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NRTidalv2 D taper and Pv2 dispatch follow-up — 29 September 2026

Disposition: No source-backed production change. The pinned binary_compatible D amplitude remains a historical binary-compatibility choice, while the published 2019 D composition remains phase-only. The nonzero-tide D taper binary gate retains its frozen 5e-5 limit and strict expected failures. Complete Pv2 BNS dispatch remains pending. This receipt adds a reproducible black-box taper discriminator and a source boundary audit; it does not promote either approximant's qualification status.

Sources and competing explanations

Dietrich et al. (2019), Table II and Eqs. (24)–(25) assign the additive tidal amplitude to Pv2, not D, and taper the amplitude from the merger frequency to 1.2 f_mrg. The older Dietrich et al. (2018), Eqs. (10)–(11) print the merger-frequency fit, saying that kappa_eff^T replaces kappa_2^T in the LAL implementation. The independent SymPy/mpmath reference in src/diffgw_reference/nrtidalv2_amplitude.py uses those printed coefficients and the published Planck function. The earlier provenance audit algebraically rejected the coupling substitution as a complete explanation: it changes the equal-mass case by exactly zero and the unequal-mass printed merger fit by -594.064 ppm, compared with observed effective shifts near -25 ppm. It also found no published normalization for the default D tidal amplitude.

This follow-up checked three further possibilities without reading LAL implementation source or deriving constants from its binary:

Hypothesis Decisive observation Status
A fixed merger-frequency rescaling explains the binary taper Effective shift is zero at zero tide, then varies from -10.0140 to -60.1647 ppm across equal-mass tidal strengths Rejected as a single fixed scale
The discrepancy is specific to LALSuite 7.26.15 Isolated 7.25.1 and 7.26.15 binary wheels give identical printed diagnostic rows Rejected for these two releases only
Unprinted precision in the published merger coefficients could explain it Independent interval arithmetic around the last printed digit allows approximately ±190 ppm at kappa_eff^T=75 and ±253 ppm at 225, holding the zero-tide prefactor fixed Numerically possible; no unique source-backed replacement coefficients

For that interval check, each of the four nonconstant Eq. (11) coefficients was independently moved by at most half a unit of its last printed decimal: n1=0.03354±0.000005, n2=0.00004315±0.000000005, d1=0.07542±0.000005, d2=0.0002236±0.00000005. Since the numerator increases and denominator decreases monotonically with those choices for positive coupling, the endpoint calculation bounds all combinations within those decimal intervals. It establishes only that rounding can contain the observed shift, not that the binary uses a particular unprinted value.

Dense black-box result

On len, the checked-out fcff4626 tree was copied to /home/xangma/tmp/diffgw-nrtidalv2-d-pv2-20260929. The historical, one-off diagnostic sampled 151 frequencies from 0.9 to 1.2 times each printed-paper merger frequency. It queried only the LAL binary API for |h_plus(D_NRTidalv2)|/|h_plus(D)|, divided by the native untapered quotient, and compared the resulting effective window with the independently specified Planck function. The diagnostic then inverted that window on 61 interior bins to express the mismatch as an equivalent boundary displacement. This inversion is conditional on the native untapered quotient continuing to approximate the binary quotient inside the taper; its median is not an estimate of a production coefficient.

(m1,m2; Lambda1,Lambda2) Printed f_mrg Hz Pre-taper maximum quotient error Interior maximum window error Median equivalent shift ppm
(1.35,1.35; 0,0) 4291.579158 0 2.22e-16 0
(1.35,1.35; 100,100) 2830.445551 1.03e-7 1.10e-4 -10.0140
(1.35,1.35; 200,200) 2401.755992 1.38e-7 1.68e-4 -15.2494
(1.35,1.35; 400,400) 2037.930727 1.79e-7 2.81e-4 -25.5376
(1.35,1.35; 800,800) 1732.535794 2.27e-7 4.90e-4 -44.4509
(1.35,1.35; 1200,1200) 1572.344865 2.54e-7 6.63e-4 -60.1647
(1.6,1.2; 200,800) 1709.953767 1.21e-7 2.77e-4 -25.1381

Rows agree at displayed precision for LALSuite 7.26.15 (lal 7.7.1, lalsimulation 6.2.1) and isolated 7.25.1 (lal 7.6.1, lalsimulation 6.1.0). Across the interior inversion bins, the equivalent shifts are nearly constant within each case (for example, [-25.5536,-25.4512] ppm at Lambda=400); a median-shifted Planck function leaves a maximum window residual of 2.69e-7 there. This pattern localizes the large mismatch to a merger-boundary-like difference. It does not identify the binary's internal formula, full-precision coefficients, or the default D amplitude's provenance.

The frozen focused binary comparison still gives maximum amplitude quotient errors 0.000153757344 for equal masses and 0.000189164604 for unequal masses inside the nonzero-tide taper, above the unchanged 0.00005 limit. The zero-tide taper passes. These numbers are a separate, predeclared grid from the dense effective-window diagnostic and should not be interchanged.

Pv2 public dispatch boundary

Dietrich et al. (2019), Sec. III.4, directs finite-size corrections to the aligned point-particle carrier before Pv2 rotation. The conditional carrier and supplied-angle positive-22 projection have scalar references and Torch/JAX checks in the existing public assembly boundary. The public Pv2 technical note specifies BBH frame and angle ingredients but does not select a BNS Fourier carrier time/phase origin or merger-slope rule. Its NNLO spin input and printed orbital-angular-momentum coefficient also differ from the current native BBH compatibility drivers, as mapped in that boundary document. Consequently those checked components do not justify a complete, unaligned IMRPhenomPv2_NRTidalv2 BNS dispatch. No angle, origin, or coefficient was chosen from a binary residual.

Historical run and maintained checks

The remote environment was /home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python with JAX_ENABLE_X64=1, OMP_NUM_THREADS=1, and PYTHONPATH=src:tests from the scratch checkout. The dense scan's one-off replay script is not maintained; the frozen amplitude comparison below remains a maintained regression and does not replay the per-bin frequency inversion.

For isolated LALSuite 7.25.1, PYTHONPATH=lalsuite-7.25.1:src:tests was used, with the binary wheel installed in the scratch target directory. The full outputs are retained on len at /home/xangma/tmp/diffgw-nrtidalv2-d-pv2-20260929/taper_probe_7.26.15_clean.log and taper_probe_7.25.1_clean.log. The frozen comparison was reproduced with DIFFGW_REQUIRE_LAL_BINARY=1 PYTHONPATH=src:tests JAX_ENABLE_X64=1 OMP_NUM_THREADS=1 python -m pytest -q -s tests/test_nrtidalv2_amplitude_lal_binary.py -k frontend_taper_amplitude: 2 passed, 6 strict xfailed, 24 deselected on 7.26.15. The expected failures remain failures. The full amplitude binary file yielded 14 passed, 18 strict xfailed, recorded in focused_binary_7.26.15.log. The amplitude math-reference, conditional Pv2 aligned-carrier, and supplied-angle projection files yielded 31 passed, recorded in focused_math_pv2.log. No model, gate, CI, catalogue, or shared qualification-status file was changed; nothing was deployed.