NSBH remnant paper-precision interval
Scope and status
nsbh.remnant.rounding_interval/v1 is a component qualification of the
Jiménez-Forteza et al. BBH remnant fit followed by the Zappa et al. NSBH tidal
correction. It checks the final mass and spin returned by the native Torch and
JAX remnant providers on five frozen, calibrated, guard-inactive inputs. It is
not a claim of numerical-relativity accuracy, physical fit uncertainty,
extrapolation behavior, or whole-waveform qualification.
Inputs, conventions, and options
Use \(m_{\rm NS}=1.4\) in nominal solar-mass units, \(m_{\rm BH}=q m_{\rm NS}\), \(\chi_{\rm NS}=0\), and the ordered \((q,\chi_{\rm BH},\Lambda)\) cases
| Case | \(q\) | \(\chi_{\rm BH}\) | \(\Lambda\) |
|---|---|---|---|
| A | 3 | 0 | 2500 |
| B | 3 | 0.5 | 2500 |
| C | 5 | 0.5 | 1000 |
| D | 5 | 0.75 | 100 |
| E | 5 | 0.75 | 2500 |
All have \(\nu=q/(1+q)^2\) in \([0.109,0.222]\), \(\Lambda\) in \([100,2500]\), and \(a_{\rm BH}\) in \([-0.5,0.75]\), the reported Zappa calibration ranges. Inputs are exact decimal/rational values for the scalar reference and FP64 values for native evaluation. The NS spin is zero, as in the Zappa calibration.
Mathematics and components
Jiménez-Forteza et al. (2017), arXiv:1611.00332v2 give the BBH final-spin fit in Eqs. (7)–(11), (13), (15)–(19), Tables 1–4, and the radiated-energy fit in Eqs. (21)–(24), (26)–(28), Tables 7–10. Use \(\hat S=(m_1^2\chi_1+m_2^2\chi_2)/(m_1^2+m_2^2)\), \(S=(m_1^2\chi_1+m_2^2\chi_2)/(m_1+m_2)^2\), and \(\Delta\chi=\chi_1-\chi_2\). Their final spin is \(S+L'_{\rm orb}\); their final mass ratio is \(1-E_{\rm rad}\). The constrained coefficients \(f_{i3}=64-64f_{i0}-16f_{i1}-4f_{i2}\) for spin and \(f_{i2}=16-16f_{i0}-4f_{i1}\) for energy are derived algebraically, not independently rounded. The paper's Eqs. (13) and (26) likewise derive spin \(f_{11}\) and energy \(f_{10}\) from other printed coefficients; their printed constraint multipliers carry the same rounding intervals. Explicit zero coefficients are exact zeros.
Zappa et al. (2019), arXiv:1903.11622v2 give, in Supplementary Eqs. (4)–(6) and Table 1, the mass/spin factor
The final mass is \((m_1+m_2)(1-E_{\rm rad})G_M\) and the final spin is
\((S+L'_{\rm orb})G_\chi\). For each printed decimal coefficient, including
the scaling constants in Jiménez-Forteza Eqs. (7), (8), and (22), define the
closed interval centered on that decimal with half-width one half of its
last displayed decimal place. Thus 3.833 denotes [3.8325,3.8335],
and -1.83e-3 denotes [-1.835e-3,-1.825e-3]. This conventional
round-to-nearest interpretation bounds omitted digits; it is not a reported
statistical error or a reconstruction of unpublished coefficients. Exact
integers, the zero constraints, and \(\sqrt2,\sqrt3\) remain exact. The scalar
reference propagates every independent printed interval through the paper
equations by conservative interval arithmetic. Correlations from constraints
are preserved by deriving those coefficients from their printed inputs.
Implementation mapping
The independent scalar interval reference lives in
src/diffgw_reference/nsbh_remnant_rounding.py; it imports neither frontend.
The native providers are bbh_remnant_uib2016 and
zappa_remnant_properties in each of
src/torchwave/approximants/imrphenom_nsbh.py and
src/jaxwave/approximants/imrphenom_nsbh.py. The comparison first checks
that each native literal fit coefficient rounds to the matching printed
table entry, then that native BBH and NSBH outputs lie inside the scalar
intervals. This audits implementation of the published fit at its printed
precision, not the provenance of unpublished native digits.
Evidence and limitations
The case list and the following acceptance conditions were frozen before native evaluation. For each case, both scalar Zappa-factor intervals must be strictly below one and both scalar BBH mass/spin intervals positive; otherwise the gate fails instead of silently testing a guard branch. The native mass ratio, spin, and final mass/spin must lie within their corresponding scalar interval, enlarged by \(2\times10^{-12}\) absolute on each side solely for FP64 evaluation. No fit-dependent tolerance or outcome-selected cases are permitted. A source-only interval width is reported for every case. Interval arithmetic may overestimate the set of jointly attainable outputs, so passing is a conservative consistency check, not proof of exact coefficient identity. Paper coefficient standard errors and NR residuals quantify a different uncertainty and are not substituted for last-digit rounding bounds.
Zappa's supplementary text does not define a complete algorithm for all extrapolation guards. Consequently this gate excludes those branches, and does not certify the native fallback/clipping policy, remnant calibration against NR, derivatives, FP32, or remnant-driven whole waveforms.
Reproduce the checks
On len CPU FP64 with the current PyCBC-capable environment, run
PYTHONPATH=src /home/xangma/.cache/diffgw-xp-pycbc-venv/bin/python -m pytest -q tests/test_nsbh_remnant_rounding_math_reference.py.
The six-heading documentation check is
PYTHONPATH=src python3 scripts/generate_waveform_library_table.py --check.