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

Official public reference library:GitHub repository: https://github.com/devinromberger123-prog/rgl-scalingSoftware DOI: https://doi.org/10.5281/zenodo.19212391 As of current, the combined 12 articles that were posted have a total of 754 views and 475 downloads within 1 month or less of being public. I truly hope this has been helpful to your work. I will be the first to admit that I am a private researcher without grant funding, doing this on my own time and money. I do not have the privilege of publishing in large peer-reviewed journals (yet). For these reasons, are why I chose to publish here. Please forgive me as I know everything may not be perfect, but I will actively make corrections. I sincerely thank you all for taking the time to review my work. If anyone would be willing to sponsor my work, and/or even be willing to collaborate, I would be extremely grateful. If not, all I ask is to give credit where credit is due. Please reach me personally at http://linkedin.com/in/devin-romberger-92385420a. My goal was to make this work open source to the public. Now, please respect that. Please do the right thing. Reference your sources. Thank you. --------------------------------------------------------------------------------------------------------------------------------------------- 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. Keywords: Universality Classes Renormalization Group Theory Scaling Exponents Stochastic Perturbation Critical Transitions Bifurcation Theory Nonlinear Dynamics