Multiscale DAGI Validation in Holographic Stabilizer Codes: Möbius Decomposition Confirms Entanglement Wedge Thresholds

Context: This manuscript belongs to the computational validation track of the DAGI (Directed Acyclic Graph Interpretation) research program at Whytics. It provides a mathematically exact confirmation of holographic entanglement wedge reconstruction using multiscale information theory. Abstract: We validate the entanglement wedge reconstruction property in a holographic stabilizer code using a multiscale information-theoretic approach. In a 16-qubit stabilizer graph code, we identify a bulk qubit whose information can only be recovered from a specific minimum set of five boundary qubits (its "entanglement wedge"). We employ the Directed Acyclic Graph Interpretation (DAGI) framework and a Möbius inversion-based decomposition of mutual information to quantify how information about the bulk is distributed among boundary subsets. Our analysis confirms that no information about the bulk qubit is accessible from any proper subset of its five-qubit wedge or from disjoint outside regions. Only when all five qubits in the entanglement wedge are present does the mutual information rise to its maximum (2 bits), corresponding to a perfect quantum correlation. Moreover, a Möbius decomposition reveals that this 2-bit mutual information is an irreducible five-party correlation: all lower-order contributions (one-body, two-body, etc.) are zero. We thus explicitly confirm that the bulk qubit's information is encoded entirely in a five-body entanglement, providing a quantitative, multiscale verification of entanglement wedge reconstruction in the code. Key Highlights: Exact Holographic Validation: Quantitatively confirms the entanglement wedge threshold in a 16-qubit hyperbolic graph code using exact algebraic rank methods. Synergy Verification: Proves via Möbius inversion that bulk information manifests entirely as an irreducible 5-body synergistic correlation, with strictly zero information present in lower-order marginals. Open Source Framework: The complete Python computational pipeline—including graph-state generation, Möbius inversion, and visualization routines—is included in this release to guarantee reproducibility.