The Structural Non-Existence of Odd Perfect Numbers under the Strong Goldbach Conjecture v2

This paper demonstrates the formal non-existence of Odd Perfect Numbers ( by applying the Strong Goldbach Conjecture to the prime distribution of We define as the largest prime number strictly less than $m$ ($p < m$). We show that the resulting even gap must be representable as the sum of two primes (). Through a nested modular "Kill-Chain," we prove that this additive construction $m = p + P_i + P_n$ is arithmetically incompatible with the multiplicative density and square-factor requirements necessary for a perfect number.