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NRTidalv2 spinning paper-D composition receipt — 27 September 2026

Result: The frozen positive-Lambda, nonzero-spin complex quotient gate passed for Torch and JAX CPU FP64 across the printed premerger-to-taper boundary. It is conditional on the printed equations and the existing IMRPhenomD carrier. The full waveform is not thereby qualified.

The specification freezes three cases, 12 frequencies per case, both polarizations, the scalar phase/self-spin/taper composition, and a 1e-10 absolute complex quotient limit without phase/time alignment or amplitude fitting. The printed-fit merger frequencies are about 2102.760106 Hz for the equal case and 1673.800358 Hz for both unequal labelings. The strictly post-endpoint quotient is exactly zero. The test is tests/test_nrtidalv2_paper_d_composition_math_reference.py.

Execution: host len, cwd /home/xangma/tmp/diffgw-nrtidalv2-paper-d-composition-20260927, Linux CPU FP64, Python 3.12.3, Torch 2.14.0+cpu, JAX 0.11.2, pytest 9.1.1, mpmath 1.3.0. Command:

PYTHONPATH=src:tests JAX_ENABLE_X64=1 OMP_NUM_THREADS=1 \
/home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python -m pytest -q \
  tests/test_nrtidalv2_paper_d_composition_math_reference.py \
  tests/test_nrtidalv2_self_spin_math_reference.py \
  tests/test_nrtidalv2_phase_math_reference.py \
  tests/test_nrtidalv2_amplitude_math_reference_native.py \
  tests/test_nrtidal.py

Result: 75 passed, 1 skipped in 22.08 s. The skip is the existing optional LALSimulation/PyCBC comparison in tests/test_nrtidal.py. Output is paper_d_composition.log under that cwd. The foreground command completed in 24.4 s including SSH; no process remains.

No pinned-LAL binary gate was added: its D option does not have the exact paper Table II amplitude contract, and its nonzero-tide effective merger boundary differs from the printed fit. The paper's Fig. 7 example also conflicts with Eqs. (28)–(29). Those are source/binary disagreements rather than failures of this conditional printed-equation composition gate; see the self-spin receipt and merger provenance audit. A spinning paper-D binary or independent physical/NR gate remains open.