The Abiotic Loom: Discrete Morse Theory and the Geometric Resolution of Levinthal’s Paradox in the Chrysene Tensor Space

Abstract

The classical formulation of protein folding treats the polypeptide as a continuous chain free to explore an exponentially large space of dihedral angles. Levinthal’s paradox records the resulting temporal impossibility: an unguided search cannot reach a unique native structure in biologically relevant time. Continuous stochastic models remain indispensable for describing local thermal motion, yet they lack absolute spatial bounds that would render the search finite.

This paper supplies those bounds. The physical molecule already shown to co-synthesize nucleic acids and phospholipid membranes—the 3,6,9,12-tetrasubstituted chrysene of U.S. Patent 12,195,423—is abstracted into a discrete, non-commutative lattice called the Chrysene Tensor Space Ic. The interstitial voids of this lattice function as an abiotic loom. Continuous thermal exploration continues inside the open cells, but any trajectory that intersects a lattice wall is assigned infinite steric energy. The resulting discrete Morse filtration admits only two families of critical configurations: right-handed alpha-helices and extended beta-strands. A proton-coupled electron transfer operator then locks these geometrically selected arrangements into covalent permanence.

The conformational measure therefore collapses from an exponentially growing continuum to a finite discrete set whose cardinality is independent of chain length. Levinthal’s paradox is resolved not by discarding continuous dynamics, but by confining them to the active interstitium of a geometrically rigid molecular loom whose architecture is identical to the patented precursor of the genetic and membrane systems.