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TaylorF2_HM minimal multimode oracle boundary — 2026-09-27

Candidate and decision

The smallest useful external waveform gate is the nonspinning, unwindowed (2,2)+(3,3) composition at unequal mass. The (3,3) leading amplitude is proportional to the signed mass difference in Mishra et al., Eqs. (9)–(12h) and Mezzasoma and Yunes, Eqs. (20)–(21i), so unequal masses distinguish this candidate from a dominant-only carrier. Use chi1=chi2=0, f_ref=None, and f_isco_cutoff=False, and require direct complex per-mode (h_plus,h_cross) and their sum with pinned Fourier, polarization, phase, time, distance, and angular conventions. The previously declared maximum normalized complex error is 4e-10 in FP64 for each mode and sum, with no fitted alignment. This two-mode gate would establish only that slice, not the other six modes or any spin/reference-frequency/cutoff option.

No external same-model (2,2)+(3,3) complex waveform output was found in the reviewed sources. The checksum-pinned Mishra author supplement provides symbolic expressions, not a separately emitted numerical series; the maintained source-composed test already exercises all eight leading nonspinning modes and summed polarizations in both frontends. Re-evaluating that composition for just two modes cannot supply a new independent oracle. The public LAL TaylorF2 documentation describes a frequency-domain TaylorF2 waveform, but the pinned binary returns one carrier series and offers no TaylorF2 FD-mode generator. IMRPhenomXHM and TEOBResumSPA are different waveform models, so their higher-mode values cannot serve as binwise TaylorF2_HM parity targets. This is a dated boundary, not a claim that no future independent release can exist.

Reproducible public-binary check

On len (Linux x86_64), the private staging copy was /home/xangma/tmp/diffgw-tf2hm-minimal-oracle-20260927. The environment was /home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python with LAL 7.7.1, LALSimulation 6.2.1, Torch 2.14.0+cpu, JAX/JAXLIB 0.11.2, SymPy 1.14.0, and mpmath 1.3.0. tests/test_taylorf2_hm_external_api.py now uses unequal (1.7,1.2) solar-mass components. At 30:0.25:500 Hz, the public SimInspiralTaylorF2 output has 2001 bins; inserting mode arrays [(2,2)], [(2,2),(3,3)], or [(2,2),(3,2)] leaves that series exactly unchanged (max |delta| = 0 for each). The separate public SimInspiralChooseFDModes request for TaylorF2 raises a generator/argument error. These observations verify the API boundary, not a two-mode waveform.

The command below passed 54/54 on len, with no skips or expected failures:

cd /home/xangma/tmp/diffgw-tf2hm-minimal-oracle-20260927
env PYTHONPATH=src:tests:. JAX_ENABLE_X64=true JAX_PLATFORM_NAME=cpu \
  XLA_PYTHON_CLIENT_PREALLOCATE=false \
  /home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python -m pytest -q -ra \
  tests/test_taylorf2_hm_external_api.py \
  tests/test_taylorf2_hm_author_supplement_math_reference.py \
  tests/test_taylorf2_hm_math_reference.py \
  tests/test_taylorf2_hm_paper_math_reference.py tests/test_oracle_ci.py

The external multimode verdict remains UNRESOLVED_ORACLE. A qualifying future release would need a reproducible, independently maintained same-model complex series or published numerical table with sufficient precision and explicit redistribution terms. Its two mode values and sum must be compared directly against both frontends at fixed physical inputs and conventions.