{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:TIQ7PT6QZS4ADSPV6W4YH7G7G7","short_pith_number":"pith:TIQ7PT6Q","schema_version":"1.0","canonical_sha256":"9a21f7cfd0ccb801c9f5f5b983fcdf37ef2e4bd63e3cb473b26d8ce83ae1b9de","source":{"kind":"arxiv","id":"2303.12386","version":1},"attestation_state":"computed","paper":{"title":"Generalized quasi-shuffle products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Masataka Satoh","submitted_at":"2023-03-22T08:52:11Z","abstract_excerpt":"In this paper, we introduce the notion of generalized quasi-shuffle products and give a criterion for their associativity. These extend the quasi-shuffle products introduced by Hoffman, which are often used to describe the stuffle and shuffle product for multiple zeta values. For $q$-analogues of multiple zeta values, the description of an analogue for the shuffle product can often not be described with the classical notion of quasi-shuffle products. We show that our generalization gives a natural extension to also include these types of products and we prove a generalization of a duality betw"},"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":"2303.12386","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-03-22T08:52:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9b90e354292c9aea491fcb2da63401d169dbc5fb7813e1046bbd01d9d5e73e5a","abstract_canon_sha256":"d3b63c318594aec3f15b62e9ee6514eb66113b4b1840a22375350a5efaf4bbf8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:53:40.690984Z","signature_b64":"vYkGqCuipvz3PMZAaZdMBq8uOz6+3qrWXD0DAUsKy7G/NrleSUt2cb7CweQOpjQtJbU8o2LWVYReiKzen+WqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a21f7cfd0ccb801c9f5f5b983fcdf37ef2e4bd63e3cb473b26d8ce83ae1b9de","last_reissued_at":"2026-07-05T05:53:40.690544Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:53:40.690544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized quasi-shuffle products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Masataka Satoh","submitted_at":"2023-03-22T08:52:11Z","abstract_excerpt":"In this paper, we introduce the notion of generalized quasi-shuffle products and give a criterion for their associativity. These extend the quasi-shuffle products introduced by Hoffman, which are often used to describe the stuffle and shuffle product for multiple zeta values. For $q$-analogues of multiple zeta values, the description of an analogue for the shuffle product can often not be described with the classical notion of quasi-shuffle products. We show that our generalization gives a natural extension to also include these types of products and we prove a generalization of a duality betw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12386","kind":"arxiv","version":1},"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/2303.12386/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":"2303.12386","created_at":"2026-07-05T05:53:40.690602+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.12386v1","created_at":"2026-07-05T05:53:40.690602+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.12386","created_at":"2026-07-05T05:53:40.690602+00:00"},{"alias_kind":"pith_short_12","alias_value":"TIQ7PT6QZS4A","created_at":"2026-07-05T05:53:40.690602+00:00"},{"alias_kind":"pith_short_16","alias_value":"TIQ7PT6QZS4ADSPV","created_at":"2026-07-05T05:53:40.690602+00:00"},{"alias_kind":"pith_short_8","alias_value":"TIQ7PT6Q","created_at":"2026-07-05T05:53:40.690602+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/TIQ7PT6QZS4ADSPV6W4YH7G7G7","json":"https://pith.science/pith/TIQ7PT6QZS4ADSPV6W4YH7G7G7.json","graph_json":"https://pith.science/api/pith-number/TIQ7PT6QZS4ADSPV6W4YH7G7G7/graph.json","events_json":"https://pith.science/api/pith-number/TIQ7PT6QZS4ADSPV6W4YH7G7G7/events.json","paper":"https://pith.science/paper/TIQ7PT6Q"},"agent_actions":{"view_html":"https://pith.science/pith/TIQ7PT6QZS4ADSPV6W4YH7G7G7","download_json":"https://pith.science/pith/TIQ7PT6QZS4ADSPV6W4YH7G7G7.json","view_paper":"https://pith.science/paper/TIQ7PT6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.12386&json=true","fetch_graph":"https://pith.science/api/pith-number/TIQ7PT6QZS4ADSPV6W4YH7G7G7/graph.json","fetch_events":"https://pith.science/api/pith-number/TIQ7PT6QZS4ADSPV6W4YH7G7G7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TIQ7PT6QZS4ADSPV6W4YH7G7G7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TIQ7PT6QZS4ADSPV6W4YH7G7G7/action/storage_attestation","attest_author":"https://pith.science/pith/TIQ7PT6QZS4ADSPV6W4YH7G7G7/action/author_attestation","sign_citation":"https://pith.science/pith/TIQ7PT6QZS4ADSPV6W4YH7G7G7/action/citation_signature","submit_replication":"https://pith.science/pith/TIQ7PT6QZS4ADSPV6W4YH7G7G7/action/replication_record"}},"created_at":"2026-07-05T05:53:40.690602+00:00","updated_at":"2026-07-05T05:53:40.690602+00:00"}