Endpoint Tangents and a New Universal Lower Bound for the Ropelength of Nontrivial Knots

Preprint; not peer reviewed. This work sharpens the optimized universal diameter-normalized ropelength bound of Denne, Diao and Sullivan. Obstacle tangent cones, endpoint deficits, circular-turn comparisons, two-moving-point constraints, evolving-polar recovery, and a common-continuation estimate produce an auxiliary joint functional. Directed interval certificates prove 0.09548 <= Delta* < 0.095675 and hence Rop(K) > 15.75608926 for every nontrivial knot K. Version 5.0.0 includes frozen verifier source, manifests, local-support evidence, the complete global-cover receipt, an independent source/receipt audit with bounded fresh arithmetic, and a neutral archival preprint.