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/useVoteFormula.ts

@@ -0,0 +1,98 @@
+/**
+ * Composable for real-time vote formula computation.
+ *
+ * Re-exports and wraps the threshold utility functions for reactive use
+ * in Vue components. Provides convenient methods for threshold calculations,
+ * inertia factor, required ratio, and adoption checks.
+ */
+import { wotThreshold, smithThreshold, techcommThreshold } from '~/utils/threshold'
+
+export interface FormulaParams {
+  majority_pct: number
+  base_exponent: number
+  gradient_exponent: number
+  constant_base: number
+}
+
+export function useVoteFormula() {
+  /**
+   * Compute the WoT threshold for a given set of parameters.
+   */
+  function computeThreshold(wotSize: number, totalVotes: number, params: FormulaParams): number {
+    return wotThreshold(
+      wotSize,
+      totalVotes,
+      params.majority_pct,
+      params.base_exponent,
+      params.gradient_exponent,
+      params.constant_base,
+    )
+  }
+
+  /**
+   * Compute the inertia factor: 1 - (T/W)^G
+   * Ranges from ~1 (low participation) to ~0 (full participation).
+   */
+  function computeInertiaFactor(
+    totalVotes: number,
+    wotSize: number,
+    gradientExponent: number,
+  ): number {
+    if (wotSize <= 0 || totalVotes <= 0) return 1.0
+    const participationRatio = totalVotes / wotSize
+    return 1.0 - Math.pow(participationRatio, gradientExponent)
+  }
+
+  /**
+   * Compute the required ratio of "pour" votes at a given participation level.
+   * requiredRatio = M + (1 - M) * inertiaFactor
+   */
+  function computeRequiredRatio(
+    totalVotes: number,
+    wotSize: number,
+    majorityPct: number,
+    gradientExponent: number,
+  ): number {
+    const M = majorityPct / 100
+    const inertia = computeInertiaFactor(totalVotes, wotSize, gradientExponent)
+    return M + (1.0 - M) * inertia
+  }
+
+  /**
+   * Check whether a vote is adopted given all criteria.
+   * A vote is adopted when it passes the WoT threshold AND
+   * any applicable Smith/TechComm criteria.
+   */
+  function isAdopted(
+    votesFor: number,
+    threshold: number,
+    smithVotesFor?: number,
+    smithThresholdVal?: number,
+    techcommVotesFor?: number,
+    techcommThresholdVal?: number,
+  ): boolean {
+    // Main WoT criterion
+    if (votesFor < threshold) return false
+
+    // Smith criterion (if applicable)
+    if (smithThresholdVal !== undefined && smithThresholdVal > 0) {
+      if ((smithVotesFor ?? 0) < smithThresholdVal) return false
+    }
+
+    // TechComm criterion (if applicable)
+    if (techcommThresholdVal !== undefined && techcommThresholdVal > 0) {
+      if ((techcommVotesFor ?? 0) < techcommThresholdVal) return false
+    }
+
+    return true
+  }
+
+  return {
+    computeThreshold,
+    computeInertiaFactor,
+    computeRequiredRatio,
+    isAdopted,
+    smithThreshold,
+    techcommThreshold,
+  }
+}