9.1.1.

The gate conditions on the native-supplied final spin/QNM pair and the declared PhenomD fit rows with digits beyond the printed Khan table. It therefore qualifies the explicit phase composition at those inputs, not the remnant/QNM fit or its coefficient provenance. The legacy grid-dependent phase offsets, disruption-dependent amplitude, conflicting published/native amplitude variants, complex whole waveform, and NR validation remain open.