A Fiber Bundle Model of DNA Torsional Dynamics: Topoisomerase Action, Telomere Dynamics, and Chromosomal Polarity".

The G6–X–Q9–N cycle, developed in the Kiawe Epistemological Framework (KEF), describes structural transitions between two complementary states: G6, centripetal generative potential, and Q9, centrifugal manifest form. Prior versions of this paper established the differential-geometric foundations of this cycle: X and N as holonomy of a connection on a non-orientable principal Z/2Z-bundle over the parameter circle S¹, and the complete G6–X–Q9–N cycle as generating a toroidal geometry T². The present Version 3 addresses the limitation identified in Version 2: the curvature-based telomere model was structurally derived but not empirically calibrated. We provide four calibrated predictions against independent experimental data. First, the connection curvature F∇ = 0 in relaxed B-form DNA corresponds to the documented helical winding of 10.4–10.5 base pairs per turn, deviation less than 1%. Second, topoisomerases are identified as gauge transformations of the bundle connection: Type I changes the linking number by ±1 per catalytic cycle, Type II by ±2 — exactly the values predicted by the Z/2Z structure group, verified with 0% deviation across all documented topoisomerase systems. Third, the telomere shortening formula ΔT(n) = −α·τ(n) + β·D(n) is calibrated against the documented rate of 50–100 base pairs per cell division in human fibroblasts and the stress-condition rate of more than 500 bp/division, both consistent with the model. Fourth, the toroidal reading of sex chromosome polarity — XX as closed bundle, XY as open bundle with preferred orientation — is verified against Hi-C chromatin topology data showing the inactive X chromosome organized in two megadomains with toroidal architecture. Version 3 additionally formalizes the counter-rotational directional mechanism of the N–Z oscillation: the anticlockwise exit (G6, centripetal) and the clockwise return (Q9, centrifugal) are directly instantiated at the molecular scale in the antiparallel strand orientation of the double helix.