Add conditioning diagnostics for multimode fits - #155
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Adds ringdown.conditioning with two utilities: - mode_gaps(modes, chi): pairwise distances between mode frequencies in the complex plane, dimensionless or in 1/s. - conditioning_report(modes, chi): per-pair error-amplification factors for three estimation tasks (amplitudes with fixed frequencies ~ 1/gap, free frequencies ~ 1/gap^2, amplitudes with free frequencies ~ 1/gap^3), sorted by gap, with the smallest-gap pair flagged. Includes tests anchored on the known (2,2,5)-(2,2,6) avoided crossing (gap 0.0667 at chi ~ 0.897). No existing file is changed.
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What this adds
A small module
ringdown.conditioningwith two utilities meant to be run before or alongside a fit:mode_gaps(modes, chi): pairwise distances between the mode frequencies of a fit model in the complex plane (dimensionless, or in 1/s when a mass is given).conditioning_report(modes, chi): for each mode pair, the gap and the error-amplification factors for three different estimation tasks, sorted by gap, with the smallest-gap pair flagged.The amplification exponents encode how hard each task gets as two modes approach each other:
Example numbers
The first line is one way to see, quantitatively, why overtone amplitudes with free frequencies are so fragile even for a loud event, and the second why nobody separates n = 5 from n = 6 near the crossing.
Where the exponents come from
The 1/gap scaling for fixed-frequency amplitudes was measured on SXS waveforms across the (2,2,5) and (2,2,6) avoided crossing, and the full task hierarchy (1, 2, 3) was measured in a controlled synthetic study; both live at https://github.com/maiconburn/recoverability-criticality (DOI 10.5281/zenodo.22156019). The 1/gap^2 frequency case matches the Fisher forecast scaling of arXiv:2605.16199, and the 1/gap^3 case matches the classical Prony-type super-resolution scaling. The exponents are stated up to mode-dependent prefactors, so the factors are most meaningful when compared between pairs or across spins.
Tests
Four tests included, anchored on the known (2,2,5)-(2,2,6) crossing (gap 0.0667 at chi about 0.897). On my machine
tests/test_conditioning.pyandtests/test_qnms.pypass together (21 tests); the data-dependent test files need the download scripts and were not touched.Happy to adjust naming, API, or placement, or to wire the report into Fit if that would be useful.