From e82091a66fc81e37a59b0da64a5b5112613d97d0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 8 Sep 2026 15:50:37 +0530 Subject: [PATCH 1/4] Order the C52 upper bounds by tightness. --- constants/52a.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/constants/52a.md b/constants/52a.md index 796250a..a073838 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 | +| 4.506 | [DBM2000] || | 4.490 | [DKMP2009] || +| 4.453 | [MS2008] |Under an extra hypothesis,
see Additional Comments (1) below | From cc3206f26ce72faf0b197edc902561cf2eb0f4d3 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 8 Sep 2026 15:50:37 +0530 Subject: [PATCH 2/4] Mark the MS2008 4.453 bound as conditional. --- constants/52a.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/constants/52a.md b/constants/52a.md index a073838..4edb1b8 100644 --- a/constants/52a.md +++ b/constants/52a.md @@ -36,7 +36,7 @@ $\liminf_{n \to \infty} r_{3,n}$. | 4.571 | [KKSVZ2007]|| | 4.506 | [DBM2000] || | 4.490 | [DKMP2009] || -| 4.453 | [MS2008] |Under an extra hypothesis,
see Additional Comments (1) below | +| 4.453 | [MS2008] |Under an extra hypothesis,
see Additional Comments (1) below. Not an unconditional record. | From 990892bd9b7570ebeeda50098cd9f6725a698fc5 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 8 Sep 2026 15:50:37 +0530 Subject: [PATCH 3/4] Note that 4.490 remains the last unconditional upper bound. --- constants/52a.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/constants/52a.md b/constants/52a.md index 4edb1b8..40f15f8 100644 --- a/constants/52a.md +++ b/constants/52a.md @@ -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. From bc381bca701d08c5fea66a54c8218181323f7be1 Mon Sep 17 00:00:00 2001 From: Taksh Date: Tue, 8 Sep 2026 15:50:37 +0530 Subject: [PATCH 4/4] Label 4.490 as the tabulated unconditional record. --- constants/52a.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/constants/52a.md b/constants/52a.md index 40f15f8..63173b7 100644 --- a/constants/52a.md +++ b/constants/52a.md @@ -35,7 +35,7 @@ $\liminf_{n \to \infty} r_{3,n}$. | 4.596 | [JSV2000] || | 4.571 | [KKSVZ2007]|| | 4.506 | [DBM2000] || -| 4.490 | [DKMP2009] || +| 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. |