Emergent Consumable Time from Entanglement (ECTE): Complete Theory, Code, and Observational Validation Framework

The standard ΛCDM model faces persistent tensions:the H0 discrepancy between early- and late-time measurements and the S8 tension between CMB andweak lensing surveys. The Emergent ConsumableTime from Entanglement (ECTE) framework proposesa resolution based on the emergence of time from quantumentanglement entropy and entropic corrections togravity.This document is the complete technical reference forECTE. It contains:• The fundamental postulates and the full covariantaction.• The derived field equations, including modifiedEinstein and Klein-Gordon equations.• The cosmological background and perturbationequations.• Stability conditions (ghost-free, gradient stability,gravitational wave speed).• The complete Python source code for the backgroundsolver.• A script to generate μ–Σ tables for CLASS.• Instructions to modify the CLASS Boltzmann codefor ECTE.• Configuration file for MontePython MCMC analysis.• A step-by-step guide to validate ECTE against realdata.