fix: scoring & game logic bugs — arena modifiers, human timeout, validated prompts

- scoring.ts: wire arena damage modifiers (speed_2x, roast_2x, etc.) into applyModifiers()
- human-responses.ts: use challenge.timeout_ms instead of hardcoded 8s
- FightPage.vue: add route watcher for clean state reset on navigation
- Validated all 800 prompts: 0 duplicates, all factual have answers, all choices have 4 items

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

server/src/engine/scoring.ts

@@ -174,13 +174,34 @@ export function scoreRound(
   }
 }
 
+const ARENA_MODIFIER_TYPES: Record<string, string[]> = {
+  speed_2x: ['speed_blitz'],
+  efficiency_buff: ['token_economy'],
+  roast_2x: ['roast_battle'],
+  accuracy_buff: ['hallucination_check'],
+  wrestling_2x: ['wrestling_match', 'roast_battle'],
+  food_2x: ['food_fight'],
+  magic_2x: ['magic_duel', 'medieval_combat'],
+  meme_2x: ['meme_war'],
+  space_2x: ['space_war'],
+  demo_2x: ['demolition', 'vehicle_mayhem'],
+  music_2x: ['music_battle'],
+  nature_2x: ['nature_clash', 'animal_kingdom'],
+  hack_2x: ['hack_battle'],
+  sports_2x: ['sports_showdown'],
+}
+
 function applyModifiers(
   damage: number,
-  _challenge: Challenge,
-  _arenaModifier: string | null,
+  challenge: Challenge,
+  arenaModifier: string | null,
   combo: number,
 ): number {
   let d = damage
+  // Arena modifier: 2x damage when challenge type matches
+  if (arenaModifier && ARENA_MODIFIER_TYPES[arenaModifier]?.includes(challenge.type)) {
+    d *= 2
+  }
   if (combo > 0) {
     d *= 1 + Math.min(combo, 5) * 0.2
   }