Voyage by Catamaran: Effecting Semantic Network "Bricolage" via Infinite-Dimensional Zero-Divisor Ensembles

TL;DR

This paper explores the mathematical foundations of scale-free networks using zero-divisor structures in complex systems, revealing new insights into network fractality and potential for cross-domain infiltration.

Contribution

It introduces a novel zero-divisor ensemble framework based on infinite-dimensional structures, linking algebraic properties to network topology and bricolage processes.

Findings

Identifies spandrel structures linked to scale-free networks

Shows recursive embedding of octonions within zero-divisor ensembles

Proposes a new algebraic approach to network bricolage

Abstract

Continuing arguments presented [1] or announced [2][3] in "Complex Systems," zero-divisor (ZD) foundations for "scale-free" networks (evinced, in particular, in the "fractality" of the Internet) are decentralized. Spandrels, quartets of ZD-free or "hidden" box-kite-like structures (HBKs) in the 2^(N+1)- ions, are "exploded" from (and uniquely linked to) each standard box-kite in the 2^N-ions, N > 3. Any HBK houses, in a "cowbird's nest," exactly one copy of the (ZD-free) octonions, the recursive basis for all ZD ensembles. Each is a potential waystation for alien-ensemble infiltration in the large, or metaphor-like jumps in the small. Cowbirding models what evolutionary biologists [4], and structural mythologist Claude Levi-Strauss before them [5], term bricolage: the opportunistic co-opting of objects designed for one purpose to serve others unrelated to it. Such arguments entail switching focus, from the octahedral box-kite's four triangular "sails," to its trio of square "catamarans" and their box-kite-switching "twist products."