Calibration Defects from Endpoint Tangents, and a Stronger Ropelength Bound for Non-Trivial Knots

Preprint — not peer reviewed. This preprint recovers a quantitative calibration defect from endpoint tangent data and applies it to the essential middle arc arising from an essential alternating quadrisecant. In the Denne–Diao–Sullivan diameter-thickness convention, the main result is Rop(K) ≥ LDDS + 149/5000 > 15.69040926 for every non-trivial knot K. A deterministic standard-library Python certificate, using exact fixed-point interval arithmetic with outward rounding, verifies all 967,680 boxes in the finite two-variable numerical step and encloses the obstacle bound without assuming its monotonicity. Automated verification of the finite calculation is not a substitute for expert review of the geometric and topological argument. The archived release includes the PDF, exact LaTeX and text source, certificate and tests, machine-readable outputs, reproduction instructions, licenses, citation metadata, SHA-256 checksums, and a self-contained release ZIP.