Logarithmic Curvature as an Asymptotic Diagnostic: A Structural Framework for Growth Classification
Year: 2026
Type: preprint
Abstract: We study the scale-normalized curvature of logarithmic growth, \mathcal{C}(n) = \frac{n\Phi''(n)}{\Phi'(n)}, as a structural diagnostic for asymptotic behavior. By defining the curvature index as the elasticity of the logarithmic slope, we provide a unified framework for identifying polynomial, exponential, and super-exponential regimes. The work connects regular variation theory to Large Deviation Theory via curvature-Legendre duality and proposes an empirical method for predicting the growth of sequences with unknown asymptotics."
Author: Sahai, Adhrit Mohan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7133201673