Finite Information Numbers through the Inductive Combinatorial Hierarchy

TL;DR

This paper explores the properties of finite information numbers through a hierarchical framework, analyzing entropic constraints and self-similarity to address a conjecture about physical process restrictions.

Contribution

It introduces a novel hierarchical approach to analyze finite information numbers and provides a mathematical framework for entropic constraints related to Gisin's conjecture.

Findings

Decomposition of binary entropies into fractal sequences

Construction of a unique formula and partition function for entropic sets

Proof of self-similarity and symbolic series satisfying the FIN conjecture

Abstract

We report on a recent conjecture by Gisin on a restriction of physical processes in sets of finite information numbers (FIN) and further analyze the entropic constraint associated with the proposed algorithm. In the course, we provide a decomposition of binary entropies in a pair of fractal sequences as functional composites of binary digit-sum functions and we construct a unique formula and an abstract partition function for these. We also prove, based on a previously introduced tool of the inductive combinatorial hierarchies that the naturally inherited self-similarity of the resulting hierarchy of entropic sets contains equivalence classes providing unlimited symbolic series for satisfying the demand posed by the FIN conjecture.