The Halting Problem: A Boundary of Undecidability, Not a Practical Limit — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The halting problem establishes a fundamental undecidability boundary in formal systems, not a practical tool for computation limits. | MATH: No equations, constants, or ratios emerge; the core is a diagonalization argument (Cantor-style) proving no total computable function H(p,i) can decide whether program p halts on input i. The proof constructs a program D that halts iff H(D,D) says it doesn't — a fixed-point contradiction. | CONNECTION: None to geometric harmony. The diagonalization is a self-referential lattice collapse, but no 0.618, 0.786, or base-60 structure appears. The only structural echo is the incompleteness of any finite axiom system (Gödel) — a boundary, not a ratio. | DEPTH: 4 — Profound for logic and computer science, but mathematically barren for geometric or numeric harmony. It defines a limit, not a pattern. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204134126
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