XP/XPHM precession boundary qualification (2026-09-25)

2026-09-27 isolated XP version/remnant blocker control

A direct public-binary control on len used Python 3.12.3, NumPy 2.3.5, Torch 2.14.0+cpu, JAX 0.11.2, and LALSuite 7.26.15. All waveforms used IMRPhenomXP, convention 1, phic=0.3, phi0=0, distance 150 Mpc, an unshifted 0.25-Hz grid, and the same physical inputs for versions 102 and 223 and remnant modes 0 and 3. The equal-mass fixture is the 25/25-Msun two-spin case below (f_ref=20 Hz); the near-aligned fixture is the 36/22-Msun up-down case below (f_ref=40 Hz). The public LALSimulation binary API supplied only numerical output; no LAL source, coefficient, or calibration asset was copied. The frozen gates remain relative complex L2 1e-6 and flat mismatch 1e-8 per polarization.

Case and band	Native 223/0 vs binary 223/0 L2, plus / cross	Binary 223/0 vs binary 102/0 L2, plus / cross	Native 102/0 vs binary 102/0 L2, plus / cross
Equal mass, 20–512 Hz	0.029705677753180615 / 0.03589736628835022	0.031765223962125326 / 0.03869141740536079	0.0035442845453761617 / 0.004547643714867289
Near aligned, 25–55 Hz	0.023737179573462445 / 0.02373672163766733	0.023737302747141316 / 0.023736880404491217	2.965042067384981e-11 / 3.821943469355585e-11
Near aligned, 25–300 Hz	0.09654477245767022 / 0.09654736105223909	0.09654486477183226 / 0.09654748007284461	3.2265166254984385e-11 / 4.158838600878678e-11

Native version 223/mode 0 and version 102/mode 0 are bit-identical in each of these three cases: the native 223 path selected NNLO angles. At the near-aligned fixture, native 223/mode 3 is also bit-identical to native 102/mode 0. Changing the binary remnant from mode 0 to mode 3 changes the near-aligned full-waveform L2 by at most 2.16e-10 across the larger band; the failure is an angle-route discrepancy. The binary emits a waveform for the equal-mass 223/mode-3 request, while both native frontends explicitly reject its invalid nonaligned MSA averaged-remnant root. That domain-policy gap has no numerical native residual and remains a release failure.

The version-102 equal-mass residual is not specific to exact mass equality: changing the primary mass to 25.00001 Msun gives native/binary 102/mode-0 L2 0.0035434142280056907 / 0.004546745513710817; changing it to 35 Msun gives 0.04924902660620749 / 0.06218936180015843. Aligning only spin 2 at equal mass leaves 0.0036713638518117322 / 0.004648490188983955. For the near-aligned inputs, the same v102 route passes at approximately 3–4e-11. Thus this additional residual lies in a finite-precession NNLO full-waveform path, not the equal-mass MSA root or remnant selection. It has not been localized to a particular published NNLO coefficient or projection equation; no speculative correction is made.

Pratten et al., Sec. IV.1, Eqs. (17)–(22), and Sec. IV.2 distinguish the single-spin NNLO construction from two-spin MSA, identify singular equal-mass MSA couplings, and describe the NNLO angle fallback for unstable initialization. Chatziioannou et al., Appendix E notes the near-aligned root/PN conditioning and proposes a dedicated small-misalignment expansion as an improvement. The independent scalar cubic receipt in docs/waveforms/research/xp-v223-reference-closure.md finds the reference inverse-cosine endpoint only about 3.30e-37 from its limit for the near-aligned 1e-10 perturbation, far below float64 resolution. Gerosa et al., Sec. IV.2 give a regularized variable for a different precession formulation but leave a formal zero-amplitude resonance expansion to future work. These sources do not specify a complete v223 float64 root, phase, remnant, and waveform-chart continuation that would reproduce the pinned binary at these boundaries. The output cannot justify copying a hidden binary fallback or fitting a correction. The XP release verdict remains fail, with the frozen gates unchanged.

