Structural Derivation of the QCD Correction Coefficient in the PDL Mass Ratio Formula and Completion of the εG Conjecture: Gate 2 Resolved

The εG conjecture of D28 expressed Newton's gravitational constant as G = (ħc/mₚ²) · (εGB) ¹8, with εGB ∈ ℚ (√5) accurate to 17 ppm, contingent on proving two steps: (a) that 155/11017 follows from the PDL axioms (resolved in D29), and (b) that the coefficient 2 in the isospin correction 2Δmᵢso/mₚ is a structural consequence of the PDL axioms rather than a numerical fit. This paper resolves step (b) and thereby proves the εG conjecture under the minimal PDL–QCD interface, closing Gate 2. The central result is Lemma 2: the PDL engagement coefficient a = 2 is forced by charge constraint C4 applied to the proton quintuplet, because only mixed triangles of type (1 up-core, 2 down-cores) satisfy the (A) ∧ (B) stability criterion with net charge +1. The identification Δmᵢso = md − mᵤ is forced uniquely by PDL charge constraint C1, making it the minimum irreducible external parameter at the PDL–QCD interface. Under this minimal identification, the full factorisation δμ = (155/11017) · (1 − 2Δmᵢso/mₚ) + O (47 ppm) follows from PDL axioms together with Δmᵢso, and the conjecture εG = εGB ∈ ℚ (√5) is proved to 17 ppm. As a consequence, Newton's gravitational constant G = (ħc/mₚ²) · (εGB) ¹8 is a fully combinatorial prediction from the proton quintuplet (24, 28, 930, 10087, 11017), with Δmᵢso as the sole irreducible external input.