{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VWGCUJT6C4Z6J77DE77EP25LX2","short_pith_number":"pith:VWGCUJT6","canonical_record":{"source":{"id":"1210.3120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-11T04:25:37Z","cross_cats_sorted":[],"title_canon_sha256":"edf2f86205d9d31c88a2fc1b0b93f113d8b2c0a364f2be037e4a9cb616790412","abstract_canon_sha256":"d35c0b22b3b45cea76586d3b2722a870a5dada871529b1cd37b961ab7024445d"},"schema_version":"1.0"},"canonical_sha256":"ad8c2a267e1733e4ffe327fe47ebabbead1361518c5fe48b2d5e8dabd700c804","source":{"kind":"arxiv","id":"1210.3120","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3120","created_at":"2026-05-18T03:43:29Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3120v1","created_at":"2026-05-18T03:43:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3120","created_at":"2026-05-18T03:43:29Z"},{"alias_kind":"pith_short_12","alias_value":"VWGCUJT6C4Z6","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VWGCUJT6C4Z6J77D","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VWGCUJT6","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VWGCUJT6C4Z6J77DE77EP25LX2","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-11T04:25:37Z","cross_cats_sorted":[],"title_canon_sha256":"edf2f86205d9d31c88a2fc1b0b93f113d8b2c0a364f2be037e4a9cb616790412","abstract_canon_sha256":"d35c0b22b3b45cea76586d3b2722a870a5dada871529b1cd37b961ab7024445d"},"schema_version":"1.0"},"canonical_sha256":"ad8c2a267e1733e4ffe327fe47ebabbead1361518c5fe48b2d5e8dabd700c804","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:29.011909Z","signature_b64":"57JtkgLgZQ+9/ScsKS2ZYob3kqMg2SR14TuKxbfUGPbOFUi1N2KI0s0E0hxxNuT59TYP9hrp5K/tDJnf2F0RCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad8c2a267e1733e4ffe327fe47ebabbead1361518c5fe48b2d5e8dabd700c804","last_reissued_at":"2026-05-18T03:43:29.011349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:29.011349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3120","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9brVaWKomJ64qXPCyw/VPNTGWFpKIFMROzJb5bXO9BKPSryWGkVGcVlD/n9pLfXeKEDu1WRHJKIuDMAQz3GoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:46:43.620557Z"},"content_sha256":"b479473d6c6d92d3391033040a4ab9d10d6cd1979c0ad97057574b7686337f33","schema_version":"1.0","event_id":"sha256:b479473d6c6d92d3391033040a4ab9d10d6cd1979c0ad97057574b7686337f33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VWGCUJT6C4Z6J77DE77EP25LX2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hopf monoids in the category of species","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Marcelo Aguiar, Swapneel Mahajan","submitted_at":"2012-10-11T04:25:37Z","abstract_excerpt":"A Hopf monoid (in Joyal's category of species) is an algebraic structure akin to that of a Hopf algebra. We provide a self-contained introduction to the theory of Hopf monoids in the category of species. Combinatorial structures which compose and decompose give rise to Hopf monoids. We study several examples of this nature. We emphasize the central role played in the theory by the Tits algebra of set compositions. Its product is tightly knit with the Hopf monoid axioms, and its elements constitute universal operations on connected Hopf monoids. We study analogues of the classical Eulerian and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3120","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QBWa2Y1EiotDRHij0i64dhsT3VH6xojCiIsHA3jdQRvc/aqlAy8AtI0m6g9erHd3h5TFIMXcurEYmTXmtJWnDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:46:43.620904Z"},"content_sha256":"c468f833a468e4517ae6d14963579999ab7f25c02f3a25ae0ceded88c735601e","schema_version":"1.0","event_id":"sha256:c468f833a468e4517ae6d14963579999ab7f25c02f3a25ae0ceded88c735601e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VWGCUJT6C4Z6J77DE77EP25LX2/bundle.json","state_url":"https://pith.science/pith/VWGCUJT6C4Z6J77DE77EP25LX2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VWGCUJT