Time as a Discrete Information Ledger: A Topological Framework for Quantum Delayed-Choice, Entanglement, and Observer-Dependent Reality

The incompatibility between General Relativity and Quantum Mechanics necessitates a reevaluation of spacetime ontology. This paper proposes a Discrete Dynamic Ledger (DDL) model, defining time as a sequence of discrete state-nodes within a directed acyclic graph. Based on Wheeler’s delayed-choice experiment, we argue that historical states lack absolute determinacy until retroactively fixed by present observations, and predictions based on past states are merely decohered "abandoned futures." We introduce "Local Causal Closure": entangled particles and the observer's physical operation share a single topological node in the fundamental ledger. Through partial trace and quantum channel formulations, it is demonstrated that this synchronization requires no superluminal signaling. The observer is strictly defined by the macroscopic irreversible physical entanglement (Lindblad decoherence) formed by the unification of decision and action, independent of consciousness. Integrating the Holographic Principle and the ER=EPR conjecture, a modified interference phase formula is derived at the Planck scale. Overwritten histories are shown to transform into a "Static Information Ground State"—an eternal stillness (Ataraxia) that preserves information without energy inflation.