Bivariate Scaling Relationship Between Stochastic Perturbation and Critical Proximity in Nonlinear Dynamical Systems

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 document records a mathematical scaling relationship describing how stochastic perturbations interact with proximity to critical transitions in nonlinear dynamical systems. An empirically observed bivariate scaling form is stated, along with a derived perturbation threshold relationship and a hub-dependent geometric correction factor. A validation taxonomy is provided to delineate confirmed empirical baselines from theoretical predictions. This memorandum places the mathematical relationships into the public scientific record to establish definitive prior art and ensure open accessibility. Keywords: nonlinear dynamicscritical transitionsscaling lawstochastic perturbationFeigenbaumuniversalityinstability threshold