Phi and Alzheimer's Disease: Is the Tree Drawing Test for diagnosing cognitive impairment an inner view of the golden proportion?”

Phi and Alzheimer's Disease: Is the Tree Drawing Test for diagnosing cognitive impairment an inner view of the golden proportion?” | 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 Phi and Alzheimer's Disease: Is the Tree Drawing Test for diagnosing cognitive impairment an inner view of the golden proportion?” Michelangelo Stanzani Maserati, Fabiana Zama This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8069544/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 12 You are reading this latest preprint version Abstract The golden ratio (φ ≈ 1.618) exhibits unique autosimilarity properties that appear throughout biological systems, including human physiology and neural organization. The Tree Drawing Test (TDT), a simple cognitive assessment tool that mainly implies visuospatial, praxic and executive functions, may capture φ-based organizational principles that become disrupted in neurodegenerative conditions. This study examined the relationship between golden ratio proportions and cognitive impairment in tree drawings through quantitative analysis of a large cohort of cognitively impaired patients. We evaluated 613 Alzheimer’s disease (AD) patients, 328 mild cognitive impairment (MCI) patients, and 438 healthy controls who completed the TDT. Novel golden ratio-based deviation indices were developed to quantify proportional relationships between trunk and crown dimensions. Classification quality metrics including Distance-to-Diameter Ratio (DDR), Fisher Ratio (FR), and Overlap Coefficient (OC) were employed to assess discriminative power across diagnostic groups. Among five proposed indices, the trunkbased measure H/φ − T emerged as the optimal classifier, achieving DDR exceeding 0.54 and FR above 0.56. The most remarkable finding was the emergence of Fibonacci sequence patterns in empirical data, with mean values across diagnostic groups (AD ≈ 5, MCI ≈ 12–13, healthy controls ≈ 33– 34) closely approximating consecutive Fibonacci numbers (5, 13, 34). Intergroup ratios consistently approached φ2 ≈ 2.618, suggesting that cognitive decline in TDT may follow discrete mathematical states along a Fibonacci progression. All pairwise diagnostic comparisons achieved statistical significance (p < 0.0001), with robust performance maintained across demographic stratifications. TDT golden ratio-based deviation measures provide mathematically discriminators for cognitive impairment assessment. The spontaneous emergence of Fibonacci patterns suggests that cognitive decline, diagnosed through the TDT, may follow mathematically predictable trajectories respecting deep structural constraints, establishing a foundation for developing φ-based biomarkers of neurological health and supporting the hypothesis that the TDT provides an “inner view” of golden proportion organization within cognitive architecture. Health sciences/Biomarkers Biological sciences/Computational biology and bioinformatics Health sciences/Diseases Health sciences/Neurology Biological sciences/Neuroscience Full Text Additional Declarations No competing interests reported. Supplementary Files Supplementary1.pdf Supplementary2.pdf Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 17 Feb, 2026 Reviews received at journal 07 Feb, 2026 Reviews received at journal 01 Feb, 2026 Reviewers agreed at journal 25 Jan, 2026 Reviewers agreed at journal 22 Jan, 2026 Reviewers agreed at journal 22 Jan, 2026 Reviewers agreed at journal 16 Dec, 2025 Reviewers invited by journal 02 Dec, 2025 Editor invited by journal 13 Nov, 2025 Editor assigned by journal 10 Nov, 2025 Submission checks completed at journal 10 Nov, 2025 First submitted to journal 09 Nov, 2025 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-8069544","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":554192456,"identity":"2a7b6d27-e71a-4ce7-bc31-a20eaf0cdfd6","order_by":0,"name":"Michelangelo Stanzani Maserati","email":"","orcid":"","institution":"Istituto delle Scienze Neurologiche di Bologna","correspondingAuthor":false,"prefix":"","firstName":"Michelangelo","middleName":"Stanzani","lastName":"Maserati","suffix":""},{"id":554192457,"identity":"92b70edf-9e06-477d-b703-68726b8008a6","order_by":1,"name":"Fabiana 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The Tree Drawing Test (TDT), a simple cognitive assessment tool that mainly implies visuospatial, praxic and executive functions, may capture φ-based organizational principles that become disrupted in neurodegenerative conditions. This study examined the relationship between golden ratio proportions and cognitive impairment in tree drawings through quantitative analysis of a large cohort of cognitively impaired patients. We evaluated 613 Alzheimer’s disease (AD) patients, 328 mild cognitive impairment (MCI) patients, and 438 healthy controls who completed the TDT. Novel golden ratio-based deviation indices were developed to quantify proportional relationships between trunk and crown dimensions. Classification quality metrics including Distance-to-Diameter Ratio (DDR), Fisher Ratio (FR), and Overlap Coefficient (OC) were employed to assess discriminative power across diagnostic groups. Among five proposed indices, the trunkbased measure H/φ − T emerged as the optimal classifier, achieving DDR exceeding 0.54 and FR above 0.56. The most remarkable finding was the emergence of Fibonacci sequence patterns in empirical data, with mean values across diagnostic groups (AD ≈ 5, MCI ≈ 12–13, healthy controls ≈ 33– 34) closely approximating consecutive Fibonacci numbers (5, 13, 34). Intergroup ratios consistently approached φ2 ≈ 2.618, suggesting that cognitive decline in TDT may follow discrete mathematical states along a Fibonacci progression. All pairwise diagnostic comparisons achieved statistical significance (p \u003c 0.0001), with robust performance maintained across demographic stratifications. TDT golden ratio-based deviation measures provide mathematically discriminators for cognitive impairment assessment. 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