Finite Information, Two-Layer Geometry, and Informational Adjacency

Abstract

Central Thesis: Graph connectivity α determines quantum decoherence rate γ via γ = α×γlink when environmental noise couples to edges rather than nodes. The icosahedron (α = 5) has lower connectivity than the cubic lattice (α = 6), predicting 20% longer coherence time: τ5/τ6 = 6/5 = 1.20. This ratio is testable in neutral atom arrays with engineered bond noise. Derivation: We derive γ ∝ α from a bond-coupled bath Hamiltonian under explicit assumptions: Born-Markov (A1), secular (A2), identical edge baths (A3), and uncorrelated noise (A4). Numerical simulation confirms the ratio at 2% accuracy. Experimental Test: We propose comparing icosahedral and cuboctahedral 12-atom configurations in optical tweezers. Error budget analysis shows the predicted 20% difference exceeds estimated uncertainty by a factor of 7. Geometric Foundation: The icosahedron is selected by group theory (A5 is the unique maximal finite SO(3) subgroup with complex conjugate 3D irreps) and energy minimization (Thomson problem for N = 12).

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