Auditing coherence through the principle of a single functional mapping

Auditing coherence through the principle of a single functional mapping | 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 Auditing coherence through the principle of a single functional mapping Hedayat Haddadi, Adam Kloskowski, Piotr Mironowicz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8072048/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 The reliability of scientific conclusions is increasingly challenged by combining diverse datasets and evaluating predictive models. Apparent consensus can hide structural breaks or hidden disorder, leading to miscalibration and incorrect inferences. We introduce the Agreement–Entropy Map (AEM), a rigorously developed classifier that combines overlap-gated structural tests with entropy-based disorder detection. The framework supports the principle of a single functional mapping: only subsets or models that are consistent in both structure and disorder are considered reliable. Formal derivations show that entropy predictably rises with variance imbalance, slope offsets, or multimodality, complementing the Chow test, which does not detect such disorder. When applied to predictive models, the AEM measures coherence with physical laws and offers a systematic way to audit physics-informed machine learning. In doing so, it adds a missing axis of reliability for modern science—one that differentiates genuine coherence from apparent agreement amid vast, diverse data. Physical sciences/Mathematics and computing/Statistics Physical sciences/Chemistry/Cheminformatics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryInformation9.docx Auditing coherence through the principle of a single functional mapping 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-8072048","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":545543979,"identity":"055f412d-b04e-45eb-bc8a-8a58c8f8baaf","order_by":0,"name":"Hedayat 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