Path-Dependent Geometrogenesis: Emergent Bulk Topology from Quantum Circuit Histories

Standard models in holographic duality assume that spatial connectivity in the bulk comes directly from the instantaneous entanglement entropy of a boundary state, typically tracked by the Ryu-Takayanagi formula. However, this static approach creates a blind spot: completely different state-preparation pathways can end up mapping to identical macroscopic spatial surfaces. We present an informational-physiological alternative framework termed Path-Dependent Geometrogenesis. Our core hypothesis positions the emergent bulk spacetime metric tensor g_μν as an operational ledger. Rather than registering immediate state correlations, it encodes the specific, time-ordered unitary history, the actual quantum circuit, that generated those correlations. By decoupling instantaneous Dynamical Entanglement from State-Encoded History, this model breaks the geometric degeneracy found in states with identical Von Neumann entropies. We model spacetime as an evolving, self-regulating topological network, providing a fresh perspective on how to localize bulk degrees of freedom and track the structural persistence of emergent network bottlenecks.