feat(rithmomachia): add CaptureContext for capture dialog state management

Add centralized context provider for capture dialog subsystem. Provides:
- Layout configuration (targetPos, cellSize, gap, padding)
- Piece references (mover, target, helper)
- Selection state (selectedRelation, closing)
- Helper functions (findValidHelpers, selectRelation, selectHelper, dismissDialog)

This eliminates 8-15 props from each capture component and provides a
single source of truth for capture state.

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

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

apps/web/src/arcade-games/rithmomachia/contexts/CaptureContext.tsx

@@ -0,0 +1,75 @@
+'use client'
+
+import { createContext, type ReactNode, useContext } from 'react'
+import type { Piece, RelationKind } from '../types'
+
+/**
+ * Layout information for the capture dialog
+ */
+export interface CaptureLayout {
+  targetPos: { x: number; y: number }
+  cellSize: number
+  gap: number
+  padding: number
+}
+
+/**
+ * Pieces involved in the current capture attempt
+ */
+export interface CapturePieces {
+  mover: Piece
+  target: Piece
+  helper: Piece | null
+}
+
+/**
+ * Context value for the capture dialog subsystem
+ */
+export interface CaptureContextValue {
+  // Layout (calculated once, shared by all capture components)
+  layout: CaptureLayout
+
+  // Pieces involved in capture
+  pieces: CapturePieces
+
+  // Capture state
+  selectedRelation: RelationKind | null
+  closing: boolean
+
+  // All pieces on the board (for validation)
+  allPieces: Piece[]
+
+  // Helper functions
+  findValidHelpers: (moverValue: number, targetValue: number, relation: RelationKind) => Piece[]
+
+  // Actions
+  selectRelation: (relation: RelationKind) => void
+  selectHelper: (pieceId: string) => void
+  dismissDialog: () => void
+}
+
+const CaptureContext = createContext<CaptureContextValue | null>(null)
+
+/**
+ * Hook to access capture context
+ */
+export function useCaptureContext(): CaptureContextValue {
+  const context = useContext(CaptureContext)
+  if (!context) {
+    throw new Error('useCaptureContext must be used within CaptureProvider')
+  }
+  return context
+}
+
+/**
+ * Provider for capture dialog context
+ */
+export function CaptureProvider({
+  children,
+  value,
+}: {
+  children: ReactNode
+  value: CaptureContextValue
+}) {
+  return <CaptureContext.Provider value={value}>{children}</CaptureContext.Provider>
+}