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/routers/protocols.py

@@ -1,4 +1,4 @@
-"""Protocols router: voting protocols and formula configurations."""
+"""Protocols router: voting protocols, formula configurations, and simulation."""
 
 from __future__ import annotations
 
@@ -10,13 +10,20 @@ from sqlalchemy.ext.asyncio import AsyncSession
 from sqlalchemy.orm import selectinload
 
 from app.database import get_db
+from app.engine.smith_threshold import smith_threshold as compute_smith_threshold
+from app.engine.techcomm_threshold import techcomm_threshold as compute_techcomm_threshold
+from app.engine.threshold import wot_threshold as compute_wot_threshold
 from app.models.protocol import FormulaConfig, VotingProtocol
 from app.models.user import DuniterIdentity
 from app.schemas.protocol import (
     FormulaConfigCreate,
     FormulaConfigOut,
+    FormulaConfigUpdate,
+    FormulaSimulationRequest,
+    FormulaSimulationResult,
     VotingProtocolCreate,
     VotingProtocolOut,
+    VotingProtocolUpdate,
 )
 from app.services.auth_service import get_current_identity
 
@@ -39,6 +46,17 @@ async def _get_protocol(db: AsyncSession, protocol_id: uuid.UUID) -> VotingProto
     return protocol
 
 
+async def _get_formula(db: AsyncSession, formula_id: uuid.UUID) -> FormulaConfig:
+    """Fetch a formula config by ID, or raise 404."""
+    result = await db.execute(
+        select(FormulaConfig).where(FormulaConfig.id == formula_id)
+    )
+    formula = result.scalar_one_or_none()
+    if formula is None:
+        raise HTTPException(status_code=status.HTTP_404_NOT_FOUND, detail="Configuration de formule introuvable")
+    return formula
+
+
 # ── Voting Protocol routes ──────────────────────────────────────────────────
 
 
@@ -102,6 +120,30 @@ async def get_protocol(
     return VotingProtocolOut.model_validate(protocol)
 
 
+@router.put("/{id}", response_model=VotingProtocolOut)
+async def update_protocol(
+    id: uuid.UUID,
+    payload: VotingProtocolUpdate,
+    db: AsyncSession = Depends(get_db),
+    identity: DuniterIdentity = Depends(get_current_identity),
+) -> VotingProtocolOut:
+    """Update a voting protocol (meta-governance).
+
+    Only provided fields will be updated. Requires authentication.
+    """
+    protocol = await _get_protocol(db, id)
+
+    update_data = payload.model_dump(exclude_unset=True)
+    for field, value in update_data.items():
+        setattr(protocol, field, value)
+
+    await db.commit()
+
+    # Reload with formula config
+    protocol = await _get_protocol(db, protocol.id)
+    return VotingProtocolOut.model_validate(protocol)
+
+
 # ── Formula Config routes ───────────────────────────────────────────────────
 
 
@@ -137,3 +179,90 @@ async def create_formula(
     await db.refresh(formula)
 
     return FormulaConfigOut.model_validate(formula)
+
+
+@router.get("/formulas/{id}", response_model=FormulaConfigOut)
+async def get_formula(
+    id: uuid.UUID,
+    db: AsyncSession = Depends(get_db),
+) -> FormulaConfigOut:
+    """Get a single formula configuration."""
+    formula = await _get_formula(db, id)
+    return FormulaConfigOut.model_validate(formula)
+
+
+@router.put("/formulas/{id}", response_model=FormulaConfigOut)
+async def update_formula(
+    id: uuid.UUID,
+    payload: FormulaConfigUpdate,
+    db: AsyncSession = Depends(get_db),
+    identity: DuniterIdentity = Depends(get_current_identity),
+) -> FormulaConfigOut:
+    """Update a formula configuration (meta-governance).
+
+    Only provided fields will be updated. Requires authentication.
+    """
+    formula = await _get_formula(db, id)
+
+    update_data = payload.model_dump(exclude_unset=True)
+    for field, value in update_data.items():
+        setattr(formula, field, value)
+
+    await db.commit()
+    await db.refresh(formula)
+
+    return FormulaConfigOut.model_validate(formula)
+
+
+# ── Simulation ──────────────────────────────────────────────────────────────
+
+
+@router.post("/simulate", response_model=FormulaSimulationResult)
+async def simulate_formula(
+    payload: FormulaSimulationRequest,
+) -> FormulaSimulationResult:
+    """Simulate a WoT threshold formula computation.
+
+    Pure calculation endpoint -- no database access needed.
+    Accepts WoT size, total votes, and formula parameters,
+    returns the computed thresholds and derived values.
+    """
+    # Compute WoT threshold
+    wot_thresh = compute_wot_threshold(
+        wot_size=payload.wot_size,
+        total_votes=payload.total_votes,
+        majority_pct=payload.majority_pct,
+        base_exponent=payload.base_exponent,
+        gradient_exponent=payload.gradient_exponent,
+        constant_base=payload.constant_base,
+    )
+
+    # Compute derived values for transparency
+    w = payload.wot_size
+    t = payload.total_votes
+    m = payload.majority_pct / 100.0
+    g = payload.gradient_exponent
+
+    participation_rate = t / w if w > 0 else 0.0
+    turnout_ratio = min(t / w, 1.0) if w > 0 else 0.0
+    inertia_factor = 1.0 - turnout_ratio ** g if t > 0 else 1.0
+    required_ratio = m + (1.0 - m) * inertia_factor
+
+    # Smith threshold (optional)
+    smith_thresh = None
+    if payload.smith_wot_size is not None and payload.smith_exponent is not None:
+        smith_thresh = compute_smith_threshold(payload.smith_wot_size, payload.smith_exponent)
+
+    # TechComm threshold (optional)
+    techcomm_thresh = None
+    if payload.techcomm_size is not None and payload.techcomm_exponent is not None:
+        techcomm_thresh = compute_techcomm_threshold(payload.techcomm_size, payload.techcomm_exponent)
+
+    return FormulaSimulationResult(
+        wot_threshold=wot_thresh,
+        smith_threshold=smith_thresh,
+        techcomm_threshold=techcomm_thresh,
+        participation_rate=round(participation_rate, 6),
+        required_ratio=round(required_ratio, 6),
+        inertia_factor=round(inertia_factor, 6),
+    )