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/FormulaDisplay.vue

@@ -0,0 +1,110 @@
+<script setup lang="ts">
+/**
+ * Display vote formula with KaTeX rendering.
+ *
+ * Renders the WoT threshold formula using KaTeX when available,
+ * falling back to a code display. Shows parameter values and
+ * optional Smith/TechComm criteria formulas.
+ */
+import type { FormulaConfig } from '~/stores/protocols'
+
+const props = defineProps<{
+  formulaConfig: FormulaConfig
+  showExplanation?: boolean
+}>()
+
+const showExplain = ref(props.showExplanation ?? false)
+
+/**
+ * Render a LaTeX string to HTML using KaTeX, with code fallback.
+ */
+function renderFormula(tex: string): string {
+  if (typeof window !== 'undefined' && (window as any).katex) {
+    return (window as any).katex.renderToString(tex, { throwOnError: false, displayMode: true })
+  }
+  return `<code class="text-sm font-mono">${tex}</code>`
+}
+
+/** Main threshold formula in LaTeX. */
+const mainFormulaTeX = 'Seuil = C + B^W + \\left(M + (1-M) \\cdot \\left(1 - \\left(\\frac{T}{W}\\right)^G\\right)\\right) \\cdot \\max(0,\\, T - C)'
+
+/** Smith criterion formula. */
+const smithFormulaTeX = computed(() => {
+  if (props.formulaConfig.smith_exponent === null) return null
+  return `Seuil_{Smith} = \\lceil W_{Smith}^{${props.formulaConfig.smith_exponent}} \\rceil`
+})
+
+/** TechComm criterion formula. */
+const techcommFormulaTeX = computed(() => {
+  if (props.formulaConfig.techcomm_exponent === null) return null
+  return `Seuil_{TechComm} = \\lceil W_{TechComm}^{${props.formulaConfig.techcomm_exponent}} \\rceil`
+})
+
+const mainFormulaHtml = computed(() => renderFormula(mainFormulaTeX))
+const smithFormulaHtml = computed(() => smithFormulaTeX.value ? renderFormula(smithFormulaTeX.value) : null)
+const techcommFormulaHtml = computed(() => techcommFormulaTeX.value ? renderFormula(techcommFormulaTeX.value) : null)
+
+const parameters = computed(() => [
+  { label: 'Duree', code: 'D', value: `${props.formulaConfig.duration_days} jours`, description: 'Duree du vote en jours' },
+  { label: 'Majorite', code: 'M', value: `${props.formulaConfig.majority_pct}%`, description: 'Ratio de majorite cible a haute participation' },
+  { label: 'Base', code: 'B', value: String(props.formulaConfig.base_exponent), description: 'Exposant de base (B^W tend vers 0 si B < 1)' },
+  { label: 'Gradient', code: 'G', value: String(props.formulaConfig.gradient_exponent), description: 'Exposant du gradient d\'inertie' },
+  { label: 'Constante', code: 'C', value: String(props.formulaConfig.constant_base), description: 'Plancher fixe de votes requis' },
+  ...(props.formulaConfig.smith_exponent !== null ? [{
+    label: 'Smith', code: 'S', value: String(props.formulaConfig.smith_exponent), description: 'Exposant du critere Smith',
+  }] : []),
+  ...(props.formulaConfig.techcomm_exponent !== null ? [{
+    label: 'TechComm', code: 'T', value: String(props.formulaConfig.techcomm_exponent), description: 'Exposant du critere TechComm',
+  }] : []),
+])
+</script>
+
+<template>
+  <div class="space-y-4">
+    <!-- Main formula -->
+    <div class="p-4 bg-gray-50 dark:bg-gray-800 rounded-lg overflow-x-auto">
+      <div v-html="mainFormulaHtml" class="text-center" />
+    </div>
+
+    <!-- Smith criterion -->
+    <div v-if="smithFormulaHtml" class="p-3 bg-blue-50 dark:bg-blue-900/20 rounded-lg overflow-x-auto">
+      <p class="text-xs font-semibold text-blue-600 dark:text-blue-400 mb-2">Critere Smith</p>
+      <div v-html="smithFormulaHtml" class="text-center" />
+    </div>
+
+    <!-- TechComm criterion -->
+    <div v-if="techcommFormulaHtml" class="p-3 bg-purple-50 dark:bg-purple-900/20 rounded-lg overflow-x-auto">
+      <p class="text-xs font-semibold text-purple-600 dark:text-purple-400 mb-2">Critere TechComm</p>
+      <div v-html="techcommFormulaHtml" class="text-center" />
+    </div>
+
+    <!-- Parameters grid -->
+    <div class="grid grid-cols-2 md:grid-cols-3 lg:grid-cols-4 gap-3">
+      <div
+        v-for="param in parameters"
+        :key="param.code"
+        class="p-3 bg-gray-50 dark:bg-gray-800 rounded-lg"
+      >
+        <div class="flex items-center gap-2 mb-1">
+          <span class="font-mono font-bold text-primary text-sm">{{ param.code }}</span>
+          <span class="text-xs font-medium text-gray-700 dark:text-gray-300">{{ param.label }}</span>
+        </div>
+        <div class="text-lg font-semibold text-gray-900 dark:text-white">{{ param.value }}</div>
+        <p v-if="showExplain" class="text-xs text-gray-500 mt-1">{{ param.description }}</p>
+      </div>
+    </div>
+
+    <!-- Explanation toggle -->
+    <div class="flex justify-end">
+      <UButton
+        variant="ghost"
+        color="neutral"
+        size="xs"
+        :icon="showExplain ? 'i-lucide-eye-off' : 'i-lucide-eye'"
+        @click="showExplain = !showExplain"
+      >
+        {{ showExplain ? 'Masquer les explications' : 'Afficher les explications' }}
+      </UButton>
+    </div>
+  </div>
+</template>