We introduce PoSME (Proof of Sequential Memory Execution), a cryptographic primitive that enforces sustained sequential computation via latency-bound pointer chasing over a mutable arena. Each step reads data-dependent addresses, writes a block whose value and causal hash are mutually dependent (symbiotic binding), and chains the result into a global transcript. This yields three properties: (1) strict linear sequential memory-step enforcement, (2) high time-memory trade-off resistance (a tenfold penalty at a write density of 4, with a formal space-time lower bound that scales quadratically with the number of steps), and (3) a tight ASIC advantage bound by DRAM random-access latency rather than bandwidth. Benchmarks across 17 CPU platforms and 4 GPU architectures demonstrate that hash computation is under 3.5 percent of step cost and GPU hardware is 14 to 19 times slower than a consumer CPU. POSME requires no trusted setup and provides a foundation for verifiable delay, authorship attestation, and Sybil resistance.

翻译：我们提出PoSME（顺序内存执行证明），一种通过可变区域上的延迟边界指针追踪强制执行持续顺序计算的密码学原语。每一步读取数据依赖的地址，写入一个值与其因果哈希相互依赖（共生绑定）的数据块，并将结果链接到全局记录中。这产生三个性质：（1）严格的线性顺序内存步执行强制；（2）高时间-内存权衡抵抗性（在写密度为4时产生十倍惩罚，且形式化的时空下界与步数呈二次方缩放）；（3）基于DRAM随机访问延迟（而非带宽）的紧致ASIC优势界。对17个CPU平台和4个GPU架构的基准测试表明，哈希计算占步成本的3.5%以下，且GPU硬件比消费级CPU慢14至19倍。PoSME无需可信设置，为可验证延迟、作者身份证明和女巫攻击抵抗提供了基础。