perf(snake): cache survival rollout state

- Cache occupancy bitboards for repeated multiplayer rollout positions.
- Memoize position evaluations to avoid duplicate flood-fill calculations.
- Reuse shared values while ranking simultaneous enemy responses.
- Include evaluation hits in Prism rollout telemetry.
- Document the optimization and bump Prism to version 1.4.0.

snakes/strategies/prism.py

@@ -1,4 +1,4 @@
-"""PrismBattleSnake_GPT_5_6_Sol v1.3.0
+"""PrismBattleSnake_GPT_5_6_Sol v1.4.0
 
 Built on ApexBattleSnake v1.0.0.  All strategic logic is inherited.
 Performance improvement: all spatial primitives (flood fill, territory,
@@ -30,6 +30,7 @@ Key speedups:
   S16: Compact adversarial multiplayer rollout advances plausible enemy replies.
   S17: Rollout memoization and adaptive depth spend time on ambiguous positions.
   S18: Prism uses a deeper tactical horizon while retaining Apex's timeout reserve.
+  S19: Rollout occupancy and evaluation caches avoid repeated flood-fill work.
 """
 
 from __future__ import annotations
@@ -53,7 +54,7 @@ class PrismBattleSnake_GPT_5_6_Sol(
   BitboardSpatialMixin,
   ApexBattleSnake,
 ):
-  VERSION = "1.3.0"
+  VERSION = "1.4.0"
 
   def __init__(self) -> None:
     super().__init__()
@@ -162,6 +163,7 @@ class PrismBattleSnake_GPT_5_6_Sol(
         thinking["prism_rollout_nodes"] = self._survival_search_context.nodes
         thinking["prism_rollout_cache_hits"] = (
           self._survival_search_context.cache_hits
+          + self._survival_search_context.evaluation_cache_hits
         )
         thinking["prism_rollout_deadline_exits"] = (
           self._survival_search_context.deadline_exits