Extended_Meta_Architectural_Formulas__Cross_Domain_Applications_of_Novel_Scaling_Laws
Year: 2025
Type: article
Abstract: The Ukachi Scaling Laws: Fundamental Limits in Complex Systems We present the Ukachi Scaling Laws, a family of scaling relations describing system responses to exponentially growing inputs. From three complementary first-principles derivations (random-walk state exploration, renormalization-group scaling, and information-theoretic processing limits) we derive the canonical Ukachi form R(I) = k[logI]α, explain its domain of validity, and introduce a hybrid extension R(I) = k1[logI]α +k2Iβ, which couples information-limited amplification with classical allometric (power-law) behavior. We test the forms against simulated real-world datasets motivated by biology, physics, economics and neuroscience, present best-fit constants and goodness-of-fit metrics, and discuss the conceptual novelty and problems solved by this universality class. The manuscript includes reproducible fitting code snippets and tables with the simulated-data comparisons
Author: Ukachi Nmachuwku, Treasure
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7092626707
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