Atlas — Volume 3: The Hologram and the Atomic Model
Year: 2026
Type: preprint
Abstract: The third volume of the Atlas series studies a family of finite monoids and the constructions they allow — coordinates, evolutions, commutation graphs, projections, catalogues of laws, and atomic models — in order to understand which mechanisms arise from simple composition rules, and then to examine the scope of their physical interpretation. At its centre is the odometer monoid M_L(A_K), presented by K idempotent generators; its (K+1)! states are indexed by permutations. The book consistently separates computation — a general proof, a cited classical theorem, or an exact check at the enumerated ranks, labelled [P] — from physical interpretation, a proposed hypothesis or correspondence, labelled [BRIDGE]: no conclusion is stronger than what it establishes, and counterexamples hold a central place. The work is reproducible: every result carries a standalone kit (standard library only) — command, blocking checks, and expected output — and a computation companion (a REPL) lets the reader re-run and compare each verification. A preface and twenty-eight chapters, in three movements: the substrate, the hologram, and the atomic model.
Author: Allaghi, Sami
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222579278
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