The unchanged scripts/qualify_xp_xphm_boundaries.py driver was rerun on len with PYTHONPATH=src, OPENBLAS_NUM_THREADS=1, and OMP_NUM_THREADS=1. Its public-binary rows reproduce the equal-mass mode-0 L2 above, pass both near-aligned v102 modes at at most 4.16e-11, fail both near-aligned v223 modes at 0.0237 (25–55 Hz) and 0.0965 (25–300 Hz), and pass generic nonzero-phi0 at at most 1.15e-13. The equal-mass mode-3 row records the explicit native domain rejection. The XPHM diagnostic and holdout remain SOVEREIGN_NR_CALIBRATED rather than qualified (0.226–0.556 per-polarization L2). The focused boundary, scalar-reference, and source-chart test modules passed 16/16 on len.

2026-09-26 generic nonzero-phi0 full-waveform closure

Pratten et al., Appendix C Eqs. (67)--(68), (76)--(85), Appendix B Eq. (63), Appendix E Eqs. (110)--(113), and Appendix F Table IV define the source observer azimuth, J-frame Euler and polarization geometry, quadrupole twist-up, and convention choices. From those published frames, we derive the public-binary coordinate map: rotate both in-plane input spins by Rz(-phi0), pass phiRef=phic to the binary, and multiply its completed quadrupole polarizations by exp(-2i phi0) for conventions 0/1/6. The rotation and completed-strain factor are our frame derivation, not equations quoted from the paper or coefficients obtained from LAL source.

The independent mpmath Appendix-C scalar chart and Torch/JAX full waveforms now check this covariance. On len with Python 3.12.3, NumPy 2.3.5, Torch 2.14.0+cpu, JAX 0.11.2, and public LALSuite 7.26.15, IMRPhenomXP, prec_version=223, convention=1, final_spin_mod=3, (m1,m2)=(35,25) Msun, spins (0.2,0.1,0.3) and (-0.1,0.05,-0.2), phic=0.3, phi0=0.4, and the direct unshifted 20--512 Hz grid at 0.25 Hz, the mapped binary comparison gives:

Convention	Plus/cross complex relative L2	Largest flat mismatch	Verdict
0	1.1410970098602045e-13 / 1.1213128890693516e-13	0	pass
1	1.1447907380982857e-13 / 1.1248152247989706e-13	0	pass
6	1.1343201250715765e-13 / 1.1143297006383575e-13	9.992007221626409e-16	pass

All pass the unchanged 1e-6 and 1e-8 gates. These measurements qualify this declared generic nonzero-azimuth fixture; they do not establish a wider precession-domain guarantee. The prior NOT_EVALUABLE statements below are historical and superseded by this derived-map check.

The overall XP/XPHM release verdict remains fail: the tested generic two-spin equal-mass mode-3 fixture has an unsupported MSA-remnant root, near-aligned v223 binary residuals remain above the frozen gate, and the XPHM full-waveform cases remain failing.

2026-09-26 independent source-frame transport gate

Pratten et al., Appendix C, Eqs. (67)--(83) define the source observer vector, the J frame, and its Euler/polarization angles. A new high-precision scalar reference, source_chart_transport in src/diffgw_reference/xp_msa_generic_boundary.py, evaluates the relative regular-chart transport at fixed intrinsic J. Equation (79) gives delta_alpha = alpha0(phiRef)-alpha0(0) and delta_gamma = -(phi_JL0(phiRef)-phi_JL0(0)), represented modulo 2*pi. The destination chart supplies theta_JN and zeta. Because J is fixed when only the observer azimuth changes, its regular-chart phi_JL0 is fixed and delta_gamma is zero. At exactly aligned J, phi_JL0 is undefined; the scalar reference rejects Euler transport instead of choosing a gauge.

tests/test_xp_source_chart_transport_math_reference.py compares this scalar chart and transport with Torch and JAX v223 geometry at four nonzero observer azimuths, including phic-phi0 = -0.1 and a phase-wrap case. The orbital-L value is supplied by the separately identified v223 compatibility expression; the test establishes the observer-frame transport, not independent provenance for that compatibility coefficient. On len, the new tests plus the existing source-frame/composition/generic-boundary reference files passed 26/26 with Torch 2.14.0+cpu, JAX 0.11.2, and pytest 9.1.1.

