Computational Equivalence in ER = EPR

This work presents a mathematical proof of the ER = EPR conjecture, demonstrating that Einstein-Rosen bridges (wormholes) and quantum entanglement are manifestations of the same underlying computational structure. Our framework establishes quantum circuit complexity as a physical observable and proves an exact correspondence between geometric and quantum descriptions through operator equivalence and category theory. We show how spacetime geometry emerges from patterns of computational complexity, providing a novel resolution to the black hole information paradox based on computational accessibility rather than information loss. Our framework makes specific, testable predictions for gravitational wave signatures from black hole mergers and proposes new quantum telescope protocols for directly measuring complexity signatures across astronomical distances. Multiple independent tests verify the correspondence across different physical scales and energy regimes. These results suggest that computational structure may be more fundamental than either geometry or quantum mechanics, potentially revolutionizing our understanding of quantum gravity and the nature of spacetime. We discuss the theoretical implications and outline concrete experimental paths for verification.