No Dris Conjecture Sources Found; Only Standard Number-Theory Identities Retrieved — E8 Intelligence Research

FINDING: Search returned only pedagogical number-theory content (divisor function d(n), σ(n), Möbius inversion) plus one unrelated LIGO paper; no source addressing the Dris conjecture or the q^k < n ↔ m² < n biconditional was retrieved. | MATH: Standard identities recovered: d(n) = ∏(aᵢ+1) for n = ∏pᵢ^aᵢ; σ(n) = ∏(pᵢ^(aᵢ+1)−1)/(pᵢ−1); ∑_{d|n} μ(d) = [n=1] (Möbius inversion identity). No Dris-specific content: the target claim (odd perfect n ⇒ q^k < n ⟺ m² < n, where n = q^k m², q ≡ k ≡ 1 mod 4, gcd(q,m)=1) is absent. | CONNECTION: None supported by evidence. The retrieved identities are multiplicative-arithmetic, not geometric. No ratios (0.382, 0.618, 0.786, 1.618, 2.618), base-60, crystallographic, root-system, or lattice content appears. | DEPTH: 1 — The search failed to surface the requested theorem; findings are textbook-level and do not advance the Dris conjecture. Recommend re-query with "odd perfect number Euler prime q^k m²" and "Dris 2012 arXiv" to obtain the actual proof. 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
2026-10-31
DOI
https://doi.org/10.5281/zenodo.23830715
Primary Topic
Analytic Number Theory Research
Type
preprint
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No Dris Conjecture Sources Found; Only Standard Number-Theory Identities Retrieved — E8 Intelligence Research

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

No Dris Conjecture Sources Found; Only Standard Number-Theory Identities Retrieved — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search returned only pedagogical number-theory content (divisor function d(n), σ(n), Möbius inversion) plus one unrelated LIGO paper; no source addressing the Dris conjecture or the q^k < n ↔ m² < n biconditional was retrieved. | MATH: Standard identities recovered: d(n) = ∏(aᵢ+1) for n = ∏pᵢ^aᵢ; σ(n) = ∏(pᵢ^(aᵢ+1)−1)/(pᵢ−1); ∑_{d|n} μ(d) = [n=1] (Möbius inversion identity). No Dris-specific content: the target claim (odd perfect n ⇒ q^k < n ⟺ m² < n, where n = q^k m², q ≡ k ≡ 1 mod 4, gcd(q,m)=1) is absent. | CONNECTION: None supported by evidence. The retrieved identities are multiplicative-arithmetic, not geometric. No ratios (0.382, 0.618, 0.786, 1.618, 2.618), base-60, crystallographic, root-system, or lattice content appears. | DEPTH: 1 — The search failed to surface the requested theorem; findings are textbook-level and do not advance the Dris conjecture. Recommend re-query with "odd perfect number Euler prime q^k m²" and "Dris 2012 arXiv" to obtain the actual proof. 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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