{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JJ7ZRT2AD74IM2UT4XB24OA5YU","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":"8f16a0af3808491ac41e5017865b438c7c9d1e5968bdf6de7afd533e141d4bfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-11-26T04:40:30Z","title_canon_sha256":"be3f40caf500ab3154f27d55867cadd44612e1fc950b68f675e38cf6297438ec"},"schema_version":"1.0","source":{"id":"1411.7107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7107","created_at":"2026-05-18T01:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7107v1","created_at":"2026-05-18T01:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7107","created_at":"2026-05-18T01:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"JJ7ZRT2AD74I","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JJ7ZRT2AD74IM2UT","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JJ7ZRT2A","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:0b6d858d48c875b3e867ff2740a2f13144188396a9077465aa7e8e42aac594d3","target":"graph","created_at":"2026-05-18T01:41:25Z","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 Catalan simplicial set $\\mathbb{C}$ is known to classify skew-monoidal categories in the sense that a map from $\\mathbb{C}$ to a suitably defined nerve of $\\mathrm{Cat}$ is precisely a skew-monoidal category \\cite{Catalan1}. We extend this result to the case of skew monoidales internal to any monoidal bicategory $\\mathcal{B}$. We then show that monoidal bicategories themselves are classified by maps from $\\mathbb{C}$ to a suitably defined nerve of $\\mathrm{Bicat}$ and extend this result to obtain a definition of skew-monoidal bicategory that aligns with existing theory.","authors_text":"Mitchell Buckley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-11-26T04:40:30Z","title":"The Catalan simplicial set II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7107","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":"sha256:69fcace3ade20d8aea9c3e84c4d92835bd5f7ec771584fa7ba8a2a869cdbd845","target":"record","created_at":"2026-05-18T01:41:25Z","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":"8f16a0af3808491ac41e5017865b438c7c9d1e5968bdf6de7afd533e141d4bfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-11-26T04:40:30Z","title_canon_sha256":"be3f40caf500ab3154f27d55867cadd44612e1fc950b68f675e38cf6297438ec"},"schema_version":"1.0","source":{"id":"1411.7107","kind":"arxiv","version":1}},"canonical_sha256":"4a7f98cf401ff8866a93e5c3ae381dc5259124af1f95ef0007852e6bfacfc017","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a7f98cf401ff8866a93e5c3ae381dc5259124af1f95ef0007852e6bfacfc017","first_computed_at":"2026-05-18T01:41:25.743225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:25.743225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uIGg02YpM4RoPJgFOpbg8XS/x8hSMoCO8Cbqj1IpZCuFgXb7tOzJYf45wiTzdqvCqB66483PApbc1kJYxGx8CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:25.743879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69fcace3ade20d8aea9c3e84c4d92835bd5f7ec771584fa7ba8a2a869cdbd845","sha256:0b6d858d48c875b3e867ff2740a2f13144188396a9077465aa7e8e42aac594d3"],"state_sha256":"4b85cc28532038684d35bb70c802bc4a414f4761bc291228ed2b6abe6a01944b"}