An Unconditional Proof of the Goldbach Conjecture via the P * ∞ Fixed-point Framework

Abstract

We introduce an arithmetic-dynamical framework for Goldbach's Conjecture that reformulates hypothetical counterexamples 2N > 6 in terms of a recursive prime divisor mapping D(S) = p∈S {q ∈ P | q | (2N-p)}. Under the counterexample hypothesis, the iterated set sequence P * (n + 1) = D(P * (n)) forms a monotonically non-increasing finite nested chain P * (0) ⊇ P * (1) ⊇. .. that converges in finitely many steps to a non-empty stationary limit set P * ∞ = D(P * ∞) bounded strictly inside P ≤ 2N-5 3. We prove that every minimal terminal component I ⊆ P * ∞ forms an irreducible, strongly connected directed graph G = (I, R) governed by an exponent matrix M ∈ Z k×k ≥0 with zero diagonal (Tr(M) = 0). Through modular growth constraints, trace nullity propagation (c 1 = c 2 = c 3 = 0), Perron-Frobenius spectral radius bounds (ρ(M) ≥ 2), and the Spectral Decoupling Barrier (U Large 2.