We introduce \textit{OptChain}, a permissionless blockchain state machine replication (SMR) protocol that achieves optimal throughput. We first establish a theoretical upper bound on the throughput of any SMR protocol under a fixed error probability, and OptChain is the first protocol to approach this limit. Conceptually, OptChain is a sharding protocol that optimizes both vertical and horizontal scalability. Vertically, we introduce \textit{Shardis}, a novel permissionless verifiable information dispersal mechanism that maximizes intra-shard throughput to its physical limit, determined by the fastest node's bandwidth within each shard. Horizontally, we propose \textit{diffusion mining}, which ensures security as long as each shard includes at least one honest node, thereby allowing for the maximum number of shards. We provide a formal security and efficiency analysis, demonstrating that OptChain approaches the established upper bound while maintaining robust security. Finally, we implement a full prototype of OptChain and deploy it on AWS EC2 nodes across various regions. Experimental results indicate that OptChain outperforms state-of-the-art permissionless protocols and closely approaches the theoretical optimal throughput.

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