Standalone waveform family: provisional research ledger

This is a research specification, not a catalog definition or a whole-model verification claim. It records six non-SEOBNR standalone classes as found at foundation commit 5bc907d (2026-09-24). Five remain public; the complete TEOBResumS waveform has since been retired from releases, while scoped TEOB equation components remain. Its descriptions below are a historical code audit, not current usage instructions. The IDs are proposed component identities, not registered catalog IDs. Source locations and carrier behavior are deliberately separate. pending means the equation or convention has not been resolved; conditional means declared input or assets are required; executable means a stated independent scalar expression exists; diagnostic means a check or prototype that does not establish production mathematics. The CW quadrupole amplitude, conditional Kerr 220 carrier, angular projection, selected QNM inputs, dominant-22 memory, leading EMRI Peters flux, and ppE inspiral amplitude/phase and dispersion now have independent scalar references.

Scope and status

Class	Surface at the foundation snapshot and narrow scope	Qualification blocker
KerrRingdown	Torch/JAX time- and frequency-domain causal damped modes, default (2,2,0) with arbitrary unit coefficient; physical-energy option for one positive-m mode and its mirror. Main Torch/JAX waveform dispatch is narrower than the direct class API.	Extend the independently checked canonical physical-energy (2,2,0) case mode by mode; do not transfer it to arbitrary overtones, superpositions, or angular bases.
TEOBResumS	Torch/JAX frequency-domain prototype from an EOB trajectory. Default fixed-step diagnostic integration, leading quadrupole and merger taper. Torch only selects a separate clean vacuum route for scalar zero-spin, zero-tide inputs with matching_method="continuous" or integration_mode="clean".	Full published factorized modes, calibrated NQC, tidal/spin sectors, event and postmerger composition need separate references and tests.
ContinuousWave	Torch/JAX detector time series for a triaxial, principal-axis 2 f_rot carrier with a simplified Earth orbit/rotation model. Exported from approximants, but absent from the main waveform-name dispatcher.	Accurate barycentric timing and detector response, a stated epoch, and amplitude/phase convention checks. No F-statistic is implemented.
MemoryWaveform	Torch/JAX transform of supplied oscillatory strain into an accumulated memory correction; evaluate_22 accepts a physical h22 and explicit SI distance for a versioned dominant-pair direct-class slice. It does not generate the oscillatory carrier. Exported from approximants; absent from the main dispatcher.	General angular mode-pair coupling and all memory output modes remain pending; the legacy polarization-only path retains heuristic flux and scaling. Dominant-22 component derivation.
EMRIKludge	Torch/JAX short-time harmonic prototype plus optional LISA antenna projection. Exported at top level; absent from the main dispatcher. Its leading Peters p,e flux has a scoped scalar gate.	Generic orbital/geodesic evolution, published harmonics and a declared LISA response remain open. It is neither a Babak numerical kludge nor a fully relativistic EMRI waveform.
ParameterizedPostEinstein	Torch/JAX frequency-domain amplitude and phase multiplier around a supplied carrier (default IMRPhenomD). Exported at top level; absent from the main dispatcher. Its inspiral amplitude/phase, massive-graviton distance/phase and negative-phase adapter have scoped scalar gates.	Published merger/ringdown branches and physical fidelity of the selected carrier remain open.

The frozen legacy ledger reports KerrRingdown 1/1 only for the canonical physical-energy (2,2,0) waveform and TEOBResumS 0/1, with continuous NQC spline attachment described only at component level (provenance ledger). The current research page does not reinterpret those historical scores as new checks. The ppE amplitude/phase/dispersion specification records separate component-level scalar gates.

