NSBH low-tidal ringdown-width gate — 27 September 2026

The six-section v1 specification was frozen in a78e646 before adding the independent scalar reference, production-called Torch/JAX helpers, or native tests. It transcribes the closed \(0\leq\Lambda\leq1\) branch of Thompson et al. (2020), Eq. (29), and Eq. (28). The scalar code uses mpmath and imports neither native backend nor LAL. The native refactor keeps the original polynomial operation order and the historical public branch selection.

Validated on len CPU FP64. No numerical tests or scientific compute were run on the Mac for this slice. The frozen test spans 112 supplied input tuples, 70/90-digit scalar stability, both endpoint identities, Torch/JAX CPU FP64 values, six conditional partials, and domain rejection. The expected limits are \(10^{-30}\) for scalar stability, \(2\times10^{-13}\) for native values, and \(2\times10^{-12}\) for native partials, all absolute.

From a clean len checkout containing both commits, use the existing Torch/JAX/mpmath environment:

JAX_PLATFORMS=cpu JAX_ENABLE_X64=1 PYTHONPATH=src /home/xangma/repos/diffgw-worktrees/xas-whole-waveform-gate/.venv/bin/python -m pytest -q -s tests/test_nsbh_low_lambda_width_math_reference.py tests/test_nsbh_amplitude_variant_provenance_math_reference.py tests/test_nsbh_amplitude_window_sum_math_reference.py tests/test_nsbh_clean_amplitude.py tests/test_clean_room_nsbh.py tests/parity/test_nsbh_parity.py
/home/xangma/repos/diffgw-worktrees/xas-whole-waveform-gate/.venv/bin/python scripts/generate_waveform_library_table.py --check
/home/xangma/repos/diffgw-worktrees/xas-whole-waveform-gate/.venv/bin/python -m ruff check src/diffgw_reference/nsbh_low_lambda_width.py src/torchwave/approximants/nsbh_clean_amplitude.py src/torchwave/approximants/imrphenom_nsbh.py src/jaxwave/approximants/imrphenom_nsbh.py tests/test_nsbh_low_lambda_width_math_reference.py

The integrated checkout at 582414b was archived at /home/xangma/tmp/diffgw-integration-gate-20260927i. The focused command above ran there with JAX_PLATFORMS=cpu, JAX_ENABLE_X64=1, OMP_NUM_THREADS=1, and PYTHONPATH additionally including the separate PyCBC 2.11.0 package directory. It passed 104/104 tests in 54.04 s, with no skips or expected failures. Both backends reached maximum absolute value and partial errors of 1.137e-13 against the scalar. The log is nsbh-low-lambda-focused.log in that directory. Versions were Torch 2.14.0+cpu, JAX 0.11.2, mpmath 1.3.0, and PyCBC 2.11.0. The catalog generator --check and Ruff commands above passed on len. The len compute environment did not have MkDocs; a strict documentation build passed on the local documentation environment, with no local scientific compute.

This passing component gate covers only the source-unambiguous low-\(\Lambda\) correction and width on supplied inputs. The large-\(\Lambda\) Eq. (29) sign and Eq. (26) provenance, joining-center discrepancy, upstream provider guards, full amplitude, and whole waveform remain unqualified.