NRTidalv2 Pv2 positive-22 projection receipt — 27 September 2026

Result: The published supplied-mode positive-frequency (2,2) projection passed against an independent 80-digit scalar reference in both Torch and JAX CPU FP64. This qualifies the operator boundary only; it is not a native IMRPhenomPv2_NRTidalv2 waveform gate.

The frozen specification uses Pratten et al. (2020), Eqs. (11)–(13), (53), (93)–(94) for three nondegenerate angle sets and complex supplied modes. Both complex polarizations must agree to 1e-12 relative to maximum input-mode magnitude, without alignment or fitting. The pre-rotation identity P(H+D)=P(H)+P(D) has the same limit, and the chosen angles make direct addition of D to final polarizations observably wrong. The maintained test is tests/test_nrtidalv2_pv2_projection_math_reference.py.

Execution: host len, cwd /home/xangma/tmp/diffgw-nrtidalv2-pv2-projection-20260927, Linux CPU FP64, Python 3.12.3, Torch 2.14.0+cpu, JAX 0.11.2, pytest 9.1.1, mpmath 1.3.0. Read-only hostname, disk, environment, and process checks preceded the temporary checkout copy. The remote state-changing commands created this temporary directory and copied the isolated checkout into it; no package update was needed. After the final test assertion, the validation command was:

PYTHONPATH=src:tests JAX_ENABLE_X64=1 OMP_NUM_THREADS=1 \
/home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python -m pytest -q \
  tests/test_nrtidalv2_pv2_projection_math_reference.py \
  tests/test_nrtidalv2_pv2_aligned_additive_terms_math_reference.py \
  tests/test_precession_twisting_positive_clean.py \
  tests/test_phenompv2_sourceframe_clean.py \
  tests/test_phenompv2_waveform_clean.py

Final result: 36 passed, 1 skipped in 11.01 s. The skip is the pre-existing optional LAL/PyCBC test in the neighboring Pv2 suite. All jobs were foreground SSH commands and completed; no PID remains.

The catalog generator's --check currently fails on the already-tracked docs/math/imrphenomxhm-projection.md, whose four section headings do not match the required six-section outline. This new spec has all six sections; the unrelated page was not changed here.

The remaining block is concrete: native Pv2 has a BBH carrier/projector, but no IMRPhenomPv2_NRTidalv2 assembly that inserts the printed full self-spin and signed Eq. (24) amplitude into the correct supplied mode, then rotates it. The Eq. (24) absolute-to-mode normalization and the published-versus-binary angle/basis contract need independent qualification. The paper-D and historical binary-compatible variants remain separate and untouched; no LAL source or fitted correction was used.