Unity as Closure Capacity: The Borwein Threshold

Zenodo (CERN European Organization for Nuclear Research) 2026 Preprint Open access

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Authors: Clifford Keeble
DOI: 10.5281/zenodo.18132552
Cited by: 6

Abstract

The Borwein integrals demonstrate that mathematical patterns can break at finite points. The breaking condition is unity: when contributions sum to more than 1, the pattern fails. This paper provides a rigorous foundation for closure capacity, connecting the Borwein theorem to the Bootstrap Universe framework. For the canonical odd sequence, exactly 6 = 3! = D! terms fit before breakdown — the dimensional signature of D = 3.

Fields of Study & Subjects

Cellular Automata and Applications Quasicrystal Structures and Properties semigroups and automata theory

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
2 January 2026
Document type
Preprint