Operational ER ↔ EPR Connection within the TAGC-LQG-RG Framework: Theoretical Framework and Reversible Traversability Criteria

We present an operational theoretical framework for evaluating the reversible traversability of Einstein-Rosen bridges (wormholes) within the TAGC-LQG-RG research programme (Theory of Anchored Gravity through Complexity - Loop Quantum Gravity - Renormalization Group). The work integrates concepts from loop quantum gravity, information theory, and irreversible thermodynamics to derive quantitative criteria determining when an entanglement-connected throat configuration (ER = EPR) admits informational coherence preservation during a round-trip process. We introduce a quantified critical threshold Kc = 2.04±0.05, threshold-activated GKSL master equations, and a gravitational Landauer-type energy cost. The formalism is expressed through an informational Hessian operator whose spectrum determines viable connecting modes. We establish three complementary operational criteria: temporal coherence (Γψτtrav ≪ 1), Landauer energy balance (Eavail ≥ ζEthroat), and spectral robustness (measured by Rgap). The framework is computationally falsifiable through simulations on LQG-type discrete networks. We include numerical protocols for sensitivity analysis, phase diagrams, and statistical robustness tests. The interpretation of “reversible traversability” is defined strictly in the informational sense: the capacity to preserve quantum coherence during information transfer, without necessarily implying classical matter transport or macroscopic signal transmission. The work establishes connections with the Multibang programme through mappings between coarse-graining parameters and cosmological scales, and proposes verifiable observational predictions related to critical throat masses of the order of the Planck mass.