From a conjecture of Collatz to Thompson's group F, via a conjunction of Girard

Peter Hines

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arXiv · 2202.04443

From a conjecture of Collatz to Thompson's group F, via a conjunction of Girard

Peter Hines

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Abstract

The famous 3x + 1 problem of L. Collatz needs no introduction; however, this paper concerns a lesser-known, but similarly unresolved, precursor problem : the Original Collatz Conjecture, or OCC. We demonstrate that the core arithmetic operator from the OCC, when combined with a conjunction of J.-Y. Girard from his Geometry of Interaction system, leads to a realisation of R. Thompson's group F as congruential functions, in the sense of J. Conway. We also give the underlying category theory that accounts for this, and describe the core operator from the OCC as a canonical coherence isomorphism.

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Peter Hines. 2022-02-09. From a conjecture of Collatz to Thompson's group F, via a conjunction of Girard. https://arxiv.org/abs/2202.04443

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