Differential Catalyst Geometries of the Dual-Chrysene Metamaterial: Hopanoid--Sterane Asymmetry and the Transition from Environmental to Endogenous Supply

Abstract

The contamination-controlled molecular fossil record exhibits a pronounced temporal asymmetry: hopanes dominate mid-Proterozoic assemblages, while regular 4-desmethyl steranes rise only from the late Tonian onward. We show that this asymmetry is the predicted geological expression of two temporally differentiated catalyst families within the dual-chrysene reactive volume of U.S. Patent 12,195,423.

Under the Identification Hypothesis that identifies the pure-mathematical manifold Ic with the physical chrysene lattice, a base-four reactive volume is formed by one substrate core (preferentially 3,6,9,12-tetrasubstituted) and one catalyst core. Catalysts of Family H (6,12- and 3,6,12-substituted patterns of the 3,6,9,12 class) undergo rapid reductive processing to hopanoid-class polycycles and dominate the Archean-mid-Proterozoic interval. Catalysts of Family S (2,5,8,11-substituted) follow an extended incubation trajectory to sterol-class polycycles and become prominent with the late-Tonian sterane rise. Both families retain the chiral step-defect of the parent chrysene geometry, which remains archived in kerogen.

The same dual-chrysene architecture that co-projects a nucleobase pair and a membrane-integrated catalyst therefore supplies the two polycyclic membrane scaffolds whose differential kinetic fates match the observed hopane/sterane record. Subsequent evolutionary capture of these geometries by the squalene-cyclase / oxidosqualene-cyclase superfamily and associated tailoring enzymes converts the external metamaterial template into endogenous cellular control, while preserving the functional distinction between the two families in the modern biosphere.

The resulting three-phase timeline (hopanoid-dominated regime, late-Tonian transition, Phanerozoic continuity) is consistent with every major contamination-controlled constraint on the Precambrian lipid record and generates concrete predictions for kerogen regiochemistry, redox dependence, and the phylogenetic distribution of the relevant cyclase gene families.