Newtonian eccentric EMRI source strain evidence — 2026-09-29
Executed environment and results
Host len (Linux), scratch cwd /home/xangma/diffgw-emri-scope-20260929, base checkout 64e6661 plus the scoped files in this commit, venv Python /home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python. Versions: PyTorch 2.14.0+cpu, JAX 0.11.2, SymPy 1.14.0, mpmath 1.3.0, NumPy 2.5.3, pytest 9.1.1. JAX x64 is enabled by the test module. Only CPU float64 results are reported.
| Check | Reproduction command after cd to the scratch cwd |
Observed result | Remote log |
|---|---|---|---|
| Paper-derived reference, both native frontends, and existing Peters flux | PYTHONPATH=src /home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python -m pytest -q tests/test_emri_newtonian_quadrupole_reference.py tests/test_emri_peters_flux_math_reference.py |
20 passed in 22.90s |
emri-focused-final.log |
| Legacy EMRI API and specialized EMRI parity | PYTHONPATH=src /home/xangma/.cache/diffgw-taylorf2-hm-venv/bin/python -m pytest -q tests/test_emri_kludge.py tests/parity/test_specialized_parity.py -k EMRI |
8 passed, 277 deselected in 10.67s |
emri-legacy-final.log |
The focused reference covers exact SymPy circular identities; mpmath source strain at e=0,0.2,0.55, fixed observer angles and sampled times; independent high-precision five-point derivatives in p0,e0,iota,gamma; Torch batch values; JAX batched jit; RK4 grid stability; and the Bessel truncation edge N=8,e=0.6,p0=12.1. Relative/absolute value tolerances are 3e-12/2e-34; derivative tolerances are 4e-10/1e-34. These are sampled implementation comparisons, not a uniform error certificate. The initial development run failed five checks because mp.diff drove perturbations beneath the fixed mpmath evaluator precision and a convergence-ratio assertion sampled a floating-point plateau. The independent gradient oracle was changed to an explicit high-precision five-point stencil, and the grid check now asserts stability at 1e-12; the final gates above passed.
Source and implementation provenance
src/diffgw_reference/emri_newtonian_quadrupole.py defines emri-newtonian-eccentric-quadrupole/v1 from Peters (1964), Eqs. (5.6)–(5.7) and Barack–Cutler (2004), Sec. III B, Eqs. (2)–(10), (27). Its symbolic flux dependency is the independent emri-peters-leading-flux/v1 reference. The reference uses SymPy expressions, mpmath Bessel evaluation, and high-precision fixed-grid RK4. Native Torch and JAX use their own tensor code and a 21-term integer Bessel series. Both native strains match this same finite Newtonian option at the sampled values. The common RK4 stepping choice leaves shared integration truncation error possible.
Public model comparison and open gates
FastEMRIWaveforms v2.1.1 exposes separate Schwarzschild eccentric flux, Kerr eccentric equatorial flux, and PN5 AAK waveform options; its trajectory guide describes their distinct inspiral equations. The diffgw definition checked here has Newtonian Peters flux, Kepler phase, finite quadrupole harmonics, and fixed source-frame observer projection. FEW's options have relativistic or higher-PN trajectory and amplitude choices, so this receipt makes no numerical FEW equivalence or same-model external-binary claim. No FEW code or output was used.
The generic Kerr/AK/NK orbit, precession, higher-order or self-force flux, all-harmonic amplitude, LISA/TDI response, longer inspiral accuracy, and JAX JIT runtime-domain rejection gates remain open. The older EMRIKludge still has only its leading flux component checked against a mathematical reference. Neither class is promoted to the public catalog by this receipt. No deployment or external publication was performed.