Abstract: Blockchains usually pay for authenticated reads by maintaining a structure that spans the entire state. We show how validators can support historical membership and exclusion proofs by authenticating each block's writes instead. A Block Update Digest (BUD) commits a write log whose predecessor pointers link successive modifications of each key. A SuperBUD summarizes last writes over a window; an exponential hierarchy turns long unchanged intervals into short proofs. The digest count is logarithmic in the gap within the hierarchy's range, with one additional digest per top-level window beyond it. We prove soundness against adversarial provers and up to f Byzantine validators, and completeness for queries anchored by a post-deployment modification, assuming archive, attestation, and committee evidence is available. Across a 50x increase in state size, the measured base-BUD path rises by 1.24x, compared with 3.1x and 69.5x for in-memory and cache-bounded disk-backed Merkle Patricia tries. On the synthetic trace, two-digest read-layer payloads stay below 800 bytes, and warm hash-path verification takes at most 146 microseconds at p99.