IMRPhenomHM complex intrinsic-mode assembly — 2026-09-27

The conditional hm.intrinsic.complex-assembly.eq3.v1 gate passed on len. The standalone SymPy/mpmath reference composes London's amplitude and phase equations with the previously specified frequency map, PN ratio, and phase offset components. Its public adapter accounts for the native Fourier sign, odd-mode sign, and nonzero orbital-phase and time gauges. The test compares full complex unprojected modes, including their amplitude scale, with both Torch and JAX. It does not compare polarizations or claim NR accuracy.

The CPU-FP64 fixture uses masses (35,20) solar masses and aligned spins (0.2,-0.1), all six positive-frequency HM modes, and both london_2018 and phenomd_runtime transition selections. Each mode uses 11 frequencies spanning the low-frequency amplitude and phase joins and the mode ringdown join, including one point on each side. It fixes f_ref=None, phic=0.37, and tc=0.008 seconds, and explicitly selects the Mishra-source 1.5PN variants for (2,1), (3,2), and (4,3). The test checks each complex sample against its own nonzero expected amplitude, with maximum relative error required below 3e-8; this is 264 frontend samples. Scalar checks separately verify the symbolic Eq. (3), the paper's positive-exponent convention, the exact symmetric odd-mode undefined ratio, and the public symmetry-zero/time-gauge contract.

Focused run: host len; cwd /tmp/diffgw-hm-intrinsic-20260927/repo; command JAX_ENABLE_X64=1 JAX_PLATFORMS=cpu PYTHONPATH=src /tmp/diffgw-waveform-library-1315f6e/venv-latest/bin/python -m pytest -q tests/test_imrphenomhm_intrinsic_modes_math_reference.py --reference-device=cpu -ra; result 6 passed in 21.49 s. The foreground command completed, with no running PID or log to poll. Environment: Python 3.12.3, Torch 2.14.0+cu130, JAX 0.11.2, SymPy 1.14.0, mpmath 1.3.0, NumPy 2.3.5, SciPy 1.16.3, pytest 9.1.1; both frontends ran on CPU.

The adjacent HM math-reference suite passed 289 tests in 155.34 s on len from the same cwd and environment. Command: JAX_ENABLE_X64=1 JAX_PLATFORMS=cpu PYTHONPATH=src /tmp/diffgw-waveform-library-1315f6e/venv-latest/bin/python -m pytest -q tests/test_imrphenomhm_*math_reference.py --reference-device=cpu -ra. PID 2392236 has completed; log: /tmp/diffgw-hm-intrinsic-20260927/all-hm.log; exit-status file: /tmp/diffgw-hm-intrinsic-20260927/all-hm.exit contains 0. The next check is complete and there is no scheduled poll. If that job were still running, its stop command would be ssh len 'kill 2392236'. The new source and test pass Ruff, and the docs pass mkdocs build --strict.

The D carrier amplitude and phase, alpha fit coefficients, remnant and QNM frequencies come from the public frontends and are supplied inputs to the scalar reference. This gate can catch a wrong composition of those inputs, but shared upstream errors remain possible. It does not cover another mass/spin region, a finite f_ref, negative-frequency reconstruction, polarization projection, binary-library agreement, or physical mismatch against NR. See the mathematical specification.