Can prison officials be held liable for failing to properly assess the risk posed by an inmate to the public under the Eighth Amendment?

Thus, if prison officials "did not know of the underlying facts indicating a sufficiently substantial danger," and "were therefore unaware of the danger," or if "they knew the underlying facts but believed (albeit unsoundly) that the risk to which the facts gave rise was unsubstantial or nonexistent," they may not be held liable. Farmer, 511 U.S. at 844; see also Gibson v. County of Washoe, Nevada, 290 F.3d 1175, 1188 (9th Cir. 2002) (noting that a prison official who "should have been aware of the risk, but was not, ... has not violated the Eighth Amendment, no matter how severe the risk.").