feat(snake): optimize duels and persist customizations

- Add deadline-aware iterative duel search with bitboards and tuple bodies.

- Reuse transposition bounds and move-order hints across search depths.

- Persist snake colors, heads, and tails in SQLite and PostgreSQL.

- Restore customization metadata when hydrating dashboard replays.

- Cover duel deadlines, cache reuse, schema storage, and replay output.

tests/snakes/test_PrismBattleSnake_GPT_5_6_Sol.py

@@ -1,9 +1,11 @@
 import unittest
+from time import perf_counter
 
 from snakes import SnakeBuilder, get_snake_version
 from snakes.ApexBattleSnake import ApexBattleSnake
 from snakes.PrismBattleSnake_GPT_5_6_Sol import PrismBattleSnake_GPT_5_6_Sol
 from snakes.bitboard import BitBoard
+from snakes.bitboard_duel_search import BitboardDuelSearch
 
 class TestBitBoard(unittest.TestCase):
 
@@ -64,5 +66,51 @@ class TestPrismBattleSnake_GPT_5_6_Sol(unittest.TestCase):
     self.assertEqual(open_count, 9)
     self.assertEqual(trapped_count, 1)
 
+  def test_bitboard_duel_search_values_length_advantage(self):
+    snake = PrismBattleSnake_GPT_5_6_Sol()
+    my_body = [{"x": 1, "y": 0}, {"x": 0, "y": 0}, {"x": 0, "y": 1}]
+    enemy_body = [{"x": 1, "y": 2}, {"x": 0, "y": 2}]
+
+    value = snake._minimax_sim(
+      my_body=my_body, enemy_body=enemy_body,
+      food_set=set(), hazard_set=set(),
+      my_health=100, enemy_health=100,
+      hazard_damage=15, hazard_count={},
+      width=3, height=3, depth=2,
+      alpha=-1e9, beta=1e9, deadline=None,
+    )
+
+    self.assertGreater(value, 0)
+
+  def test_bitboard_duel_search_reuses_transpositions(self):
+    board = BitBoard(5, 5)
+    search = BitboardDuelSearch(
+      board=board, food=set(), hazards=set(), hazard_count={},
+      hazard_damage=15, deadline=perf_counter() + 1.0,
+    )
+    my_body = [{"x": 1, "y": 1}, {"x": 1, "y": 0}, {"x": 0, "y": 0}]
+    enemy_body = [{"x": 3, "y": 3}, {"x": 3, "y": 4}, {"x": 4, "y": 4}]
+
+    search.search_depth(my_body, enemy_body, 100, 100, 3, set())
+    hits_before = search.cache_hits
+    search.search_depth(my_body, enemy_body, 100, 100, 3, set())
+
+    self.assertGreater(search.cache_hits, hits_before)
+
+  def test_bitboard_duel_search_respects_deadline(self):
+    board = BitBoard(11, 11)
+    search = BitboardDuelSearch(
+      board=board, food=set(), hazards=set(), hazard_count={},
+      hazard_damage=15, deadline=perf_counter() - 0.001,
+    )
+    my_body = [{"x": 2, "y": 2}, {"x": 2, "y": 1}, {"x": 2, "y": 0}]
+    enemy_body = [{"x": 8, "y": 8}, {"x": 8, "y": 9}, {"x": 8, "y": 10}]
+
+    started = perf_counter()
+    _, depth = search.search(my_body, enemy_body, 100, 100, 6, set())
+
+    self.assertEqual(depth, 0)
+    self.assertLess(perf_counter() - started, 0.05)
+
 if __name__ == "__main__":
   unittest.main()