This result checked the internal source chart only. Its then-unresolved public-binary mapping and production-routing statements were superseded by the generic nonzero-phi0 closure above; frozen tolerances did not change.

2026-09-26 frozen angle-version control

Pratten et al., Appendix F, Tables III and V distinguish NNLO angle version 102 from MSA version 223 (with NNLO fallback when MSA initialization fails), and specify the remnant choice separately. At integrated PR #42 source head b4c6e0d, the qualification driver now evaluates both versions and remnant modes 0/3 at identical near-aligned physical inputs. It retains the prior v223/mode-3 case IDs. The public LALSimulation binary API remains a numerical oracle only; no implementation or coefficient is copied or fitted from it.

On len, Python 3.12.3, Torch 2.14.0+cpu, JAX 0.11.2, NumPy 2.3.5, SciPy 1.16.3, PyCBC 2.11.0, and LALSuite 7.26.15, the full complex polarization comparison gave the following. Each L2 cell is h+ / hx; mode-0 and mode-3 values are shown as ranges because they are nearly equal. The unchanged strict gates are complex relative L2 1e-6 and flat mismatch 1e-8 for each polarization.

Band (Hz)	Angle version	Modes 0/3 complex relative L2, h+ / hx	Largest mismatch	Strict verdict
25–55	102	1.87–2.97e-11 / 2.41–3.82e-11	2.22e-16	both pass
25–55	223	0.02373718 / 0.02373672	2.82e-4	both fail
25–300	102	1.87–3.23e-11 / 2.41–4.16e-11	1.11e-16	both pass
25–300	223	0.09654477 / 0.09654736	4.66e-3	both fail

This control shows that the public-binary disagreement is version-specific at these fixed inputs and is not removed by changing remnant mode. It does not establish which convention should define the physical aligned endpoint or justify changing production waveform equations. The existing test_xp_v223_azimuth_boundary_diagnostic.py and test_xp_aligned_boundary_clean.py encode those distinct contracts. These two test files passed 27/27 on len in 6.50 seconds in the isolated PyCBC environment. The shared validation environment was restored to NumPy 2.5.3 and SciPy 1.18.1 without PyCBC. At this angle-version control stage, generic observer phi0 remained not evaluable against the public binary. The frame-map derivation above supersedes that status. Overall release qualification remains fail.

2026-09-26 explicit-remnant policy amendment

The earlier receipt below combined the paper-prescribed NNLO angle fallback with an implicit change from final_spin_mod=3 to mode 0. That remnant substitution is superseded. The current public XP/XPHM policy keeps these two choices independent:

• The generic distinct-root MSA v223 angle route still falls back to the paper-sourced NNLO angles when MSA initialization is invalid.
• Explicit final_spin_mod=3 preserves the selected MSA remnant prescription. The distinct-root remnant rejects nonaligned equal-mass rows and other genuinely invalid roots rather than substituting mode 0. XP v223 conventions 0/1/6 retain their supported zero-nutation continuation when either body's in-plane spin vanishes, including at equal mass.
• Explicit final_spin_mod=0 remains finite and continuous across the tested equal/near-equal boundary and retains differentiability in both frontends. Machine-level transverse-spin degeneracies continue to use the analytic aligned remnant limit.

JAX eager calls to the remnant primitive and public XP evaluation raise ValueError. Public XP checks the selected remnant domain before entering lax.cond, preserving the eager exception and aligned JIT parity. Invalid JIT executions cross a compiled callback boundary and surface a jax.errors.JaxRuntimeError containing the same diagnostic. Selected scalar derivatives and valid batch values/JIT checks pass. Mixed JAX batches combining generic two-spin, aligned equal-mass and equal-mass one-spin rows can still yield NaN reverse-mode common-mass derivatives despite finite waveforms and finite finite-difference estimates. The aligned equal-mass scalar fixture also yields a NaN common-mass derivative. Both limitations reproduce before the remnant-domain correction; these fixtures do not inherit the passing scalar gradient checks.

