feat(server): complete phase 6 local verification

Game/scripts/arena_registry.gd

@@ -24,3 +24,26 @@ const ARENAS := [
 static func random_path() -> String:
 	var candidates := ARENAS.filter(func(arena): return arena["random"])
 	return candidates[randi() % candidates.size()]["path"]
+
+
+# The arenas a server may rotate through, in declaration order. Same filter as
+# random_path(): an elevated-goal variant is Free-Play-only until a checkpoint
+# trained on it is promoted, and a dedicated server rotating onto one would
+# hand every bot-filled slot an arena it cannot score in.
+static func rotation_paths() -> Array:
+	return ARENAS.filter(func(arena): return arena["random"]).map(func(arena): return arena["path"])
+
+
+# Task 6.5's arena rotation, as pure arithmetic so it is unit-testable without
+# a server: given how many matches have already been played, which arena is
+# next. `random` deliberately still uses the global RNG (the caller wants
+# variety, not reproducibility); `sequential` is a pure function of the count,
+# which is what makes "the server cycles arenas" an assertable claim rather
+# than an observation about luck.
+static func path_for_match(match_index: int, mode: String) -> String:
+	var paths := rotation_paths()
+	if paths.is_empty():
+		return ARENAS[0]["path"]
+	if mode == "random":
+		return paths[randi() % paths.size()]
+	return paths[posmod(match_index, paths.size())]