The Principle of Minimal Historical Action: Local Closure of O2 in the EPPQ Framework

The EPPQ (Emergent Pre-Quantizable) framework seeks to derive spacetime andquantum mechanics from a purely relational substrate governed by a primordial distinctionα and the Principle of Absolute Historicity (PAH). While previous work (O1) established aconditional reconstruction of Riemannian geometry, the open problem O2—the emergenceof a causal, unidirectional temporal dynamics—has remained unresolved. The PAH, inits original form, is a static constraint; it prohibits ahistorical configurations but doesnot furnish a rule for selecting the actual historical trajectory among many admissibleones. This ambiguity is a manifestation of the Axiom of Choice in the relational setting:without a dynamical principle, the system’s evolution is either arbitrary or requires external,non-relational oracles. In this paper, we establish a rigorous local dynamics for O2 by elevating the PAH toa variational principle: the Principle of Minimal Historical Action (PMAH). We define adiscrete action functional that penalizes both local inconsistencies and the “forgetting” ofhistorical depth. We then introduce the Axiom of Relational Causality (ACR), which selectsthe physical, Markovian solution among the many non-causal extrema of the action. Underempirically motivated structural hypotheses (energy gap, monotonicity of the historicalcost), we prove a local well-posedness theorem: in the vicinity of a low-energy metamode,the PMAH+ACR dynamics is deterministic, uniquely defined, and converges exponentiallyto a fixed point via a contraction mapping. This result transforms the PAH from a passiverestriction into an active, time-generating engine. It resolves the local Axiom of Choiceambiguity and establishes the arrow of time as a consequence of historical dissipation. Thetheorem provides the rigorous dynamical foundation required for the emergence of quantummechanics (O3) and, ultimately, for closing the geometric problem O1.