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TaylorF2_HM independent-oracle search — 2026-09-26

Outcome

No qualifying published numerical oracle was located. No external-parity test or numerical claim was added. The existing author-source, paper-fidelity, scalar-reference, Torch/JAX-parity, angular, and dominant-mode gates retain their narrower labels.

This was a bounded clean-room search. A same-equation SymPy evaluation, a translation of the Mishra supplement, a LAL-derived series, or a fit to diffGW output was rejected as independent evidence.

Reduced nonspinning gate

Restricting the claim to chi1=chi2=0, f_ref=None, and f_isco_cutoff=False removes the spin-recipe, reference-frequency, and per-mode-mask requirements below. It does not supply an independent eight-mode numerical oracle. Before the diagnostic run, the candidate gate was fixed to all eight listed modes, direct unaligned complex per-mode \((h_+,h_\times)\) and their sum in FP64 Torch and JAX, and a maximum complex error of \(4\times10^{-10}\) per unmasked mode and sum, normalized by the corresponding reference magnitude (or summed mode magnitudes for a polarization sum). No fitted phase, time, amplitude, or frequency shift is permitted. Concrete sample inputs are the three binaries and frequencies in tests/data/taylorf2_hm_mishra2016_samples.json, with distance 410 Mpc, \(t_c=0.0041\) s, \(\phi_c=0.23\), and orientations \((\iota,\phi_0)=(0.91,0.37),(1.32,-0.44)\).

The existing author-supplement test already evaluates precisely this nonspinning, unwindowed slice as a source-composed complex check: it extracts the leading terms and nonspinning phase from the pinned symbolic supplement, adapts their convention, and supplies the polarization projection from García-Quirós et al. Eqs. (8)–(9). Its \(8\times10^{-10}\) component threshold establishes agreement with that composition, not independent numerical parity. Re-evaluating those same expressions in another interpreter would check parsing or arithmetic but would still share the symbolic source and the locally supplied composition.

The Mishra et al. author source contains symbolic amplitudes and phasing, but no separately emitted complex mode or polarization table. The public WF4Py restricted TaylorF2 and gwfast feature inventory give a dominant-only TaylorF2; gwfast's listed higher modes belong to its different TEOBResumSPA model. LAL's public TaylorF2 API returns one carrier; its FD-mode dispatch has no TaylorF2 generator, as checked by the maintained tests/test_taylorf2_hm_external_api.py black-box test. Searches for TaylorF2HM, TaylorF2_HM, the Mishra supplement identifier, and nonspinning eight-mode TaylorF2 numerical data found no independently maintained exact model. These are dated negative observations, not a proof of nonexistence.

Thus the reduced numerical-oracle gate remains open. A qualifying output may omit spins, finite \(f_{\rm ref}\), and cutoff samples, but must provide all eight complex modes or both polarizations per mode and their sum with fixed physical inputs, units, phase, Fourier, tetrad, and mode conventions. The comparison must be direct and reproducible from a pinned, suitably redistributable published table or independently maintained executable. The (2,2) LAL carrier and angular-basis checks cannot substitute for the other seven modes.

On len (Linux x86_64), the existing bounded checks passed 46/46 in 24.79 s using Python 3.12.3, Torch 2.14.0+cu130 on CPU, JAX/JAXLIB 0.11.2, SymPy 1.14.0, mpmath 1.3.0, LAL 7.7.1, and LALSimulation 6.2.1. The command was env PYTHONPATH=src:. JAX_ENABLE_X64=true JAX_PLATFORM_NAME=cpu XLA_PYTHON_CLIENT_PREALLOCATE=false python -m pytest -q -ra followed by 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_taylorf2_hm_external_api.py, and tests/test_oracle_ci.py in the private staging checkout /home/xangma/tmp/diffgw-tf2hm-nonspin-oracle-20260926. No new numerical gate, fixture, or verification claim was added.

Required oracle record

A closing record must supply all of the following without inference or fitted convention alignment:

  • complex frequency-domain values, or per-mode \((h_+,h_\times)\) plus their exact sum, for (2,2), (2,1), (3,1), (3,2), (3,3), (4,2), (4,3), and (4,4);
  • component masses, nonzero aligned spins, distance, inclination, phase and time origins, frequency grid and units;
  • a finite f_ref, its phase definition, and the Fourier, tetrad, spin-weighted-harmonic, and signed-mode conventions;
  • the termination rule for every mode, with samples below, at, and above each per-mode cutoff;
  • an author-published table or independently maintained executable, versioned provenance and hashes, and explicit redistribution terms.

The comparison must be direct, complex, per mode and on the sum in both Torch and JAX. A dominant carrier, angular basis, magnitude-only ratio, or post-hoc phase/time alignment cannot close the gate.

Sources examined

Source Published material found Missing for this gate
Mishra et al., arXiv:1601.05588v1 and its checksum-pinned source bundle Paper plus supl-mkaf16.m; the bundle contains the TeX, bibliography, and symbolic Mathematica supplement No independently emitted numerical modes or polarizations; no finite-f_ref table; no native signed-mode projection; no cutoff-boundary samples; the arXiv license grants distribution to arXiv, not a downstream MIT grant
Mezzasoma and Yunes, arXiv:2203.15934v1 and its source bundle Paper formulas; the bundle contains TeX and bibliography only No numerical data or executable; the GR amplitude review used here is nonspinning; no finite-f_ref and per-mode-cutoff oracle
LALSuite TaylorF2 public documentation and the maintained public-API probe One TaylorF2 frequency series with a documented finite f_ref; public mode dispatch does not provide this eight-mode TaylorF2 model Not an all-eight independent mode record; LAL source/copies and fitted adapters were outside the acceptance boundary
WF4Py and PyCBC waveform interface Restricted TaylorF2 in WF4Py; a LAL-backed interface in PyCBC Neither supplies an independent all-eight oracle with the required options

Registry/repository checks used both arXiv identifiers, titles and DOIs. Zenodo returned no matching records; GitHub repository search returned no exact matches; Crossref exposed no related data/code objects; DataCite returned only the arXiv DOI records. These negative results are dated observations, not proof that no future or unindexed oracle exists.

Frozen fixture provenance

tests/data/taylorf2_hm_mishra2016_samples.json stores generated amplitude ratios and a normalized nonspinning TF28Phasing. The latter is a symbolic transformation of checksum-pinned supl-mkaf16.m, not an independently authored numerical output. The original .m file is absent, but that does not make the transformed expression MIT work. Because no explicit downstream redistribution or MIT grant was found, the fixture now records its terms as unresolved and THIRD_PARTY_NOTICES.md excludes it from the repository's MIT claim.