Long 4-uniform tight cycles C_L^(4) with L not divisible by 4 have Turán density 1/2.
Mantel, Problem 28, Wiskundige Opgaven 10 (1907), 60–61
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The Tur\'an Density of 4-Uniform Tight Cycles
Long 4-uniform tight cycles C_L^(4) with L not divisible by 4 have Turán density 1/2.