{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:R4U3HV3ELLAD4WVSOI2HSJ7NBK","short_pith_number":"pith:R4U3HV3E","canonical_record":{"source":{"id":"1506.02962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T15:34:50Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"549c6fa33c9c187eadd662ff7ee0eb315ad730be1f14d70120b9d3caee1039c5","abstract_canon_sha256":"6ffb4529b7ccb3eebbe2993152d97ffa987d963d31df573d14947c225204e8a8"},"schema_version":"1.0"},"canonical_sha256":"8f29b3d7645ac03e5ab272347927ed0a99f8e70714c0c482971ae4a99df95e99","source":{"kind":"arxiv","id":"1506.02962","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02962","created_at":"2026-05-18T01:25:11Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02962v2","created_at":"2026-05-18T01:25:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02962","created_at":"2026-05-18T01:25:11Z"},{"alias_kind":"pith_short_12","alias_value":"R4U3HV3ELLAD","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"R4U3HV3ELLAD4WVS","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"R4U3HV3E","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:R4U3HV3ELLAD4WVSOI2HSJ7NBK","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T15:34:50Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"549c6fa33c9c187eadd662ff7ee0eb315ad730be1f14d70120b9d3caee1039c5","abstract_canon_sha256":"6ffb4529b7ccb3eebbe2993152d97ffa987d963d31df573d14947c225204e8a8"},"schema_version":"1.0"},"canonical_sha256":"8f29b3d7645ac03e5ab272347927ed0a99f8e70714c0c482971ae4a99df95e99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:11.726270Z","signature_b64":"Jdnyd/TGDRSjGBgs6lfK90U6cpHIuUR5hA/b2UKMkV1auffLaM8fHzBV3+TtBe7KMObWqI/EpNlT14t22H+1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f29b3d7645ac03e5ab272347927ed0a99f8e70714c0c482971ae4a99df95e99","last_reissued_at":"2026-05-18T01:25:11.725792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:11.725792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02962","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5hwolkw73r6OZT0zG3RHwNimKf4xhHktd7VbrbEZgUoGwAjo5qBOhRb4hslEXPGda7MGHYYDVVTX71Hntx2ECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:11:27.215621Z"},"content_sha256":"fb32256401f9f951bf4efd57f92b05e08ee4597772ac4966c5b5a9d32a86808e","schema_version":"1.0","event_id":"sha256:fb32256401f9f951bf4efd57f92b05e08ee4597772ac4966c5b5a9d32a86808e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:R4U3HV3ELLAD4WVSOI2HSJ7NBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A uniform generalization of some combinatorial Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"Jia Huang","submitted_at":"2015-06-09T15:34:50Z","abstract_excerpt":"We generalize the Hopf algebras of free quasisymmetric functions, quasisymmetric functions, noncommutative symmetric functions, and symmetric functions to certain representations of the category of all finite Coxeter systems and its dual category. We investigate their connections with the representation theory of 0-Hecke algebras of finite Coxeter systems. Restricted to type B and D we obtain dual graded modules and comodules over the corresponding Hopf algebras in type A."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02962","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ey6gpduY73qy7p2wZzLbxuWRjcuXM7IoGDlqJOvgDGtkQRYkElXBpTvzwTSwq9BqCJ2U1IvBaWm469mJbVfQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:11:27.215969Z"},"content_sha256":"1a09f3d1d00a768c4ee244a9f57ed85712b07de6cebf8c0ddb06394c6d4d8283","schema_version":"1.0","event_id":"sha256:1a09f3d1d00a768c4ee244a9f57ed85712b07de6cebf8c0ddb06394c6d4d8283"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4U3HV3ELLAD4WVSOI2HSJ7NBK/bundle.json","state_url":"https://pith.science/pith/R4U3HV3ELLAD4WVSOI2HSJ7NBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4U3HV3ELLAD4WVSOI2HSJ7NBK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T23:11:27Z","links":{"resolver":"https://pith.science/pith/R4U3HV3ELLAD4WVSOI2HSJ7NBK","bundle":"https://pith.science/pith/R4U3HV3ELLAD4WVSOI2HSJ7NBK/bundle.json","state":"https://pith.science/pith/R4U3HV3ELLAD4WVSOI2HSJ7NBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4U3HV3ELLAD4WVSOI2HSJ7NBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:R4U3HV3ELLAD4WVSOI2HSJ7NBK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6ffb4529b7ccb3eebbe2993152d97ffa987d963d31df573d14947c225204e8a8","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T15:34:50Z","title_canon_sha256":"549c6fa33c9c187eadd662ff7ee0eb315ad730be1f14d70120b9d3caee1039c5"},"schema_version":"1.0","source":{"id":"1506.02962","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02962","created_at":"2026-05-18T01:25:11Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02962v2","created_at":"2026-05-18T01:25:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02962","created_at":"2026-05-18T01:25:11Z"},{"alias_kind":"pith_short_12","alias_value":"R4U3HV3ELLAD","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"R4U3HV3ELLAD4WVS","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"R4U3HV3E","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:1a09f3d1d00a768c4ee244a9f57ed85712b07de6cebf8c0ddb06394c6d4d8283","target":"graph","created_at":"2026-05-18T01:25:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We generalize the Hopf algebras of free quasisymmetric functions, quasisymmetric functions, noncommutative symmetric functions, and symmetric functions to certain representations of the category of all finite Coxeter systems and its dual category. We investigate their connections with the representation theory of 0-Hecke algebras of finite Coxeter systems. Restricted to type B and D we obtain dual graded modules and comodules over the corresponding Hopf algebras in type A.","authors_text":"Jia Huang","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T15:34:50Z","title":"A uniform generalization of some combinatorial Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02962","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fb32256401f9f951bf4efd57f92b05e08ee4597772ac4966c5b5a9d32a86808e","target":"record","created_at":"2026-05-18T01:25:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6ffb4529b7ccb3eebbe2993152d97ffa987d963d31df573d14947c225204e8a8","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T15:34:50Z","title_canon_sha256":"549c6fa33c9c187eadd662ff7ee0eb315ad730be1f14d70120b9d3caee1039c5"},"schema_version":"1.0","source":{"id":"1506.02962","kind":"arxiv","version":2}},"canonical_sha256":"8f29b3d7645ac03e5ab272347927ed0a99f8e70714c0c482971ae4a99df95e99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f29b3d7645ac03e5ab272347927ed0a99f8e70714c0c482971ae4a99df95e99","first_computed_at":"2026-05-18T01:25:11.725792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:11.725792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jdnyd/TGDRSjGBgs6lfK90U6cpHIuUR5hA/b2UKMkV1auffLaM8fHzBV3+TtBe7KMObWqI/EpNlT14t22H+1CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:11.726270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02962","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb32256401f9f951bf4efd57f92b05e08ee4597772ac4966c5b5a9d32a86808e","sha256:1a09f3d1d00a768c4ee244a9f57ed85712b07de6cebf8c0ddb06394c6d4d8283"],"state_sha256":"7851725748d9a0416f19a412cc1c2112d33b935647364b3bfeaeab2b77376a6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S5RmPySn7uvAwEKRBqDMAAXtstJPs1wH6eKseahuvB9j/G9gc1+c0PKNt+gaEYhhBQkY5HP5ANie25I6OLhHAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:11:27.218014Z","bundle_sha256":"c848c768fceaa7fd25353e113fc11fbfe9ea78c0be310f9b21b4dcd59dd40b54"}}