{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T07:09:05Z","timestamp":1750230545496,"version":"3.41.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T00:00:00Z","timestamp":1710720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["Distrib. Ledger Technol."],"published-print":{"date-parts":[[2024,3,31]]},"abstract":"<jats:p>\n            We introduce the\n            <jats:bold>SPRIG (Smart Proofs via Recursive Information Gathering)<\/jats:bold>\n            protocol. SPRIG allows agents to propose, question, and defend mathematical proofs in a decentralized fashion. A structure of stakes and bounties aims at producing debates in good faith and if those persist, they must go down to machine-level details, where they can be settled automatically. This combination of economic incentives and an oracle is designed to promote succinct and informative proofs. SPRIG can run autonomously as a smart contract on a blockchain platform, and hence it does not rely on a central trusted institution.\n          <\/jats:p>\n          <jats:p>We translate SPRIG into a general game-theoretic model and prove that the protocol satisfies two desirable properties: no spamming and monotonicity. We then characterize analytically the equilibrium of a simple two-player specification of the model: this provides important insights into the impact of the protocol\u2019s parameters on the probabilities that it induces type I\/II errors. We conclude by discussing the main attacks SPRIG\u2019s designers will need to take into account.<\/jats:p>","DOI":"10.1145\/3595298","type":"journal-article","created":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T12:00:25Z","timestamp":1684324825000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Smart Proofs via Recursive Information Gathering: Decentralized Refereeing by Smart Contracts"],"prefix":"10.1145","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5240-3918","authenticated-orcid":false,"given":"Sylvain","family":"Carr\u00e9","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris-Dauphine, Universit\u00e9 PSL, LEDa, CNRS, IRD, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9510-1135","authenticated-orcid":false,"given":"Franck","family":"Gabriel","sequence":"additional","affiliation":[{"name":"Univ Lyon, Universit\u00e9 Claude Bernard Lyon 1, Laboratoire de Sciences Actuarielle et Financi\u00e8re LSAF, ISFA, Lyon, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6224-2035","authenticated-orcid":false,"given":"Cl\u00e9ment","family":"Hongler","sequence":"additional","affiliation":[{"name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Institute of Mathematics, Chair of Statistical Field Theory, Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-4181-4480","authenticated-orcid":false,"given":"Gustavo","family":"Lacerda","sequence":"additional","affiliation":[{"name":"Independent, Asheville, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4086-4842","authenticated-orcid":false,"given":"Gloria","family":"Capano","sequence":"additional","affiliation":[{"name":"Independent, Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,3,18]]},"reference":[{"key":"e_1_3_4_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3419614.3423251"},{"key":"e_1_3_4_3_1","doi-asserted-by":"publisher","DOI":"10.21428\/58320208.c9738e64"},{"key":"e_1_3_4_4_1","doi-asserted-by":"publisher","DOI":"10.5555\/648231.752823"},{"key":"e_1_3_4_5_1","doi-asserted-by":"publisher","DOI":"10.1215\/ijm\/1256049011"},{"key":"e_1_3_4_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/2600057.2602888"},{"key":"e_1_3_4_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhy095"},{"key":"e_1_3_4_8_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v29i1.9317"},{"key":"e_1_3_4_9_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2102.03044"},{"key":"e_1_3_4_10_1","unstructured":"Ethereum. 2022. Optimistic rollups. (2022). https:\/\/ethereum.org\/en\/developers\/docs\/scaling\/optimistic-rollups\/."},{"key":"e_1_3_4_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759729"},{"key":"e_1_3_4_12_1","unstructured":"Scott Garrabrant Tsvi Benson-Tilsen Andrew Critch Nate Soares and Jessica Taylor. 2016. Logical induction. (2016). https:\/\/intelligence.org\/files\/LogicalInduction.pdf."},{"key":"e_1_3_4_13_1","doi-asserted-by":"publisher","DOI":"10.1086\/288169"},{"key":"e_1_3_4_14_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022058209073"},{"key":"e_1_3_4_15_1","doi-asserted-by":"publisher","DOI":"10.5750\/jpm.v1i1.417"},{"key":"e_1_3_4_16_1","article-title":"AI safety via debate","author":"Irving Geoffrey","year":"2018","unstructured":"Geoffrey Irving, Paul Christiano, and Dario Amodei. 2018. AI safety via debate. arXiv:1805.00899 (2018). https:\/\/arxiv.org\/pdf\/1805.00899.pdf.","journal-title":"arXiv:1805.00899"},{"key":"e_1_3_4_17_1","article-title":"Arbitrum: Private, scalable smart contracts","author":"Kalodner Harry","year":"2018","unstructured":"Harry Kalodner, Steven Goldfeder, Xiaoqi Chen, S. Matthew Weinberg, and Edward W. Felten. 2018. Arbitrum: Private, scalable smart contracts. Proceedings of the 27th USENIX Security Symposium (2018). https:\/\/www.usenix.org\/system\/files\/conference\/usenixsecurity18\/sec18-kalodner.pdf.","journal-title":"Proceedings of the 27th USENIX Security Symposium"},{"key":"e_1_3_4_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICBC54727.2022.9805513"},{"key":"e_1_3_4_19_1","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhaa075"},{"key":"e_1_3_4_20_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1971.10482346"},{"key":"e_1_3_4_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(64)90223-2"},{"key":"e_1_3_4_22_1","article-title":"MathCoin: A blockchain proposal that helps verifying mathematical theorems in public","author":"Su Borching","year":"2018","unstructured":"Borching Su. 2018. MathCoin: A blockchain proposal that helps verifying mathematical theorems in public. Cryptology ePrint Archive Report 2018\/271 (2018). https:\/\/ia.cr\/2018\/271.","journal-title":"Cryptology ePrint Archive Report 2018\/271"},{"key":"e_1_3_4_23_1","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1908.04756"},{"key":"e_1_3_4_24_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1994-00502-6"},{"key":"e_1_3_4_25_1","unstructured":"Bill White. 2016. Qeditas: A formal library as a Bitcoin spin-off. (2016). https:\/\/qeditas.org\/docs\/qeditas.pdf."},{"key":"e_1_3_4_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24849-1_24"}],"container-title":["Distributed Ledger Technologies: Research and Practice"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3595298","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3595298","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T17:49:08Z","timestamp":1750182548000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3595298"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,18]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,3,31]]}},"alternative-id":["10.1145\/3595298"],"URL":"https:\/\/doi.org\/10.1145\/3595298","relation":{},"ISSN":["2769-6480","2769-6480"],"issn-type":[{"type":"print","value":"2769-6480"},{"type":"electronic","value":"2769-6480"}],"subject":[],"published":{"date-parts":[[2024,3,18]]},"assertion":[{"value":"2022-11-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-04-10","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-03-18","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}