Initial commit — Cortex API + Inara identity

Cortex: FastAPI backend serving Inara via Claude/Gemini CLI backends.
Includes SSE streaming chat, session persistence, Google Chat webhook
handler, and Docker support.

Inara: Identity files (persona, soul, protocols, memory, context tiers)
mounted read-only into the container at runtime.

Features in initial cut:
- /chat endpoint with SSE keepalive + LLM fallback
- Session store with rolling history window
- Markdown rendering, copy-to-clipboard, links open in new tab
- Stacked right-column input controls (height selector, enter toggle,
  note mode with public/private) — semi-hidden until textarea grows
- /note endpoint for injecting public context into session history
- Docker Compose config (local dev runs natively; Docker for server)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

cortex/main.py

@@ -0,0 +1,41 @@
+from contextlib import asynccontextmanager
+from fastapi import FastAPI
+from fastapi.staticfiles import StaticFiles
+from fastapi.responses import FileResponse
+import uvicorn
+
+from config import settings
+from routers import chat, google_chat
+
+
+@asynccontextmanager
+async def lifespan(app: FastAPI):
+    yield
+    from llm_client import cleanup
+    await cleanup()
+
+
+app = FastAPI(title="Cortex Dispatcher", lifespan=lifespan)
+
+app.include_router(chat.router)
+app.include_router(google_chat.router)
+app.mount("/static", StaticFiles(directory="static"), name="static")
+
+
+@app.get("/")
+async def index() -> FileResponse:
+    return FileResponse("static/index.html")
+
+
+@app.get("/health")
+async def health() -> dict:
+    return {"status": "ok"}
+
+
+if __name__ == "__main__":
+    uvicorn.run(
+        "main:app",
+        host=settings.host,
+        port=settings.port,
+        reload=True,
+    )