Operational Bounds and Null Tests for Phase-Quantization Residuals in Spinor Readout

Operational Bounds and Null Tests for Phase-Quantization Residuals in Spinor Readout | 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 Operational Bounds and Null Tests for Phase-Quantization Residuals in Spinor Readout Atsushi Otsuka This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8982870/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 specify an explicit readout-layer interface for coarse-grained phase reporting by introducing a non-anticipating phase-quantizer map ΠΔt with sampling increment Δt and declared phase step δθ = ωΔt. A declared digital pipeline produces a pre-quantized estimate ˜θ from recorded data and metadata and reports ˆθ = ΠΔt(˜θ) on a phase grid. We define the projection residual as a reportable component, εproj = ΠI(˜θ − ˆθ), under a declared principal-interval convention ΠI. For canonical non-anticipating reporting using a floor-type quantizer, the residual at a spinor landmark θ⋆ = π (mod 2π) admits the explicit scalar form εproj = π − δθ⌊π/δθ⌋ and the sharp universal bound 0 ≤ εproj < δθ, independent of platform-specific noise models. The residual vanishes only on the countable commensurability set δθ = π/n (n ∈ N), yielding explicit refutation targets under controlled δθ-sweeps. Using the established SU(2) spinor periodicity U(2π) = −I as a geometric guarantee of a robust π-landmark, we propose falsifiable null-test protocols based on local contrasts between commensurate and nearby incommensurate steps and provide minimal decision rules suitable for measurement reports. No Hamiltonians, commutators, or microscopic dynamics are modified; the testable content resides entirely in the declared readout/interface map and its predicted sweep signature. phase-quantization residual non-anticipating readout commensurability null test spinor holonomy declared measurement model quantum phase estimation Full Text Additional Declarations No competing interests reported. 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. 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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-8982870","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":597861550,"identity":"1b5a9d5c-596f-4ec0-af70-41cbc5bc0185","order_by":0,"name":"Atsushi Otsuka","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVRIiWNgGAWjYJACxgYY9QFIsbETUs+GpIVxBkiAmXgtDAzMPGCSgA5++fZnkjNqGOR0Zzc3f7b5tU2ej5mB8cPHHNxaJNt4zCQ3HGMwNrtzsE06t++2YRszA7PkzG24tRgc42GTfMDGkLjtRmIbc27PbUagFjZmXrxa2J9JPvgH1tL82bLntj0RWhjMJDe2gbU0SDP8uJ1IUItkW46x5cw+CWMzoMMkextuJ7cxMzbj9Qs/8/GHN3u+2ciZ3Uh//OHHn9u289ubD374iEcLFEhAKMY2MNlAUD0S+EOK4lEwCkbBKBgpAAAx3k7L06zZngAAAABJRU5ErkJggg==","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Atsushi","middleName":"","lastName":"Otsuka","suffix":""}],"badges":[],"createdAt":"2026-02-27 03:10:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8982870/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8982870/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106686782,"identity":"69a9a231-5175-4eaa-987d-e43a8d178bb6","added_by":"auto","created_at":"2026-04-11 16:40:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":350467,"visible":true,"origin":"","legend":"","description":"","filename":"Submission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8982870/v1_covered_37ff0e2c-5bff-4c18-b526-4a873e181042.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\nOperational Bounds and Null Tests for Phase-Quantization Residuals in Spinor Readout","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":"phase-quantization residual, non-anticipating readout, commensurability null test, spinor holonomy, declared measurement model, quantum phase estimation","lastPublishedDoi":"10.21203/rs.3.rs-8982870/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8982870/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe specify an explicit readout-layer interface for coarse-grained phase reporting by introducing a non-anticipating phase-quantizer map ΠΔt with sampling increment Δt and declared phase step δθ = ωΔt. 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