IMRPhenomXPNR published components, version 1.0.0

Scope and status

This is a research component specification, not a qualified full IMRPhenomXPNR waveform. xpnr-published-components-sympy-1.0.0 independently encodes the published algebra as 37 executable SymPy expressions with mpmath evaluation. Components that require a transition spin, calibration value, boundary track, or carrier input accept it explicitly. The current public Torch/JAX waveform remains provisional; see the family ledger.

Inputs, conventions, and options

Frequencies f, f0, f1, and fc are dimensionless Mf; angles and spins are dimensionless. m1 >= m2, the spin vectors chi_i = S_i/m_i², and unit Lhat must refer to the same caller-supplied transition frame. eta, chi, c = cos(theta_LS), q, boundary values and derivatives, and ringdown parameters are explicit scalar inputs. f0 < f1, positive frequencies, and a nonzero base beta at the final-rescaling join are preconditions. The zero-spin map sets c=0 as a numerical extension because the published angle is undefined there. Piecewise derivatives mean derivatives within a branch; join checks use the appropriate one-sided limits.

The optional reference needs SymPy and mpmath. Native attachment kernels take Torch/JAX tensors, support float64 CPU values and autodiff, and do not import the reference. The tests exercise JAX JIT and vmap and Torch broadcasting. No inherited A/B/Bf tensor is an input to the independent test expectations.

Mathematics and components

Component ID	Pinned primary equations	Reference expressions	Native implementation	Status
XPNR-MAP/1	XPNR Eqs. 3–6	map.*	Existing Torch/JAX precession PNR map	Conditional on transition state
XPNR-FIT/1	XO4a Eq. 35; XPNR Eq. 22	calibration_polynomial, fit.eta_frozen, fit.chi_frozen	Existing PNR fit evaluators	Conditional on independently sourced coefficients
XPNR-MR/1	XO4a Eqs. 25–34; XPNR Eqs. 15–16	fit.a*, fit.b*, fit.beta_rd, angles.*	Existing PNR angle kernels	Algebra executable; fit assets conditional
XPNR-ATTACH/1	Final Twist Eqs. 41–45, 56–58, 62; XO4a Eq. 37 and denominator correction; XPNR Eqs. 17–21	attach.*	pnr_attachment.py in Torch/JAX	Algebra executable; full boundary construction pending
XPNR-CARRIER/1	XPNR Eqs. 7–8, 10–13	carrier.*	None for XPNR carrier modification/asymmetry	Conditional on u_k, calibrated carrier and asymmetry inputs
XPNR-HMMAP/1	XO4a Eqs. 50–52	higher_mode.frequency_map	Existing PNR higher-mode mapping	Executable component
XO4A-WINDOW/1	XO4a Eq. 38	window.endpoint_complete	Existing PNR window	Explicit endpoint-completing interpretation

The bound uses Final Twist Eq. 62 with p=0.002, algebraically evaluated as pi/2 + (beta-pi/2) [atan(t)/t]^p, where t = ((beta-pi/2)/(pi/2)^(1-p))^(1/p) and its center limit is beta. This even integer power form avoids a distribution term when differentiated symbolically. Native kernels use equivalent small/large forms to stay finite in float64. The public waveform still clips beta rather than calling this standalone bound.

Implementation mapping

The versioned specification is xpnr_symbolic.py. The independently written float64 scalar forms are xpnr_angles.py. Native attachment forms live in the Torch and JAX modules. The reference accepts caller-supplied carrier deviations and asymmetry amplitudes; neither native frontend composes the XHM-CP deviations, adjusted ringdown, or dominant-mode asymmetry into the public route. Endpoint-completing window behavior is an explicit interpretation of XO4a Eq. 38, not a literal copy of its printed trigonometric argument.

Evidence and limitations

The maintained symbolic test checks all 37 expressions against separately constructed scalar expectations, exact rational polynomial coefficients, four join values/slopes, and high precision derivative stability. Eleven isolated attachment kernels pass value and gradient comparison in Torch and JAX on CPU float64; JAX JIT/vmap and Torch batch behavior are also checked. On 2026-09-29, the focused XPNR suite passed 164 tests on len with SymPy 1.14.0, mpmath 1.3.0, Torch 2.14.0+cu130, JAX 0.11.2, and LALSuite 7.26.15. Four default-option LAL binary/PyCBC optimized plus-polarization comparisons passed their declared match >= 0.99 threshold over 20–400 Hz; they are diagnostics only.

The transition sampling event and complete SpinTaylor integration, beta input tracks and landmark/root decisions, 80-waveform fit targets and licensed tensor release, XHM-CP u_k mapping, and dominant-mode asymmetry remain unavailable from the examined public primary assets. The unchanged strict inherited XHM/XPHM binary catalog and holdout gates record failures. No DiffGW-to-NR physical comparison is claimed. Equation and native component passes do not qualify the public waveform.

Reproduce the checks

On len, from /tmp/diffgw-xpnr-qualification-332f, run:

PYTHONPATH=src JAX_ENABLE_X64=1 JAX_PLATFORMS=cpu OMP_NUM_THREADS=1 /tmp/diffgw-xpnr-portability-0172-pypi-clean/.venv/bin/python -m pytest -q tests/test_xpnr_symbolic_reference.py tests/test_xpnr_attachment_math_reference.py tests/test_xpnr_component_evidence.py tests/test_xpnr_attachment_gate.py tests/test_xpnr_coefficient_provenance.py tests/test_imrphenom_xpnr.py

The optional binary cases skip without LALSuite/PyCBC. The published expression version must change if an equation, branch convention, or input meaning changes; recheck the independent scalar expectations and both native frontends before updating the machine-readable qualification.