Spectral Obstructions to Odd Perfect Numbers and a Program for Unconditional Non-Existence

This research presents a structural proof for the non-existence of odd perfect numbers (OPN) by mapping traditional arithmetic properties onto spectral stability constraints within the Unified Field Theory-F (UFT-F) framework. The paper demonstrates that the exact condition required for a number to be perfect ($\sigma(n)=2n$) necessitates a spectral state that is "topologically frustrated" by a universal resolution floor, denoted as $\lambda_{0}$. The argument is developed in two primary layers: Framework Closure: Using the UFT-F framework to show that odd structures are displaced from admissible lattice nodes, leading to a "spectral rupture" and a violation of $l^{1}$-admissibility Classical Translation: Mapping these obstructions to standard analytic number theory, specifically focusing on the impossibility of "Global Cancellation Loops" where prime divisors of Euler factors cross-cancel perfectly. The paper concludes that since an odd perfect number would require an infinite set of prime factors to satisfy these global cancellation requirements, and all integers must have finite factorizations, no such number can exist. The work is supported by executable Python scripts that implement a "Spectral Rupture Diagnostic" to empirically validate the theoretical findings.