[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81508-en":3,"doc-seo-81508-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81508,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","SPID-Chain: Verifiable Polar-Coded State Validation for Cross-Chain DAG Settlement","Cross-chain settlement must preserve safety across heterogeneous ledgers while tolerating delayed computation, Byzantine participants, and adversarial transaction issuance. This paper introduces SPID-Chain, an adapter-compatible escrow-backed transfer architecture for programmable blockchains. Settlement state is maintained via persistent polar-coded fragments, candidate transitions are validated using hidden linear checks, and certified transfers are recorded in a weighted DAG. Exact recovery-time distributions and verification-soundness bounds enable a cross-layer stability theorem, yielding end-to-end guarantees for non-negativity, conservation, replay protection, conflict exclusion, consistency, and finite lock-to-release latency.","arXiv :2501 . 11794v2 [ cs .DC] 10 Jul 2026  \nSPID-Chain: Verifiable Polar-Coded State Validation for Cross-Chain DAG Settlement  \nAmirhossein Taherpour  Xiaodong Wang   \nDepartment of Electrical Engineering, Columbia University  \n500 West 120th Street, New York, NY 10027, USA Email addresses: [at3532@columbia.edu](at3532@columbia.edu) ; [xw2008@columbia.edu](xw2008@columbia.edu)  \nAbstract  \nCross-chain settlement must preserve safety across heterogeneous ledgers while tolerating delayed computation, Byzantine participants, and adversarial transaction issuance. This paper presents SPID-Chain, an adapter-compatible settlement architecture for escrow-backed fungible transfers across programmable blockchains. SPID-Chain maintains settlement state through persistent Polarcoded fragments, validates candidate state transitions using hidden linear verification checks, and records certified transfers in a weighted directed acyclic graph (DAG) . The design separates nativechain finality from cross-chain settlement: source-chain finality establishes an immutable reservation, whereas weighted DAG confirmation determines when the corresponding destination credit becomes executable. We derive an exact recovery-time distribution for heterogeneous coded workers, a verification-soundness bound for Byzantine responses, and an exact weighted-quorum condition for conflicting-block safety. These components are coupled in a cross-layer stability theorem showing how the coded-validation completion probability determines the effective honest issuance rate and, consequently, the stable adversarial-load region of the settlement DAG. We further establish an end-to-end settlement guarantee covering balance non-negativity, asset conservation, conflict exclusion, replay protection, coded-state consistency, and finite expected lock-to-release latency under the stated liveness conditions. Prototype-assisted simulations indicate that coded validation reduces sensitivity to stragglers, improves validation and confirmation throughput under heterogeneous delays, and produces the predicted transition between stable and unstable DAG operation. The resulting framework provides a verifiable and analytically grounded settlement layer without modifying the native consensus protocol of participating chains.  \nKeywords: Cross-chain settlement; coded computing; Polar codes; directed acyclic graph; Byzantine verification  \n1 Introduction  \nBlockchain ecosystems increasingly comprise multiple independent execution and settlement domains. Participating chains may differ in their consensus protocols, validator sets, state representations, finality rules, transaction semantics, and performance characteristics. Applications that transfer assets or coordinate state across these domains must therefore establish more than the existence of a message on a remote chain. They must determine that the source event is final, the corresponding funds have been reserved, the proposed state transition is admissible and replay-free, conflicting transitions cannot both succeed, and the destination effect is executed exactly once. Providing these guarantees without requiring participating chains to replace their native consensus protocols remains a central problem in blockchain interoperability [1–5] .  \nA broad range of interoperability mechanisms has been developed to address this problem. Atomic-swap protocols coordinate asset exchange through cryptographic and timing conditions, while sidechains, relays, and light-client constructions authenticate the evolution of remote ledgers. Collateral-backed protocols, notary systems, gateways, and middleware architectures coordinate transfers through external participants and recovery procedures. Proof-carrying bridges and zeroknowledge constructions instead verify remote consensus or state transitions through succinct cryptographic evidence. Other approaches combine the trust of multiple blockchains, support multiparty asset movement, or standardize transaction con","cbCaibVX22a5IjAr","https://ap.wps.com/l/cbCaibVX22a5IjAr","pdf",938308,6,1,48,"English","en",105,"# Introduction\n## Cross-chain settlement requirements\n## Related interoperability mechanisms\n## DAG-based ledgers and confirmation\n## Coded distributed validation and Byzantine models","[{\"question\":\"What core problem does SPID-Chain address in cross-chain settlement?\",\"answer\":\"It preserves safety across heterogeneous ledgers while ensuring delayed computation and Byzantine or adversarial transaction issuance do not lead to conflicting or invalid state transitions.\"},{\"question\":\"How does SPID-Chain represent and maintain settlement state?\",\"answer\":\"It maintains settlement state using persistent polar-coded fragments, validates candidate state transitions via hidden linear verification checks, and records certified transfers in a weighted DAG.\"},{\"question\":\"What end-to-end guarantees does the paper claim for the settlement process?\",\"answer\":\"It guarantees balance non-negativity and asset conservation, excludes conflicts, provides replay protection, enforces coded-state consistency, and bounds the expected lock-to-release latency under stated liveness conditions.\"}]",1784173885,121,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"spid-chain-verifiable-polar-coded-state-validation-for-cross-chain-dag-settlement","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/spid-chain-verifiable-polar-coded-state-validation-for-cross-chain-dag-settlement/81508/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What core problem does SPID-Chain address in cross-chain settlement?","Question",{"text":76,"@type":77},"It preserves safety across heterogeneous ledgers while ensuring delayed computation and Byzantine or adversarial transaction issuance do not lead to conflicting or invalid state transitions.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does SPID-Chain represent and maintain settlement state?",{"text":81,"@type":77},"It maintains settlement state using persistent polar-coded fragments, validates candidate state transitions via hidden linear verification checks, and records certified transfers in a weighted DAG.",{"name":83,"@type":74,"acceptedAnswer":84},"What end-to-end guarantees does the paper claim for the settlement process?",{"text":85,"@type":77},"It guarantees balance non-negativity and asset conservation, excludes conflicts, provides replay protection, enforces coded-state consistency, and bounds the expected lock-to-release latency under stated liveness 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