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>

backend/app/schemas/vote.py

@@ -55,6 +55,74 @@ class VoteSessionOut(BaseModel):
     created_at: datetime
 
 
+class VoteSessionListOut(BaseModel):
+    """Lighter vote session representation for list endpoints (no nested votes)."""
+
+    model_config = ConfigDict(from_attributes=True)
+
+    id: UUID
+    decision_id: UUID | None = None
+    item_version_id: UUID | None = None
+    voting_protocol_id: UUID
+
+    # Snapshot at session start
+    wot_size: int
+    smith_size: int
+    techcomm_size: int
+
+    # Dates
+    starts_at: datetime
+    ends_at: datetime
+
+    # Status
+    status: str
+
+    # Tallies
+    votes_for: int
+    votes_against: int
+    votes_total: int
+    threshold_required: float
+    result: str | None = None
+
+    created_at: datetime
+
+
+# ── Threshold Details ────────────────────────────────────────────
+
+
+class ThresholdDetailOut(BaseModel):
+    """Detailed threshold computation result for a vote session."""
+
+    wot_threshold: int
+    smith_threshold: int | None = None
+    techcomm_threshold: int | None = None
+    votes_for: int
+    votes_against: int
+    votes_total: int
+    wot_passed: bool
+    smith_passed: bool | None = None
+    techcomm_passed: bool | None = None
+    overall_passed: bool
+    participation_rate: float
+    formula_params: dict
+
+
+# ── Vote Result ──────────────────────────────────────────────────
+
+
+class VoteResultOut(BaseModel):
+    """Structured vote result response."""
+
+    session_id: UUID
+    result: str | None = None  # adopted, rejected
+    threshold_required: float
+    votes_for: int
+    votes_against: int
+    votes_total: int
+    adopted: bool
+    nuanced_breakdown: dict | None = None  # for nuanced votes
+
+
 # ── Vote ─────────────────────────────────────────────────────────