Axis Journal of Mathematical Statistics and Modelling
Goldbach Entropy and Analytic Compression: A Structural Theory of Additive Arithmetic
Abstract
Dhruva Janardana
This paper develops a foundational framework for understanding the structural limitations of analytic methods in additive number theory, using the binary Goldbach problem as a case study. We formalize how generating functions, Dirichlet series, circle-method asymptotics, and sieve bounds encode arithmetic information through averaging and smoothing (analytic compression). We define Goldbach entropy as a local invariant capturing representation structure, reformulate Goldbach as a uniform non-vanishing condition, and establish impossibility results explaining why average control cannot certify universal predicates.
