We prove that Cypher 25, the graph query language of Neo4j, is Turing-complete. The proof shows that a single RETURN statement using reduce(), CASE expressions, and list comprehensions can simulate any 2-counter machine (Minsky 1967). We address the bounded-step objection via two complementary resolutions and present a third graph-native simulation using quantified path patterns (QPP) with allReduce. All three constructions were verified on a live Neo4j Aura instance.

翻译：我们证明了Neo4j的图查询语言Cypher 25是图灵完备的。该证明表明，使用reduce()、CASE表达式和列表推导式的单条RETURN语句能够模拟任意二计数器机（Minsky 1967）。我们通过两种互补的解决方案解决了有限步数异议，并提出了第三种使用带allReduce的量词化路径模式（QPP）的图原生模拟方法。所有三种构造均在活跃的Neo4j Aura实例上验证通过。