The Ternary Balance Function: A Philosophical Framework Unifying Goldbach and Riemann Hypothesis

We present a novel mathematical-philosophical framework, dubbed”Cosmic Mathematics,” grounded in the concept of a cosmic trinity.From this philosophical foundation, we construct a Balance Function,B(N), that offers a unified perspective on Goldbach’s Conjecture andthe Riemann Hypothesis. While our model does not claim to provideabsolute, independent mathematical proofs, it demonstrates thatwithin a coherent and self-contained axiomatic system, these conjecturesemerge as necessary consequences. We rigorously distinguish betweenresults derived within our model (model-dependent theorems)and traditional, universally accepted mathematical proofs. Our approachintroduces key concepts such as a neutral pole, ternary balancerepresentations of even numbers, spectral balance functions, anda complex-analytic extension of B(N) to B(z), establishing strikingstructural parallels with known problems in analytic number theory.This work provides a theoretical model where Goldbach’s Conjectureand the Riemann Hypothesis emerge as natural consequences of aternary balance principle. While not absolute proofs, our results suggestdeep structural connections.