Continuous, State-Dependent Temporal Response Scales in GNSS Satellite Clock Residuals

Continuous, State-Dependent Temporal Response Scales in GNSS Satellite Clock Residuals | 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 Research Article Continuous, State-Dependent Temporal Response Scales in GNSS Satellite Clock Residuals Takahiro Mitsui This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9191253/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 We investigate whether GNSS satellite clock residuals are better described by a purely instantaneous response or by a finite temporal response with a characteristic time scale τ . Using event-centered stacks built around apoapsis and periapsis passages, we compare an immediate model with exponential and Gaussian kernel-response models. Across the strongest candidate satellites, the finite-response models consistently outperform the immediate model, with continuous best-fit response scales spanning approximately 15.66 min and improvements of up to ΔAIC . 78. A continuous-τ optimization shows that the preferred scales are not evidence for strict quantized time modes; rather, they form a continuous, state-dependent response spectrum whose local maxima cluster around a few tens of minutes. Resolution tests using coarsened sampling indicate that the strongest candidates remain finite-response dominated, although the inferred τ can shift when temporal resolution is degraded. The results therefore support a conservative interpretation: GNSS clock residuals contain reproducible signatures consistent with finite, state-dependent temporal response scales, while stronger claims such as discrete eigenmodes are not required by the present data. These findings motivate a continuous temporal-response extension of Time- Field General Relativity (TFGR), in which scale dependence and finite memory coexist without contradiction. Theoretical Physics GNSS satellite clock residuals temporal response time-domain analysis kernel response models state dependence model selection AIC Full Text Additional Declarations The authors declare no competing interests. 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. 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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-9191253","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":610129288,"identity":"7f9c62f4-14ee-42ff-98c6-5754b1842bce","order_by":0,"name":"Takahiro Mitsui","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYHACNiCqSTBgb2A8kFAB5DMzN+BVzwPRcizBgOcAw4EPZ0BaGInSwpxgIJHAcHBmG0iMgBZ7sQNsjwvK2PLMGdIfHOadVxvN3w7U8qNiG25bpBPYjWeckym2bDhjcJh32/HcGYcZGxh7ztzGp4VNmreNLXHDwR4GoJZjuQ1ALcyMbQS1MCduOMwOdNicY7nziddyjMHg4MyGmtwNBLXcTmyT5jl3rNiyh8fgwIdjB3I3ArUcxOcX9tnJx6R5ymryzOWfP3yQUFOXO+/84YMPflTg1oIeC4fB5AE86jFAHSmKR8EoGAWjYIQAABoUXQvcwduMAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0006-6576-0352","institution":"Independent Researcher, Japan","correspondingAuthor":true,"prefix":"","firstName":"Takahiro","middleName":"","lastName":"Mitsui","suffix":""}],"badges":[],"createdAt":"2026-03-22 12:41:21","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9191253/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9191253/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105752209,"identity":"992e0c50-b858-44ce-b20e-7760d3967eb1","added_by":"auto","created_at":"2026-03-30 15:55:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":479658,"visible":true,"origin":"","legend":"","description":"","filename":"ContinuousStateDependentTemporalResponseScalesinGNSSSatelliteClockResiduals.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9191253/v1_covered_4fc29eae-4414-402c-a180-65bfc6f11aa2.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eContinuous, State-Dependent Temporal Response Scales in GNSS Satellite Clock Residuals\u003c/p\u003e","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":"GNSS, satellite clock residuals, temporal response, time-domain analysis, kernel response models, state dependence, model selection, AIC","lastPublishedDoi":"10.21203/rs.3.rs-9191253/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9191253/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe investigate whether GNSS satellite clock residuals are better described by a purely instantaneous response or by a finite temporal response with a characteristic time scale τ . 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