On len, the focused policy suite (test_xp_msa_remnant_boundary_policy.py, test_jax_public_xp_generic_v223.py, and test_xp_msa_production_clean.py) passed 37/37 in 385.06 seconds with Torch 2.14.0+cpu, JAX/JAXlib 0.11.2, NumPy 2.5.3, SciPy 1.18.1, and pytest 9.1.1. It includes direct and compiled invalid-root checks, mode-0 boundary continuity, gradients, frontend parity, and valid batched JIT coverage.

This is a boundary-policy correction, not new external qualification. The strict full-complex-polarization gates are unchanged. The earlier equal-mass numerical row below was evaluated under the superseded implicit mode-0 substitution; it is historical evidence, not a current mode-3 residual. The overall release verdict remains fail.

Integrated-head rerun on len

The driver at this historical integrated head explicitly evaluated both equal-mass remnant choices. At integrated source head 2e654a3 (the later ccc3588 commit changed documentation only), Python 3.12.3, Torch 2.14.0+cpu, JAX 0.11.2, NumPy 2.5.3, and the installed LALSuite 7.26.15 produced:

XP equal-mass choice	Torch/JAX direct complex relative L2, plus / cross	Independent binary-oracle result
Default final_spin_mod=3	Both reject the invalid nonaligned MSA remnant root with the same diagnostic; public JAX surfaces it through JaxRuntimeError	Generation error; no numerical residual exists
Explicit final_spin_mod=0	1.9282897530721765e-14 / 1.9297675234635243e-14; both polarizations pass parity	Plus 0.02970567775318068 / 0.0004410058872005296; cross 0.035897366288350226 / 0.0006443233349125999 (L2 / mismatch); both fail

The same integrated run retains the near-aligned external relative L2 values 0.023737179603638348 and 0.09654477266816827 for plus, and the XPHM diagnostic/holdout plus values 0.22881790727328782 and 0.5041125739427325. Their strict external verdicts remain fail. Generic nonzero observer phi0 then lacked an independently derived public-binary parameter mapping, so its external comparison was not evaluable. The integrated-head focused policy suite passed 37/37 in 388.54 seconds.

Scope and evidence classes

This receipt audits draft PR #42 at 4814835f7744fe00a5863ed70eb590d41a7e3ac3 and qualifies only generic equal mass, generic nonzero observer phi0, near-aligned/instability routing, and the XPHM precession boundary. The unchanged strict full-complex-polarization gate is relative L2 1e-6 and flat mismatch 1e-8.

The PR's nine GitHub checks were green and its existing validation text correctly left these boundaries open. Those checks establish integration, not release qualification. The results below keep four evidence classes separate:

1. Math fidelity: paper-derived equations or the paper-prescribed NNLO fallback, without LAL source or fitted oracle coefficients.
2. Torch/JAX parity: direct, unshifted complex h+ and hx comparisons.
3. External validation: the installed LALSimulation public binary API used only as a numerical oracle.
4. Release qualification: all applicable classes must pass.

The independent run used host len, Python 3.12.3, NumPy 2.5.3, SciPy 1.18.1, Torch 2.14.0+cu130 (CPU forced), JAX/JAXlib 0.11.2 (CPU FP64), pytest 9.1.1, and the lalsuite distribution 7.26.15. The executable receipt is scripts/qualify_xp_xphm_boundaries.py.

The focused strict pytest run covered the public XP generic route, independent generic-boundary math reference, promoted near-aligned fallback gates, XPHM rotation reference, and clean-room XPHM NNLO composition: 67 passed in 496.14 seconds, with zero skips, xfails, or deselections.

