An Exact Maximum for Ternary Non-overlapping Codes of Length 19

We establish the exact unrestricted maximum S(3,19) = 17,238,401 for ternary non-overlapping (cross-bifix-free) codes of length 19. An explicit construction gives the lower bound, independently verified on all 17,238,401 codewords. Using the published structural reduction of Stanovnik, Moškon and Mraz, a full overflow-guarded exact C++ certificate checks 3,028,326 early profiles and 512 late orientations each, totaling 1,550,502,912 cases, with no failures. Independent tests of the quadratic reduction and a negative control are included. The result is an exact finite-parameter computer-assisted optimum conditional on the published structural reduction and source-code correctness, not a solution to the general non-overlapping code problem. Independent historical priority and peer review remain open.