标题： 安全低带宽SPV：简化支付验证协议与安全界限的形式化处理 显示英文标题

标题： Safe Low Bandwidth SPV: A Formal Treatment of Simplified Payment Verification Protocols and Security Bounds

摘要： 本文提出了对简化支付验证（SPV）的完整形式化规范、协议描述和数学证明结构，该定义最初在比特币白皮书中提出\cite{nakamoto2008}。 与流行实现中传播的错误描述形成鲜明对比，我们表明，在有界对手假设下，SPV不仅安全，而且对于需要可扩展和可验证交易包含的数字现金系统来说是严格最优的。 我们从基本原理出发重新构建了SPV协议，将验证模型建立在符号自动机、Merkle成员关系和链式证明支配谓词之上。 通过严格的概率和博弈论分析，我们推导出协议在其中安全运行的经济边界，并在部分连接性、敌对中继网络和对手传播延迟条件下验证其活性和安全性属性。 我们的规范进一步引入了低带宽优化，如自适应轮询和压缩头同步，同时保持正确性。 本文既作为安全SPV实现的蓝图，也是对非验证客户端常见误解的反驳。 显示英文摘要

摘要： This paper presents a complete formal specification, protocol description, and mathematical proof structure for Simplified Payment Verification (SPV) as originally defined in the Bitcoin whitepaper \cite{nakamoto2008}. In stark contrast to the misrepresentations proliferated by popular implementations, we show that SPV is not only secure under bounded adversarial assumptions but strictly optimal for digital cash systems requiring scalable and verifiable transaction inclusion. We reconstruct the SPV protocol from first principles, grounding its verification model in symbolic automata, Merkle membership relations, and chain-of-proof dominance predicates. Through rigorous probabilistic and game-theoretic analysis, we derive the economic bounds within which the protocol operates securely and verify its liveness and safety properties under partial connectivity, hostile relay networks, and adversarial propagation delay. Our specification further introduces low-bandwidth optimisations such as adaptive polling and compressed header synchronisation while preserving correctness. This document serves both as a blueprint for secure SPV implementation and a rebuttal of common misconceptions surrounding non-validating clients.