Angular Endpoint Stability and a Stronger Universal Ropelength Bound for Non-Trivial Knots

Preprint — not peer reviewed. This preprint proves that every non-trivial knot K satisfies Rop(K) > LDDS + 0.026 > 15.68660926 by coupling two arc estimates arising from an essential alternating quadrisecant. A deterministic standard-library Python certificate uses exact fixed-point interval arithmetic with outward rounding to verify all 12,800 boxes in the finite two-variable numerical step. Automated verification of that finite calculation is not a substitute for expert review of the geometric argument. The archived materials include the PDF, complete LaTeX source, certificate and tests, text and JSON certificate outputs, reproduction instructions, licenses, citation metadata, and SHA-256 checksums.