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NRTidal v1 merger-fit source boundary — 27 September 2026

Decision: No author-published source checked here supplies the full-precision merger-fit parameters or an alternative NRTidal v1 variant that identifies the pinned public binary's nonzero-tide taper frequency. The published Eq. (11) remains the mathematical reference. The frozen nonzero-tide binary gate still fails; this audit does not qualify the fully tapered carrier.

Sources and scope

  • Dietrich et al. (2018), Eq. (11) and its preceding and following paragraphs print \(\omega_0=0.3586\), \(n_1=3.354\times10^{-2}\), \(n_2=4.315\times10^{-5}\), \(d_1=7.542\times10^{-2}\), and \(d_2=2.236\times10^{-4}\). The authors explicitly say that LAL substitutes \(\kappa_{\rm eff}^T\) for \(\kappa_2^T\), and set the Planck taper from \(f_{\rm mrg}\) to \(1.2 f_{\rm mrg}\). The article's arXiv v1 source archive has the same printed digits in paper20180406.tex; its other entries are figures and the bibliography, with no coefficient table or companion code. The accepted manuscript also prints the same precision. No separate author or publisher supplement with additional digits was found in the checked records; this is a bounded search result, not a claim that unpublished fit data do not exist.
  • Bernuzzi et al. (2014), merger-frequency fit gives an earlier, different rational fit for moderate mass ratios. In particular, it has no \(d_2\) term. It is not a higher-precision version of Dietrich et al. (2018), Eq. (11).
  • Dietrich et al. (2019), Eq. (25) refers back to the 2018 merger frequency and \(1.2 f_{\rm mrg}\) taper. The later author review, Eq. (89) repeats the merger-fit coefficients at the same precision; neither supplies the missing digits or defines a separate v1 public-binary fit.

What the frozen diagnostic establishes

The public-interface convention diagnostic shows that one merger-frequency shift explains the pinned LALSuite 7.26.15 binary's Planck-window modulus at seven taper samples. On five nonzero-tide systems, the binary-implied frequency is \(2.51\times10^{-5}\) to \(4.87\times10^{-5}\) below the printed Eq. (11) fit in relative terms; the zero-tide system agrees. The \(\kappa_2^T\) alternative fails the unequal-mass cases and cannot explain an equal-mass difference. Rounding intervals of the printed parameters can contain a discrepancy of this size, but the binary diagnostic does not identify which parameter differs or establish its unpublished value. No coefficient has been extracted from LAL source or fitted to its binary output.

Missing contract and next gate

The missing source contract is either (a) the author-published, sufficiently precise joint tuple \((\omega_0,n_1,n_2,d_1,d_2)\) for the Eq. (11) fit used by the specified NRTidal v1 variant, together with its coupling convention, or (b) a published, complete variant definition that fixes the binary's merger frequency independently. A single inferred \(f_{\rm mrg}\), or one coefficient chosen within a rounding interval, cannot supply that contract. If such a source becomes available, freeze its equation, domain, cases, and tolerance before adding a separate scalar/Torch/JAX and public-binary gate. Until then, keep the source-derived scalar-to-native checks and the failed nonzero-tide boundary diagnostic distinct; do not change native constants or relax the frozen tolerance.