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NRTidalv2 D amplitude and taper provenance audit — 27 September 2026

Disposition: No source-backed change to the waveform or its frozen gates. The default binary_compatible D variant remains pinned-binary verified, but its tidal-amplitude normalization is not derived from the published model. The explicit paper_2019 D phase-only variant and the separate Eq. (24) amplitude component retain their distinct source-scoped contracts. This is a follow-up to the 26 September qualification receipt, not a new qualification claim. No LAL implementation source or constants were used in this audit.

Can the historical 1/2 be derived?

Dietrich et al. (2019), Eq. (24) specifies the frequency-domain additive tidal amplitude with the prefactor sqrt(5*pi*nu/24) * M^2/D_L; Eq. (23) and Kawaguchi et al. (2018), Eq. (2.25) have the same leading normalization. In particular, (27/16)*sqrt(160*pi*nu/27) = 9*sqrt(5*pi*nu/24), with no extra 1/2. Equation (25) adds that correction once to the BBH amplitude and then tapers the sum. Table II marks tidal amplitude absent for IMRPhenomD_NRTidalv2, present for IMRPhenomPv2_NRTidalv2.

The same paper's Appendix A.2, Eq. (40), does contain a 1/2, in the stationary-phase conversion of a time-domain amplitude. Equations (40)–(45) develop a different amplitude prescription; the paragraph after Eq. (45) explicitly says the main-text Eq. (24) prescription was chosen for implementation. Therefore Eq. (40) does not authorize multiplying Eq. (24) by a second 1/2 or adding a nonzero tidal amplitude to the paper's D composition. The frozen default's M_sec^2/(2 D_sec) prefactor remains a historical binary-compatible observation, not a sourced paper coefficient. For the frozen equal- and unequal-mass cases, the historical/published component scale ratios are respectively 1.236077446 and 1.248886881 (earlier receipt). A single polarization projection cannot account for both at fixed inclination.

The 2019 paper describes public CoRe numerical-relativity waveforms but does not identify an independently licensed companion implementation of its NRTidalv2 D amplitude or full-precision taper fit. A bounded search of the paper and public author-artifact records found no such artifact. This is an absence of provenance found in this audit, not proof that none exists.

Can a published merger-frequency convention explain the taper difference?

Dietrich et al. (2018), Eqs. (10)–(11) give a merger-frequency fit in kappa_2^T and explicitly state that their LAL implementation substitutes kappa_eff^T. Using their Eq. (10), Lambda_i = (2/3) k_2^i/C_i^5, and Dietrich 2019 Eq. (8), independent algebra gives

kappa_2^T   = 3 [X_A^4 X_B Lambda_A + X_B^4 X_A Lambda_B]
kappa_eff^T = (3/13) [(X_A + 12 X_B) X_A^4 Lambda_A
                       + (X_B + 12 X_A) X_B^4 Lambda_B].

For the frozen equal-mass (1.35,1.35;400,400) case, both couplings are exactly 75; substitution changes the Eq. (11) merger frequency by zero. For (1.6,1.2;200,800) and its exchanged ordering, they are respectively 73.683584220860 and 73.496848840456; using kappa_2^T instead of kappa_eff^T changes the printed Eq. (11) frequency by -594.064 ppm. The earlier public-binary diagnostic yielded only -25.54 ppm equal-mass and -25.14 ppm unequal-mass equivalent boundary shifts, conditional on the untapered amplitude continuing to agree inside the taper. The published coupling substitution cannot explain both cases and should not be changed to fit them.

The papers specify a taper from f_mrg to 1.2 f_mrg. Printed Eq. (11) coefficients have only four significant digits. At kappa_eff^T = 75, moving one coefficient at a time by half a unit of its last printed digit changes the merger frequency by up to approximately 100 ppm (n1), 7.5 ppm (n2), 47 ppm (d1), or 36 ppm (d2). Thus unpublished precision could explain a nonzero-tide ~25 ppm discrepancy while leaving the zero-tide boundary unchanged; this is a sensitivity bound, not evidence that the pinned binary uses such precision. No unprinted coefficient was inferred or added.

Exact remaining gate and next discriminating evidence

The frozen binary_compatible default passed unchanged strict len catalog 19/19 and holdout 14/14 with LALSuite distribution 7.26.15; its focused scalar/backend tests passed 67, with 18 strict xfails. The paper_2019 D composition differs from the same pinned binary at nonzero tide, and the default's nonzero-tide high-frequency taper quotient retains the two strict expected failures: maximum absolute ratio errors 0.000153757344 equal-mass and 0.000189164604 unequal-mass versus the unchanged 0.00005 limit. Host, commands, logs, and remaining test coverage are in the earlier receipt. These failures prevent a claim that the taper is both paper-grounded and binary-qualified; the D amplitude provenance prevents a paper-grounded claim for the default despite its binary parity.

The next read-only discriminator is a public-binary, dense-frequency taper comparison for equal masses at several nonzero Lambda values, plus zero tide, repeated across documented LALSuite releases. Compare each output to the printed Eq. (11) and independently checked Planck window, without fitting a production coefficient. This can distinguish a version-dependent or tide-dependent effective boundary from a fixed convention. Promoting a different coefficient would still require an author-published full-precision fit or another independently licensed source. Resolving the D amplitude contract would require a published correction or author artifact that explicitly assigns a nonzero amplitude and its normalization to D.