Inputs, conventions, and options

KerrRingdown

times are seconds, frequencies Hz, final_mass solar masses, dimensionless final_spin, t0 seconds, and sky angles radians. The frequency transform uses ∫h(t)e^{-2πift}dt; output is a real TD pair or complex FD pair. Each supplied positive-m (l,m,n) coefficient has an equatorial-symmetry mirror. The default angular basis is spherical; spheroidal evaluates the spin-weighted angular Teukolsky function. Cook–Zalutskiy Eqs. (47), (48b–c), (49) fix the angular phase and mirror reflection: both projected terms carry exp(+imφ), and the spheroidal projection reduces to the spherical one at zero spin. The default QNM backend is independent; an optional Berti fit exists. energy_fraction and amplitudes exclude each other; physical-energy normalization additionally needs distance in Mpc and the spheroidal basis. Without energy_fraction, unit amplitude is merely a coefficient, not a distance-calibrated strain. The mirror energy convention and onset derivative exclude the artificial step discontinuity. The generated QNM data asset is kerr_qnm_generated.py, SHA-256 82da71c19c50defeab4c32b6950141d845214909e9f52342e3f1cf3b46f08326, generated in-repo from Kerr eigenvalue equations under MIT terms; it is not a downloaded Cook table. The JAX angular eigensolver uses a pure differentiable inverse-iteration and Rayleigh quotient implementation without CPU callbacks, enabling native reverse-mode autodiff with respect to Kerr spin \(a\) and complex oblateness via jax.grad.

TEOBResumS

f is Hz; component masses are solar masses, aligned chi1/chi2 dimensionless, lambda1/lambda2 dimensionless tidal deformabilities, cq1/cq2 spin quadrupole coefficients, distance Mpc, angles radians, tc seconds. Outputs are complex FD polarizations. Default dt_geom=0.5, num_steps=1500, integration_mode="diagnostic_fixed", matching_method="diagnostic_fixed"; this duration is not a physical merger time. physical_event finds an orbital-frequency peak and uses a piecewise-linear Fourier integral, with different Torch and JAX peak localization. The Torch-only clean nonspinning vacuum route uses continuous attachment; its NQC spline and ringdown pieces must be qualified as a distinct variant. JAX accepts the matching/integration arguments but has no clean-route dispatch. f_lower defaults to the smallest positive requested frequency. Tidal fallback applies a heuristic merger taper (taper_width_ratio=0.1), not a calibrated postmerger. The source-to-code identity of several numerical fit coefficients remains to be audited; no external author fit asset is declared by this prototype.

ContinuousWave

The selected monochromatic H1 whole-class composition now has a separate versioned specification. This ledger continues to track the wider class and unresolved alternatives.

t and t0 are GPS seconds; f0 is GW Hz (twice rotation frequency), f1 Hz/s, f2 Hz/s², right ascension/declination and polarization/initial phase radians, cos_iota dimensionless. h0 is dimensionless strain; otherwise ellipticity, distance in meters, and default Izz=10^38 kg m² construct it. Output is detector strain, not a polarization pair. The orbit is a circular 1-AU approximation plus diurnal position, with no ephemeris, Einstein/Shapiro or binary timing correction. Both class wrappers now pass a nondefault i_zz to the ellipticity amplitude path. Time/phase origin and antenna conventions have direct detector-level verification only for the linked H1 monochromatic slice, whose v2 survey gate checks source precision rather than all inherited coordinate digits.

MemoryWaveform

times are seconds. Inputs are a dictionary of oscillatory complex modes or supplied h_plus,h_cross; the class wrapper accepts the latter only. A supplied distance is guessed to be Mpc below 10^15 and meters otherwise. If omitted, a small flux estimate triggers an assumed 100-Mpc scale. scale_factor is an unconstrained multiplier. These branches make physical units ambiguous. The helper uses a first-sample time spacing for derivatives and cumulative trapezoidal integration, and sets memory to zero at the first sample. h_cross^mem=0 and the angular pattern is sin² i; this is an l=2,m=0 truncation, not the full angular dependence. Torch uses .item() for branch decisions, limiting traced/compiled and derivative behavior. A reusable independent reference must require an explicit unit system and distance rather than reproducing the heuristic.

The new evaluate_22(times, h22, distance_m, inclination) path in both classes does require an explicit distance in meters. It assumes the symmetric negative-m mirror and uses the published dominant-pair formula, including the l=4,m=0 part of the full plus pattern. This method has no scale_factor calibration option. The older __call__/forward path remains a diagnostic proxy with the branch behavior described above.

EMRIKludge

The central and secondary masses are solar masses, p0 in central-mass units, eccentricity dimensionless, spin dimensionless, angles radians, t seconds and distance Mpc. n_harmonics=5 by default. The trajectory uses initial fluxes to form linear p(t),e(t) and clamps them; phases are rectangular cumulative sums on the first time spacing. The e argument to kerr_geodesic_frequencies does not affect its frequencies. The computed nodal phase is not included in the emitted n φ+2γ harmonic phase. project_to_lisa multiplies the polarizations by static A/E/T antenna patterns; that alone is not a demonstrated time-delay-interferometry transfer function. Differentiability at clamps and long-time validity are unresolved.

ParameterizedPostEinstein

f is Hz, masses solar masses, distance Mpc, lambda_g meters, redshift dimensionless, alpha_ppe dimensionless and a_ppe the paper's exponent of u=π𝓜f, beta_ppe dimensionless and b_ppe the native velocity exponent (default -2, paper exponent -2/3). The default carrier is IMRPhenomD, with other callable FD carriers accepted; source-level deformation is only as well qualified as the selected carrier. The helpers clamp nonpositive frequencies to 10^-15 Hz; the qualified physical domain is positive frequency. It multiplies both GR polarizations by (1+αu^a)exp[-i(δΨ_ppE+δΨ_disp)], the carrier's Fourier sign, whereas the paper writes exp(+iΨ) for its detector response. lambda_g=∞ zeros the dispersion term. An optional explicit d_alpha supplies D0 in meters; otherwise the native helper evaluates the published flat matter/Λ distance-integral ratio. Merger/ringdown ppE branches are absent.

Mathematics and components

Primary sources used here are Leaver 1985, Cook & Zalutskiy 2014, Berti, Cardoso & Will 2006, Ruiz et al. 2008, Nagar et al. 2018, Jaranowski, Królak & Schutz 1998, Favata 2010, Talbot et al. 2018, Barack & Cutler 2004, Babak et al. 2007, Peters & Mathews 1963, Peters 1964, Yunes & Pretorius 2009, and Mirshekari, Yunes & Will 2012. A paper citation identifies the proposed mathematical target, not proof that carrier code implements it.

