IMRPhenomHM N61 six-mode QNM off-grid receipt — 27 September 2026
The hm.qnm.n61.offgrid-six-mode/v1 specification
was evaluated for the n61_main clean-room refit, whose coefficient
payload SHA-256 is afcb21b634efacbc1ed0b44f24fda5df5ab08e236f3b7cbfdc7e71d3452d6525.
This is the explicitly hypothesized 61-node variant; it is not identified
with historical author training data or coefficients.
On len, the independent Cook--Zalutskiy solver generated 18 strict roots:
the six fundamental modes (2,2,0), (2,1,0), (3,3,0), (3,2,0), (4,4,0),
(4,3,0) at oriented remnant spins -0.71, 0.37, and 0.79. The minimum
distance to the hypothesized training grid is 0.00643 in spin. No native
fit coefficient or waveform function entered root generation. The solver
source SHA-256 is 36792fc5ad7201cfd5e4cac5221d48ca0db70f38b9d6fec4c3232caf60f84717;
the frozen roots
have SHA-256 febbad662efb5209691d3e26fa311eaf03d855510470019b2201d18b7761222a.
Every root reports the large-ell WKB/separation/spin continuation branch,
continued-fraction depth 1024, maximum estimated frequency error
1.54×10⁻¹⁵, and maximum angular truncation error 7.11×10⁻¹⁴.
The maximum |omega_N61 - omega_root|/|omega_root| across the three spins
for each mode was:
| Mode | Max complex relative error | Max real-part relative error | Max damping relative error |
|---|---|---|---|
| (2,2,0) | 0.000676 | 0.000637 | 0.001423 |
| (2,1,0) | 0.000810 | 0.000503 | 0.002661 |
| (3,3,0) | 0.000468 | 0.000448 | 0.001093 |
| (3,2,0) | 0.000163 | 0.000106 | 0.000739 |
| (4,4,0) | 0.000429 | 0.000412 | 0.001214 |
| (4,3,0) | 0.000106 | 0.000103 | 0.000546 |
All 18 points meet the predeclared 0.01 complex relative-error bound.
Torch and JAX returned identical FP64 fit values at these points to the
displayed precision (maximum complex relative difference 0 in this run).
The public IMRPhenomHM.mode_qnm_frequencies total-mass conversion passed
on all six modes in both frontends with supplied M_f=57.6, a=0.37, and
M_total=60. The supplied remnant state isolates the QNM adapter; it is not
a test of the remnant provider.
The CPU FP64 focused test on len passed 67/67 in 3.33 s:
cd /home/xangma/tmp/diffgw-hm-qnm-offgrid-20260927
env JAX_ENABLE_X64=1 JAX_PLATFORMS=cpu PYTHONPATH=src:tests OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 \
/home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python -m pytest -q \
tests/test_imrphenomhm_qnm_n61_offgrid_math_reference.py --reference-device=cpu -ra
The root-generation command was PYTHONPATH=src OMP_NUM_THREADS=1
OPENBLAS_NUM_THREADS=1 .../python -u
scripts/generate_hm_qnm_n61_offgrid_reference.py --output
tests/data/hm_qnm_n61_offgrid_roots.json; its job PID was 3328567 and
the complete log is hm_qnm_n61_roots.log in the same remote working
directory. It finished successfully before the focused test. Environment:
Python 3.12.3, NumPy 2.5.3, SciPy 1.18.1, Torch 2.14.0+cpu, JAX 0.11.2,
pytest 9.1.1. JAX used CpuDevice(id=0).
This receipt establishes selected off-grid QNM input agreement and Torch/JAX evaluation and scaling for the named N61 artifact. It does not establish historical London fit provenance, full-spin or near-extremal accuracy, remnant-fit accuracy, mode assembly, polarizations, or whole-waveform physical validity.