{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:OKTPCMTKP4ENBVARAYUUVAJOZK","short_pith_number":"pith:OKTPCMTK","schema_version":"1.0","canonical_sha256":"72a6f1326a7f08d0d41106294a812ecab3673904f7fb267e05494624431a1c5c","source":{"kind":"arxiv","id":"2411.08536","version":3},"attestation_state":"computed","paper":{"title":"Extended Shuffle Product for Multiple Zeta Values","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.NT","authors_text":"Bin Zhang, Hongyu Xiang, Li Guo, Wenchuan Hu","submitted_at":"2024-11-13T11:34:07Z","abstract_excerpt":"The shuffle algebra on positive integers encodes the usual multiple zeta values (MZVs) (with positive arguments) thanks to the representations of MZVs by iterated Chen integrals of Kontsevich. Together with the quasi-shuffle (stuffle) algebra, it provides the algebraic framework to study relations among MZVs.\n  This paper enlarges the shuffle algebra uniquely to what we call the extended shuffle algebra that encodes convergent multiple zeta series with arbitrary integer arguments, not just the positive ones in the usual case. To achieved this goal, we first replace the Rota-Baxter operator of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.08536","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2024-11-13T11:34:07Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"7f061aff25983d4941ea3f086d0c752c443f055b386a5deb86b40770390a8dad","abstract_canon_sha256":"2c1879c9121603c14abc13c63fb870e953b743c787ce98d3b4946904c27f7c29"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:18.260067Z","signature_b64":"uOjcV81RgQicWUSM7bCL2s5umCnAa7J3wLjF+7t7HHP25tPXuA+yl8debtNBocgWOfUYt6/mr6IM5LoyQ+rFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72a6f1326a7f08d0d41106294a812ecab3673904f7fb267e05494624431a1c5c","last_reissued_at":"2026-07-05T11:15:18.259327Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:18.259327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extended Shuffle Product for Multiple Zeta Values","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.NT","authors_text":"Bin Zhang, Hongyu Xiang, Li Guo, Wenchuan Hu","submitted_at":"2024-11-13T11:34:07Z","abstract_excerpt":"The shuffle algebra on positive integers encodes the usual multiple zeta values (MZVs) (with positive arguments) thanks to the representations of MZVs by iterated Chen integrals of Kontsevich. Together with the quasi-shuffle (stuffle) algebra, it provides the algebraic framework to study relations among MZVs.\n  This paper enlarges the shuffle algebra uniquely to what we call the extended shuffle algebra that encodes convergent multiple zeta series with arbitrary integer arguments, not just the positive ones in the usual case. To achieved this goal, we first replace the Rota-Baxter operator of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.08536","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.08536/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2411.08536","created_at":"2026-07-05T11:15:18.259407+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.08536v3","created_at":"2026-07-05T11:15:18.259407+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.08536","created_at":"2026-07-05T11:15:18.259407+00:00"},{"alias_kind":"pith_short_12","alias_value":"OKTPCMTKP4EN","created_at":"2026-07-05T11:15:18.259407+00:00"},{"alias_kind":"pith_short_16","alias_value":"OKTPCMTKP4ENBVAR","created_at":"2026-07-05T11:15:18.259407+00:00"},{"alias_kind":"pith_short_8","alias_value":"OKTPCMTK","created_at":"2026-07-05T11:15:18.259407+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OKTPCMTKP4ENBVARAYUUVAJOZK","json":"https://pith.science/pith/OKTPCMTKP4ENBVARAYUUVAJOZK.json","graph_json":"https://pith.science/api/pith-number/OKTPCMTKP4ENBVARAYUUVAJOZK/graph.json","events_json":"https://pith.science/api/pith-number/OKTPCMTKP4ENBVARAYUUVAJOZK/events.json","paper":"https://pith.science/paper/OKTPCMTK"},"agent_actions":{"view_html":"https://pith.science/pith/OKTPCMTKP4ENBVARAYUUVAJOZK","download_json":"https://pith.science/pith/OKTPCMTKP4ENBVARAYUUVAJOZK.json","view_paper":"https://pith.science/paper/OKTPCMTK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.08536&json=true","fetch_graph":"https://pith.science/api/pith-number/OKTPCMTKP4ENBVARAYUUVAJOZK/graph.json","fetch_events":"https://pith.science/api/pith-number/OKTPCMTKP4ENBVARAYUUVAJOZK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OKTPCMTKP4ENBVARAYUUVAJOZK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OKTPCMTKP4ENBVARAYUUVAJOZK/action/storage_attestation","attest_author":"https://pith.science/pith/OKTPCMTKP4ENBVARAYUUVAJOZK/action/author_attestation","sign_citation":"https://pith.science/pith/OKTPCMTKP4ENBVARAYUUVAJOZK/action/citation_signature","submit_replication":"https://pith.science/pith/OKTPCMTKP4ENBVARAYUUVAJOZK/action/replication_record"}},"created_at":"2026-07-05T11:15:18.259407+00:00","updated_at":"2026-07-05T11:15:18.259407+00:00"}