Proposed component ID/version	Source equation or algorithm, and carrier variant	Status	Scalar reference	Torch/JAX carrier	Main gate
kerr.qnm.v0	Leaver/Cook radial-angular continued fractions; generated spline of complex Mω; optional Berti fit is a different option	selected 220 scalar check	kerr-220-qnm-scalar/v1, independent mpmath radial/angular solve	evaluate_qnm	Selected moderate spins and derivatives pass; other modes, near-extremal spins, and domain-wide interpolation remain open
kerr.angular.v0	Spin-weight -2 spherical/spheroidal harmonics and mirror projection	selected scalar check	kerr-angular-projection-scalar/v1, independent Wigner-d/quadrature	_ringdown_projection	Selected spherical/spheroidal values and angle derivatives pass; all modes and JAX spheroidal oblateness derivatives remain open
kerr.causal_poles.v0	Causal 220 mode/mirror projection and exact two-pole transform, u=t-t0	scoped conditional check	kerr-220-energy-carrier-conditional/v1 with mpmath quadrature	kerr220_td/kerr220_fd in Torch/JAX	Extend beyond 220 and independently verify QNM/angular inputs
kerr.energy.v0	Ruiz et al. Eq. (2.8), Berti et al. Eq. (3.18) coefficient mapping under stated convention	scoped conditional check	kerr-220-energy-carrier-conditional/v1 scalar finite-Q coefficient	ringdown_amplitude_from_energy_fraction and JAX counterpart	Other modes and excitation; FH doubled-time waveform is a different convention
teob.dynamics.v0	Nagar et al. EOB potentials/Hamiltonian and dissipative evolution; carrier mixes clean vacuum and spin/tide fallback	pending	pending	TEOBResumSHamiltonian, TEOBResumSRadiationReaction	Audit every fit/coefficient, initial conditions, flux, regularization
teob.attachment.v0	Nagar et al. Eq. (14) NQC factor and Eq. (15) timing; Appendix F postmerger; carrier continuous spline is a narrower component	pending	pending	Torch clean conditioned branch only; JAX absent	Reproduce calibration, modes, peak/event and postmerger joins
teob.prototype_fd.v0	Project adapter: RK4 finite horizon, leading h22∝ηv², fixed FFT or event transform, taper	diagnostic	pending diagnostic oracle	TEOBResumS.__call__ / JAX evaluate	Convergence and branch parity; never substitute for published TEOBResumS
cw.quadrupole_h0/v1	JKS v1 PDF Eqs. (23)–(24): 16π²G I ε f_rot²/(c⁴d)=4π²G I ε f0²/(c⁴d)	scoped scalar check	diffgw_reference.continuous_wave_quadrupole	continuous_wave_h0 and class wrappers	SI benchmark, frequency derivative, inertia propagation; detector response remains separate
cw.phase_response.paper/v1	JKS v1 PDF Eqs. (1)–(6), (10)–(14), (18)–(22): arm response, geometric delay, first-order Roemer phase and 2f_rot projection	scoped conditional scalar; three source-variant diagnostics remain strict xfails	diffgw_reference.continuous_wave_phase_response	continuous_wave_phase, continuous_wave_basis, continuous_wave_strain	Native H1 arms match Anderson 2001 Table I print precision and tensor response passes for Torch/JAX; JKS Table 1 geometry, paper-truncated spin-down identity and physical epoch remain open
memory.mode_coupling.v0	Talbot et al. Eqs. (1)–(9): time integral of mode-pair derivative products with angular Γ kernel	pending	pending general mode-coupling quadrature	compute_memory_h20 is not equivalent	Restore coupling and all required memory modes
memory.dominant_22/v1	Favata v1 Sec. 6.2 Eq. (21), consistent with Talbot v2 Eqs. (1)–(9): symmetric ±22 pair and full angular projection	executable, scoped	memory_dominant_22 mpmath projection and exact linear-mode value/derivative	compute_memory_h20_22, memory_polarizations_22, MemoryWaveform.evaluate_22	Explicit SI distance, both frontends, full projection, nonuniform grid; no general-mode claim
memory.carrier_h20.v0	Carrier h20=(1/√6)∫Σ|ḣ_lm|²dt plus heuristic unit branches	diagnostic	strict expected-failure comparison to the published ±22 coefficient	compute_memory_h20	Multimode discrepancies remain unquantified
memory.projection.v0	_{-2}Y_{20}=√(15/32π) sin²i; Favata Eq. (21) dominant-22 full pattern adds (17+cos²i)	diagnostic truncation	harmonic projection checked for dominant ±22 only	memory_polarizations	Legacy projection lacks the l=4,m=0 contribution; use memory_polarizations_22 for the scoped full pattern
emri.orbit.v0	Barack–Cutler analytic kludge evolution versus Babak et al. numerical geodesic kludge	pending	pending chosen AK/NK equations	kerr_geodesic_frequencies, orbital_trajectory	Choose one model, recover eccentricity and orbital-plane dynamics
emri.flux.peters_leading.v1	Peters 1964 Eqs. (5.6)-(5.7), exact semimajor-axis to p conversion	scoped executable	emri-peters-leading-flux/v1	peters_mathews_radiation_reaction	CPU float64 value/derivative evidence only; frozen-rate trajectory remains unqualified
emri.harmonics.v0	Published eccentric harmonics use Bessel coefficients; carrier uses hand-set e powers	diagnostic	pending literal diagnostic only	polarizations	Replace or explicitly bound harmonic truncation and angular response
emri.lisa.v0	Detector response/TDI needs a specified transfer convention	pending	pending	project_to_lisa	Independent A/E/T time-delay response and sky-frame tests
ppe.inspiral.phase/v1	Yunes–Pretorius Eq. (1): u=π𝓜 f, δΨ=βu^b; native b_ppe=3b	scoped scalar check	ppe-phase-dispersion/v1, paper-literal chirp-mass scalar	ppe_phase_shift uses chirp-mass v=(π𝓜 f)^{1/3}	Positive-frequency value and derivative in Torch/JAX; merger branch remains open
ppe.inspiral.amplitude/v1	Yunes–Pretorius v2 Eqs. (1), (47): signed 1+α(π𝓜 f)^a	scoped scalar check	ppe-inspiral-amplitude/v1, 70-digit scalar	ppe_amplitude_factor in Torch/JAX	Positive-frequency value and four derivatives; paper response mapped conditionally to two carrier polarizations
ppe.dispersion.massive_graviton/v1	Mirshekari et al. Eqs. (14)–(16), (28)–(31): cosmological D0, δΨ=-πD0c/[λ_g²(1+z)f], separate Lorentz-violating term zero	scoped scalar check	ppe-phase-dispersion/v1, independent mpmath integral	modified_dispersion_phase_shift	Flat matter/Λ, supplied D_L,z, explicit D0, value/derivative in Torch/JAX; other dispersion terms/cosmologies open
ppe.wrapper.carrier/v1	Project adapter h̃_{+,×}=h̃^GR_{+,×}e^{-i(δΨ_ppE+δΨ_disp)} in negative-phase carrier convention	scoped conditional check	ppe-phase-dispersion/v1 scalar multiplier	ParameterizedPostEinstein.forward	Both polarizations, stub carrier, explicit D0; real carrier and broad-band physical fidelity open
ppe.wrapper.carrier/v2	Project adapter h̃_{+,×}=h̃^GR_{+,×}(1+αu^a)e^{-i(δΨ_ppE+δΨ_disp)}; amplitude signed, phase convention reversed	scoped conditional check	ppe-inspiral-amplitude/v1 composed with phase scalar	ParameterizedPostEinstein.forward	Batched two-polarization stub; applied across caller grid although source amplitude is inspiral-only
ppe.wrapper.taylorf2_inspiral/v1	Yunes–Pretorius v2 Eq. (1), inspiral branch below f_IM, composed with the project's negative-phase TaylorF2 carrier	scoped ratio gate; len CPU FP64 passed	real-carrier ratio and derivative grid	Torch/JAX ParameterizedPostEinstein(TaylorF2())	Equal-mass nonspinning four-bin inspiral ratio only; cancels carrier and does not qualify absolute TaylorF2 or merger/ringdown

