In the context of rapidly evolving cloud service systems and blockchain ecosystems, certain lightweight edge client nodes responsible for continuous generation or transmission of streaming data often exhibit limited computational prowess. Traditional dynamic integrity audit schemes, which rely on one-time initialization frameworks and incur high client-side over-heads, are ill-suited to this scenario. To address these challenges, this paper introduces Iterative Proof of Retrievability (IPoR), an integrity verification scheme for periodic incremental data via optimistic tags generation. We propose a publicly verifiable tripartite IPoR system framework comprised of SDC, EAP and SSP, where the majority of the stream data tagging process is attributed to the SSP responsible for data storage. To ensure the verifiability of the EAP's stream data tag generation process, we introduce a fraud proof based on SMT, the latter substantially decreasing the computational load on public validators. We formally prove under the random oracle model that IPoR satisfies storage integrity and tag generation completeness. Theoretical performance analysis and experimental results demonstrate that our IPoR construction can help clients save over 90% on initial computational overhead.