Schrödinger Dynamics from the (A)∧(B) Coupling Criterion in the PDL Framework

The Projective Dynamic Logo (PDL) framework derives physical reality from four axioms on finite signed graphs, without presupposing space, time, or wavefunctions. This paper shows that the Schrödinger equation emerges from the (A)∧(B) stability criterion — the condition characterising stable mixed triangles between K₄ closures and proton vertices — without any additional quantum mechanical postulate. The key result is Proposition 2: the amplitude coefficient b = −iħΔt/(2m_e(Δx)²) is derived from condition (B) together with the Compton pulsation scale, with no free parameter. From this coefficient, the full time-dependent Schrödinger equation iħ∂ψ/∂t = [−ħ²/(2m_e)∇² − α_PDL·ħc/r]ψ follows by the continuum limit, with the fine-structure constant α_PDL entering from the PDL proton quintuplet. The S₄ transitivity established in D31 forces isotropy of the transition amplitudes, ensuring spatial homogeneity of the derived dynamics. The non-relativistic limit is self-consistent, using the same α_PDL and m_e as the full theory. This result closes open problem OP6 of D31 and constitutes the first derivation of a quantum dynamical equation from the PDL closure axioms. Conditions (A)∧(B) are identified as the natural entry point for the relativistic extension to the Dirac equation, addressed in D33