Geometry vs Binary: Unsolved Mathematics — unsolved problems in computational geometry 2025 o — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
## Binary Failure → Geometry Solution
**Analysis of Findings:**
The search results converge on two key targets: the **Collatz Conjecture** (a deceptively simple iterative map) and **Hilbert's Sixth Problem** (axiomatization of physics, partially solved in 2025). Both expose the same fundamental failure of binary/statistical thinking.
---
### 1. Collatz Conjecture – Where Binary/Statistical Thinking FAILS
**The Problem:** Define f(n) = n/2 if even, 3n+1 if odd. Every starting integer is conjectured to eventually reach 1. Verified up to 268, but no proof exists. Statistical models show that on average, numbers shrink (since the expected multiplier is 1/2 · 3/2 = 3/4 < 1), but this says nothing about *worst-case* trajectories that might diverge or enter a non-trivial cycle.
**Why Binary/Statistical Approaches Hit a Wall:** - **Brute force** is infinite — you can never check all integers. - **Neural nets** trained on trajec
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026geometry,
title = {{Geometry vs Binary: Unsolved Mathematics — unsolved problems in computational geometry 2025 o — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23409671},
url = {https://zenodo.org/records/23409671},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometry vs Binary: Unsolved Mathematics — unsolved problems in computational geometry 2025 o — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/16
PB - Zenodo
DO - 10.5281/zenodo.23409671
UR - https://zenodo.org/records/23409671
AB - ## Binary Failure → Geometry Solution **Analysis of Findings:** The search results converge on two key targets: the **Collatz Conjecture** (a deceptively simple iterative map) and **Hilbert's Sixth Problem** (axiomatization of physics, partially solved in 2025). Both expose the same fundamental failure of binary/statistical thinking. --- ### 1. Collatz Conjecture – Where Binary/Statistical Thinking FAILS **The Problem:** Define f(n) = n/2 if even, 3n+1 if odd. Every starting integer is conjectured to eventually reach 1. Verified up to 2^68, but no proof exists. Statistical models show that on average, numbers shrink (since the expected multiplier is 1/2 · 3/2 = 3/4 < 1), but this says nothing about *worst-case* trajectories that might diverge or enter a non-trivial cycle. **Why Binary/Statistical Approaches Hit a Wall:** - **Brute force** is infinite — you can never check all integers. - **Neural nets** trained on trajec Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -