Paper T23: Multipartite Entanglement and Triadic Tensor Networks

Paper T23 extends Holosphere Theory’s angular-phase coherence framework to multipartite entanglement using a real-valued, triadic network model. Each subsystem is represented by a unit triadic spin vector in R3\mathbb{R}^3R3, and the multipartite state is defined as a constraint structure StateN=(G,{v⃗i},θc)\mathsf{State}_N=(G,\{\vec{v}_i\},\theta_c)StateN=(G,{vi},θc) rather than as a complex-amplitude superposition. The paper uses R3N\mathbb{R}^{3^N}R3N as a configuration register for joint triad orientations while treating entanglement as coherence-graph connectivity, admissibility thresholds, and optional triadic closure constraints. GHZ-type and W-type regimes are characterized as distinct corridor topologies (global phase locking versus distributed redundancy), and separability is identified with coherence-graph disconnection. Decoherence is modeled as a deterministic structural transition driven by angular strain, implemented as threshold crossings that delete edges and increase coherence rank. The result is a topology-first, real-valued interpretation of multipartite correlations that aligns with Holosphere determinism and provides operational metrics (coherence functional, strain, coherence rank, and fragmentation) for classification and future evaluation on public data.