DNA offers high-density, durable storage by encoding digital information into synthetic strands and retrieving it through sequencing. Sequence reconstruction combines noisy copies of each strand before downstream decoding. Conventional offline methods typically reconstruct completed read clusters, separating reconstruction from ongoing read collection. Streaming reconstruction offers a way to overlap evidence processing with sequencing and reduce the computation remaining before downstream decoding. We present ACOR, a streaming consensus reconstruction method that records $k$-mer transitions and boundary support in a persistent ledger, then decodes through length-constrained beam search and priority-based selection at cluster closure. Evaluation on real and simulated DNA-storage datasets showed competitive recovery. On our own short-read next-generation sequencing (NGS) wet-lab library, ACOR combined near-complete recovery with second-scale reconstruction of more than ten million reads. A smaller public benchmark was completed in a fraction of a second. Parallel ACOR achieved speedups of tens to over a thousand-fold relative to the tested serial baseline configurations. Sparse storage reduced high-context memory requirements, while parallel execution accelerated reconstruction computation. ACOR is designed for streaming readout pipelines that process assigned reads while sequencing continues.

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