{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QSQLVBNDVHWI5I4BNAB7R76QJI","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":"efa57889608717c244d5e1a53d1146613e565afa66e1a1c63b3e33a561aa4691","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-19T16:37:12Z","title_canon_sha256":"a77b46d1e8cd8084e479a991c038d5fe1856f7af1684c577890d4e91d6688f1f"},"schema_version":"1.0","source":{"id":"1109.4084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4084","created_at":"2026-05-18T03:48:59Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4084v1","created_at":"2026-05-18T03:48:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4084","created_at":"2026-05-18T03:48:59Z"},{"alias_kind":"pith_short_12","alias_value":"QSQLVBNDVHWI","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QSQLVBNDVHWI5I4B","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QSQLVBND","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:54c3bd0b73abb6459352382da2b71161b649f5eb5ac1b9ae4a012131c3b57a02","target":"graph","created_at":"2026-05-18T03:48:59Z","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 consider a theory of centers and homotopy centers of monoids in monoidal categories which themselves are enriched in duoidal categories. Duoidal categories (introduced by Aguillar and Mahajan under the name 2-monoidal categories) are categories with two monoidal structures which are related by some, not necessary invertible, coherence morphisms. Centers of monoids in this sense include many examples which are not `classical.' In particular, the 2-category of categories is an example of a center in our sense. Examples of homotopy center (analogue of the classical Hochschild complex) include ","authors_text":"M. Batanin, M. Markl","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-19T16:37:12Z","title":"Centers and homotopy centers in enriched monoidal categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4084","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:a3db72f5dce7912ed7c300bfbae239db7f0f5b17b44a1877d96380faeeeeaa60","target":"record","created_at":"2026-05-18T03:48:59Z","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":"efa57889608717c244d5e1a53d1146613e565afa66e1a1c63b3e33a561aa4691","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-19T16:37:12Z","title_canon_sha256":"a77b46d1e8cd8084e479a991c038d5fe1856f7af1684c577890d4e91d6688f1f"},"schema_version":"1.0","source":{"id":"1109.4084","kind":"arxiv","version":1}},"canonical_sha256":"84a0ba85a3a9ec8ea3816803f8ffd04a08deee1181fe31908687f3ff681d9eb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84a0ba85a3a9ec8ea3816803f8ffd04a08deee1181fe31908687f3ff681d9eb6","first_computed_at":"2026-05-18T03:48:59.087468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:59.087468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/zEN4ymp5g8NBiI0mmMFKU/gCnr0vWvK28dG9hn0Z8cLAil/pp/pqjAbd430x1sAG7iC3rPClEL7brBCHKE2Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:59.088332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3db72f5dce7912ed7c300bfbae239db7f0f5b17b44a1877d96380faeeeeaa60","sha256:54c3bd0b73abb6459352382da2b71161b649f5eb5ac1b9ae4a012131c3b57a02"],"state_sha256":"eceac6a26fc7d0116e8ac44a9cb4c6742c86ad01d49701031bd54aec0764b2f8"}