diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index efbdc9e..5910ab7 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -34,9 +34,9 @@
               "type": "pdf",
               "state": {
                 "file": "Concurrent Systems/slides/class 3.pdf",
-                "page": 13,
+                "page": 16,
                 "left": -26,
-                "top": 31,
+                "top": 472,
                 "zoom": 0.57541567695962
               },
               "icon": "lucide-file-text",
@@ -216,11 +216,11 @@
       "companion:Toggle completion": false
     }
   },
-  "active": "6edd4157a160e462",
+  "active": "02dff467d5bcbba5",
   "lastOpenFiles": [
+    "Concurrent Systems/notes/3.md",
     "Pasted image 20250310172134.png",
     "Concurrent Systems/slides/class 3.pdf",
-    "Concurrent Systems/notes/3.md",
     "Pasted image 20250310103703.png",
     "Concurrent Systems/notes/1 - CS Basics.md",
     "Concurrent Systems/notes/1 - CS Basics2.md",
@@ -248,7 +248,6 @@
     "Concurrent Systems/notes/images/Pasted image 20250304084537.png",
     "Concurrent Systems/slides/class 1.pdf",
     "Concurrent Systems/notes/images/Pasted image 20250303093116.png",
-    "Concurrent Systems/notes/images/Pasted image 20250303100953.png",
     "Foundation of data science/notes/1 CV Basics.md",
     "Foundation of data science/notes/7 Autoencoders.md",
     "Foundation of data science/notes/6 PCA.md",
diff --git a/Concurrent Systems/notes/3.md b/Concurrent Systems/notes/3.md
index 20e2b67..d9d6f35 100644
--- a/Concurrent Systems/notes/3.md	
+++ b/Concurrent Systems/notes/3.md	
@@ -260,7 +260,8 @@ Let's consider the execution of $p_i$ leading to its CS:
 so by this, the very worst possible case is that my lock experiences that.
 
 It looks like I can experience at most $2n-1$ other critical sections, but it is even better, let's see:
-...
+- $p_n$ invokes lock alone, completes its CS (the first after the reset) and its new DATE is n+1
+- all processes invoke lock simultaneously
 
 
 #### Improvement of Aravind’s algorithm