Debunking the False Link Between Maynard–Tao Sieve and Golden Ratio — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Search results conflate Maynard–Tao sieve theory with golden-ratio geometry; no direct evidence links sieve weights to 0.618 optimality. | MATH: Maynard–Tao sieve uses multidimensional weights W(n) = ∑di | n+hi λd1,…,dk with λ chosen to maximize ∑n≤ x (∑i=1k 1n+hi prime − ρ ) W(n)2, yielding k-tuples with liminf (pn+k−pn) ≪ k ek (Maynard 2013). No constant 0.618 appears in the sieve construction; optimal smoothing is polynomial (e.g., P(log x)), not golden. | CONNECTION: The golden ratio appears only in unrelated Numberphile videos and a paper on self-application (arXiv:2510.08934) — no mathematical bridge to sieve theory. The only shared feature is the number 1.618 as a ratio, but sieve weights are optimized via linear programming and Selberg's Λ2, not via geometric proportion. | DEPTH: 2 — The search query itself is a false premise; the results are a
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026debunking,
title = {{Debunking the False Link Between Maynard–Tao Sieve and Golden Ratio — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23465032},
url = {https://zenodo.org/records/23465032},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Debunking the False Link Between Maynard–Tao Sieve and Golden Ratio — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23465032
UR - https://zenodo.org/records/23465032
AB - FINDING: Search results conflate Maynard–Tao sieve theory with golden-ratio geometry; no direct evidence links sieve weights to 0.618 optimality. | MATH: Maynard–Tao sieve uses multidimensional weights W(n) = ∑_d_i | n+h_i λ_d_1,…,d_k with λ chosen to maximize ∑_n≤ x (∑_i=1^k 1_n+h_i prime − ρ ) W(n)^2, yielding k-tuples with liminf (p_n+k−p_n) ≪ k e^k (Maynard 2013). No constant 0.618 appears in the sieve construction; optimal smoothing is polynomial (e.g., P(log x)), not golden. | CONNECTION: The golden ratio appears only in unrelated Numberphile videos and a paper on self-application (arXiv:2510.08934) — no mathematical bridge to sieve theory. The only shared feature is the number 1.618 as a ratio, but sieve weights are optimized via linear programming and Selberg's Λ^2, not via geometric proportion. | DEPTH: 2 — The search query itself is a false premise; the results are a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -