BB(5) Resolved: Maximum Halting Steps = 47,176,870 — E8 Intelligence Research

FINDING: The exact value of the 5‑state Busy Beaver function BB(5) has been determined, establishing a concrete upper bound on what any Turing machine can compute before halting. MATH: BB(5) = 47 176 870 (the maximum number of steps executed by any halting 5‑state, 2‑symbol Turing machine before termination). CONNECTION: No explicit link to geometric harmonics (φ‑ratios, base‑60, crystallographic symmetries) is reported in the supplied sources. DEPTH: 8 – The result resolves a long‑standing open problem in computability theory, providing a finite, non‑trivial benchmark that illustrates the sharp boundary between computable and non‑computable growth rates. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-08
DOI
https://doi.org/10.5281/zenodo.24048988
Primary Topic
Computability, Logic, AI Algorithms
Type
preprint
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BB(5) Resolved: Maximum Halting Steps = 47,176,870 — E8 Intelligence Research

Andrew Stewart Caldin
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Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
preprint

BB(5) Resolved: Maximum Halting Steps = 47,176,870 — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: The exact value of the 5‑state Busy Beaver function BB(5) has been determined, establishing a concrete upper bound on what any Turing machine can compute before halting. MATH: BB(5) = 47 176 870 (the maximum number of steps executed by any halting 5‑state, 2‑symbol Turing machine before termination). CONNECTION: No explicit link to geometric harmonics (φ‑ratios, base‑60, crystallographic symmetries) is reported in the supplied sources. DEPTH: 8 – The result resolves a long‑standing open problem in computability theory, providing a finite, non‑trivial benchmark that illustrates the sharp boundary between computable and non‑computable growth rates. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
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