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) > 6.32. Consequently, the infimum within every non-trivial knot type is at least 6.32. The proof combines an acyclic essential-secant bootstrap, exact compatible affine radial transfers, covered joint-radius propagation, exact profile convolution, ordered failure boundaries, and retained distortion constraints through a common interior knot point. The complete computer-assisted certificate chain was run independently at 96-bit and 192-bit precision; each run certified 2,024,886 boxes across 52 sequential stages and 132 uniform regional results, with all 26 verification-source hashes frozen. This record contains the 19-page version 1.0 preprint and its complete reproducible source and verification package. The preprint has not been submitted to or accepted by a journal.