Minimalist Conjecture Unproven: Rank-29 Discovery, Conditional High-Rank Density Limits — E8 Intelligence Research

FINDING: Minimalist conjecture (50/50 rank distribution) remains unproven; recent progress includes rank-29 curve discovery and explicit rank≥5 families, but density-zero results for high ranks are still conditional on BSD and GRH. MATH: - Minimalist conjecture: \( \lim_{X\to\infty} \frac{\#\{E: \text{rank}(E)=0, \text{cond}(E) 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
2026-09-01
DOI
https://doi.org/10.5281/zenodo.22230181
Primary Topic
Intelligence, Security, War Strategy
Type
preprint
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preprint

Minimalist Conjecture Unproven: Rank-29 Discovery, Conditional High-Rank Density Limits — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Intelligence, Security, War Strategy
preprint

Minimalist Conjecture Unproven: Rank-29 Discovery, Conditional High-Rank Density Limits — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Minimalist conjecture (50/50 rank distribution) remains unproven; recent progress includes rank-29 curve discovery and explicit rank≥5 families, but density-zero results for high ranks are still conditional on BSD and GRH. MATH: - Minimalist conjecture: \( \lim_{X\to\infty} \frac{\#\{E: \text{rank}(E)=0, \text{cond}(E) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Intelligence, Security, War Strategy
DOIOpen Access PDFOpenAlex
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