Holographic Constraint Network Spectral Flow Program D; Graph-Theoretic Semantics of Quantum Error-Correcting Codes– From Tensor Networks to Condensation-Rewiring Dualities of Black Hole Singularities

changzheng zhou, ZIQING zhou

Published Jul 9, 2026• 0 citations

Abstract

This paper unifies holographic quantum error-correcting codes, the internaldynamics of black holes, and the Einstein–Rosen bridge within a mathematicalframework centered on the category of constraint networks and spectral flow. Byencoding tensor networks as weighted hypergraphs and introducing a faithful functor, a strict duality between bulk spacetime geometry and boundary quantuminformation is established. In this framework, the code distance is determined bythe Cheeger isoperimetric lower bound and is shown to be equivalent to the invariant features of the Laplacian spectral flow under coarse-graining; black holeevaporation is described as a percolation phase transition caused by the failure ofinternal entanglement structures, where the failure of the condensation operatorautomatically triggers the splitting operator, leading to branching of quantum extremal surfaces and quantitative constraints on information release governed by theinformation conservation axiom; the formation of the ER bridge corresponds to atopological mutation induced by the rewiring functor, whose throat area is rigidlydetermined by the information-potential difference across the boundary and thenetwork compression ratio. The two axioms of information conservation and computability run throughout the entire treatment, reducing all geometric connectivitydecision problems to polynomial-time solvable graph algorithms. We further givespecific numerical predictions for the code-distance enhancement of non-Abeliansymmetric tensor networks, the acceleration of wormhole connectivity computability, and the critical behavior of the condensation–splitting phase transition, anddesign a simulation verification scheme independent of external datasets.

DOI: 10.5281/zenodo.21272336

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