No Unsolved Competition Problem Found; Collatz Conjecture Dominates Search Results — E8 Intelligence Research

FINDING: Search returned no unsolved competition problem; dominant result is the Collatz Conjecture — an open problem, not a competition problem — plus a benchmark dataset and routine Olympiad content. | MATH: Collatz map T(n) = n/2 if n≡0 (mod 2); T(n) = 3n+1 if n≡1 (mod 2). Conjecture: ∀n∈ℤ⁺, ∃k: Tᵏ(n)=1. Verified computationally to ~2⁶⁸. No proof of termination or of any nontrivial cycle exists. | CONNECTION: None supported. No 0.382/0.618/0.786/1.618/2.618, no base-60, no crystallographic/root-system/lattice structure appears in the evidence. The 3n+1 map is a piecewise-linear dynamical system on ℤ; its known invariant is the 2-adic parity vector, not a geometric ratio. | DEPTH: 2 FINDING: The MATH dataset (Hendrycks et al., arXiv:2103.03874) is the only substantive technical artifact — 12,500 competition problems with full step-by-step solutions, built to measure machine mathematical reasoning. | MATH: 12,500 problems; 7 subject areas; difficulty levels 1–5; answer format is a si Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-27
DOI
https://doi.org/10.5281/zenodo.23690519
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

No Unsolved Competition Problem Found; Collatz Conjecture Dominates Search Results — E8 Intelligence Research

Andrew Stewart Caldin
11 links
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

No Unsolved Competition Problem Found; Collatz Conjecture Dominates Search Results — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search returned no unsolved competition problem; dominant result is the Collatz Conjecture — an open problem, not a competition problem — plus a benchmark dataset and routine Olympiad content. | MATH: Collatz map T(n) = n/2 if n≡0 (mod 2); T(n) = 3n+1 if n≡1 (mod 2). Conjecture: ∀n∈ℤ⁺, ∃k: Tᵏ(n)=1. Verified computationally to ~2⁶⁸. No proof of termination or of any nontrivial cycle exists. | CONNECTION: None supported. No 0.382/0.618/0.786/1.618/2.618, no base-60, no crystallographic/root-system/lattice structure appears in the evidence. The 3n+1 map is a piecewise-linear dynamical system on ℤ; its known invariant is the 2-adic parity vector, not a geometric ratio. | DEPTH: 2 FINDING: The MATH dataset (Hendrycks et al., arXiv:2103.03874) is the only substantive technical artifact — 12,500 competition problems with full step-by-step solutions, built to measure machine mathematical reasoning. | MATH: 12,500 problems; 7 subject areas; difficulty levels 1–5; answer format is a si Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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No Unsolved Competition Problem Found; Collatz Conjecture Dominates Search Results — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS