NSBH amplitude variant provenance — 27 September 2026
The source decision and diagnostic limits
were frozen in commit c8520fd before this diagnostic run. The audited
primary sources are Thompson et al. (2020), final arXiv v2
and its cited Pannarale et al. (2015).
Thompson v1 and v2 have the same relevant Table I / Eq. (26) / Eq. (29)
forms. Pannarale Eq. (26) corroborates the low/no-torus mixed PN center;
its Eq. (20) also uses a minus ringdown-width window. Thompson explicitly
corrects a factor of two in the latter but does not print a sign correction.
No audited paper equation or erratum uniquely licenses all three native
compatibility variants. This is a provenance blocker, not a failed
attempt to fit binary output.
An independent mpmath reference evaluated both variants at 70 and 90 decimal digits. Every scalar value satisfied the frozen \(10^{-30}\) absolute stability limit. The controlled inputs gave:
| Quantity | Printed paper | Native compatibility | Difference |
|---|---|---|---|
| Low/no-torus \(\widetilde f_0\), \(q=3\), \(\widetilde f_{\rm RD}=0.09\), \(f_{\rm tide}=0.06\), \(\epsilon_{\rm ins}=0.8\) | 0.076 | 0.0608 | 20% relative |
| Eq. (26) polynomial at \(\Lambda=1\) from below | 0.25 | 1.25 | 1.0 absolute |
| Eq. (29) factor at \(x=x_3+d_3/4\) | 0.09684999 | 0.71563001 | 0.61878002 absolute |
Torch and JAX CPU FP64 agreed with the independent compatibility scalar
variant at all three points (maximum reported relative error 0.000e+00,
below the frozen \(2\times10^{-13}\) bound). This is a drift check only; the
paper-literal variants do not pass a native equality gate. The diagnostic
does not resolve the additional question of whether Thompson Eq. (26)'s
\(\gamma'_1\) is meant to multiply baseline \(\gamma_1\).
On len (x86_64 Linux CPU), cwd
/home/xangma/tmp/diffgw-nsbh-variant-20260927, Python 3.12.3,
Torch 2.14.0+cpu, JAX 0.11.2, NumPy 2.5.3, mpmath 1.3.0, and pytest 9.1.1,
the focused command
JAX_ENABLE_X64=1 PYTHONPATH=src python -m pytest -q -s tests/test_nsbh_amplitude_variant_provenance.py
passed 3/3. The neighboring run with that file plus
test_nsbh_joining_frequencies.py, test_nsbh_branch_amplitude_fits.py,
test_nsbh_branch_reference.py, test_nsbh_torus_reference.py,
test_nsbh_disruption_reference.py, test_nsbh_clean_amplitude.py,
test_clean_room_nsbh.py, and tests/parity/test_nsbh_parity.py passed
107/107 in 78.00 s, with no skips or expected failures; its log is
nsbh-neighbor.log in the scratch cwd. Local Ruff, git diff --check, and
strict MkDocs build passed.
On integration, the same diagnostic was renamed to
tests/test_nsbh_amplitude_variant_provenance_math_reference.py so the
strict mathematical-reference CI job collects it. The historical len
commands above retain the original filename used for that run.
The native defaults are unchanged. The low/no-torus PN center and Eq. (26)/(29) paper variants remain unqualified; consequently the next amplitude assembly gate cannot be declared source-supported. The remnant/QNM provider, amplitude windows, phase composition, and whole NSBH waveform still require their own independent qualification.