fix: inject /blog into Gradio's internal FastAPI router at position 0

gr.mount_gradio_app + uvicorn was ignored by HF Spaces (expects demo.launch).
Use prevent_thread_lock=True to get the live FastAPI app, then insert the
static-files Mount at index 0 so it is checked before Gradio's catch-all.

app.py

@@ -1077,9 +1077,15 @@ with gr.Blocks(title="PaperProf", css=CSS) as demo:
 print("✅ Gradio demo defined successfully")
 
 print("✅ Launching demo...")
-_fastapi = FastAPI()
-_fastapi.mount("/blog", StaticFiles(directory="blog", html=True), name="blog")
-app = gr.mount_gradio_app(_fastapi, demo, path="/")
-
-if __name__ == "__main__":
-    uvicorn.run(app, host="0.0.0.0", port=7860)
+app, local_url, _ = demo.launch(
+    server_name="0.0.0.0",
+    server_port=7860,
+    prevent_thread_lock=True,
+)
+
+# Insert /blog BEFORE Gradio's catch-all route so it takes priority
+from starlette.routing import Mount
+app.router.routes.insert(0, Mount("/blog", StaticFiles(directory="blog", html=True), name="blog"))
+print(f"✅ Blog mounted at {local_url}blog")
+
+demo.block_thread()