6C4Z6J77DE77EP25LX2/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":"2026-05-27T14:46:43Z","links":{"resolver":"https://pith.science/pith/VWGCUJT6C4Z6J77DE77EP25LX2","bundle":"https://pith.science/pith/VWGCUJT6C4Z6J77DE77EP25LX2/bundle.json","state":"https://pith.science/pith/VWGCUJT6C4Z6J77DE77EP25LX2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VWGCUJT6C4Z6J77DE77EP25LX2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VWGCUJT6C4Z6J77DE77EP25LX2","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":"d35c0b22b3b45cea76586d3b2722a870a5dada871529b1cd37b961ab7024445d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-11T04:25:37Z","title_canon_sha256":"edf2f86205d9d31c88a2fc1b0b93f113d8b2c0a364f2be037e4a9cb616790412"},"schema_version":"1.0","source":{"id":"1210.3120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3120","created_at":"2026-05-18T03:43:29Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3120v1","created_at":"2026-05-18T03:43:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3120","created_at":"2026-05-18T03:43:29Z"},{"alias_kind":"pith_short_12","alias_value":"VWGCUJT6C4Z6","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VWGCUJT6C4Z6J77D","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VWGCUJT6","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:c468f833a468e4517ae6d14963579999ab7f25c02f3a25ae0ceded88c735601e","target":"graph","created_at":"2026-05-18T03:43:29Z","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":"A Hopf monoid (in Joyal's category of species) is an algebraic structure akin to that of a Hopf algebra. We provide a self-contained introduction to the theory of Hopf monoids in the category of species. Combinatorial structures which compose and decompose give rise to Hopf monoids. We study several examples of this nature. We emphasize the central role played in the theory by the Tits algebra of set compositions. Its product is tightly knit with the Hopf monoid axioms, and its elements constitute universal operations on connected Hopf monoids. We study analogues of the classical Eulerian and ","authors_text":"Marcelo Aguiar, Swapneel Mahajan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-11T04:25:37Z","title":"Hopf monoids in the category of species"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3120","kind":"arxiv","version":1},"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:b479473d6c6d92d3391033040a4ab9d10d6cd1979c0ad97057574b7686337f33","target":"record","created_at":"2026-05-18T03:43:29Z","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":"d35c0b22b3b45cea76586d3b2722a870a5dada871529b1cd37b961ab7024445d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-10-11T04:25:37Z","title_canon_sha256":"edf2f86205d9d31c88a2fc1b0b93f113d8b2c0a364f2be037e4a9cb616790412"},"schema_version":"1.0","source":{"id":"1210.3120","kind":"arxiv","version":1}},"canonical_sha256":"ad8c2a267e1733e4ffe327fe47ebabbead1361518c5fe48b2d5e8dabd700c804","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad8c2a267e1733e4ffe327fe47ebabbead1361518c5fe48b2d5e8dabd700c804","first_computed_at":"2026-05-18T03:43:29.011349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:29.011349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"57JtkgLgZQ+9/ScsKS2ZYob3kqMg2SR14TuKxbfUGPbOFUi1N2KI0s0E0hxxNuT59TYP9hrp5K/tDJnf2F0RCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:29.011909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b479473d6c6d92d3391033040a4ab9d10d6cd1979c0ad97057574b7686337f33","sha256:c468f833a468e4517ae6d14963579999ab7f25c02f3a25ae0ceded88c735601e"],"state_sha256":"721d16827cd51b4addf6023efdfc3559fa900e6db7aa69e0d568907aff2bbf5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p7WGnQayeGRo495em5sHlWAkPieOlNoyFjsZBhJG15v1HOY9O1hVNUJNRQTa3R+q1o9lCJr17Ydz+tNk74ZYCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:46:43.623230Z","bundle_sha256":"99c4c903d2a9d2a500647d32704036ffbde3d9c62a840f323f810be1c60c0e02"}}