Geometric Validation of the Abiotic Loom: Discrete Morse Predictions versus PDB Secondary-Structure Statistics and Ramachandran Densities
Keywords:
abiotic loom, Chrysene Tensor Space, secondary structure, Ramachandran plot, PDB validation, Levinthal’s paradoxAbstract
Paper 1 (Schaper, C. D. (2026). The Abiotic Loom: Discrete Morse Theory and the Geometric Resolution of Levinthal’s Paradox in the Chrysene Tensor Space. Annals of the Chrysene Formalism, 1(1), 273--282. https://chrysene.com/index.php/acf/article/view/23) of this series derived two families of critical secondary-structure geometries---right-handed alpha-helices and extended beta-strands---as the only configurations admitted by a steric Morse filtration on the Chrysene Tensor Space. The present work translates those abstract critical simplices into explicit, parameter-free angular windows on the classical Ramachandran torus and evaluates their occupancy against a curated, high-resolution, non-redundant subset of the public Protein Data Bank.
The lattice-derived windows concentrate the observed helical and strand populations relative to the background density of all residues, yielding moderate-to-strong enrichment ratios ((Ealpha = 3.07\), (Ebeta = 2.65)) and recovering approximately 72% of secondary-structure residues. The residual population lying outside the windows is consistent with geometric distortions at segment termini and with the theoretical capacity of proton-coupled electron transfer to form connectors outside the tightly tethered zones.
No new laboratory experiments are performed and no adjustable parameters are introduced beyond the fixed lattice geometry of the basis tensor. The empirical support reported here is restricted to the secondary-structure level. Tertiary packing, side-chain quantization, and active-site geometry are deferred to subsequent papers in the series.
