>[!warning] >This content has not been peer reviewed. # Ryu–Takayanagi Metric — RST application The RT formula is a concrete case where **entanglement determines geometry**. RST uses this as an engine design rule: define an **effective distance** directly from an entanglement / coherence proxy, and let the simulation’s connectivity update that distance dynamically. This folder provides a runnable toy implementation: maintain \(E_{ij}\) and define \(d_{ij} = -\log(E_{ij} + \epsilon)\); update \(E_{ij}\) upward when nodes share coherent workload and let it decay otherwise. --- ## I. Mapping to RST | Classical concept | RST reading | |:---|:---| | Entanglement entropy ↔ area | Connectivity / coherence ↔ distance / “metric”. | | Minimal surface | Least-cost coupling surface (operational proxy). | | Geometry from entanglement | Engine distance derived from shared workload. | --- ## II. Script and verification - Script: **[[Ryu-Takayanagi Metric - Code]]** (`rst_rt_metric_entanglement_distance.py`) - Output: `rt_metric_entanglement_distance.png` - Result note: **[[Ryu-Takayanagi Metric Results]]**