The Post-AI Hyperedge Execution Model: Verifiable Computational Causality, Structural Grounding, and the Physics of Admitted State

Abstract

For over fifty years, computing has operated under an amnesic, bipartite abstraction: source code is an ungrounded string, and execution is an ephemeral process whose evidence is destroyed upon termination. In the era of autonomous AI agents, this produces an epistemic void where claims of execution cannot be adjudicated against physical reality. We establish The Post-AI Hyperedge Execution Model, operationalized through Git-Ontic-Trace (got), replacing lossy binary edges with an 8-ary Ontic Hyperedge: e_{exec} = . We prove two foundational theorems: Theorem 1 (Irreducibility of Execution Causality / Pairwise Decomposition Fallacy), showing that binary graph projections synthesize false transitive executions at an empirical 75.00% rate; and Theorem 2 (Invariant Enclosure & Intent Admission), proving that state transitions must strictly satisfy topological boundary enclosure Delta S subseteq R(D) under active capability deeds. Across an empirical Monte Carlo ablation experiment of N=1,000 execution events on heterogeneous hardware, we measure a 75.00% false attribution rate in relational graph projections, 3.90% silent state corruption in standard POSIX models, and 25.80% cybernetic attribution void. We formulate the Four Topological Orders of Execution (Micrograph, Hypergraph, Supergraph, Intergraph), model continuous 3D field dynamics on the Celestial Realm manifold M = , and demonstrate zero-overhead native reduction to practice on Git Content-Addressed Storage (refs/got/traces/*). This repository contains the canonical whitepaper, foundational theoretical monographs, and the complete runnable CPython 3.14 formal proof and ablation suite.