NRTidal v1 public-binary taper convention diagnostic — 27 September 2026

Result: The pinned LALSuite 7.26.15 binary uses the published descending Planck-window shape for all six declared systems, but its nonzero-tide window begins at a merger frequency below the value obtained from the coefficients printed in Dietrich et al. (2018), Eq. (11). The source does not give a higher-precision coefficient set sufficient to identify the binary's frequency. This does not qualify the nonzero-tide tapered carrier.

This is a follow-up to the frozen boundary failure. The historical, one-off diagnostic called only the public SimInspiralChooseFDWaveformSequence interface. It sampled the modulus of the binary BNS/BBH quotient at seven frequencies \(f/f_{\rm mrg}^{\rm paper}=1.025,1.05,1.075,1.1,1.125,1.15,1.175\). It inverted McKechan et al. (2010), Eq. (7) at the central sample to infer one merger frequency, then checked the other six without fitting the window shape. The printed merger fit and the \(\kappa_2^T\to\kappa_{\rm eff}^T\) substitution come from Dietrich et al. (2018), Eq. (11) and preceding paragraph.

System	Printed-fit \(f_{\rm mrg}\) Hz	Inferred binary \(f_{\rm mrg}\) Hz	Relative shift	Maximum modulus error, printed / inferred
Equal, \(1.35/1.35\), \(\Lambda=400/400\)	2037.930727302	2037.878643198	\(-2.55573474\times10^{-5}\)	\(2.81138\times10^{-4}\) / \(7.77\times10^{-16}\)
Unequal, \(1.6/1.2\), \(\Lambda=200/800\)	1709.953767101	1709.910763599	\(-2.51489269\times10^{-5}\)	\(2.76645\times10^{-4}\) / \(8.33\times10^{-16}\)
Exchanged bodies	1709.953767101	1709.910763599	\(-2.51489269\times10^{-5}\)	\(2.76645\times10^{-4}\) / \(8.33\times10^{-16}\)
Zero tide, \(1.35/1.35\)	4291.579157959	4291.579157959	\(0\)	\(1.05\times10^{-15}\) / \(1.05\times10^{-15}\)
Holdout unequal, \(1.48/1.22\), \(\Lambda=600/250\)	1766.115917226	1766.062949709	\(-2.99909630\times10^{-5}\)	\(3.29910\times10^{-4}\) / \(1.44\times10^{-15}\)
Holdout equal, \(1.25/1.25\), \(\Lambda=900/900\)	1819.558741158	1819.470113491	\(-4.87083296\times10^{-5}\)	\(5.35818\times10^{-4}\) / \(1.11\times10^{-15}\)

Independent inversion of each of the seven interior samples gives a merger-frequency spread no greater than \(7.42\times10^{-10}\) Hz (including zero tide). Thus a single frequency shift explains the observed modulus throughout the taper; a different Planck-window shape is unnecessary for these cases. The explicit alternative of using \(\kappa_2^T\) instead of \(\kappa_{\rm eff}^T\) gives errors of \(6.26\times10^{-3}\) and \(2.77\times10^{-2}\) in the two unequal-mass cases. It cannot explain the equal-mass mismatch because those couplings coincide there.

The printed coefficient \(d_2=2.236\times10^{-4}\) has a half-last-digit rounding interval of \(5\times10^{-8}\). Varying only that coefficient over its printed rounding interval contains all inferred frequencies. This is a precision illustration, not evidence that \(d_2\) alone differs in the binary: the paper does not publish the binary's full-precision coefficients, and other printed coefficients also have rounding intervals. We did not extract or fit a replacement coefficient from the binary. The paper-derived scalar reference and Torch/JAX tests retain the printed coefficients, and the strict nonzero-tide boundary failure remains open.

The run used host len, cwd /home/xangma/tmp/diffgw-nrtidalv1-phase-20260927, and the pinned environment documented in the earlier receipt. The foreground diagnostic completed normally in 3.3 s with CPU JAX float64 and single-threaded OpenMP. Its one-off replay script is not maintained. The maintained tests/test_nrtidalv1_taper_math_reference.py and tests/test_nrtidalv1_taper_lal_binary.py check the published expression and frozen boundary gate; they do not replay the binary frequency inversion.

This is a diagnostic receipt outside the required strict mathematical reference selection. No passing binary taper gate is inferred from the frequency inversion, which uses the binary's own output.