Testing the Density Profile of the Unified Informational Theory (TURI) on the Proton/Neutron: A Contribution to the Unification of Scales of Order 1034

Testing the Density Profile of the Unified Informational Theory (TURI) on the Proton/Neutron: A Contribution to the Unification of Scales of Order 1034 | 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 Testing the Density Profile of the Unified Informational Theory (TURI) on the Proton/Neutron: A Contribution to the Unification of Scales of Order 10 34 Amine Chbihi Moukit This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8932672/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 Starting from a cyclic universe and the strict conservation of total entropy (ΔS cycle = 0), we derived in a previous publication [1] the universal density profile ρ(r) = ρ₀ · sech⁸(r / r e ), which structurally resolves the Core-Cusp problem in galactic dynamics. The present work tests its application at the nuclear scale on the proton and neutron. For the proton, the triple convolution of valence quarks exactly reproduces the electric RMS radius r E = 0.84 fm, consistent with the CODATA 2022/CREMA consensus. The asymmetric approach (valence + chiral component δ M = 0.074, r e_cloud = 4.00 fm) reproduces r Magn ≈ 0.811 fm and improves G M /μ p at intermediate Q², but strongly underestimates at high Q² (no sea quarks, no perturbative QCD). G E (Q²) captures the initial slope but underestimates curvature at 0.05–0.10 GeV² relative to PRad 2019; this tension is less constraining than the PRad vs. Mainz 2010 discordance. The extension to the neutron reproduces ⟨r²⟩ E n ≈ −0.115 fm² and r M n ≈ 0.82 fm within uncertainties, via an adjusted chiral fraction (δ n = 0.12, r e_val ≈ 1.29–1.30 fm), naturally capturing isospin breaking and the non-vanishing of G E n (Q²). Falsifiable predictions: positive curvature of G E from Q² = 0.020 GeV² (+5.8% vs. Taylor, accentuated to +14.3% at Q² = 0.050), testable by PRad-II; perfect lepton universality (MUSE); stability of the ratio R = μ p G E /G M ≈ 2.78–2.79 up to Q² ≈ 2 GeV² (EIC phase 1). If confirmed, these signatures would validate sech⁸ universality and a unification of scales of order 10 34 . Nuclear Physics Proton neutron charge radius TURI density form factor non-perturbative QCD isospin breaking sech⁸ universality 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-8932672","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":594834362,"identity":"2c60e6e1-1bee-402e-a8f2-3df841730dc2","order_by":0,"name":"Amine Chbihi Moukit","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIie3SMQrCMBSA4dRAXFK7JijtFSpeqJncXDraoRKIizhKF+/gESqBXqId6tLJoZO4KCbo4hLjJph/eISQj7cEAJfrJ/NyNcoEEW/VqoO+aa0Jj58ExjarygQQgIgVCXZStH3WLEZjLpY4a8IAQNSbCKnZelpUXYomR1HjqpvRHMLCuKZmYuznkgnCFEGSHcpAGkWkye1FUnzXBEIjiTXxXgT6woJMFaGbSqaIME73Wzmj/AMJ63lHrplcRMX81J8vMgyG3EzeGmA9vwDqI1y/ee1yuVx/0wMHB08p9Y5A/QAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-5566-3376","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Amine","middleName":"Chbihi","lastName":"Moukit","suffix":""}],"badges":[],"createdAt":"2026-02-21 10:30:10","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-8932672/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8932672/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103506056,"identity":"20a27c6d-363e-4022-8ac8-b219d0d7a734","added_by":"auto","created_at":"2026-02-26 13:33:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":536556,"visible":true,"origin":"","legend":"","description":"","filename":"ArticleUITProtonNeutronAng.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8932672/v1_covered_4056d04c-9472-4aee-a7c0-114a4129785e.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eTesting the Density Profile of the Unified Informational Theory (TURI) on the Proton/Neutron: A Contribution to the Unification of Scales of Order 10\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e34\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Independent Researcher","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":"Proton, neutron, charge radius, TURI density, form factor, non-perturbative QCD, isospin breaking, sech⁸ universality","lastPublishedDoi":"10.21203/rs.3.rs-8932672/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8932672/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eStarting from a cyclic universe and the strict conservation of total entropy (ΔS\u003csub\u003ecycle\u003c/sub\u003e = 0), we derived in a previous publication [1] the universal density profile ρ(r) = ρ₀ · sech⁸(r / r\u003csub\u003ee\u003c/sub\u003e), which structurally resolves the Core-Cusp problem in galactic dynamics. The present work tests its application at the nuclear scale on the proton and neutron.\u003c/p\u003e\n\u003cp\u003eFor the proton, the triple convolution of valence quarks exactly reproduces the electric RMS radius r\u003csub\u003eE\u003c/sub\u003e = 0.84 fm, consistent with the CODATA 2022/CREMA consensus. The asymmetric approach (valence + chiral component δ\u003csub\u003eM\u003c/sub\u003e = 0.074, r\u003csub\u003ee_cloud\u003c/sub\u003e = 4.00 fm) reproduces r\u003csub\u003eMagn\u003c/sub\u003e ≈ 0.811 fm and improves G\u003csub\u003eM\u003c/sub\u003e/μ\u003csub\u003ep\u003c/sub\u003e at intermediate Q², but strongly underestimates at high Q² (no sea quarks, no perturbative QCD). G\u003csub\u003eE\u003c/sub\u003e(Q²) captures the initial slope but underestimates curvature at 0.05–0.10 GeV² relative to PRad 2019; this tension is less constraining than the PRad vs. Mainz 2010 discordance.\u003c/p\u003e\n\u003cp\u003eThe extension to the neutron reproduces ⟨r²⟩\u003csub\u003eE\u003c/sub\u003e\u003csup\u003en\u003c/sup\u003e ≈ −0.115 fm² and r\u003csub\u003eM\u003c/sub\u003e\u003csup\u003en\u003c/sup\u003e ≈ 0.82 fm within uncertainties, via an adjusted chiral fraction (δ\u003csub\u003en\u003c/sub\u003e = 0.12, r\u003csub\u003ee_val\u003c/sub\u003e ≈ 1.29–1.30 fm), naturally capturing isospin breaking and the non-vanishing of G\u003csub\u003eE\u003c/sub\u003e\u003csup\u003en\u003c/sup\u003e(Q²).\u003c/p\u003e\n\u003cp\u003eFalsifiable predictions: positive curvature of G\u003csub\u003eE\u003c/sub\u003e from Q² = 0.020 GeV² (+5.8% vs. Taylor, accentuated to +14.3% at Q² = 0.050), testable by PRad-II; perfect lepton universality (MUSE); stability of the ratio R = μ\u003csub\u003ep\u003c/sub\u003e G\u003csub\u003eE\u003c/sub\u003e/G\u003csub\u003eM\u003c/sub\u003e ≈ 2.78–2.79 up to Q² ≈ 2 GeV² (EIC phase 1). If confirmed, these signatures would validate sech⁸ universality and a unification of scales of order 10\u003csup\u003e34\u003c/sup\u003e.\u003c/p\u003e","manuscriptTitle":"Testing the Density Profile of the Unified Informational Theory (TURI) on the Proton/Neutron: A Contribution to the Unification of Scales of Order 1034","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-24 06:13:10","doi":"10.21203/rs.3.rs-8932672/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"87815572-66c8-4e9f-b265-e7e514004096","owner":[],"postedDate":"February 24th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63422351,"name":"Nuclear Physics"}],"tags":[],"updatedAt":"2026-02-24T06:13:10+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-24 06:13:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8932672","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8932672","identity":"rs-8932672","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}