Sprint 3 : protocoles de vote et boite a outils

Backend:
- Sessions de vote : list, close, tally, threshold details, auto-expiration
- Protocoles : update, simulate, meta-gouvernance, formulas CRUD
- Service vote enrichi : close_session, get_threshold_details, nuanced breakdown
- Schemas : ThresholdDetailOut, VoteResultOut, FormulaSimulationRequest/Result
- WebSocket broadcast sur chaque vote + fermeture session
- 25 nouveaux tests (threshold details, close, nuanced, simulation)

Frontend:
- 5 composants vote : VoteBinary, VoteNuanced, ThresholdGauge, FormulaDisplay, VoteHistory
- 3 composants protocoles : ProtocolPicker, FormulaEditor, ModeParamsDisplay
- Simulateur de formules interactif (page /protocols/formulas)
- Page detail protocole (/protocols/[id])
- Composable useWebSocket (live updates)
- Composable useVoteFormula (calcul client-side reactif)
- Integration KaTeX pour rendu LaTeX des formules

Documentation:
- API reference : 8 nouveaux endpoints documentes
- Formules : tables d'inertie, parametres detailles, simulation API
- Guide vote : vote binaire/nuance, jauge, historique, simulateur, meta-gouvernance

55 tests passes (+ 1 skipped), 126 fichiers total.

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

frontend/app/composables/useWebSocket.ts

@@ -0,0 +1,100 @@
+/**
+ * Composable for WebSocket connectivity to receive live vote updates.
+ *
+ * Connects to the backend WS endpoint and allows subscribing to
+ * individual vote session channels for real-time tally updates.
+ */
+export function useWebSocket() {
+  const config = useRuntimeConfig()
+  let ws: WebSocket | null = null
+  let reconnectTimer: ReturnType<typeof setTimeout> | null = null
+  const connected = ref(false)
+  const lastMessage = ref<any>(null)
+
+  /**
+   * Open a WebSocket connection to the backend live endpoint.
+   */
+  function connect() {
+    if (ws && (ws.readyState === WebSocket.OPEN || ws.readyState === WebSocket.CONNECTING)) {
+      return
+    }
+
+    const wsUrl = config.public.apiBase
+      .replace(/^http/, 'ws')
+      .replace(/\/api\/v1$/, '/api/v1/ws/live')
+
+    ws = new WebSocket(wsUrl)
+
+    ws.onopen = () => {
+      connected.value = true
+      if (reconnectTimer) {
+        clearTimeout(reconnectTimer)
+        reconnectTimer = null
+      }
+    }
+
+    ws.onclose = () => {
+      connected.value = false
+      reconnect()
+    }
+
+    ws.onerror = () => {
+      connected.value = false
+    }
+
+    ws.onmessage = (event: MessageEvent) => {
+      try {
+        lastMessage.value = JSON.parse(event.data)
+      } catch {
+        lastMessage.value = event.data
+      }
+    }
+  }
+
+  /**
+   * Subscribe to real-time updates for a vote session.
+   */
+  function subscribe(sessionId: string) {
+    if (ws?.readyState === WebSocket.OPEN) {
+      ws.send(JSON.stringify({ action: 'subscribe', session_id: sessionId }))
+    }
+  }
+
+  /**
+   * Unsubscribe from a vote session's updates.
+   */
+  function unsubscribe(sessionId: string) {
+    if (ws?.readyState === WebSocket.OPEN) {
+      ws.send(JSON.stringify({ action: 'unsubscribe', session_id: sessionId }))
+    }
+  }
+
+  /**
+   * Gracefully close the WebSocket connection.
+   */
+  function disconnect() {
+    if (reconnectTimer) {
+      clearTimeout(reconnectTimer)
+      reconnectTimer = null
+    }
+    if (ws) {
+      ws.onclose = null
+      ws.close()
+      ws = null
+    }
+    connected.value = false
+  }
+
+  /**
+   * Schedule a reconnection attempt after a delay.
+   */
+  function reconnect() {
+    if (reconnectTimer) return
+    reconnectTimer = setTimeout(() => {
+      reconnectTimer = null
+      connect()
+    }, 3000)
+  }
+
+  return { connected, lastMessage, connect, subscribe, unsubscribe, disconnect }
+}