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

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 + Pᵢ + Pₙ is arithmetically incompatible with the multiplicative density and square-factor requirements necessary for a perfect number.