Spectral and geometric refinements of the Fibonacci recursion operator

Refine the spectral analysis of the Fibonacci recursion operator by characterizing its relationships with the eigenvalue and eigenvector distributions of the empirical Gram matrix, effective rank, and kernel alignment, to reveal deeper connections between golden-ratio dynamics, information propagation in ensembles, and the geometry of high-dimensional learning.

Background

The paper develops spectral stability conditions and mode decomposition for the second-order recursive ensemble operator, linking behavior to golden-ratio asymptotics.

The Future Work section proposes deeper spectral and geometric analysis by relating the recursion operator to Gram-matrix spectra, effective rank, and kernel alignment, aiming to illuminate how golden-ratio dynamics govern information propagation and ensemble geometry in high dimensions.

References

Several directions remain open and are, in our view, both challenging and promising.

— On Fibonacci Ensembles: An Alternative Approach to Ensemble Learning Inspired by the Timeless Architecture of the Golden Ratio  (2512.22284 - Fokoué, 25 Dec 2025) in Section “Future Work: From One-Dimensional Harmony to High Dimensional Practice”