Structural Parallels Between NP-Completeness and Rank-2 Root Systems — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The search results span two distinct mathematical domains — computational complexity (P vs NP, NP-hardness) and Lie theory (root systems) — with no direct evidence linking them in the provided sources. | MATH: No explicit equations, constants, or ratios are given in the abstracts; only structural concepts: NP-hardness (decision problems reducible in polynomial time), complexity classes (P, NP, NP-complete), root systems of rank 2 (finite reflection groups, Cartan matrices, Dynkin diagrams), and Tetris clearing/survival complexity (single-piece-type restriction). | CONNECTION: Root systems are crystallographic by definition — their Weyl groups are finite reflection groups with integer Cartan integers (2, -1, 0 for A₂, B₂, G₂). The rank-2 root systems exhibit angles 60°, 90°, 120°, 150° — yielding ratios of squared lengths 1:1, 1:2, 1:3. These are not the golden-ratio family (0.382, 0.618, 0.786, 1.618, 2.618) nor base-60. No geometric harmony link is supported by the given abst Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204941084
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