diff --git a/constants/52a.md b/constants/52a.md index 796250a..63173b7 100644 --- a/constants/52a.md +++ b/constants/52a.md @@ -32,11 +32,11 @@ $\liminf_{n \to \infty} r_{3,n}$. | 4.758 | [KMPS1995] || | 4.643 | [DB1997] || | 4.602 | [KKKS1998] || -| 4.506 | [DBM2000] || | 4.596 | [JSV2000] || | 4.571 | [KKSVZ2007]|| -| 4.453 | [MS2008] |Under an extra hypothesis,
see Additional Comments (1) below | -| 4.490 | [DKMP2009] || +| 4.506 | [DBM2000] || +| 4.490 | [DKMP2009] | Unconditional record among the tabulated upper bounds | +| 4.453 | [MS2008] |Under an extra hypothesis,
see Additional Comments (1) below. Not an unconditional record. | @@ -55,7 +55,7 @@ $\liminf_{n \to \infty} r_{3,n}$. ## Additional comments -1. The extra hypothesis used in [MS2008] is about the satisfying assignments of formulas with density below and close to the threshold. +1. The extra hypothesis used in [MS2008] is about the satisfying assignments of formulas with density below and close to the threshold. That 4.453 bound is therefore listed after the unconditional 4.490 record. 2. In [CF1986], the probability of satisfiability is shown to be only a positive constant. However, this, by Friedgut's result of 1999, implies that the probability is actually 1.