Independent Sets in Two-Regular Uniform Hypergraphs

For every integer r >= 2, we prove the Balogh-Bollobas-Narayanan independent-set bound for finite simple r-uniform, 2-regular hypergraphs. If such a hypergraph has n vertices, its number of weak independent sets is at most (2^(2(r-1)) + 3(2^(r-1)-1)^2)^(n/(2r)). The proof uses the edge-cover dual and regional entropy inequalities of Sarantis, Tetali and Zheng. An edge-and-odd-cycle factor can be chosen with all its odd cycles induced, by reducing chords. A uniform transfer-matrix estimate handles the remaining closed cycles. This extends the previously stated degree-two cases, odd r and r = 4, to all uniformities without a finite rooted-region enumeration. The general-degree conjecture for d >= 3 is not resolved. This is a self-audited, AI-assisted, unrefereed preprint; no independent review, formal certification or exhaustive priority determination is asserted.