diff --git a/.gitea/workflows/compile.yml b/.gitea/workflows/compile.yml
new file mode 100644
index 0000000..c2a6226
--- /dev/null
+++ b/.gitea/workflows/compile.yml
@@ -0,0 +1,25 @@
+name: Build LaTeX on Host
+on: [push]
+
+jobs:
+  build:
+    # Tell Gitea to use your host runner
+    runs-on: self-hosted
+
+    steps:
+      - name: Check out the repository
+        uses: actions/checkout@v4
+
+      - name: Compile LaTeX using local TeX Live
+        # These commands run directly in your machine's shell
+        run: |
+          echo "Compiling document..."
+          latexmk distribution.tex
+          latexmk Notes_SODA23.tex
+          latexmk SDP.tex
+
+      - name: Upload PDF artifact
+        uses: actions/upload-artifact@v3
+        with:
+          name: distribution.pdf
+          path: distribution.pdf
\ No newline at end of file
diff --git a/.gitignore b/.gitignore
index b2b403a..b69b9fa 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,6 +1,6 @@
 .vscode/
 .ds_store
-
+/*.pdf
 ## Core latex/pdflatex auxiliary files:
 *.aux
 *.lof
diff --git a/distribution.pdf b/distribution.pdf
deleted file mode 100644
index 02dddd5..0000000
Binary files a/distribution.pdf and /dev/null differ
diff --git a/distribution.tex b/distribution.tex
index 62f6583..bf4fbb2 100644
--- a/distribution.tex
+++ b/distribution.tex
@@ -60,4 +60,6 @@ One thing we can try is to tighten the second line.
 Recall that for each dimension $i$ a random subset $S_i\subset X$ is selected and the value of $f_i(x)$ is $\min_{s\in S_i} d(x,s)$.
 We want to show that for any fixed $x,y\in X$ and any dimension $i$ the event that distance $|f_i(x)-f_i(y)|^2$ is much smaller than $d(x,y)^2$ happends with high probability.
 
+Now consider a subset $S_i$ by sampling each node in $X$ iid with probability $2^{-i}$.
+
 \end{document}
\ No newline at end of file