The Maslov-GCD Soliton: Topological Protection and Number-Theoretic Stability in Coupled Oscillator Networks

Introduced is a foundational model of three oscillators coupled on orthogonal torusknots, where the collective stability is governed by the greatest common divisor(GCD) of their frequency differences. Also proved is a Universal Period Theorem:the fundamental period of the system is Tfund = 2π/M, where M = gcd(|∆sij|).Through a canonical asymmetric geometry, it is demonstrated that systems withinteger M ≥ 2 occupy “Bosonic” ground states—stable, low-variance orbits—whilehalf-integer and irrational configurations exhibit “Topological Frustration” characterized as a dynamical indecision between adjacent topological sectors. Crucially,we identify the stationary oscillator (spin 0) as a Topological Anchor that reducesthe critical coupling threshold for synchronization by orders of magnitude. Theseresults suggest that number theory provides the discrete selection rules for stabilityin nonlinear frequency networks