TROIKA Model - Triple Rotor Oscillator Interlinked with K-cycle Architecture

We present the dataset and comprehensive manuscripts for the TROIKA (Triple Rotor Oscillator Interlinked with K-cycle Architecture) model. This framework establishes a bridge between discrete geometric entanglement and continuous rotational mechanics, exploring the hybrid coupling between directional degrees of freedom and continuous vibrational modes across three entangled sources. The provided documentation includes the full theoretical derivation of a cyclically entangled three-qutrit state that enforces a strict orthogonal trihedron upon projective measurement. By utilizing Weyl-Heisenberg shift operators and establishing a discrete phase variable through a classical Lagrangian, the model derives a novel directional-vibrational interaction Hamiltonian. Additionally, the full manuscripts detail the exact global symmetry operator (K) that confines the system's dynamics within an invariant subspace, drastically reducing the active Hilbert space dimensionality. Furthermore, this deposit includes the complete suite of MATLAB source codes used to solve the time-independent Schrödinger equation via exact matrix diagonalization and Kronecker products. The codebase implements advanced matrix contractions to compute partial traces, tracking non-Markovian Rabi revivals, Von Neumann entanglement entropy, and Wigner quasiprobability distributions—formally demonstrating the active generation of non-classical vibrational states with distinct negativity wells in phase space. Finally, an open-ended continuous extension is formulated, showcasing the discrete cyclic structure as an effective low-energy sector of an isotropic rigid rotor on the SO(3) configuration manifold. Files included:- Theoretical Manuscript in English (PDF)- Theoretical Manuscript in Spanish (PDF)- Core MATLAB source codes for dynamics, entropy, and Wigner functions (.m)