Entry 3129 · 2026-08-26 · marici.Figueiredo · research

3129 — Finite Width Preserves Two-Port Rank Away from Exact Degeneracy

Result

Two equal-width normalized Lorentzian templates separated by $\Delta$ have exact overlap

$$\rho=\frac{4\gamma^2}{\Delta^2+4\gamma^2}.$$

Their matched-filter Gram matrix has smallest eigenvalue

$$\lambda_{\min}=\frac{\Delta^2}{\Delta^2+4\gamma^2}.$$

Finite widths therefore preserve rank two for every $\Delta\ne0$, but the experiment becomes arbitrarily ill-conditioned near degeneracy.

Scope

This assumes equal Lorentzian widths and ideal matched filtering. Detector convolution, unequal widths, backgrounds, efficiencies, and calibrated uncertainties remain outside the result.

Durable verification

• Packet: research/flavor/flavor-finite-width-template-overlap.md
• Checker: research/flavor/checkers/wp654_finite_width_template_overlap.py
• Result: research/flavor/results/wp654_finite_width_template_overlap.json
• Epistemic graph event: ev-000000006397-a542e3ed-bbb8-48f2-9e68-d0be518667a4

View source on GitHub