A Predictive Roadmap for Stochastic Scaling Exponents Across Universality Classes: Identifying the Mathematical Gaps

A Predictive Roadmap for Stochastic Scaling Exponents Across Universality Classes: Identifying the Mathematical Gaps | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 24 March 2026 V1 View latest version Share on A Predictive Roadmap for Stochastic Scaling Exponents Across Universality Classes: Identifying the Mathematical Gaps Author : Devin Romberger 0000-0002-3550-3199 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.177437413.35916861/v1 149 views 60 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This memorandum serves as a predictive roadmap for the application of the universal bivariate scaling law, V_eff(μ, σ) = μ^γ * F(σ / μ^κ), across divergent topological routes to chaos. By isolating the universal scaling architecture from class-specific geometric constants, we identify the solved eigenvalues for established universality classes and explicitly define the unmapped stochastic eigenvalues required to resolve higher-order and non-unimodal critical transitions. A validation taxonomy is provided to delineate confirmed empirical baselines from theoretical predictions. This work is a preprint. The original data record and timestamped version are archived at Zenodo: https://doi.org/10.5281/zenodo.18825703 Supplementary Material File (edit 3.0.pdf) Download 154.52 KB Information & Authors Information Version history V1 Version 1 24 March 2026 V2 Version 2 01 April 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords bifurcation theory critical transitions nonlinear dynamics renormalization group theory stochastic perturbation universality classes Authors Affiliations Devin Romberger 0000-0002-3550-3199 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 149 views 60 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Devin Romberger. A Predictive Roadmap for Stochastic Scaling Exponents Across Universality Classes: Identifying the Mathematical Gaps. Authorea . 24 March 2026. DOI: https://doi.org/10.22541/au.177437413.35916861/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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