We prove uniqueness of the infinite entangled component for bond percolation on the three-dimensional cubic lattice above the entanglement critical probability. This improves earlier results by Grimmett and Holroyd.
"Uniqueness of the infinite entangled component in three-dimensional bond percolation." Ann. Probab. 29 (1) 127 - 136, February 2001. https://doi.org/10.1214/aop/1008956325