PEDLER: A Deterministic Event–Hypergraph Foundation for Quantum Mechanics, Gravity, and Cosmology

This research poster advances PEDLER (Point Event-Driven Learner) from an initial conceptual blueprint to a structured axiomatic research programme for a deterministic foundation of modern physics. Building upon the proposed primitive ontology of finite typed directed event hypergraphs and deterministic local rewrite dynamics, the poster organizes the mathematical architecture required to derive quantum mechanics, gravity, gauge theory, particle physics, black holes, and cosmology from a common causal substrate. The programme distinguishes formal definitions, axioms, rewrite rules, conserved information invariants, lemmas, conjectures, target theorems, and experimentally falsifiable predictions, explicitly separating established mathematical structures from open research problems. It introduces the required categorical framework, hypergraph-to-geometry mappings, simplicial constructions, discrete differential geometry, continuum convergence programme, metric reconstruction, Lorentzian signature, Einstein gravity, quantum histories, amplitude functionals, Hilbert space emergence, Born rule derivation, particle topology, internal symmetries, gauge bosons, entanglement, decoherence, black holes, inflation, dark energy, and cosmological evolution within a unified dependency architecture. Rather than claiming completed derivations, the poster identifies the precise mathematical, computational, and experimental milestones necessary to rigorously establish each stage of the programme, providing a comprehensive axiomatic roadmap for investigating whether the known laws of physics can emerge from deterministic event–hypergraph dynamics.