Deterministic Growth Dynamics of Causal Graphs IV: Derivation of Quantum Mechanics

The present paper continues the DGDCG I–III programme by deriving quantum dynamics and Lorentz invariance from a single axiom — the Coverage Principle. A deterministic mechanism for the emergence of quantum uncertainty is proposed for the first time: it is interpreted as the operational ambiguity of coarse-graining at finite structural resolution r∗, rather than as fundamental stochasticity. On this basis, the uncertainty relation, the Born rule, unitary evolution, and the Schrödinger equation are rigorously derived. The Lorentzian signature (− + ++) and the group SO(3, 1) emerge as the unique structure compatible with the complex phase of the geometric action and the irreversibility of Frontier growth. All results follow from a variational principle without additional physical postulates.