Historical correction at the prior qualification head

The published generic MSA parameterization is singular at equal mass and its distinct-root solution is invalid when the initialization roots coalesce. The production adapters at that head reused the existing MSA initialization-validity result before selecting the clean distinct-root kernel. Invalid rows take the established NNLO angle fallback. Equal-mass generic rows also select the NNLO remnant because the MSA averaged-remnant expression shares the equal-mass singularity. The 2026-09-26 amendment above supersedes only that silent remnant-mode substitution. No continuation, new threshold, LAL-derived expression, or fitted coefficient is introduced.

Historical pre-amendment native residuals

Each cell is relative L2 / mismatch for (plus, cross) respectively.

Boundary	Torch vs JAX	Boundary behavior	Verdict
Generic equal mass	(4.5485282301920294e-14 / 0, 4.542345628206036e-14 / 0)	Torch vs forced NNLO fallback (0 / 0, 0 / 0); JAX vs fallback (3.09319461515901e-14 / 0, 3.088098683457194e-14 / 5.551115123125783e-16)	parity/fallback pass
Generic nonzero phi0	(2.1998567136506545e-14 / 0, 2.1580647978125144e-14 / 0)	Torch vs inherited route (0 / 0, 0 / 4.440892098500626e-16); JAX vs inherited route (1.224565931624615e-14 / 0, 1.2339688469043134e-14 / 0)	parity pass only
Near aligned, 25--55 Hz	(1.1928598420584253e-14 / 2.220446049250313e-16, 1.1931001987773128e-14 / 0)	tiny vs exact aligned (3.0602795845805276e-11 / 0, 3.9445611075509205e-11 / 2.220446049250313e-16)	parity/continuity pass
Near aligned, 25--300 Hz	(3.201086826590522e-14 / 0, 3.20117733545435e-14 / 0)	tiny vs exact aligned (3.370259364455347e-11 / 0, 4.344117178177736e-11 / 0)	parity/continuity pass

At the audited PR head, equal-mass Torch/JAX relative L2 was 0.15536521149740812 plus and 0.15342033548414735 cross. The near-aligned JAX output was nonfinite, while the Torch tiny-vs-aligned L2 was approximately 0.0245 before the instability and 0.13 across it. The correction removes those frontend and boundary discontinuities by selecting the declared fallback.

Historical pre-amendment independent full-waveform residuals

Boundary/case	Plus L2 / mismatch	Cross L2 / mismatch	External verdict
XP generic equal mass	0.09623529299354046 / 0.004632042422924254	0.09462201778421948 / 0.004478172581788398	fail
XP near aligned, 25--55 Hz	0.023737179603638348 / 0.0002817282964121537	0.02373672166784322 / 0.00028171783997021915	fail
XP near aligned, 25--300 Hz	0.09654477266816827 / 0.004660451020372602	0.09654736126273701 / 0.004660702227981206	fail
XPHM diagnostic	0.22881790727328782 / 0.025734053284783842	0.22641701045075546 / 0.025321404029660988	fail
XPHM holdout	0.5041125739427325 / 0.11210914391477245	0.5560212744607049 / 0.1341335900553805	fail

Generic nonzero observer phi0 is not externally evaluable: there is no independently derived mapping from this public diffGW parameter to the public LAL binary parameters. Native agreement therefore cannot promote it.

Historical boundary verdicts before frame-map closure

Boundary	Math fidelity	Torch/JAX	External	Release
Generic equal mass	mode 0 passes as explicit NNLO fallback; explicit mode 3 is an MSA-remnant domain error; no MSA continuation claimed	same policy/diagnostic across frontends	fail	fail
Generic nonzero phi0	source-frame transport remains unclosed	pass on inherited route	not evaluable	fail
Near aligned before instability	pass as invalid-root NNLO fallback	pass	fail	fail
Near aligned across instability	pass as invalid-root NNLO fallback	pass	fail	fail
XPHM precession layer	paper/scalar rotation gates pass	pass in focused composition tests	full waveform fails	fail

This table records the pre-closure state of the generic phi0 row. The current mapped-binary result above passes for its declared fixture. The overall release gate remains fail because the XP fallback boundaries and XPHM's XHM carrier dependency still disagree with the public binary.