Emergent Discreteness from Stability Boundaries in Reversible Dynamics

Emergent Discreteness from Stability Boundaries in Reversible Dynamics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Emergent Discreteness from Stability Boundaries in Reversible Dynamics andrei ursachi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8790240/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Discrete spectra are traditionally postulated as axiomatic in quantum theory. Here we demonstrate that discreteness can emerge generically as a consequence of dynamical stability in reversible, non-integrable systems under weak perturbations. We identify robust parameter plateaus (locking shelves) across quantum Floquet chains, classical area-preserving maps, and wave-transfer matrices. Crucially, every tested system follows the same boundary logic: shelves occur only within elliptic stability islands and collapse under irreversibility, strong noise, or hyperbolic instability. We do not derive quantum theory; we identify a cross-domain stability mechanism that generically selects discrete responses. This stability-selection principle provides a concrete bridge between classical mode-locking, Floquet many-body scars, discrete time crystals, and dynamical localization—suggesting that discreteness is a selected dynamical outcome rather than a fundamental axiom. Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Nonlinear phenomena Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8790240","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":588709260,"identity":"4e380d41-63a0-408e-bbc9-55cc853b16ab","order_by":0,"name":"andrei ursachi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYBADOSA2ACMgYGNIwK+asQGo1Jh0LYkNMPVgLfgAf3vv8Qc/av6k989u3vbhQ8HhfPn2w88ePGCwARmCFUicOZfY2HPMIHfGnWPFM2cYHLbccCbN3CCBIQ2nFgOJHMMG3gaD3IYbOcbMPAaHDQwYctgkEhgO49XS+LfBIF0epOUPUIt8/xuQlv94tTQDbUkwAGlhAGphuAG25QAev5wxnC1zzNhw4420YsYeg3QDgxvPzCQSDJKNcWnhb+8x+PimRk5e7kbyZoYff6yBDkt+Jvmjwk4WlxZcwICwklEwCkbBKBgFuAEA7plXE1d03eMAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0002-6114-5011","institution":"noce","correspondingAuthor":true,"prefix":"","firstName":"andrei","middleName":"","lastName":"ursachi","suffix":""}],"badges":[],"createdAt":"2026-02-04 21:05:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8790240/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8790240/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102963784,"identity":"b7d260a7-b6a6-4f28-8600-7ad1154e916b","added_by":"auto","created_at":"2026-02-19 04:20:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":324173,"visible":true,"origin":"","legend":"Article File","description":"","filename":"EmergentDiscretenessNaturePhysicsFINALv6.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8790240/v1_covered_be6b50c9-ab91-4d5e-b127-c695ed507c67.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Emergent Discreteness from Stability Boundaries in Reversible Dynamics","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8790240/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8790240/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDiscrete spectra are traditionally postulated as axiomatic in quantum theory. 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