The Kerr 220 carrier checks condition on supplied QNM and angular inputs. conditional alone does not imply validation of other rows.

Implementation mapping

The native files are torchwave/approximants and jaxwave/approximants, with matching basenames kerr_ringdown.py, teobresums.py, continuous_wave.py, memory.py, emri_kludge.py, and ppe.py. Kerr energy has an additional Torch file kerr_ringdown_energy.py; JAX defines its counterpart inside kerr_ringdown.py. The independent CW scalar references are src/diffgw_reference/continuous_wave_quadrupole.py and src/diffgw_reference/continuous_wave_phase_response.py; the Kerr 220 carrier, angular projection, and selected QNM input references are src/diffgw_reference/kerr_ringdown.py, src/diffgw_reference/kerr_angular.py, and src/diffgw_reference/kerr_qnm.py. Memory, EMRI-flux, and ppE references are src/diffgw_reference/memory_dominant_22.py, src/diffgw_reference/emri_peters_flux.py, and src/diffgw_reference/ppe.py. Current in-carrier helpers named *_reference for Kerr are useful checks but are not independent scalar references.

At the foundation snapshot, the Torch and JAX main dispatchers exposed KerrRingdown and TEOBResumS. TEOBResumS has since been removed from release dispatch; the other four are direct imports from approximants. Torch top level exports EMRIKludge and ParameterizedPostEinstein, while JAX top level exports all four. These are API observations, not catalog statements. The current dispatcher enforces a Kerr physical-energy (2,2,0) scope that is narrower than direct class calls.

For Kerr, compare native QNM interpolation and spherical/spheroidal projections to independently evaluated radial-angular solutions and scalar harmonics. Its FD poles must be checked against a quadrature of the real causal TD polarization, including both poles and the t0 factor. For TEOB, split Torch's vacuum conditioned EOB mathematics from the shared fallback prototype before any shared model identity; JAX physical_event uses a grid maximum while Torch refines a bracketed maximum. For CW, use an SI amplitude scalar and a separate barycentric detector geometry; do not adopt the circular-orbit shortcut as source truth. For memory, implement Talbot's angular kernel directly from spherical-harmonic quadrature, then add oscillatory strain. For EMRI, choose and implement a published AK or NK branch from primary equations. For ppE, the independent scalar reference keeps paper-literal chirp-mass amplitude/phase and cosmological D0 equations separate from the negative-phase carrier adapter.

