NSBH conditional amplitude window-and-sum gate — 27 September 2026

The six-section v1 specification was frozen in commit be85d40 before native comparison. It transcribes Thompson et al. (2020), Eqs. (4) and (30) with independently supplied centers, width, total mass, and three carrier amplitudes. The scalar reference uses mpmath and imports neither native backend nor LAL code. The native helpers are called by the public Torch and JAX amplitude assembly. No fit coefficients or historical default changed.

On local Darwin arm64 with Python 3.13.7, Torch 2.14.0, JAX 0.11.2, NumPy 2.5.3, mpmath 1.3.0, and pytest 9.1.1, the command JAX_ENABLE_X64=1 PYTHONPATH=src /Users/xangma/repos/diffgw/.venv/bin/python -m pytest -q -s tests/test_nsbh_amplitude_window_sum_math_reference.py tests/test_nsbh_amplitude_variant_provenance_math_reference.py tests/test_nsbh_joining_frequencies_math_reference.py tests/test_nsbh_branch_amplitude_fits_math_reference.py tests/test_nsbh_clean_amplitude.py tests/test_clean_room_nsbh.py tests/parity/test_nsbh_parity.py passed 102/102 in 16.84 s. The 14 new tests cover four frozen center/width patterns, 70-versus-90-digit scalar stability, window centers and neighborhoods, Torch/JAX values and selected frequency/carrier derivatives, and two fixed pre-refactor public amplitude sample grids. The scalar difference stayed below its frozen 1e-30 absolute limit. The maximum native value error was 2.220e-16 and maximum selected partial error was 1.110e-16, below 2e-13 and 2e-12 respectively. The fixed public amplitude samples passed at 2e-13 absolute after scaling by 1e22.

The adjacent NSBH phase and reconstruction suite passed 31/31 in 3.83 s. The documentation generator's --check and Ruff on all changed Python files passed. An additional local strict LAL-binary suite produced 33 passed, 22 failed: this Mac environment lacks PyCBC, so the harness returns optimized_match=None for each strict comparison, which its existing strict gate rejects. This is an environment limitation of that suite, not a changed tolerance or evidence for a waveform discrepancy. On len with CPU FP64, the new gate, its NSBH amplitude neighbors, and the HM mapping reference passed 142/142 in 72.03 s from the integrated checkout at 6ad7663. The command used JAX_ENABLE_X64=1, JAX_PLATFORMS=cpu, and PYTHONPATH=src:tests, with --reference-device=cpu -ra; its test files were test_nsbh_amplitude_window_sum_math_reference.py, test_nsbh_amplitude_variant_provenance_math_reference.py, test_nsbh_joining_frequencies_math_reference.py, test_nsbh_branch_amplitude_fits_math_reference.py, test_nsbh_clean_amplitude.py, test_clean_room_nsbh.py, parity/test_nsbh_parity.py, and test_imrphenomhm_frequency_map_math_reference.py under tests/.

The strict public-binary NSBH remnant-mass regression was then rerun on len from that same checkout with PyCBC 2.11.0 installed in a separate package directory (NumPy 2.3.5, SciPy 1.16.3), without changing the shared Torch/JAX environment. All 24/24 tests passed in 6.87 s, including the 22 cases that could not obtain a match statistic on the Mac without PyCBC. The command was JAX_ENABLE_X64=1 JAX_PLATFORMS=cpu PYTHONPATH=/home/xangma/tmp/diffgw-pycbc-2.11.0-full/packages:src:tests OMP_NUM_THREADS=1 python -m pytest -q tests/test_nsbh_phase_mass_regression.py -ra, using the existing len venv's Python. This resolves the environment limitation above; it does not expand the conditional amplitude-window gate into whole-waveform qualification.

This gate verifies only the three-window algebra with supplied inputs. The low/no-torus joining-center discrepancy, Eq. (26)/(29) variant discrepancies, upstream PhenomC carriers and distance normalization, and the complete NSBH waveform remain unqualified.