Skip to content

Order the C52 upper bounds by tightness #181

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
Chessing234 wants to merge 4 commits into
base: main
Choose a base branch
from
Open

Order the C52 upper bounds by tightness #181

Changes from all commits
Commits
Show all changes
4 commits
Select commit Hold shift + click to select a range
e82091a
Order the C52 upper bounds by tightness.
Chessing234 Sep 8, 2026
cc3206f
Mark the MS2008 4.453 bound as conditional.
Chessing234 Sep 8, 2026
990892b
Note that 4.490 remains the last unconditional upper bound.
Chessing234 Sep 8, 2026
bc381bc
Label 4.490 as the tabulated unconditional record.
Chessing234 Sep 8, 2026
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
8 changes: 4 additions & 4 deletions constants/52a.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -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,<br> 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,<br> see Additional Comments (1) below. Not an unconditional record. |



Expand All @@ -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.

Expand Down