feat: add gameplay stats and restore Zenith rollout depth

- Add read-only gameplay statistics with filters and opponent comparisons.
- Report move-trace latency percentiles and external timeout counts.
- Pair engine latency with the preceding turn to separate timing stages.
- Adjust Zenith rollout deepening for its larger timeout reserve.
- Bump Zenith to 1.2.0 and document the fix and snake-stats command.
- Cover statistics, trace aggregation, rollout depth, and verdict budgets.

snakes/__init__.py

@@ -13,7 +13,7 @@ SNAKE_REGISTRATIONS = {
     "snakes.strategies.prism", "1.5.0"
   ),
   "ZenithBattleSnake_ClaudeOpus5_5": SnakeRegistration(
-    "snakes.strategies.zenith", "1.1.0"
+    "snakes.strategies.zenith", "1.2.0"
   ),
   "DummSnake": SnakeRegistration("snakes.legacy.DummSnake", "1.0.0"),
   "LogicSnake": SnakeRegistration("snakes.legacy.LogicSnake", "1.1.0"),

snakes/engine/survival.py

@@ -4,6 +4,10 @@ from time import perf_counter
 from snakes.engine.survival_search import CompactSurvivalSearch
 
 class BitboardSurvivalMixin:
+  # Remaining budget above which rollouts against at most two enemies may look
+  # one turn deeper. Snakes with a larger timeout reserve lower this threshold.
+  _rollout_deepen_ms = 250.0
+
   def _future_rollout_bonus(
       self, move: str, safe_moves: dict, my_body: list, other_snakes: list,
       food_set: set, is_constrictor: bool, width: int, height: int,
@@ -36,7 +40,7 @@ class BitboardSurvivalMixin:
       depth = min(self._planning_depth, 2 if len(other_snakes) > 1 else 3)
       if remaining < 90:
         depth = min(depth, 2)
-      elif remaining > 250 and len(other_snakes) <= 2:
+      elif remaining > self._rollout_deepen_ms and len(other_snakes) <= 2:
         depth = min(4, depth + 1)
       raw = self._survival_search_context.search_selected(
         my_body=my_body,

snakes/strategies/zenith.py

@@ -1,4 +1,4 @@
-"""ZenithBattleSnake_ClaudeOpus5_5 v1.1.0
+"""ZenithBattleSnake_ClaudeOpus5_5 v1.2.0
 
 Built on PrismBattleSnake_GPT_5_6_Sol v1.5.0. Prism's bitboard engine, duel
 search, and adversarial rollouts are inherited unchanged.
@@ -15,6 +15,11 @@ Z2: Proven-loss veto — a candidate whose completed search proves a loss is
     replaced by the best non-losing candidate.
 Z3: Proven-win override — a candidate whose completed search proves a win is
     played even if the heuristic preferred another move.
+Z4: Elapsed-time rollout gate — Zenith keeps a larger timeout reserve than
+    Prism. The inherited multiplayer "deepen when > 250 ms remain" gate is
+    lowered by that extra reserve, so 3-snake rollouts deepen after the same
+    elapsed time as Prism instead of never reaching depth 3. The duel gate is
+    left alone: the verdict pass already spends the duel budget.
 """
 from time import perf_counter
 
@@ -27,18 +32,22 @@ _PROVEN_WIN = BitboardDuelSearch.WIN / 2
 _PROVEN_LOSS = BitboardDuelSearch.LOSS / 2
 # Reserve kept for Apex's history bookkeeping after the verdict pass.
 _VERDICT_RESERVE_MS = 25.0
+_ZENITH_TIMEOUT_BUFFER_MS = 180
 
 class ZenithBattleSnake_ClaudeOpus5_5(ZenithSurvivalMixin, PrismBattleSnake_GPT_5_6_Sol):
-  VERSION = "1.1.0"
+  VERSION = "1.2.0"
 
   def __init__(self) -> None:
     super().__init__()
     self.name = "ZenithBattleSnake"
     self.version = self.VERSION
+    # Z4: deepen after the same elapsed time as the inherited Prism gates.
+    extra_reserve = self._get_timeout_buffer_ms() - super()._get_timeout_buffer_ms()
+    self._rollout_deepen_ms = max(120.0, self._rollout_deepen_ms - extra_reserve)
 
   def _get_timeout_buffer_ms(self):
     # Leave room for executor scheduling, history, JSON and network delivery.
-    return max(180, super()._get_timeout_buffer_ms())
+    return max(_ZENITH_TIMEOUT_BUFFER_MS, super()._get_timeout_buffer_ms())
 
   def _choose_duel_move(
     self, safe_moves, my_body, my_len, my_health, other_snakes, food_set,