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XHM and XPHM qualification boundary, 2026-09-29

Supported scope

The published XHM v2 paper constructs aligned-spin (2,2), (2,1), (3,3), (3,2), and (4,4) carriers. It inherits the XAS (2,2) carrier; the spherical (3,2) ringdown couples to spheroidal (2,2) and (3,2) carriers. The published XPHM v2 paper twists those same five coprecessing carriers using per-mode stationary-phase angles at f22 = 2 f / m', Wigner rotations, and an observer polarization-basis map.

The paper-era XPHM precession options are NNLO 101–104 and MSA 220–224, with MSA 223 the published default. The native SpinTaylor 310/311/320/321 and PNR 300/330 routes are separately sourced extensions. The supported precession option, remnant, and convention tuples and exact native reductions are in the XPHM precession closure. The XP core is an inherited dependency and is not qualified here.

Public-code comparison, pinned by version and option

Public implementation Documented capability Native DiffGW gap measured here
LALSuite 7.26 / LALSimulation 6.2.1, binary distribution 7.26.15 on len XHM aligned-spin five-mode polarizations and individual modes; PhenomXHMReleaseVersion=122022 default, 122019 selectable. XPHM precession flags include NNLO 101–104, MSA 220–224 (default 223), SpinTaylor 310/311/320/321, and PNR-related 330; remnant and convention flags are separate options. The native ordinary intermediate-amplitude algebra is reference-checked for supplied targets, but a source-pinned 122022 calibration provider is absent. The four default-option frozen full-waveform cases below fail the installed LAL binary gate. Those failures do not establish outcomes for every non-default flag tuple.
PyCBC waveform documentation, installed 2.11.0 on len Exposes XHM and XPHM approximant names in frequency and time domain; its XPHM example selects (2,2), (2,1), (3,3), (3,2), and (4,4) through mode_array. Availability depends on the processing context. The native PyCBC-style interface names alone do not demonstrate numerical equivalence to the documented XHM/XPHM provider or its selected modes. The strict comparison targets installed LAL directly, so PyCBC presentation is not an independent equation oracle.
Bilby 2.8 example Selects waveform_approximant="IMRPhenomXPHM" through bilby.gw.source.lal_binary_black_hole. This documents an analysis interface to the LAL model, not a separate calibration source. No native Bilby workflow equivalence is claimed from the DiffGW model name.
ripple README at 58c5302 Its listed JAX waveforms include XAS, D, Pv2, TaylorF2 tides, and D_NRTidalv2; the list does not include XHM or XPHM. The native JAX helper here covers one XHM algebra branch; neither its JIT/gradient checks nor ripple's XAS support establish a qualified differentiable higher-mode model. The README list is a documented-scope observation, not a claim about every experimental ripple branch.

These interfaces and options must be compared as specific configurations. An approximant name shared by two backends is not evidence of numerical parity. The XHM paper and XPHM paper supply the paper-era equations; the LALSuite 7.26 documentation supplies the current public release and option semantics. The paper-era equations alone cannot certify the later 122022 amplitude calibration.

Source and release boundary

The author's arXiv:2001.10914v2 archive supplies paper-era amplitude, phase, QNM, and mixing files, but no authoritative manifest maps those assets to the installed default XHM release 122022. LALSuite 7.26 API documentation identifies 122022 as the default and 122019 as the older version; the newer version recalibrates higher-mode amplitudes without changing phase prescriptions. A changed spheroidal (3,2) amplitude can still change the mixed spherical (3,2) phase. The paper-era archive has no verified release-122022 fit-table redistribution grant or formula-to-file mapping. Its availability cannot justify translating it into the current provider.

The regional carrier audit locates the earliest measured binary mismatch in higher-mode inspiral amplitude. Existing source-derived references verify supplied-target carrier, phase, cuts, ringdown, mixing, projection, and XPHM rotation components in their stated domains. The new intermediate-amplitude gate closes the ordinary degree-five supplied-target algebra for Torch and JAX. These component claims do not qualify the fitted surfaces or the assembled waveform.

Current-branch verification and decision

The current raw strict binary receipt was produced from base commit 64e666165b043267caa5a513a4542c40dc6718e4 plus this family-scoped addition on host len with Python 3.12.3, LALSuite 7.26.15, LALSimulation 6.2.1, Torch 2.14.0+cu130, JAX 0.11.2, and NumPy 2.3.5. It invokes the frozen catalog and holdout cases through the public SimInspiralChooseFDWaveform binary API. Each polarization must satisfy complex relative L2 <=1e-6 and flat mismatch <=1e-8. The table gives complex L2 and mismatch for plus/cross; all are strict failures.

Case Plus: L2 / mismatch Cross: L2 / mismatch
XHM catalog 0.374023 / 0.063006 0.366201 / 0.060753
XPHM catalog 0.228818 / 0.025734 0.226417 / 0.025321
XHM holdout 0.546374 / 0.127476 0.462455 / 0.094623
XPHM holdout 0.504113 / 0.112109 0.556021 / 0.134134

The strict verdict is 0/4. The harness labels these rows SOVEREIGN_NR_CALIBRATED even when legacy_oracle_passed=false; that label is not a passed binary gate. The older 2026-09-25 receipt also failed 0/4. Its waveform base changed before this branch, so the older numeric errors cannot be attributed to the new helper or used as a paired regression measurement. The helper remains unconnected to the production waveform. These binary checks measure compatibility with the pinned public LAL binary. They are not an NR physical-accuracy test.

The receipt audit disproved two shortcuts: the harness status is not the strict verdict, and the older numeric errors are not a same-base regression reference. The next decisive check is a verified 122022 amplitude provider against the same frozen cases, with the first divergent mode and frequency region isolated before any full-waveform release claim.

The focused supplied-target and native family tests passed 94/94 on len (six XHM/XPHM test modules, including the new Torch/JAX/mpmath intermediate-amplitude reference tests). This verifies those components in their tested domains, not the assembled XHM/XPHM waveform or every public option tuple. No deployment or release qualification was performed.

Further release work needs an author-published, checksum-pinned 122022 calibration package, or independently reproducible calibration data and procedure, with versioned surfaces, transition cuts, veto order, spheroidal (3,2) inputs, mixing prescription, and reuse terms. The complete carrier must then pass the unchanged catalog and holdout binary gates, followed by physical NR holdouts. XPHM full-waveform release depends on that carrier and separate precession-domain validation. Until then both full models remain unqualified for release.