Entanglement Persists at 1200 km with Attosecond Formation and Bounded Nonlocal Speed — E8 Intelligence Research

FINDING: Entanglement persists and is measured at 1200 km; formation timescale resolved to attosecond scale — no new fundamental constant, but a hard empirical bound on non-local correlation speed and decoherence limits. MATH: - Entanglement entropy (von Neumann): S = −Tr(ρ_A log ρ_A); for Bell state |Φ⁺⟩ = (|00⟩+|11⟩)/√2, S = 1 bit (maximal for 2-qubit). - Bell/CHSH inequality: |S| ≤ 2 (local realism); quantum max |S| = 2√2 ≈ 2.828. Violation ratio 2√2/2 = √2 ≈ 1.414. - Bell state amplitudes: 1/√2 ≈ 0.7071 (equal superposition coefficients). - Formation time τ ~ attoseconds (10⁻¹⁸ s) → energy scale ħ/τ ~ 10⁰–10¹ eV; consistent with ħ = 1.0546×10⁻³⁴ J·s. - 1200 km propagation: no-signaling constraint holds; correlation is non-causal, so no FTL information — consistent with relativity. CONNECTION: - √2 = 1.414 and 1/√2 = 0.7071 are the only exact ratios here; these are the diagonal/side ratio of the unit square (Pythagorean), not φ-family (0.618/1.618). - No evidence in these findings Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com