fermga

Summary: A computational investigation using spectral analysis of residue-circulant matrices has discovered that primes congruent to 1 mod 4 exhibit a vanishing "Paley gap"—the discrepancy between computed and theoretical eigenvalues reaches machine precision (10−15)). This phenomenon connects quadratic residue theory, optimal graph expansion properties (Ramanujan graphs), and Fast Fourier Transform...

Introduction: Most AI systems today optimize outputs based on probabilistic predictions. But what if, instead of optimizing outputs, an AI could reorganize its internal structure in response to symbolic input? This is the premise of TNFR (Teoría de la Naturaleza Fractal Resonante), a new computational paradigm implemented in Python and...