{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BOCH6DFTKTNJKNLN2W2BQBGIYR","short_pith_number":"pith:BOCH6DFT","schema_version":"1.0","canonical_sha256":"0b847f0cb354da95356dd5b41804c8c450228f7e18f211d4a8bf6ff9539da37b","source":{"kind":"arxiv","id":"2607.09157","version":1},"attestation_state":"computed","paper":{"title":"The Young Tableaux Hopf algebra and multiple Schur series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.NT","authors_text":"Jinbo Yu","submitted_at":"2026-07-10T07:23:36Z","abstract_excerpt":"In this paper, we introduce multiple Schur series, which are defined by Schur-type sums over semi-standard Young tableaux and generalize both Schur multiple zeta values and multiple Eisenstein series. To study their algebraic structure, we construct a connected, commutative, graded Hopf algebra of Young tableaux and identify its linearized quotient with the quasi-shuffle algebra. Within this Hopf algebra and its quotient, we establish several relations, including a hook formula and the Jacobi--Trudi formula. Furthermore, we relate this Hopf algebra to the ring of symmetric functions, which yie"},"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":"2607.09157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-10T07:23:36Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"4381143da4289fa2a7ef0db159d5489b4a9dad39fc0c173fa829f9fbc329c357","abstract_canon_sha256":"3b67d6ea8d68e7388b10fb900f3d1d3afa5b6ebe73ee91a91a4e3c19e31bfc9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T01:18:47.214256Z","signature_b64":"Bs/tlYnbhPK5Bg9+i5WrgnCuLTWTCZ/LlsN2+rVEOLBivs4nl/jyoeAnVbniuegY8bKKsA7kQJNFYU4DpHLIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b847f0cb354da95356dd5b41804c8c450228f7e18f211d4a8bf6ff9539da37b","last_reissued_at":"2026-07-13T01:18:47.213084Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T01:18:47.213084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Young Tableaux Hopf algebra and multiple Schur series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.NT","authors_text":"Jinbo Yu","submitted_at":"2026-07-10T07:23:36Z","abstract_excerpt":"In this paper, we introduce multiple Schur series, which are defined by Schur-type sums over semi-standard Young tableaux and generalize both Schur multiple zeta values and multiple Eisenstein series. To study their algebraic structure, we construct a connected, commutative, graded Hopf algebra of Young tableaux and identify its linearized quotient with the quasi-shuffle algebra. Within this Hopf algebra and its quotient, we establish several relations, including a hook formula and the Jacobi--Trudi formula. Furthermore, we relate this Hopf algebra to the ring of symmetric functions, which yie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09157","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/2607.09157/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":"2607.09157","created_at":"2026-07-13T01:18:47.213705+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.09157v1","created_at":"2026-07-13T01:18:47.213705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09157","created_at":"2026-07-13T01:18:47.213705+00:00"},{"alias_kind":"pith_short_12","alias_value":"BOCH6DFTKTNJ","created_at":"2026-07-13T01:18:47.213705+00:00"},{"alias_kind":"pith_short_16","alias_value":"BOCH6DFTKTNJKNLN","created_at":"2026-07-13T01:18:47.213705+00:00"},{"alias_kind":"pith_short_8","alias_value":"BOCH6DFT","created_at":"2026-07-13T01:18:47.213705+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/BOCH6DFTKTNJKNLN2W2BQBGIYR","json":"https://pith.science/pith/BOCH6DFTKTNJKNLN2W2BQBGIYR.json","graph_json":"https://pith.science/api/pith-number/BOCH6DFTKTNJKNLN2W2BQBGIYR/graph.json","events_json":"https://pith.science/api/pith-number/BOCH6DFTKTNJKNLN2W2BQBGIYR/events.json","paper":"https://pith.science/paper/BOCH6DFT"},"agent_actions":{"view_html":"https://pith.science/pith/BOCH6DFTKTNJKNLN2W2BQBGIYR","download_json":"https://pith.science/pith/BOCH6DFTKTNJKNLN2W2BQBGIYR.json","view_paper":"https://pith.science/paper/BOCH6DFT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.09157&json=true","fetch_graph":"https://pith.science/api/pith-number/BOCH6DFTKTNJKNLN2W2BQBGIYR/graph.json","fetch_events":"https://pith.science/api/pith-number/BOCH6DFTKTNJKNLN2W2BQBGIYR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BOCH6DFTKTNJKNLN2W2BQBGIYR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BOCH6DFTKTNJKNLN2W2BQBGIYR/action/storage_attestation","attest_author":"https://pith.science/pith/BOCH6DFTKTNJKNLN2W2BQBGIYR/action/author_attestation","sign_citation":"https://pith.science/pith/BOCH6DFTKTNJKNLN2W2BQBGIYR/action/citation_signature","submit_replication":"https://pith.science/pith/BOCH6DFTKTNJKNLN2W2BQBGIYR/action/replication_record"}},"created_at":"2026-07-13T01:18:47.213705+00:00","updated_at":"2026-07-13T01:18:47.213705+00:00"}