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A minimalist geometric model of three oscillators moving on orthogonal torus knots is introduced, each assigned an integer ``spin'' that controls its natural frequency. The greatest common divisor (GCD) of the spin differences is demonstrated to govern the system's robustness to geometric perturbations. Systems composed solely of non‑zero integer spins exhibit a boson‑like coherence: their collective rhythms remain stable under varying geometry, with area stability (the deviation of the first‑return map from an ideal value) as low as 0.11. In contrast, systems containing half‑integer spins—whether pure or mixed—show pronounced fragility, with area stability exceeding 0.2, suggesting an inherent fermionic resistance to synchronization. The special case of a zero spin (stationary particle) can artificially pin the system, masking the intrinsic behavior. These findings establish a classical analog of the boson–fermion dichotomy, where integer spins condense into protected states while half‑integers retain individuality. The invariant governing this protection is identified as the Maslov number of the Legendrian torus constructed from the three oscillators, linking the model to contact topology, Hamiltonian stability theory, and the semiclassical physics of Dirac materials. A companion paper explores the fermionic sector in depth, including the emergence of semi‑Dirac dispersion, Landau level scaling, and the mapping of the invariant to the Chern number of topological band theory. This work opens a new avenue for designing robust oscillator networks by engineering their effective ``spin'' statistics.