The Maslov-GCD Soliton: Topological Protection and Number-Theoretic Stability in Coupled Oscillator Networks
Authors/Creators
-
1.
State University of New York College of Environmental Science and Forestry
Description
Introduced is a foundational model of three oscillators coupled on orthogonal torus
knots, 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 with
integer M ≥ 2 occupy “Bosonic” ground states—stable, low-variance orbits—while
half-integer and irrational configurations exhibit “Topological Frustration” charac
terized as a dynamical indecision between adjacent topological sectors. Crucially,
we identify the stationary oscillator (spin 0) as a Topological Anchor that reduces
the critical coupling threshold for synchronization by orders of magnitude. These
results suggest that number theory provides the discrete selection rules for stability
in nonlinear frequency networks
Files
GCD_Foundations_v2.pdf
Files
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Additional details
Additional titles
- Subtitle
- A Classical Analog of Boson–Fermion Stability via the Magic Maslov Number
- Subtitle
- Topological Protection and Spin‑Difference Invariants in Oscillator Networks
Identifiers
Related works
- Is continued by
- 10.5281/zenodo.19463941 (DOI)
Dates
- Updated
-
2026-04-06This work contributes to the fields of Applied Mathematics and Dynamical Systems by introducing a number-theoretic framework for frequency locking.
Software
- Repository URL
- https://github.com/qmpath/gcd-oscillator-model
- Programming language
- Python
- Development Status
- Active
References
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