SpinTaylor whole-waveform residual diagnosis (2026-09-29)
Status: The direct complex whole-waveform comparison still fails. This read-only qualification identifies separate carrier and angle-evolution differences, but does not establish a unique paper-supported production patch. No LAL or other implementation source, private DCC note, or source-exposed SpinTaylor commit was consulted.
Historical diagnostic setup
The historical whole-waveform and angle-evolution probes ran with
PYTHONPATH=src in the len PyCBC environment. The waveform probe
compared carrier isolation, individual modes, mode sums, and constant
alpha shifts. Their one-off replay scripts are not maintained. Host:
len; checkout:
/tmp/diffgw-spintaylor-cleanroom-20260929; Python:
/home/xangma/venv-pycbc/bin/python; binary versions: lal 7.4.1,
lalsimulation 5.3.1, Torch 2.13.0+cu130. Inputs are (m1,m2)=(36,29)
Msun, spins (0.3,0.2,-0.1) and (0.1,-0.2,0.2), inclination 0.6,
distance 100 Mpc, f_ref=37.3 Hz, df=0.25 Hz, and 20–300 Hz. The LAL
XPHM binary uses precession version 320 and final-spin setting 2. All
comparisons use the same positive-frequency bins and complex plus/cross
polarizations.
Decisive waveform comparisons
Relative L2 errors below normalize by the LAL waveform norm. The fitted column maximizes complex correlation over time and constant complex scale; it is a diagnostic, not the direct fidelity gate.
| Comparison | Plus raw | Cross raw | Plus fitted | Cross fitted |
|---|---|---|---|---|
| XHM aligned, all modes | 0.164208 | 0.144298 | 0.163814 | 0.144242 |
| XHM aligned, (2,2) only | 0.009737 | 0.009718 | 0.003284 | 0.003284 |
| XPHM full precession, all modes | 0.253636 | 0.255445 | 0.059416 | 0.060229 |
| XPHM full precession, (2,2) only | 0.248621 | 0.249230 | 0.043954 | 0.043049 |
The aligned (2,2) carrier is close to its binary counterpart. The aligned
all-mode discrepancy is already substantial without precession. With a
single LAL mode-array activation, native aligned (2,1) amplitude differs
from LAL by a relative L2 of 10.696; its strain norm is 0.144 of native
plus versus 0.0131 of LAL plus. The other higher modes also differ.
Single-mode LAL outputs sum to the all-mode plus within 0.0086 relative L2
over the analysis band; native single-mode outputs sum to numerical precision.
This supports a carrier higher-mode contribution without claiming that
single-mode isolation is an exact internal decomposition of the LAL binary.
For the full XPHM waveform, the raw plus error is 0.0253 at 20–60 Hz,
0.3056 at 60–150 Hz, and 0.9848 at 150–300 Hz. The corresponding fitted
errors are 0.0175, 0.0711, and 0.1458. Removing the native higher modes
does not remove the ~25% raw precessing residual, so the aligned carrier
discrepancy is not its sole cause. Fitting time and phase lowers the full-band
error to ~6%, but the direct waveform gate remains failed.
Binary angle output and convention boundary
The public binary function SimIMRPhenomXPSpinTaylorAngles returns three
length-1121 vectors. Their values at the reference and across frequency
identify them as (alpha, cos(beta), gamma); the API docstring does not name
the vector fields. LAL returns the same alpha for conventions 0 and 1, near
zero at 37.25 Hz, while its gamma changes by about 2.95149 radians. The
native convention-1 alpha at that bin is 1.56751; native convention 0 is
-0.00689. This is a representation comparison, not proof that the
angle API returns precisely the angles used by LAL's waveform twist-up.
After removing each series' constant value at 37.25 Hz, the maximum
native–binary difference through 60 Hz is 0.1641 rad in alpha and
0.1791 rad in gamma. The maximum beta difference is 0.0304 rad.
For example, at 60 Hz LAL has alpha=1.57286 and cos(beta)=0.989286,
whereas native convention 1 has alpha=3.31032 and
cos(beta)=0.984530. These varying differences occur below the native
transition at approximately 66.98 Hz; a merger–ringdown continuation
alone cannot explain them. They do not isolate a particular RHS coefficient
from the integration method or frame conversion.
An exploratory change subtracting the 1.574396 rad XP geometric alpha
offset from native convention 1, without changing other angles or frames,
worsened the all-mode raw plus/cross errors to 1.9705/1.9662.
Therefore the standalone API's alpha offset cannot be transplanted into
native twist-up as a correction. Pratten et al., Appendix F Table IV
assigns convention 1 the PhenomPv2 alpha offset, but does not publish its
formula; Appendix C Eq. (C16) gives the distinct XP geometric offset.
Public-equation limit
Colleoni et al., §II.B, Eqs. (2.24)–(2.25)
specify that SpinTaylor alpha and beta enter merger–ringdown with inverse
frequency continuations, beta including an exponential damping factor and a
limit of 0 or pi. They attach at 0.97 f_PN,max, with f_PN,max determined
by the PN integration stop. The native calculation instead attaches at
0.98 f_MECO and holds beta constant. The LAL binary's cos(beta) rises
from 0.985562 at 150 Hz to 0.994995 at 300 Hz; native stays at
0.982350. This is a clear published-shape discrepancy above transition.
The paper does not provide the additional inspiral collocation frequency, the exact PN stop/integrator settings, or a complete normalization for the damping factor. It also describes revised coprecessing amplitude fits without publishing every calibrated coefficient needed to reconstruct the binary carrier. The Pratten twist-up equations, Eqs. (3.5)–(3.7) support the native twist-up signs and polarization rotation as written; these were not changed. No unique binary-faithful update to the reference gauge, RHS evolution, transition, or carrier follows from the allowed public material and these probes. The whole-waveform fidelity gate remains open.