A Closed-Form Value for the Generalized Uncertainty Principle Parameter: β 0 = 4 3 ln 2 from a Close-Packed Vacuum Lattice

Raghu Kulkarni

Published Aug 21, 2026• 0 citations

Abstract

The generalized uncertainty principle (GUP) modifies the Heisenberg relation by a term β₀(ℓ_P Δp/ħ)² and implies a minimal length Δx_min = √β₀ ℓ_P. Theory expects β₀ ~ 1 but does not fix its value; experiments bound it from above. Here we report a closed-form value, β₀ = (4/3) ln 2 ≈ 0.9242, obtained from two published inputs of the Selection–Stitch Model (SSM): a minimal approach distance r_min = L/√3 set by lattice geometry, and a bond length L = 2√(ln 2) ℓ_P set by an exact, codeword-independent entanglement calibration of the model's [[3L_s³, 2L_s³+2, 3]] vacuum code. The same inputs fix the model's macroscopic decoherence threshold m_soft = ħ/(Lc), which yields a bridge identity, β₀ = (1/3)(m_P/m_soft)². The identity ties two separate experimental programs — deformed-commutator tests and microgram-scale superposition tests — to one quantity, and it can be tested without adopting the model: a measured decoherence threshold predicts β₀, and conversely. All assumptions are tagged.

DOI: 10.13140/rg.2.2.30223.14245

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