The Architecture of Persistence: Stability in the Trojan Universality Class | Zenodo Skip to main Communities My dashboard Log in Sign up Published April 12, 2026 | Version v1 Preprint Open The Architecture of Persistence: Stability in the Trojan Universality Class Authors/Creators Doucette, Doug Description This paper argues that long-lived stability is not a generic consequence of nearness to equilibrium, but the expression of a specific phase-space architecture. In generic near-integrable Hamiltonian systems, persistence is partial and porous: Kolmogorov-Arnold-Moser theory preserves many invariant tori, Nekhoroshev theory yields exponentially long confinement under suitable steepness hypotheses, yet the ambient phase space remains threaded by resonance layers through which slow transport may occur. By contrast, the Trojan Universality Class (TUC), in the sense of Doucette (2026), isolates a distinct regime of persistence built around a two-degree-of-freedom elliptic-elliptic equilibrium, a persistent spectral gap, and a finite-order nonresonance structure that suppresses dangerous low-order commensurabilities. In that regime the normal form is action-dominated, the resonance web is sparse and hierarchical, and stability is protected by layered geometry rather than by perturbative smallness alone. We formulate this architecture precisely, distinguish between source-derived and newly formalized results, and show how the TUC yields a confinement law as set out. We then contrast this regime with ordinary Hamiltonian stability and develop an exit theory in which failure proceeds hierarchically through separatrix splitting, resonance overlap, spectral-gap collapse, and activation of additional modes. The central claim is architectural: TUC stability is not merely strong Hamiltonian stability, but a distinct universality class of persistence. Files The Architecture of Persistence_ Stability in the Trojan Universality Class.pdf Files (363.4 kB) Name Size Download all The Architecture of Persistence_ Stability in the Trojan Universality Class.pdf md5:22734fa952af928b4d8965b355057086 363.4 kB Preview Download 37 Views 116 Downloads Show more details All versions This version Views Total views 37 37 Downloads Total downloads 116 116 Data volume Total data volume 42.2 MB 42.2 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Details DOI DOI Badge DOI 10.5281/zenodo.19522537 Markdown [](https://doi.org/10.5281/zenodo.19522537) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19522537.svg :target: https://doi.org/10.5281/zenodo.19522537 HTML <a href="https://doi.org/10.5281/zenodo.19522537"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19522537.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19522537.svg Target URL https://doi.org/10.5281/zenodo.19522537 Resource type Preprint Publisher Zenodo Rights License Creative Commons Attribution 4.0 International The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited. Read more Citation Export Technical metadata Created April 12, 2026 Modified April 12, 2026 Jump up About About Policies Infrastructure Principles Projects Roadmap Contact Blog Blog Support Help FAQ Developers REST API OAI-PMH Contribute GitHub Donate Funded by Powered by CERN Data Centre & InvenioRDM Status Privacy policy Cookie policy Terms of Use This site uses cookies. Find out more on how we use cookies Accept all cookies Accept only essential cookies