diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 312fe25..e201e08 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -211,14 +211,14 @@
       "companion:Toggle completion": false
     }
   },
-  "active": "879210c00db77468",
+  "active": "0d64f519fd7f9420",
   "lastOpenFiles": [
+    "Concurrent Systems/slides/class 8.pdf",
     "Concurrent Systems/notes/8 - Enhancing Liveness Properties.md",
     "Concurrent Systems/slides/class 7.pdf",
     "Concurrent Systems/notes/6a - Alternatives to Atomicity.md",
     "Concurrent Systems/notes/7- MUTEX-free concurrency.md",
     "Concurrent Systems/notes/3a - Hardware primitives & Lamport Bakery algorithm.md",
-    "Concurrent Systems/slides/class 8.pdf",
     "Pasted image 20250325090735.png",
     "Concurrent Systems/notes/images/Pasted image 20250324091452.png",
     "Concurrent Systems/notes/6 - Atomicity.md",
diff --git a/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md b/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md
index a202569..02a95c5 100644
--- a/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md	
+++ b/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md	
@@ -16,8 +16,7 @@ Can we take the most basic protocol that satisfies the most basic liveness prope
 
 REMARK: the moment in which all variables contain the same leader is unknown
 
-#### From obstruction-freedom to non-blocking
-
+### From obstruction-freedom to non-blocking
 ```
 NEED_HELP[1..n] : SWMR atomic R/W boolean registers init at false
 
@@ -72,7 +71,7 @@ Guessing the time duration for suspecting a process:
 - The interval to use in the timers is the minimum Sk
 	- it can be proved that this eventually becomes ≥ $\nabla$
 
-#### From obstruction-freedom to wait-freedom
+### From obstruction-freedom to wait-freedom
 **Eventually perfect:** failure detector ♢P provides each process $p_i$ a local variable $suspected_i$ such that
 1. *(Eventual completeness)* eventually, $suspended_{i}$ contains all the indexes of crashed processes, for all correct $p_i$
 2. (*Eventual accuracy*) eventually, $suspected_{i}$ contains only indexes of crashed processes, for all correct $p_{i}$.