Symbolic Resolution of the Bunyakovsky Conjecture via AION

This paper presents a structural and symbolic resolution of the Bunyakovsky Conjecture. We introduce a symbolic framework rooted in the AION irreducibility model, where prime numbers are defined by their inability to be constructed from previous symbolic elements via multiplication. By applying this framework to polynomials with integer coefficients that are irreducible, have a positive leading term, and lack a fixed divisor, we demonstrate that such polynomials escape all symbolic multiplicative constructions infinitely often. This symbolic escape guarantees irreducibility in the AION system and thus confirms the infinite occurrence of prime outputs from the polynomial. The resolution requires no probabilistic or analytic tools and redefines primality through deterministic symbolic structure.