NRTidal family qualification boundary — 29 September 2026

Disposition: The scoped v1 D, v2 D and conditional v2 Pv2 mathematics, Torch and JAX gates pass. This receipt does not qualify a public precessing BNS waveform or resolve the known source versus pinned-binary conflicts. The native implementation was unchanged in this audit. The added executable evidence is an original-source diagnostic and derivative/JIT checks of the existing composition paths.

Versioned sources and public-code comparison

The comparison records offered options, not equivalence inferred from approximant names. The paper contracts come from Dietrich et al., arXiv:1706.02969v1, its v2 revision, the later merger-fit paper, and Dietrich et al., arXiv:1905.06011v2. Public-code offerings were checked against LALSimulation 7.26 NRTidal documentation, LALSimulation 7.26 Pv2 documentation, the PyCBC waveform list, and the Ripple model list on 29 September 2026. The numerical oracle used here was the installed LALSuite 7.26.15 distribution, not LAL implementation source.

Family and diffgw option	Published contract and native evidence	Other public-code offering and remaining gap
`IMRPhenomD_NRTidal` v1	The pinned v2 revision uses effective tidal coupling and its Eq. (7) Padé phase. The first arXiv revision prints a different \(\kappa_2^T\) mass weighting in Eq. (2); the later standard \(\kappa_2^T\) also differs from that original printed expression. The source diagnostic now demonstrates equal-mass agreement and unequal-mass divergence. Native Torch/JAX phase, taper and LAL binary gates pass to their existing bounded contracts.	LALSimulation offers `NRTidal_V` for D and PyCBC lists `IMRPhenomD_NRTidal`. Those names do not identify which printed coupling revision or every internal coefficient. diffgw does not expose the original v1 printed coupling as a waveform option; its historical taper conventions retain their documented bounds.
`IMRPhenomD_NRTidalv2`, `binary_compatible`	The default retains the historically observed D tidal amplitude and spin fit. It has pinned-binary premerger agreement, including the composed holdout, but the amplitude normalization is not derived from 2019 Eq. (24). The nonzero-tide taper binary comparisons remain expected failures.	LALSimulation offers D `NRTidalv2_V` and `NRTidalv2NoAmpCorr_V`; PyCBC lists `IMRPhenomD_NRTidalv2`. These offerings do not establish that the default diffgw option is paper-equivalent. Ripple's current README lists D NRTidalv2 with verification limited to low spins, \(\chi_{1,2}<0.05\); that claim does not qualify this option or its high-spin/taper behavior.
`IMRPhenomD_NRTidalv2`, `paper_2019`	2019 Table II assigns D no Eq. (24) tidal amplitude. The scalar reference composes the printed tidal and 2PN+3PN self-spin phases and taper. Torch/JAX complex quotients pass, as do the new 300 Hz phase-derivative and JAX JIT gates. This is a paper-math variant, with no claim of exact LAL binary parity.	LAL's `NRTidalv2NoAmpCorr_V` is a named no-amplitude option, but its full phase, spin and taper equivalence to `paper_2019` was not established. Ripple's listed D v2 model does not specify this diffgw option.
`IMRPhenomPv2_NRTidalv2`, conditional aligned carrier	2019 Eqs. (17)–(29) and Sec. III.4 add the signed Eq. (24) amplitude and 2PN+3PN+3.5PN self-spin before Pv2 rotation. An independent scalar reference checks native Torch/JAX finite-size assembly from a supplied BBH carrier, and the new fixed-carrier value/gradient/JAX JIT gate removes BBH-generator dependence from that check. Supplied-angle projection is separately gated.	LALSimulation offers `IMRPhenomPv2_NRTidalv2`; PyCBC lists it. diffgw still has no public Pv2 BNS dispatch. BNS angle evolution, phase/time origin and reference-frequency anchoring remain pending contracts; conditional assembly does not establish full waveform parity.
`IMRPhenomPv2_NRTidal` v1	No diffgw v1 Pv2 paper-math or native composition gate was added.	LALSimulation and PyCBC list this v1 Pv2 approximant. It remains a diffgw family capability gap.

PyCBC's list is evidence of exposed names, not a separately tested implementation. Ripple's README lists D v2, with its stated low-spin verification limit; it does not list v1 or Pv2 NRTidal in the checked model list. No cross-code equality is claimed from those lists.

Provenance of the executable evidence

The independent scalar modules under src/diffgw_reference/ use the cited paper equations with SymPy and high-precision mpmath. The native Torch/JAX approximants do not call those references. The new v1 diagnostic in nrtidalv1_phase.py is explicitly a printed original-source audit, not a third native coupling branch. test_nrtidalv1_phase_math_reference.py checks source-revision mass weighting and body exchange. test_nrtidalv2_paper_d_composition_math_reference.py differentiates the paper D quotient phase, and test_nrtidalv2_pv2_aligned_carrier_math_reference.py compares both native backends with an 80-digit scalar composition using a fixed complex128 BBH input. Both added derivative gates cover JAX CPU FP64 JIT; their limits are frozen in the linked math specifications. This audit introduced no LAL constants, residual fit or new native waveform branch.

Execution and observed result

Host len, owned scratch cwd /home/xangma/tmp/diffgw-nrtidal-family-qualification-20260929, Linux CPU FP64. The scratch copy came from isolated branch codex/nrtidal-family-qualification. Python was /home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python (3.12.3), with Torch 2.14.0+cpu, JAX 0.11.2, SymPy 1.14.0, mpmath 1.3.0 and LALSuite 7.26.15. The strict scoped command was:

DIFFGW_REQUIRE_LAL_BINARY=1 bash run_focus.sh

run_focus.sh set PYTHONPATH=src:tests, JAX_ENABLE_X64=1 and OMP_NUM_THREADS=1, then ran 18 files covering NRTidal v1/v2 phase, amplitude, spin, taper, paper-D, Pv2 conditional, LAL-binary and parity checks. Its retained log is focus_final.log in the scratch cwd. Result: 261 passed, 18 xfailed, 0 skipped in 81.57 s. The 18 expected failures predate this change and remain strict, especially the nonzero-tide v2 D taper binary residuals of 0.000153757344 (equal mass) and 0.000189164604 (unequal mass) against the frozen 0.00005 bound. After the final small source-assertion and test-import edits, a strict rerun of their two affected files returned 24 passed in 16.64 s. All SSH test processes exited; no running PID or stop action remains.

The existing D provenance audit records the unresolved paper/binary amplitude normalization, Love–Q and printed merger-fit conflicts. The Pv2 public-assembly boundary defines the source evidence needed before a complete precessing BNS claim. The next bounded discriminator for the D taper is the read-only multi-release, multi-tide binary comparison specified in that provenance audit; no coefficient should be inferred from a residual alone.