An improved lower bound for the distortion of a knotted curve

We prove that every non-trivial rectifiable tame knot embedding K ⊂ R³ has distortion δ(K) > 6.5321. Consequently, the infimum within every non-trivial tame knot type is at least 6.5321. This improves the 6.32 bound in version 1.0 by 0.2121. The proof combines essential-secant profiles, radial variational inequalities, ordered failure boundaries, and retained distortion constraints. The new comparison couples an actual last radial crossing on the initial arc with the same actual complementary split point, retaining both cyclic routes and common angular data. Necessary closed systems are excluded using directed interval arithmetic. Complete runs at 96-bit and 192-bit precision each certified all 54 original closed regions, testing 1,814,262 outer boxes per precision with no unresolved frontier. Independent mathematical, numerical and process-origin reviews passed. Fresh-extraction checks of the finished archive reproduced all 37 finite checks, the two-precision conditional component, and both full-receipt auditors. These checks supplement the complete original numerical runs. Version 2.0 contains the 19-page preprint and the complete reproducible LaTeX source and verification package, including frozen sources, full receipts, mathematical supplements, audit records and reproduction instructions. The package also documents structural research findings, unsuccessful approaches and remaining obstacles. No stronger global bound, knot upper bound, optimality, or proof-assistant formalization is claimed. The preprint has not been submitted to or accepted by a journal.