Axiomatic Derivation of the Leading Valence Engagement Amplitude in the PDL Framework: Gate 1 Resolved

Within the Projective Dynamic Logo (PDL) framework, the proton-to-electron mass ratio correction δμ was conjectured in D28 to factorise as (155/11017) · (1 − 2Δmᵢso/mₚ). The factor 155/11017 = rᵥal/ (Rₑ·Rₜot) was identified as the leading-order valence engagement amplitude, but its derivation from the PDL axioms remained an open problem (Gate 1). This paper closes Gate 1 by proving that δμ^ (1) = 155/11017 follows exclusively from the four PDL axioms, without external numerical input. Two lemmas are established and exhaustively verified over 768 cases with zero counter-examples. Lemma 1 proves that a mixed triangle between K₄ and a proton vertex is stable — coherent at both half-cycles of the K₄ pulsation — if and only if conditions (A) and (B) hold simultaneously: initial sign alignment (A) and phase-locking (B). Lemma 2 proves that rᵥal = 930 is the unique integer engagement satisfying net charge +1 and divisibility by Rₑ = 6, by exhaustive scan over all six admissible combinations. From these two lemmas, the theorem δμ^ (1) = rᵥal/ (Rₑ·Rₜot) = 155/11017 ∈ ℚ follows by direct construction. This result constitutes the first fully axiomatic step in the PDL derivation of Newton's gravitational constant, and provides the combinatorial foundation for the completion of the εG conjecture in D30.