The Maslov-GCD Soliton: Topological Protection and Number-Theoretic Stability in Coupled Oscillator Networks
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| Natura: | Recurso digital |
| Lingua: | inglese |
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2026
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| _version_ | 1866902060685852672 |
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| author | Abdel-Aziz, Nasri |
| author_facet | Abdel-Aziz, Nasri |
| contents | <p>Introduced is a foundational model of three oscillators coupled on orthogonal torus<br>knots, where the collective stability is governed by the greatest common divisor<br>(GCD) of their frequency differences. Also proved is a Universal Period Theorem:<br>the fundamental period of the system is Tfund = 2π/M, where M = gcd(|∆sij|).<br>Through a canonical asymmetric geometry, it is demonstrated that systems with<br>integer M ≥ 2 occupy “Bosonic” ground states—stable, low-variance orbits—while<br>half-integer and irrational configurations exhibit “Topological Frustration” charac<br>terized as a dynamical indecision between adjacent topological sectors. Crucially,<br>we identify the stationary oscillator (spin 0) as a Topological Anchor that reduces<br>the critical coupling threshold for synchronization by orders of magnitude. These<br>results suggest that number theory provides the discrete selection rules for stability<br>in nonlinear frequency networks</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19436555 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Maslov-GCD Soliton: Topological Protection and Number-Theoretic Stability in Coupled Oscillator Networks Abdel-Aziz, Nasri Mathematical physics Algebraic topology Nonlinear Dynamics Maslov-GCD Soliton Legendrian Knot Theory Topological Protection <p>Introduced is a foundational model of three oscillators coupled on orthogonal torus<br>knots, where the collective stability is governed by the greatest common divisor<br>(GCD) of their frequency differences. Also proved is a Universal Period Theorem:<br>the fundamental period of the system is Tfund = 2π/M, where M = gcd(|∆sij|).<br>Through a canonical asymmetric geometry, it is demonstrated that systems with<br>integer M ≥ 2 occupy “Bosonic” ground states—stable, low-variance orbits—while<br>half-integer and irrational configurations exhibit “Topological Frustration” charac<br>terized as a dynamical indecision between adjacent topological sectors. Crucially,<br>we identify the stationary oscillator (spin 0) as a Topological Anchor that reduces<br>the critical coupling threshold for synchronization by orders of magnitude. These<br>results suggest that number theory provides the discrete selection rules for stability<br>in nonlinear frequency networks</p> |
| title | The Maslov-GCD Soliton: Topological Protection and Number-Theoretic Stability in Coupled Oscillator Networks |
| topic | Mathematical physics Algebraic topology Nonlinear Dynamics Maslov-GCD Soliton Legendrian Knot Theory Topological Protection |
| url | https://doi.org/10.5281/zenodo.19436555 |