A Statistical Topos Model of Protein Folding: From the Peptide Monoid to Weighted Global Sections

This four-part draft series proposes a statistical topos model for protein folding. It formulates peptide sequences as words in a peptide monoid, organizes local sequence fragments, contact regions, structural motifs, and functional regions into a fragment category, and describes folding as a weighted gluing problem for local conformational sections. The series develops the algebraic and categorical base, the weighted local-to-global model, a coarse weighted-section gluing algorithm, and an interpretation of conformational ensembles, mutations, ligand binding, disordered proteins, and functional-state selection through global section distributions.