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 − 2Δm_iso/m_p). The factor 155/11017 = r_val/(R_e·R_tot) 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 r_val = 930 is the unique integer engagement satisfying net charge +1 and divisibility by R_e = 6, by exhaustive scan over all six admissible combinations. From these two lemmas, the theorem δμ^(1) = r_val/(R_e·R_tot) = 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 ε_G conjecture in D30.