Evidence and limitations

The CW amplitude slice has a scalar-to-Torch/JAX CPU float64 value and frequency-derivative test, plus a class-wrapper inertia propagation check. On len, 32 focused CW reference/parity cases and the four existing CW tests passed with Torch 2.14.0+cpu, JAX 0.11.2 and mpmath 1.3.0. Three nonzero amplitude/derivative holdouts use relative tolerance 1e-13; JKS v1 PDF Eq. (25)'s rounded 100-Hz rotation benchmark gives 4.22855608095e-25 against its quoted 4.23e-25. This is a quadrupole amplitude component claim only.

The phase/response scalar checks the paper's ideal beam geometry, the monochromatic 2f phase and frequency gradient after explicitly setting the native circular orbit phase to zero at t0, and the 2f projection conditioned on native phase and antenna inputs. An independent JKS PDF Eqs. (1)–(6) arm-tensor calculation agrees with the closed beam formula of Eqs. (10)–(13) for three JKS site-angle/sky cases. For H1 it checks that both frontends' ECEF arms round to the official four-decimal arm vectors in Anderson et al. 2001, Appendix B Table I, and agrees with native Torch/JAX beam values to absolute 2e-15 at three sky/time/polarization holdouts per frontend, conditioned on each frontend's GMST. This is a required green detector-algebra gate at the source's printed geometry precision; it does not independently verify GMST or sub-print survey digits. On len with Torch 2.14.0+cpu, JAX 0.11.2, mpmath 1.3.0, and float64 CPU inputs, the scoped CW suite had 49 passed, 254 deselected and 3 strict expected failures.

The dominant-22 memory component independently projects Favata's full angular pattern onto h20, then checks explicit-SI Torch/JAX values and amplitude/inclination derivatives at four inclinations on a nonuniform grid. On len with CPU float64, Torch 2.14.0+cpu, JAX 0.11.2, and mpmath 1.3.0, the initial combined focused run returned 5 passed, 1 strict expected failure at relative 5e-13 (absolute strain 1e-35). The separately selected strict expected failure is the old 1/√6 coefficient compared with the published symmetric ±22 coefficient. This is a scoped component gate, not general memory coupling or qualification of the polarization-only class call.

Three strict expected failures remain as source-variant diagnostics. At dt=43200 s, f1=2×10⁻¹⁰ Hz/s, f2=-10⁻¹⁵ Hz/s², and τ=219.0772992826719 s, the carrier's extra terms give a +2.363134163530285×10⁻⁵ rad residual against the paper-truncated phase. At GPS 1126259462, ra=1.1, dec=-0.3, psi=0.27, native H1 F+, F× differ from historical JKS Table 1 by -0.00753319, -0.00306511 when both use native GMST; the Table 1 diagnostic fails in both frontends at absolute 5×10⁻⁴. JKS Table 1 cites Allen 1996 for its site angles; Anderson Appendix B explicitly corrects the LIGO arm orientations in Allen and prints the vectors used by the native model. Thus those two historical-site failures are not antenna-algebra failures for the corrected vectors. PDF Appendix A Eq. (125) uses an SSB-arrival-time polynomial; Eqs. (130)–(131) truncate its delay expansion under the paper's quarter-cycle criterion and Eq. (14) is the corresponding first-order form. Native uses a simplified untruncated polynomial in dt+τ. Its additional τ² and τ³ terms should not be removed merely to match the truncated paper formula.

The paper's t=0 is an SSB reference epoch; its orbital φ_o and local sidereal φ_r must be supplied. Native t0 instead zeros orbital phase at that GPS epoch, and native GMST approximates UT1 by UTC. Native detector=None also uses H1 antenna patterns while omitting H1's diurnal phase delay. A physical GPS-to-SSB epoch and ephemeris test remains open. The Kerr 220 carrier, angular projection, selected QNM input, dominant-22 memory, leading EMRI Peters flux, and ppE phase/dispersion specifications record their separate scalar checks. Other rows remain research audits unless separate evidence says otherwise. No component here is promoted into the public WaveformDefinition catalog.

