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NRTidalv2 Pv2 public-assembly boundary

Scope and status

Specification nrtidalv2-pv2-public-assembly/v0 is a source audit and pending whole-waveform gate, not an executable waveform reference. It concerns positive-frequency, precessing IMRPhenomPv2_NRTidalv2 after the separately checked aligned BNS carrier and positive-22 projection. Neither Torch nor JAX currently dispatches that BNS approximant. This page freezes the unresolved choices rather than choosing them from a binary residual.

Inputs, conventions, and options

The proposed gate would use positive physical frequencies in Hz, component masses in solar masses, dimensionless six-component spins, nonnegative tidal deformabilities, distance in Mpc, inclination and coalescence phase in radians, and an explicit positive reference frequency in Hz. It would compare complex h_plus and h_cross in CPU FP64 without phase, time, polarization, or amplitude alignment. The inherited Pv2 note defines a J-aligned inertial frame at f_ref; its Eq. (6) sets the minimal-rotation angle derivative and its Sec. 5 fixes the observer/J chart. The native BBH drivers expose coalescence and reference_frequency carrier-phasing options. No published BNS rule examined here selects one, fixes the additive finite-size phase at f_ref, or specifies a merger-time convention for the composed BNS carrier.

Mathematics and components

Dietrich et al. (2019), Sec. III.4 instructs adding tidal corrections to the aligned point-particle model before applying the inherited Pv2 rotation. The aligned finite-size composition and supplied-angle projection are independently gated in the carrier and projection specifications. The Pv2 technical note, Eqs. (6), (13), (26), (31)–(36) defines the BBH frame/rotation, but does not prescribe a natural-cubic remnant-frequency phase slope for a BNS carrier. Dietrich's time and phase maximization in Eq. (31) is a validation overlap, not a generator origin.

Component ID/version Source equation or algorithm Variant Status Scalar reference Torch JAX Maintained check or blocker
nrtidalv2-pv2-aligned-carrier/v1 Dietrich Eqs. (17)–(29), Sec. III.4 Paper Pv2, supplied BBH carrier Conditional executable nrtidalv2_pv2_terms.assembled_carrier_from_bbh assemble_nrtidalv2_pv2_aligned_carrier Same named helper test_nrtidalv2_pv2_aligned_carrier_math_reference.py
nrtidalv2-pv2-public-angles/v0 Pv2 note Eqs. (6), (26), (31)–(36); Dietrich Sec. III.4 Paper-exact BNS angles Pending None BBH driver uses compatibility choices Same Longitudinal-spin and orbital-angular-momentum conflicts below
nrtidalv2-pv2-public-time-origin/v0 No BNS slope/interpolation or phase-origin algorithm in the cited papers BNS carrier at f_ref and merger Pending None Ten-node D-only slope in BBH driver Same Must select D-only or BNS-carrier slope, interpolation and sign
nrtidalv2-pv2-public-assembly/v0 Dietrich Sec. III.4; Pv2 note Eq. (13) Complete BNS polarizations Pending None No BNS dispatch No BNS dispatch Requires both pending contracts

The time-origin ambiguity changes the complex result. Let S' denote the derivative at f_RD of the native ten-node natural cubic. The existing BBH driver uses k_D = S'[psi_D] and multiplies its carrier by exp(i f k_D). If that same operation is instead applied to the BNS phase psi_D + psi_finite, linearity gives k_BNS - k_D = S'[psi_finite]; the two outputs differ by exp(i f S'[psi_finite]). Neither source fixes which operation, spline sample interval, or interpolation rule defines the BNS model. An overlap maximized over time cannot resolve this unaligned waveform contract.

Implementation mapping

The BBH Torch driver src/torchwave/approximants/phenompv2_waveform_clean.py and JAX driver src/jaxwave/approximants/phenompv2_waveform.py both sample the D-only phase at ten nodes on [0.8 f_RD, min(1.2 f_RD, 0.2/M)], differentiate a natural cubic at f_RD, and use a coalescence-phase D carrier by default. Their NNLO angle input is chi_eff / X_heavy; the Pv2 note Eq. (32) instead specifies the heavier body's aligned spin for those angles. The note Eq. (26) prints the 2PN orbital-angular-momentum coefficient 3.373 - 19 eta/8 - eta^2/24. The native coefficient is 27/8 - 19 eta/8 - eta^2/24, a mixed convention: the distinct Pratten et al. (2020), Eq. (27) prints 27/8 - 19 eta/8 + eta^2/24 for IMRPhenomXPHM. None of these three is silently designated the paper-exact Pv2_NRTidalv2 choice. The BBH compatibility driver and historical D default remain unchanged.

Evidence and limitations

This is a direct source/implementation audit, not a Torch/JAX numerical pass, binary comparison, or physical validation. The sources establish finite-size-before-rotation and the BBH source-frame geometry. They do not establish the D-only versus BNS slope, BNS phase/time origin, or a single angle coefficient matching the native drivers. A binary oracle may diagnose an explicitly supported IMRPhenomPv2_NRTidalv2 option, but must not supply missing mathematics by fitting a residual. The source-versus-Fig. 7 Love–Q and merger-frequency conflicts in the aligned-carrier spec remain separate.

The next qualifying step is to obtain a citable author equation/technical algorithm fixing the BNS slope and phase gauge, then name a paper-literal angle variant (including Eq. (32) and Eq. (26), or a justified correction). Freeze that variant, input chart, frequency support and strict unaligned complex tolerance before constructing a scalar reference and Torch/JAX gate. If only a binary-specific convention is available, label its gate as binary compatibility rather than published-math qualification.

Reproduce the checks

Read Dietrich Sec. III.4 and Eq. (31), Pv2 note Eqs. (6), (13), (26), (31)–(36), and Pratten Eq. (27) at the linked source revisions above. For native mapping, inspect _phase_time_shift, _L2, chil, and the carrier calls in the two driver paths named above. The executable conditional carrier/projection gates remain in their linked specs; no public BNS test is added by this source audit. A change to a source convention or origin requires versioning this pending spec before any numerical comparison.