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IMRPhenomT TaylorT3 component receipt — 2026-09-27

T-PN-T3-v1 covers the aligned (2,2) 3.5PN TaylorT3 coefficient table, frequency polynomial, and phase primitive. It does not cover pseudo-PN fits, calibrated t0, joins, modes beyond (2,2), or full waveforms.

Source and implementation

The independent scalar equations are transcribed from Estellés et al., T/TP Appendix A, Eqs. (A5a)–(A5h), and the updated THM Eqs. (8)–(11). The printed A5g omits 235925 eta³/1769472, which the pinned MIT phenomxpy author source explicitly identifies and includes. The reference exposes paper_literal and author_carrier; native Torch/JAX use the latter. See the six-section specification.

The scalar reference uses mpmath exact rationals and the paper's compact mass-fraction spin combinations. Native Torch/JAX use expanded tensor polynomials; they do not import the reference. The pre-existing collocation test now takes its six PN inputs from this scalar reference rather than from the implementation under test.

Reproduction and result

Host: len (CPU). Isolated cwd: /home/xangma/tmp/diffgw-phenomt-t3-20260927. Command:

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_taylor_t3_math_reference.py \
  tests/test_phenomt_inspiral_collocation_math_reference.py \
  --reference-device=cpu -ra

Result: 22 passed in 11.26 s, zero skipped/xfail, exit 0. Log: /home/xangma/tmp/diffgw-phenomt-t3-20260927/phenomt-t3-pytest.log. Versions: Python 3.12.3, NumPy 2.5.3, PyTorch 2.14.0+cpu, JAX 0.11.2, mpmath 1.3.0, pytest 9.1.1. The strict repository-wide --require-math-reference switch requires collection of every math-reference module and is reserved for the full integration suite.

The integrated branch at 153396e was archived to /home/xangma/tmp/diffgw-integration-gate-20260927j and reran the two modules with the same CPU FP64 settings: 22 passed in 11.18 s. The integrated files also passed Ruff, generated-catalog --check, git diff --check, and a strict documentation build.

Five physical mass/spin cases include equal masses and spins, unequal spins, q=10, and negative/positive anti-aligned combinations. Each backend's six coefficients agree with the scalar values within rtol=2e-12, atol=2e-13; frequency at theta={0.33,0.55,0.82} within the same limits; and phase within rtol=2e-12, atol=2e-12. The scalar derivative recovers frequency to relative 1e-35 at 80 digits. The paper/carrier 3PN difference is checked as an exact-rational mpmath identity. These thresholds bound float64 evaluation roundoff, not model error against numerical relativity or LAL.