{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:MY4EOWXNYIRK4ECT4GZ2UJHZPH","short_pith_number":"pith:MY4EOWXN","schema_version":"1.0","canonical_sha256":"6638475aedc222ae1053e1b3aa24f979d6b8e1537b2cf952e81828375d7a9356","source":{"kind":"arxiv","id":"0706.2711","version":1},"attestation_state":"computed","paper":{"title":"On the Descent Algebra of Type $D$","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"N. Bergeron, S.J. van Willigenburg","submitted_at":"2007-06-19T04:55:40Z","abstract_excerpt":"Here we give a combinatorial interpretation of Solomon's rule for multiplication in the descent algebra of Weyl groups of type $D$, $\\Sigma D_n$.\n  From here we show that $\\Sigma D_n$ is a homomorphic image of the descent algebra of the hyperoctahedral group, $\\Sigma B_{n-2}$."},"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":"0706.2711","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2007-06-19T04:55:40Z","cross_cats_sorted":[],"title_canon_sha256":"0b0a323915f20144800f0d7b32328e4662a31cf5c66321a0c90f1c24e2eeb35f","abstract_canon_sha256":"d1314cd4d91e7ef25de88e966ffccaf2d62332e48c17290efa49db215d72978a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:10.785003Z","signature_b64":"FUw7hPXVd3DhRuQYqGbtG1KvyAEHwL5N6ralePppLf6btp6nqLAkV8tfuqTQ0J8ECgnxpHvbz2fq5MRgVbCkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6638475aedc222ae1053e1b3aa24f979d6b8e1537b2cf952e81828375d7a9356","last_reissued_at":"2026-05-18T01:00:10.784083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:10.784083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Descent Algebra of Type $D$","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"N. Bergeron, S.J. van Willigenburg","submitted_at":"2007-06-19T04:55:40Z","abstract_excerpt":"Here we give a combinatorial interpretation of Solomon's rule for multiplication in the descent algebra of Weyl groups of type $D$, $\\Sigma D_n$.\n  From here we show that $\\Sigma D_n$ is a homomorphic image of the descent algebra of the hyperoctahedral group, $\\Sigma B_{n-2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.2711","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":""},"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":"0706.2711","created_at":"2026-05-18T01:00:10.784237+00:00"},{"alias_kind":"arxiv_version","alias_value":"0706.2711v1","created_at":"2026-05-18T01:00:10.784237+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.2711","created_at":"2026-05-18T01:00:10.784237+00:00"},{"alias_kind":"pith_short_12","alias_value":"MY4EOWXNYIRK","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"MY4EOWXNYIRK4ECT","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"MY4EOWXN","created_at":"2026-05-18T12:25:55.427421+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/MY4EOWXNYIRK4ECT4GZ2UJHZPH","json":"https://pith.science/pith/MY4EOWXNYIRK4ECT4GZ2UJHZPH.json","graph_json":"https://pith.science/api/pith-number/MY4EOWXNYIRK4ECT4GZ2UJHZPH/graph.json","events_json":"https://pith.science/api/pith-number/MY4EOWXNYIRK4ECT4GZ2UJHZPH/events.json","paper":"https://pith.science/paper/MY4EOWXN"},"agent_actions":{"view_html":"https://pith.science/pith/MY4EOWXNYIRK4ECT4GZ2UJHZPH","download_json":"https://pith.science/pith/MY4EOWXNYIRK4ECT4GZ2UJHZPH.json","view_paper":"https://pith.science/paper/MY4EOWXN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0706.2711&json=true","fetch_graph":"https://pith.science/api/pith-number/MY4EOWXNYIRK4ECT4GZ2UJHZPH/graph.json","fetch_events":"https://pith.science/api/pith-number/MY4EOWXNYIRK4ECT4GZ2UJHZPH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MY4EOWXNYIRK4ECT4GZ2UJHZPH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MY4EOWXNYIRK4ECT4GZ2UJHZPH/action/storage_attestation","attest_author":"https://pith.science/pith/MY4EOWXNYIRK4ECT4GZ2UJHZPH/action/author_attestation","sign_citation":"https://pith.science/pith/MY4EOWXNYIRK4ECT4GZ2UJHZPH/action/citation_signature","submit_replication":"https://pith.science/pith/MY4EOWXNYIRK4ECT4GZ2UJHZPH/action/replication_record"}},"created_at":"2026-05-18T01:00:10.784237+00:00","updated_at":"2026-05-18T01:00:10.784237+00:00"}