Chebyshev's Inequality vs. Bias: Search Conflation and Lattice QCD — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Search results conflate Chebyshev's inequality (probability) with Chebyshev's bias (number theory); the only lattice-related hit is a lattice QCD paper, not the prime race modulo 3. | MATH: Chebyshev's inequality: P(|X−μ| ≥ kσ) ≤ 1/k². Chebyshev's bias (unretrieved but implied by query): π(x;3,1) < π(x;3,2) for most x, with logarithmic density ~0.999...; the bias vanishes only at exceptional zeros. Lattice QCD: heavy-quark masses from Fermilab method, one-loop perturbation theory, staggered quarks — no explicit constants given. | CONNECTION: The prime race modulo 3 lives on the hexagonal lattice (roots of A₂, Eisenstein integers ℤ[ω], ω=e^{2πi/3}). The bias is tied to the sign of the Dirichlet L-function L(s,χ₃) at s=1/2 — χ₃ is the quadratic character mod 3, whose conductor 3 is the hexagonal lattice's symmetry order. The ratio 0.618 appears nowhere in the retrieved data; the lattice QCD paper uses cubic lattices, not hexagonal. | DEPTH: 3 — the search failed to retrieve the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204949590
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