IMRPhenomNSBH joining frequencies

Scope and status

Specification nsbh-joining-frequencies/v1 transcribes the joining frequencies in Thompson et al. (2020), Table I. It fixes the grid and limits before numerical native comparison. Inputs are the independently supplied \(f_{\rm tide}>0\), \(f_{\rm RD}>0\), \(\widetilde f_{\rm RD}>0\), \(q\ge1\), torus ratio \(T\ge0\), and the already qualified Table I \(\epsilon_{\rm ins}\). No remnant or QNM provider is certified by supplying these values.

Inputs, conventions, and options

The merger classification uses the unadjusted \(f_{\rm RD}\) and the closed high-frequency boundary \(f_{\rm tide}\ge f_{\rm RD}\); \(T>0\) means torus.

Mathematics and components

The paper prints:

Class	\(\widetilde f_0\)	\(\widetilde f_1\)	\(\widetilde f_2\)
high, no torus	\(\widetilde f_{\rm RD}\)	\(\widetilde f_{\rm RD}\)	\(\widetilde f_{\rm RD}\)
high, torus	\(\epsilon_{\rm ins}\widetilde f_{\rm RD}\)	\(\epsilon_{\rm ins}\widetilde f_{\rm RD}\)	\(\widetilde f_{\rm RD}\)
low, no torus	\([(q-1)\widetilde f_{\rm RD}+\epsilon_{\rm ins}f_{\rm tide}]/q\)	\([(q-1)\widetilde f_{\rm RD}+f_{\rm tide}]/q\)	—
low, torus	\(\epsilon_{\rm ins}f_{\rm tide}\)	\(f_{\rm tide}\)	—

Here “high” means \(f_{\rm tide}\ge f_{\rm RD}\); “low” means strict \(f_{\rm tide}<f_{\rm RD}\). A dash supplies no paper value and cannot be qualified numerically. The native carrier's disabled ringdown still assigns \(\widetilde f_2=\widetilde f_{\rm RD}\) in low classes; that inert value is outside this source gate.

Implementation mapping

An independent mpmath scalar evaluator implements the four printed rows. The 30 controlled inputs and 180 composition inputs are exactly the grid in the branch-factor specification, including equality and all four merger classes. The scalar joining reference consumes the independent scalar branch factors. Torch and JAX CPU FP64 consume their native branch factors. For each paper-defined frequency, 70- and 90-digit scalar evaluations must differ by at most \(10^{-30}\) absolutely. Maximum native relative error must be at most \(2\times10^{-13}\) for a row to pass. No limit may be enlarged after comparing native output.

Evidence and limitations

The existing native low/no-torus \(\widetilde f_0\) applies an additional outer \(\epsilon_{\rm ins}\) to the whole mixed expression. Table I does not print that factor. Keep the binary-compatibility adapter unchanged in this slice and report the discrepancy as a bounded diagnostic, with a nonzero controlled-grid example. Thus the other three rows may qualify, but the low/no-torus \(\widetilde f_0\) and the four-row joining-frequency component cannot yet be called paper-qualified. Its \(\widetilde f_1\) can still be checked against the printed row. This policy separates a measured source mismatch from a silently adjusted specification.

The printed signs of Appendix A Eqs. (26) and (29) also differ from the continuity-preserving native adapters. They are excluded until a published-source variant is established; this gate cannot infer a correction from binary output. Windows, amplitude assembly, and the whole waveform remain provisional.

The variant provenance gate compares the final 2020 revision with its cited 2015 amplitude model and records why these exceptions still cannot be promoted to paper-qualified amplitude gates.

Reproduce the checks

Run JAX_ENABLE_X64=1 PYTHONPATH=src pytest -q tests/test_nsbh_joining_frequencies_math_reference.py with reference, Torch and JAX extras on CPU. The validation receipt records measured errors, diagnostic, and environment.