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>

docker-compose.yml

@@ -0,0 +1,30 @@
+services:
+  cortex:
+    build:
+      context: ./cortex
+      dockerfile: Dockerfile
+    container_name: cortex
+    restart: unless-stopped
+    ports:
+      - "8000:8000"
+    volumes:
+      # Inara identity files (read-only in container)
+      - ./inara:/app/../inara:ro
+      # Session persistence (read-write)
+      - cortex_sessions:/app/data/sessions
+      # Claude CLI — needs both the config file and the directory
+      - ${HOME}/.claude.json:/root/.claude.json:ro
+      - ${HOME}/.claude:/root/.claude:ro
+      # Gemini CLI credentials
+      - ${HOME}/.gemini:/root/.gemini:ro
+      # Gemini CLI config (extensions, etc.)
+      - ${HOME}/.config/gemini:/root/.config/gemini:ro
+    env_file:
+      - ./cortex/.env
+    environment:
+      # Override paths for container layout
+      INARA_DIR: /app/../inara
+      SESSIONS_DIR: /app/data/sessions
+
+volumes:
+  cortex_sessions: