feat(complement-race): implement position broadcasting for ghost trains

Clients now broadcast their train position to server every 200ms,
allowing other clients to render ghost trains at correct locations.

Added UPDATE_POSITION move type and server-side validation to sync
client-calculated positions (from momentum physics) to server state.

This fixes the issue where ghost trains were rendering but invisible
because they all had position=0 from server.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

apps/web/src/arcade-games/complement-race/Provider.tsx

@@ -564,6 +564,23 @@ export function ComplementRaceProvider({ children }: { children: ReactNode }) {
     }
   }, [multiplayerState.currentRoute, compatibleState.style, multiplayerState.passengers.length])
 
+  // Broadcast position to server for multiplayer ghost trains
+  useEffect(() => {
+    if (!compatibleState.isGameActive || compatibleState.style !== 'sprint') {
+      return
+    }
+
+    // Send position update every 200ms
+    const interval = setInterval(() => {
+      makeMove({
+        type: 'UPDATE_POSITION',
+        data: { position: clientPosition },
+      })
+    }, 200)
+
+    return () => clearInterval(interval)
+  }, [compatibleState.isGameActive, compatibleState.style, clientPosition, makeMove])
+
   // Keep lastLogRef for future debugging needs
   // (removed debug logging)
 

apps/web/src/arcade-games/complement-race/Validator.ts

@@ -97,6 +97,9 @@ export class ComplementRaceValidator
       case 'UPDATE_INPUT':
         return this.validateUpdateInput(state, move.playerId, move.data.input)
 
+      case 'UPDATE_POSITION':
+        return this.validateUpdatePosition(state, move.playerId, move.data.position)
+
       case 'CLAIM_PASSENGER':
         return this.validateClaimPassenger(
           state,
@@ -397,6 +400,39 @@ export class ComplementRaceValidator
     return { valid: true, newState }
   }
 
+  private validateUpdatePosition(
+    state: ComplementRaceState,
+    playerId: string,
+    position: number
+  ): ValidationResult {
+    if (state.gamePhase !== 'playing') {
+      return { valid: false, error: 'Game not in playing phase' }
+    }
+
+    const player = state.players[playerId]
+    if (!player) {
+      return { valid: false, error: 'Player not found' }
+    }
+
+    // Validate position is a reasonable number (0-100)
+    if (typeof position !== 'number' || position < 0 || position > 100) {
+      return { valid: false, error: 'Invalid position value' }
+    }
+
+    const newState: ComplementRaceState = {
+      ...state,
+      players: {
+        ...state.players,
+        [playerId]: {
+          ...player,
+          position,
+        },
+      },
+    }
+
+    return { valid: true, newState }
+  }
+
   // ==========================================================================
   // Sprint Mode: Passenger Management
   // ==========================================================================

apps/web/src/arcade-games/complement-race/types.ts

@@ -143,6 +143,7 @@ export type ComplementRaceMove = BaseGameMove &
     // Playing phase
     | { type: 'SUBMIT_ANSWER'; data: { answer: number; responseTime: number } }
     | { type: 'UPDATE_INPUT'; data: { input: string } } // Show "thinking" indicator
+    | { type: 'UPDATE_POSITION'; data: { position: number } } // Sprint mode: sync train position
     | { type: 'CLAIM_PASSENGER'; data: { passengerId: string; carIndex: number } } // Sprint mode: pickup
     | { type: 'DELIVER_PASSENGER'; data: { passengerId: string } } // Sprint mode: delivery