ex(n, C_{4k+2}^{4-}) equals the number of edges in the complete odd-bipartite 4-graph for large n, and the Turán density of C_{4k+2}^4 is 1/2 for all k≥2 with stability.
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Tur\'an numbers of $4$-uniform tight even cycles minus one edge
ex(n, C_{4k+2}^{4-}) equals the number of edges in the complete odd-bipartite 4-graph for large n, and the Turán density of C_{4k+2}^4 is 1/2 for all k≥2 with stability.