Scattered Probability Bounds and CHSH-3 Randomness: No Direct Tsirelson-D4 Results — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are a scattered mix of probability-theory videos (Chernoff bounds, Markov/Tschebyscheff inequalities) and one relevant quantum information paper on CHSH-3 inequality violations for randomness generation. No direct Tsirelson-bound/D4-root-system content appears in the top results. | MATH: Chernoff bound: P(∑ Xi ≥ (1+δ)μ) ≤ exp(−δ2μ/3) for δ∈(0,1); Markov: P(X≥ a) ≤ E[X]/a; Tschebyscheff: P(|X−μ|≥ kσ) ≤ 1/k2. CHSH-3 inequality (from arXiv:2003.00124): a Bell-type inequality with three measurement settings per party; quantum violation computed via semidefinite programming (SDP) relaxations. | CONNECTION: The CHSH-3 paper's SDP hierarchy implicitly involves operator algebras and tensor products of qubit spaces — but no explicit D4 root system, golden ratio, or base-60 appears in the visible abstracts. The Chernoff bound's exponential decay has no direct geometric-harmony link. | DEPTH: 2 — The only s
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026scattered,
title = {{Scattered Probability Bounds and CHSH-3 Randomness: No Direct Tsirelson-D4 Results — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23409687},
url = {https://zenodo.org/records/23409687},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scattered Probability Bounds and CHSH-3 Randomness: No Direct Tsirelson-D4 Results — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/16
PB - Zenodo
DO - 10.5281/zenodo.23409687
UR - https://zenodo.org/records/23409687
AB - FINDING: The search results are a scattered mix of probability-theory videos (Chernoff bounds, Markov/Tschebyscheff inequalities) and one relevant quantum information paper on CHSH-3 inequality violations for randomness generation. No direct Tsirelson-bound/D4-root-system content appears in the top results. | MATH: Chernoff bound: P(∑ X_i ≥ (1+δ)μ) ≤ exp(−δ^2μ/3) for δ∈(0,1); Markov: P(X≥ a) ≤ E[X]/a; Tschebyscheff: P(|X−μ|≥ kσ) ≤ 1/k^2. CHSH-3 inequality (from arXiv:2003.00124): a Bell-type inequality with three measurement settings per party; quantum violation computed via semidefinite programming (SDP) relaxations. | CONNECTION: The CHSH-3 paper's SDP hierarchy implicitly involves operator algebras and tensor products of qubit spaces — but no explicit D4 root system, golden ratio, or base-60 appears in the visible abstracts. The Chernoff bound's exponential decay has no direct geometric-harmony link. | DEPTH: 2 — The only s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -