Topological Confinement Matrices and Asymptotically Rigid Hilbert Space Structures in Quantum Chemistry and Protein Folding (v1.0)
Year: 2026
Type: dataset
Abstract: This preprint introduces the molecular and biochemical extension of The Bell TowerArchitecture. By taking the asymptotic limit (ε → 0) of the discrete lattice Z^3, we define acontinuous rigid field Φ(z) governed by Weierstrass infinite products and Mittag-Leffler expansions. This geometric framework replaces traditional Linear Combination of Atomic Orbitals (LCAO) approximations and eliminates artificial electron-overlap singularities. When mapped onto fermionic probability density |ψ|^2 , the exact Cartesian bundle constrainty = kx + 1/(2k) identically vanishes the non-linear vortex stretching term, (ω · ∇)u ≡ 0,establishing absolute topological protection. Numerical extraction on a 150 × 150 computational mesh confirms a peak core density |ψ|^2 max = 0.9974, a regularized external vacuum integrity |ψ|^2 min = 7.7413 × 10−208, and a non-latent geometric restoring gradient of 5.9792.This structural mechanism provides a deterministic solution to Levinthal’s Paradox in protein folding, translating biochemical efficiency into an intrinsic property of a rigid Hilbert space
Author: Gabbianelli, Silvio
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
OpenAlex ID: W7207558719