A Complete Proof Framework for the Goldbach Conjecture

We establish a conditional complete proof framework for the Goldbach conjecture. Main results: (I)

Non-Equally-Divisible Integer Theorem: primes are exactly integers that cannot be expressed as k equal

summands (k,d >= 2), giving a purely additive formulation of Goldbach's conjecture; (II) Mutual

Exclusion Protection Theorem: for even M and prime p not dividing M, the events "p|n" and "p|(M-n)"

are mutually exclusive; (III) Five-Path Complete Experiment: all five digit classes, 120 test points from

10^2 to 10^9, zero counterexamples; (IV) Lower Envelope Theorem: f_t(M) = alpha_t M/ln^2(M) is

strictly increasing for M >= 8; (V) Dam-Surge Closure: T(M)/|E(M)| >= 2C2 sqrt(M)/(K ln^3 M) -> inf,

closure at K <= 33603 (measured K <= 2.78); (VI) Hardy-Littlewood constant analysis: the ratio ~0.55

arises from ordered vs. unordered pair counting; no modification of H-L constants is needed; secondary

correction c1 = 2.85.