Waveform Fidelity as an Epistemic Threshold: How Gravitational-Wave Catalog Completeness, Orbital Eccentricity Recovery, and Memory Detection Converge on a Common Measurement-Theoretic Limit

Version 2 — revised in response to an external structural review and an automated critique pass. See "Response to Review" appendix in the PDF for the change log.

The LIGO-Virgo-KAGRA collaboration has now cataloged over 300 compact binary coalescence events through GWTC-5.0, and the community simultaneously grapples with three interlocking inferential challenges: (1) recovering orbital eccentricity without systematic bias, (2) detecting nonlinear gravitational-wave memory at population scale, and (3) characterizing waveform-model systematics that propagate through every downstream astrophysical inference. This paper argues—as a heuristic reading, not a derivation—that these three challenges share a common measurement-theoretic structure: each is governed by a *signal-representation threshold*, below which the waveform model's internal approximations dominate over the physical signal. We synthesize six specific findings from recent gr-qc preprints to articulate this pattern. The SEOBNRv6EHM model (gr-qc) achieves below-or-near-2% mismatch for eccentricities up to ~0.9 across 20–200 solar masses, demonstrating that model fidelity gates eccentricity recovery. GWTC-5.0 reports 150 new candidates including the first network SNR > 70 event GW250114_082203, enabling high-fidelity tests that were previously SNR-limited. Hierarchical Bayesian inference on memory constrains the memory enhancement factor to 0.32 (+6.30/−5.12), showing that the measurement remains prior-dominated at current catalog size. Gravitational-wave parameter estimation for rotating core-collapse supernovae identifies a Cramér-Rao lower bound below 10⁻¹ for the rotational energy ratio β (specifically when β decreases with distance), quantifying the information-theoretic floor for that signal class under a specific analytical model. Across these findings, the falsification path is concrete: if waveform mismatches are reduced below ~0.5% for the full eccentricity-spin-mass parameter space, the memory enhancement factor's posterior should narrow substantially before 2,000 cumulative detections, and eccentricity Bayes factors for the five candidate eccentric events in GWTC should shift decisively. We also flag one weakly-connected source (vector-vortex light transitions in gravitational waves) as a speculative addendum rather than a load-bearing element of the thesis. ---

Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename.

Cited arXiv preprints: 2605.27223, 2605.27224, 2605.27225, 2605.27500, 2605.28715, 2605.28716, 2605.28953, 2605.29519, 2605.30446, 2605.30665