{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T09:47:04Z","timestamp":1791884824456,"version":"4.3.4"},"reference-count":42,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Blockchain-Cyber-Physical Systems (BCPSs) use sensor-generated IoT events to update ledger representations of physical assets. Authenticating individual reports does not by itself establish an admissible trajectory from the canonical predecessor or authenticate a selected historical interval. We formulate Verifiable State-Evolution Integrity (VSEI): accepted states must be reachable through ordered, device-bound, policy-compliant trajectories. HeRZ realizes this requirement through a BCPS-specific relation combining event authentication, physical guards, deterministic updates, and temporal linkage. Recursive folding preserves the relation in a fixed-width incremental proof state, while a KZG\/Groth16 Decider exposes the interval boundaries. A stateful EVM wrapper atomically consumes the canonical predecessor for forward settlement and verifies retained intervals between anchored checkpoints without publishing intermediate event records. The implementation supports both paths, producing 384-byte compressed proofs and 1156-byte settlement calldata. Mean complete online peak memory remains 27.92\u201328.68 GiB over 100\u20132000 events. At 2000 events, HeRZ reduces peak memory by 34.1% relative to the equivalent stateful FlatZK baseline, at 3.63 times its online time. Layered tests and anchored audits validate the implemented state semantics. One parameter set and deployed verifier accept different interval lengths, supporting incremental construction and selective historical auditing within a fixed protocol version. HeRZ thus provides an executable path from authenticated sensor events to canonically settled and retrospectively auditable asset histories.<\/jats:p>","DOI":"10.3390\/s26196226","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T15:20:59Z","timestamp":1790781659000},"page":"6226","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["HeRZ: Hierarchical Recursive Zero-Knowledge Verification for Canonical and Auditable Asset-State Evolution in Blockchain-Cyber-Physical Systems"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2628-1811","authenticated-orcid":false,"given":"Ningyuan","family":"Chen","sequence":"first","affiliation":[{"name":"College of Information and Intelligence Engineering, Zhejiang Wanli University, No. 8, Qianhu South Road, Yinzhou District, Ningbo 315100, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"}]},{"given":"Yibei","family":"Lin","sequence":"additional","affiliation":[{"name":"College of Information and Intelligence Engineering, Zhejiang Wanli University, No. 8, Qianhu South Road, Yinzhou District, Ningbo 315100, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Siu-Yeung","family":"Cho","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China"},{"name":"Oriensol Technology Company Limited, Hung Hom, Kowloon, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0103-0570","authenticated-orcid":false,"given":"Yu","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China"},{"name":"Oriensol Technology Company Limited, Hung Hom, Kowloon, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"data-curation","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,30]]},"reference":[{"key":"ref_1","first-page":"59","article-title":"Blockchain and the Future of Tokenization","volume":"68","author":"Bate","year":"2025","journal-title":"Res.-Technol. 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