Quantum Mechanics as Information Branching: A Formal DAG-Based Interpretation

Context: This manuscript serves as the foundational ontology paper for the Directed Acyclic Graph Interpretation (DAGI) research program at Whytics. Abstract: Quantum mechanics is remarkably successful in predicting experimental outcomes, yet it remains conceptually challenging: the status of the wavefunction, the meaning of "measurement", and the origin of the arrow of time are still debated. We propose an interpretation grounded in information theory and graph theory, representing quantum histories as a single Directed Acyclic Graph (DAG) of informational states. In this model, nodes represent quantum informational states (density operators) and directed edges represent physical interactions that update those states. Branching occurs precisely when an interaction creates a durable, distinguishable record that cannot be coherently erased at the relevant scale; decoherence corresponds to record proliferation into the environment; and quantum erasure corresponds to coherent record removal that can re-enable interference by merging previously distinguishable histories. Furthermore, we prove a Kolmogorov Consistency Theorem for finite-amplitude DAGs, guaranteeing that the framework yields a coherent probability measure on the decohered quotient graph and exactly recovers unitary Schrödinger evolution in the non-branching limit. We show how this ontology resolves standard quantum paradoxes without introducing ambiguous collapse postulates or an ontological multiplication of worlds, and we outline auxiliary operational predictions motivated by the model. In particular, DAGI motivates an "informational time dilation" program: an operational clock's inferred progress decreases with the rate of irreversible record creation under schedule-matched controls, and increases toward baseline when records are coherently erased. We additionally report initial IBM Quantum hardware results from the C1-LC program regarding light-cone transport, motivating a refined conformal hypothesis for how time and causal structure emerge from record density. Key Highlights: Novel Ontology: Replaces the ontological extravagance of the Many-Worlds Interpretation with a single, strictly causal DAG of informational records. Mathematical Rigor: Provides a mathematically rigorous Kolmogorov Consistency Theorem for finite-prefix cylinder sets, resolving standard measure-theoretic pathologies in history-based interpretations. Paradox Resolution: Resolves Wigner's Friend, Delayed Choice, and Schrödinger's Cat paradoxes through an explicit mathematical graph-refinement logic. Hardware Testability: Formulates the theoretical foundation for operational time dilation and causal-cone transport limits actively being benchmarked on IBM superconducting quantum processors.