Finite-Sample Ratio Estimator A General-Purpose Toolkit for Eigenvalue Estimation and Sequence Analysis

FSRE (Finite-Sample Ratio Estimator) is a general-purpose toolkit for extracting dominant eigenvalues from sequential data through ratio convergence analysis. Given any sequence of positive numbers, FSRE estimates the underlying exponential growth rate, quanties estimation reliability, identies known mathematical sequences, and detects special structures including integer eigenvalues, the golden ratio, rational approximations, and algebraic forms. The toolkit is applicable across domains: population dynamics, orbital mechanics, signal processing, nancial time series, recurrence relations, and any context where exponential-dominated sequences arise. FSRE provides both quick estimates for exploratory analysis and detailed diagnostics for rigorous investigation. Pass it along and share, if you want to thank me and buy me a coffee my email is : coates.research@protonmail.com