{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WQVXB7PURWDW2SB2VY7CIODISF","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":"5bceaa7fe9603fa3501382f57db9aedd0d920739389e242df23b4e264ea4bd03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-02-11T08:42:05Z","title_canon_sha256":"21c37ca480644833ed301e8ef743c39bc3d965c4d7932b6f4ac6b9f4de158c5d"},"schema_version":"1.0","source":{"id":"1902.03778","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03778","created_at":"2026-05-17T23:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03778v2","created_at":"2026-05-17T23:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03778","created_at":"2026-05-17T23:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"WQVXB7PURWDW","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WQVXB7PURWDW2SB2","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WQVXB7PU","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:2123a1dff694e708e5632e3f23f0ec42a314c8bad631729623963296bf0761c5","target":"graph","created_at":"2026-05-17T23:52:26Z","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":"The notion of 2--monoidal category used here was introduced by B.~Vallette in 2007 for applications in the operadic context. The starting point for this article was a remark by Yu. Manin that in the category of quadratic algebras (that is, \"quantum linear spaces\") one can also define 2--monoidal structure(s) with rather unusual properties. Here we give a detailed exposition of these constructions, together with their generalisations to the case of quadratic operads.\n  Their parallel exposition was motivated by the following remark. Several important operads/cooperads such as genus zero quantum","authors_text":"Bruno Vallette, Yuri I. Manin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-02-11T08:42:05Z","title":"Monoidal structures on the categories of quadratic data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03778","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:a46ced1a8bd2e591f5b4d73f8a85d11fc64475433313febae7b46797c9ea1f27","target":"record","created_at":"2026-05-17T23:52:26Z","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":"5bceaa7fe9603fa3501382f57db9aedd0d920739389e242df23b4e264ea4bd03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-02-11T08:42:05Z","title_canon_sha256":"21c37ca480644833ed301e8ef743c39bc3d965c4d7932b6f4ac6b9f4de158c5d"},"schema_version":"1.0","source":{"id":"1902.03778","kind":"arxiv","version":2}},"canonical_sha256":"b42b70fdf48d876d483aae3e243868917c938fb45db8e6ee0e35af3ddbb08a67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b42b70fdf48d876d483aae3e243868917c938fb45db8e6ee0e35af3ddbb08a67","first_computed_at":"2026-05-17T23:52:26.728866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:26.728866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"czYzpkbgawwj9hVaaHgon8TkFMTYtvsEp4/LTqPRHXlw/qK/nujRTHr53rt0qPHEg7yhKvRUGh61Lq9uh9rFDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:26.729436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03778","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a46ced1a8bd2e591f5b4d73f8a85d11fc64475433313febae7b46797c9ea1f27","sha256:2123a1dff694e708e5632e3f23f0ec42a314c8bad631729623963296bf0761c5"],"state_sha256":"4d5604b6be902c5e44aee707e6aa9fc1446ce467db0014ca52820f65c5a87756"}