Perelman and Metamonism: Topological Negation of Singularity in Mathematics and Cosmology

This paper draws a parallel between the methodology of Grigori Perelman, who proved the Poincaré conjecture through the analysis of singularities in the Ricci flow, and the principles of Metamonism—a proto-ontological model that negates the concept of a “beginning of the Universe.” The analysis shows that Perelman’s rejection of institutional recognition and his focus on the intrinsic logic of mathematical objects correlate with Metamonism’s ontological rejection of the Big Bang dogma. In both cases, singularity is treated not as an ontological fact but as a limit of method, overcome through an understanding of topological closure and the dynamics of self negation (∇U). The paper concludes by proposing a reinterpretation of key cosmological phenomena and deriving falsifiable predictions for a stationary model of an eternal field of ontological difference.