The Return of π: Circular Symmetry as an Emergent Threshold Law

Dustyn Stanley

No snc8a_v1, OSF Preprints from Center for Open Science

Abstract: This essay reframes the mathematical constant pi as an emergent feature of entropic thresholds, harmonic flows, and dimensional constraints within physical systems. Drawing from the unified 1/E^2 suppression principle, harmonic boundary theory, and thermodynamic geometry, pi is explored not simply as a Euclidean geometric ratio, but as a structural inevitability of coherence-bound systems. It is proposed that pi encodes the perimeter of phase space transitions and appears universally where closed system behavior, entropic equilibrium, and flow constraints intersect. This recontextualization offers a potential explanation for pi’s ubiquity in physical, biological, and quantum systems.

Date: 2025-04-23
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Persistent link: https://EconPapers.repec.org/RePEc:osf:osfxxx:snc8a_v1

DOI: 10.31219/osf.io/snc8a_v1

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