{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:2LRAHX2UZTBEPHKZMVPQFB3LRH","short_pith_number":"pith:2LRAHX2U","canonical_record":{"source":{"id":"0907.2460","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-07-14T21:56:20Z","cross_cats_sorted":[],"title_canon_sha256":"a7599a444bc76ed205062391d38fe68ddb16d25ffd5296173dd74c8d80b5104a","abstract_canon_sha256":"84824dd1ca7286e416d22260b8e464a5d5384503f46d67acbbfbb928177ff82e"},"schema_version":"1.0"},"canonical_sha256":"d2e203df54ccc2479d59655f02876b89d49bc5b626311dbe72cff63e6907cda8","source":{"kind":"arxiv","id":"0907.2460","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2460","created_at":"2026-05-18T04:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2460v3","created_at":"2026-05-18T04:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2460","created_at":"2026-05-18T04:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"2LRAHX2UZTBE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"2LRAHX2UZTBEPHKZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"2LRAHX2U","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:2LRAHX2UZTBEPHKZMVPQFB3LRH","target":"record","payload":{"canonical_record":{"source":{"id":"0907.2460","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-07-14T21:56:20Z","cross_cats_sorted":[],"title_canon_sha256":"a7599a444bc76ed205062391d38fe68ddb16d25ffd5296173dd74c8d80b5104a","abstract_canon_sha256":"84824dd1ca7286e416d22260b8e464a5d5384503f46d67acbbfbb928177ff82e"},"schema_version":"1.0"},"canonical_sha256":"d2e203df54ccc2479d59655f02876b89d49bc5b626311dbe72cff63e6907cda8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:47.863501Z","signature_b64":"AsJT6Y9MRA/EznhTs1vbvHXkxCycZu8gO+/xJT8eWf5CzDNeo+DZvSWPQx6a6stvJKwBEbpO6J5ryqJph0LpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2e203df54ccc2479d59655f02876b89d49bc5b626311dbe72cff63e6907cda8","last_reissued_at":"2026-05-18T04:27:47.862969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:47.862969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.2460","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:27:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FdouXX7J7ADXYyUS3QSW5v+rTLRWfMHJxHt8LOPONm21Gfy/53VO+Ad1WX/somkpdLQMkjua16pgaifVT/WHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:19:55.427561Z"},"content_sha256":"c3dbd4e73e389c602dfbd6f768d555d76bb148158b773691c1ba44bc8d9b7b8f","schema_version":"1.0","event_id":"sha256:c3dbd4e73e389c602dfbd6f768d555d76bb148158b773691c1ba44bc8d9b7b8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:2LRAHX2UZTBEPHKZMVPQFB3LRH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A unified framework for generalized multicategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"G.S.H. Cruttwell, Michael A. Shulman","submitted_at":"2009-07-14T21:56:20Z","abstract_excerpt":"Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere theories, and topological spaces. In each case, generalized multicategories are defined as the \"lax algebras\" or \"Kleisli monoids\" relative to a \"monad\" on a bicategory. However, the meanings of these words differ from author to author, as do the specific bicategories considered. We propose a unified framework: by working with monads on double categories and related structures (rather than bicategories),"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2460","kind":"arxiv","version":3},"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":"2026-05-18T04:27:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mPNP+U3AobggrMV0h/KAfShQEk6owILMNProIKHkOicJYHKawHuZ5I5xnv2OIZ1vwuwtsixMfXB/Am8hVME7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:19:55.428204Z"},"content_sha256":"1aa6e30415fd6af587fed06f0543022f09b445d63f24c6cbb98fc5255f4f055c","schema_version":"1.0","event_id":"sha256:1aa6e30415fd6af587fed06f0543022f09b445d63f24c6cbb98fc5255f4f055c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2LRAHX2UZTBEPHKZMVPQFB3LRH/bundle.json","state_url":"https://pith.science/pith/2LRAHX2UZTBEPHKZMVPQFB3LRH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2LRAHX2UZTBEPHKZMVPQFB3LRH/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":"2026-05-27T20:19:55Z","links":{"resolver":"https://pith.science/pith/2LRAHX2UZTBEPHKZMVPQFB3LRH","bundle":"https://pith.science/pith/2LRAHX2UZTBEPHKZMVPQFB3LRH/bundle.json","state":"https://pith.science/pith/2LRAHX2UZTBEPHKZMVPQFB3LRH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2LRAHX2UZTBEPHKZMVPQFB3LRH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:2LRAHX2UZTBEPHKZMVPQFB3LRH","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":"84824dd1ca7286e416d22260b8e464a5d5384503f46d67acbbfbb928177ff82e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-07-14T21:56:20Z","title_canon_sha256":"a7599a444bc76ed205062391d38fe68ddb16d25ffd5296173dd74c8d80b5104a"},"schema_version":"1.0","source":{"id":"0907.2460","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2460","created_at":"2026-05-18T04:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2460v3","created_at":"2026-05-18T04:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2460","created_at":"2026-05-18T04:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"2LRAHX2UZTBE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"2LRAHX2UZTBEPHKZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"2LRAHX2U","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:1aa6e30415fd6af587fed06f0543022f09b445d63f24c6cbb98fc5255f4f055c","target":"graph","created_at":"2026-05-18T04:27:47Z","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":"Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere theories, and topological spaces. In each case, generalized multicategories are defined as the \"lax algebras\" or \"Kleisli monoids\" relative to a \"monad\" on a bicategory. However, the meanings of these words differ from author to author, as do the specific bicategories considered. We propose a unified framework: by working with monads on double categories and related structures (rather than bicategories),","authors_text":"G.S.H. Cruttwell, Michael A. Shulman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-07-14T21:56:20Z","title":"A unified framework for generalized multicategories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2460","kind":"arxiv","version":3},"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:c3dbd4e73e389c602dfbd6f768d555d76bb148158b773691c1ba44bc8d9b7b8f","target":"record","created_at":"2026-05-18T04:27:47Z","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":"84824dd1ca7286e416d22260b8e464a5d5384503f46d67acbbfbb928177ff82e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-07-14T21:56:20Z","title_canon_sha256":"a7599a444bc76ed205062391d38fe68ddb16d25ffd5296173dd74c8d80b5104a"},"schema_version":"1.0","source":{"id":"0907.2460","kind":"arxiv","version":3}},"canonical_sha256":"d2e203df54ccc2479d59655f02876b89d49bc5b626311dbe72cff63e6907cda8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2e203df54ccc2479d59655f02876b89d49bc5b626311dbe72cff63e6907cda8","first_computed_at":"2026-05-18T04:27:47.862969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:47.862969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AsJT6Y9MRA/EznhTs1vbvHXkxCycZu8gO+/xJT8eWf5CzDNeo+DZvSWPQx6a6stvJKwBEbpO6J5ryqJph0LpBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:47.863501Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.2460","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3dbd4e73e389c602dfbd6f768d555d76bb148158b773691c1ba44bc8d9b7b8f","sha256:1aa6e30415fd6af587fed06f0543022f09b445d63f24c6cbb98fc5255f4f055c"],"state_sha256":"84bac80aabaf87615a659bb2729de2eb9cd805e187ebca7f01a73474f03d5392"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"watkRWGCMQwSRQE2RyB+8I2X3h4HNGBhDHUouLnequwGzeheTKWRa00PrRQPKd2WV3o+2kNjf4fXlp+/lrUgCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:19:55.431374Z","bundle_sha256":"ee23238f9589ee90aa2278cb8d0f71b4027b1ed1e18a7636ed160f2979713f23"}}