Source conventions and unresolved limits before qualification:

1. In the authoritative JKS gr-qc/9804014v1 PDF, detector response is Eqs. (1)–(6) and (10)–(13), first-order phase is Eq. (14), geometric delay Eq. (18), the two signal harmonics Eqs. (19)–(22), CW amplitude Eq. (23), ellipticity Eq. (24), and the numerical example Eq. (25). The arXiv HTML conversion shifts equation numbering; use the v1 PDF numbers. Using GW frequency requires f0=2f_rot; the f_rot free-precession branch is outside this principal-axis carrier. JKS Appendix A Eqs. (125), (130)–(131) explain why Eq. (14) omits higher delay powers. The native polynomial in dt+τ adds 2π[f1 τ²/2+f2 dt τ²/2+f2 τ³/6], so exact Eq. (14) identity remains a failed diagnostic. JKS Table 1 cites Allen 1996 as [25], while Anderson et al. 2001 Appendix B Table I explicitly corrects its LIGO arm orientations; native H1 arms match the latter at four-decimal precision, and independent arm-tensor response passes. The historical JKS Table 1 diagnostic remains failed without altering detector geometry.
2. The legacy memory carrier's 1/√6 sum is not Talbot's mode-pair Γ contraction. Favata Eq. (21)'s dominant-mode angular pattern is sin²i(17+cos²i), rather than the carrier's lone sin²i. Its distance inference also changes units based on sample magnitude. The separately named evaluate_22 slice fixes these issues only for a supplied symmetric ±22 pair with explicit distance; it does not accept a polarization-only input as a published memory source.
3. The EMRI provisional specification derives p=A(1-e²) from Peters 1964 Eqs. (5.6)–(5.7); the resulting de/dt coefficient is 304/15, correcting the former 604/48 in both carriers. This qualifies only leading secular flux. The frequency helper's e has no effect, and initial-rate linear evolution is neither Barack–Cutler AK nor Babak et al. NK. The former carrier citation to arXiv:2008.06071 had the wrong title and is not a mathematical source for this implementation.
4. The ppE helper formerly replaced Yunes–Pretorius' chirp-mass u=π𝓜 f with total mass; the dispersion helper formerly used D_L/(1+z) as D0 and retained an extra π after substituting u. These are corrected against the source equations in the scoped ppE component, with a retained native b_ppe=3b exponent mapping. The papers' positive Fourier-phase sign and the native carrier's negative sign remain distinct; amplitude and merger/ringdown branches remain absent. A phase overlay on IMRPhenomD at all frequencies must not be presented as the paper's complete ppE waveform.
5. TEOB's prototype h22, fixed horizon, taper and FFT do not establish Nagar et al.'s calibrated multimode/NQC/postmerger waveform. A separately checked natural cubic spline peak finder alone does not qualify the full composition.

The next independent evidence should record exact variant, parameter/domain range, float precision and device, value and derivative metrics, tolerance, negative/failed examples, and source/asset hashes. Compare Torch and JAX independently to that scalar source, then to each other; keep same-model external comparison and physical validation separate. Continue Kerr beyond the selected 220 QNM and angular inputs to other modes, overtones, and excitation physics. Every remaining whole-model claim needs its missing source-convention, component, and waveform-level gates.

Reproduce the checks

The original static audit can be repeated from foundation 5bc907d with rg -n '^def |^class ' src/{torchwave,jaxwave}/approximants/{kerr_ringdown,teobresums,continuous_wave,memory,emri_kludge,ppe}.py and direct inspection of the listed papers. The scoped CW check is PYTHONPATH=src:tests python -m pytest -q tests/test_continuous_wave_quadrupole_reference.py tests/test_continuous_wave_phase_response_reference.py tests/test_continuous_wave.py tests/parity/test_specialized_parity.py -k continuous_wave; run the two reference files without -k to include the scalar source and strict expected-failure gates. Future independent references should live under src/diffgw_reference with versioned component IDs and maintained paper-to-scalar, scalar-to-native, gradient, and backend checks. A changed equation, sign, branch, fit, or asset requires a component version increment, regenerated fixtures/docs where applicable, and review of the previous claim's exact scope before catalog publication.

The focused memory gate is PYTHONPATH=src python -m pytest -q tests/test_memory_dominant_22_math_reference.py; select the legacy strict expected failure separately with tests/test_memory_diagnostic.py. The six-section component specification gives the exact domain, source equations, gate parameters, and limitations.