IMRPhenomNSBH amplitude variant provenance

Scope and status

Specification nsbh-amplitude-variants/v1 compares the final Thompson et al. (2020), arXiv v2 with the cited Pannarale et al. (2015), arXiv v1. The source of truth for a paper-literal gate is the printed equation, not binary output. A compatible native variant may be retained without being called paper-qualified. A source-supported correction would require a published equation or explicit erratum that uniquely specifies the variant; continuity arguments and implementation behavior alone do not meet that bar.

Inputs, conventions, and options

The audit uses the papers' mass ratio \(q\ge1\), positive adjusted ringdown and tidal frequencies, nonnegative \(\epsilon_{\rm ins}\), and tidal deformability \(\Lambda\). Native outputs are compared only with the separately named compatibility variant.

Mathematics and components

The following source claims are frozen before the new numerical diagnostic:

Component	Printed source	Native compatibility variant	Provenance decision
Low/no-torus PN center	Thompson Table I: \([(q-1)\widetilde f_{\rm RD}+\epsilon_{\rm ins}f_{\rm tide}]/q\). Pannarale Eq. (26) and its following sentence give the same \(f_1\).	An additional outer \(\epsilon_{\rm ins}\) multiplies the entire mixed center.	Neither paper prints that outer factor for this branch. The general Pannarale Eq. (13) has an outer inspiral center \(\epsilon_{\rm ins}\widetilde f_0\), but its branch-specific Eq. (26) directly sets \(f_1\) and so does not uniquely license applying it again.
Small-\(\Lambda\) premerger correction	Thompson Eq. (26): \(\gamma'_1=1-0.5\Lambda-0.25\Lambda^2\) for \(\Lambda\le1\), and \(1.25\) for \(\Lambda>1\).	The polynomial is \(1+0.5\Lambda-0.25\Lambda^2\), then multiplied by baseline \(\gamma_1\).	The printed polynomial jumps from \(0.25\) to \(1.25\) at \(\Lambda=1\), despite the text's smooth-match claim. Eq. (26) also does not explicitly print the baseline \(\gamma_1\) factor. No cited source uniquely resolves both choices.
Large-\(\Lambda\) ringdown-width correction	Thompson Eq. (29): \((A/2)\omega^-_{x_3,d_3}(x)\), where \(x=(f_{\rm tide}-\widetilde f_{\rm RD})/\widetilde f_{\rm RD}\) and \(A/2=0.81248\). Pannarale Eq. (20) also prints a minus window, without the later factor-of-two correction.	\(0.81248\omega^+_{x_3,d_3}(x)\).	Thompson explicitly identifies the factor of two as a correction to Pannarale, but prints no correction of the window sign. Large-\(x\) BBH continuity favors the native sign, yet the cited published equations do not establish it.

Implementation mapping

diffgw_reference.nsbh_amplitude_variants evaluates the printed and compatibility formulas separately. The production Torch and JAX joining, premerger, and ringdown correction helpers are compared only with the compatibility scalar outputs; their numerical defaults are unchanged.

Evidence and limitations

Thompson v1 and v2 print the same three relevant variants. Its Eq. (30) defines \(\omega^\pm_{x_0,d}(x)=[1\pm\tanh(4(x-x_0)/d)]/2\). The 2015 and 2020 formulas differ elsewhere by explicit model revisions; their shared sign and mixed center are therefore corroborating source evidence, not proof that the native behavior is scientifically wrong.

Use independent 70- and 90-digit mpmath scalar evaluations with absolute agreement at most \(10^{-30}\). Evaluate three controlled, source-discriminating inputs: \((q,\widetilde f_{\rm RD},f_{\rm tide},\epsilon_{\rm ins})=(3,0.09,0.06,0.8)\); \(\Lambda=1\) approached from the small branch; and \(x=x_3+d_3/4\) for the ringdown correction. Source versus native differences must be nonzero by more than \(10^{-3}\) in their dimensionless representative values (relative for the frequency, absolute for the correction factors). Torch and JAX CPU FP64 compatibility helpers must match the independent native-variant scalar values within relative \(2\times10^{-13}\). These are discrepancy and regression checks, not a qualification of the paper-literal formulas. No limit or input may be changed after comparison.

Do not modify the native defaults or run binary fitting. With no uniquely published correction for all three variants, full amplitude assembly remains blocked. The independently printed low-\(\Lambda\) Eq. (29) branch can be gated conditionally; that does not resolve the large-\(\Lambda\) discrepancy. The disruption root, torus/ISCO, branch selection, and scoped branch factors keep their existing status; remnant/QNM supply and whole-waveform qualification remain separate gates.

Reproduce the checks

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