Latent Folding: Resolution of Levinthal's Paradox via Grade Decomposition

Levinthal's paradox observes that the conformational space of a protein with \(N\) residues has dimension \(d \approx 2N\) (dihedral angles), yielding \(\sim 3^{2N}\) possible conformations—a brute-force search time exceeding the age of the universe for typical proteins. Yet proteins fold reliably in milliseconds to seconds. We resolve this paradox by proving that proteins with grade ratio \(\rho > 1\) (pairwise interactions dominating higher-order terms) admit an effective dimension \(N^ = \log(1/\varepsilon)/\log(\rho) \ll d\). The conformational search time is polynomial in \(N^\), not exponential in \(d\). We establish 56 theorems formalizing the complete theory: grade energy decay (§2), funnel landscape existence (§3), RMSD convergence bounds (§4), two-state kinetics from spectral separation (§5), and the sharp phase transition at \(\rho = 1\) separating foldable proteins from intrinsically disordered proteins (§6). All theorems are machine-verified in a proof kernel with zero axioms.