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/components/votes/ThresholdGauge.vue

@@ -0,0 +1,114 @@
+<script setup lang="ts">
+/**
+ * Visual gauge showing votes vs threshold.
+ *
+ * Displays a horizontal progress bar with green (pour) and red (contre) fills,
+ * a vertical threshold marker, participation statistics, and a pass/fail badge.
+ */
+const props = defineProps<{
+  votesFor: number
+  votesAgainst: number
+  threshold: number
+  wotSize: number
+}>()
+
+const totalVotes = computed(() => props.votesFor + props.votesAgainst)
+
+/** Percentage of "pour" votes relative to total votes. */
+const forPct = computed(() => {
+  if (totalVotes.value === 0) return 0
+  return (props.votesFor / totalVotes.value) * 100
+})
+
+/** Percentage of "contre" votes relative to total votes. */
+const againstPct = computed(() => {
+  if (totalVotes.value === 0) return 0
+  return (props.votesAgainst / totalVotes.value) * 100
+})
+
+/** Position of the threshold marker as a percentage of total votes. */
+const thresholdPosition = computed(() => {
+  if (totalVotes.value === 0) return 50
+  // Threshold as a percentage of total votes
+  const pct = (props.threshold / totalVotes.value) * 100
+  return Math.min(pct, 100)
+})
+
+/** Whether the vote passes (votes_for >= threshold). */
+const isPassing = computed(() => props.votesFor >= props.threshold)
+
+/** Participation rate. */
+const participationRate = computed(() => {
+  if (props.wotSize === 0) return 0
+  return (totalVotes.value / props.wotSize) * 100
+})
+</script>
+
+<template>
+  <div class="space-y-3">
+    <!-- Progress bar -->
+    <div class="relative h-8 bg-gray-200 dark:bg-gray-700 rounded-full overflow-hidden">
+      <!-- Green fill (pour) -->
+      <div
+        class="absolute inset-y-0 left-0 bg-green-500 transition-all duration-500"
+        :style="{ width: `${forPct}%` }"
+      />
+      <!-- Red fill (contre) -->
+      <div
+        class="absolute inset-y-0 bg-red-500 transition-all duration-500"
+        :style="{ left: `${forPct}%`, width: `${againstPct}%` }"
+      />
+
+      <!-- Threshold marker -->
+      <div
+        v-if="totalVotes > 0"
+        class="absolute inset-y-0 w-0.5 bg-yellow-400 z-10"
+        :style="{ left: `${thresholdPosition}%` }"
+      >
+        <div class="absolute -top-5 left-1/2 -translate-x-1/2 text-xs font-bold text-yellow-600 dark:text-yellow-400 whitespace-nowrap">
+          Seuil
+        </div>
+      </div>
+
+      <!-- Percentage labels inside the bar -->
+      <div class="absolute inset-0 flex items-center px-3 text-xs font-bold text-white">
+        <span v-if="forPct > 10">{{ forPct.toFixed(1) }}%</span>
+        <span class="flex-1" />
+        <span v-if="againstPct > 10">{{ againstPct.toFixed(1) }}%</span>
+      </div>
+    </div>
+
+    <!-- Counts and threshold text -->
+    <div class="flex items-center justify-between text-sm">
+      <div class="flex items-center gap-4">
+        <span class="text-green-600 dark:text-green-400 font-medium">
+          {{ votesFor }} pour
+        </span>
+        <span class="text-red-600 dark:text-red-400 font-medium">
+          {{ votesAgainst }} contre
+        </span>
+      </div>
+
+      <div class="font-medium" :class="isPassing ? 'text-green-600 dark:text-green-400' : 'text-gray-600 dark:text-gray-400'">
+        {{ votesFor }} / {{ threshold }} requis
+      </div>
+    </div>
+
+    <!-- Participation rate -->
+    <div class="flex items-center justify-between text-xs text-gray-500">
+      <span>
+        {{ totalVotes }} vote{{ totalVotes !== 1 ? 's' : '' }} sur {{ wotSize }} membres
+        ({{ participationRate.toFixed(2) }}%)
+      </span>
+
+      <!-- Pass/fail badge -->
+      <UBadge
+        :color="isPassing ? 'success' : 'error'"
+        variant="subtle"
+        size="xs"
+      >
+        {{ isPassing ? 'Adopte' : 'Non adopte' }}
+      </UBadge>
+    </div>
+  </div>
+</template>