Paper T24: Triadic Spin Dynamics and Coherence Evolution in Small-N Systems

This paper presents explicit examples of multipartite entanglement and coherence evolution in the Holosphere framework using real-valued angular phase vectors in small-N systems. Building on the triadic tensor formalism introduced in Paper T23, we construct GHZ-type and W-type states for N = 3 and N = 4 systems and analyze their coherence graphs, strain energy, and stability under deterministic angular evolution. A class of coherence-preserving rotation operators Rθ is introduced to model strain relaxation while maintaining norm and coherence constraints. Decoherence transitions are modeled not as probabilistic collapse but as structural fragmentation, triggered when angular misalignment exceeds a critical threshold θ_c. The dropout threshold δ defines a regime of total coherence loss, creating sharp cutoffs in projection and correlation behavior. The angular strain energy S is interpreted as a geometric analog of the QCD confinement potential, and a proposed critical strain density ρ_c governs fragmentation phase transitions, drawing parallels with deconfinement in QCD. These small-N coherence networks provide a benchmark for larger-scale simulation studies and prepare the foundation for measurement theory (T25), statistical modeling (T27), and the SU(3) operator formalism in Papers 53 and 55. This work bridges geometric coherence theory with experimentally testable predictions in particle physics.