{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WO4A7XV33VEOYDRQ5XLBSBDPDY","short_pith_number":"pith:WO4A7XV3","canonical_record":{"source":{"id":"1401.7748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-01-30T05:47:11Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"10292ea620b823adda3a5ff7f82ea8d9ea4ae0a392642e62f0e252950bc462b4","abstract_canon_sha256":"66355ce230d3a4ac061b4a5dab492dfc22c69b52a9d4948ce4f689cd40f65172"},"schema_version":"1.0"},"canonical_sha256":"b3b80fdebbdd48ec0e30edd619046f1e0a54da4919f6e43260a9a969dc355b53","source":{"kind":"arxiv","id":"1401.7748","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7748","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7748v1","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7748","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"pith_short_12","alias_value":"WO4A7XV33VEO","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WO4A7XV33VEOYDRQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WO4A7XV3","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WO4A7XV33VEOYDRQ5XLBSBDPDY","target":"record","payload":{"canonical_record":{"source":{"id":"1401.7748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-01-30T05:47:11Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"10292ea620b823adda3a5ff7f82ea8d9ea4ae0a392642e62f0e252950bc462b4","abstract_canon_sha256":"66355ce230d3a4ac061b4a5dab492dfc22c69b52a9d4948ce4f689cd40f65172"},"schema_version":"1.0"},"canonical_sha256":"b3b80fdebbdd48ec0e30edd619046f1e0a54da4919f6e43260a9a969dc355b53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:38.565173Z","signature_b64":"gv7dQl7elSVLDCMhOVfMNT1A/oFVuuMtYWgldGDSIWtIQLPzHX4Te5D8sneP/id+pyXwCO4gmVvAbIxbOVmkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3b80fdebbdd48ec0e30edd619046f1e0a54da4919f6e43260a9a969dc355b53","last_reissued_at":"2026-05-18T03:00:38.564336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:38.564336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.7748","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":"2026-05-18T03:00:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQuJ4utQwuHLtbXM29GuzO9trjMN7xs6RMhGbRWOOK68GlSKLP4c7VovkTzA9W/PPbrR0dgH4/Lge3UgcfYOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:20:54.671842Z"},"content_sha256":"e3608512246686cc6203e22c4a2770546234ac22ce7b522fdc32cb658d13e9e0","schema_version":"1.0","event_id":"sha256:e3608512246686cc6203e22c4a2770546234ac22ce7b522fdc32cb658d13e9e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WO4A7XV33VEOYDRQ5XLBSBDPDY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Simplicial Nerves for Two-Dimensional Categorical Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Nathaniel Watson","submitted_at":"2014-01-30T05:47:11Z","abstract_excerpt":"The most natural notion of a simplicial nerve for a (weak) bicategory was given by Duskin, who showed that a simplicial set is isomorphic to the nerve of a $(2,1)$-category (i.e. a bicategory with invertible $2$-morphisms) if and only if it is a quasicategory which has unique fillers for inner horns of dimension $3$ and greater. Using Duskin's technique, we show how his nerve applies to $(2,1)$-category functors, making it a fully faithful inclusion of $(2,1)$-categories into simplicial sets. Then we consider analogues of this extension of Duskin's result for several different two-dimensional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7748","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":"2026-05-18T03:00:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dDy+WfVGNfQmU55VKdu7b0vJRtozX8fowMzydNcDLz+z2WcVGKKlhEls/0KzOr3W9YIw+Ve0u+lJigICfzuJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:20:54.672473Z"},"content_sha256":"159a1ef793f6c072cefec59729c5bc0124476ed42d515dc754da5f08746f61a4","schema_version":"1.0","event_id":"sha256:159a1ef793f6c072cefec59729c5bc0124476ed42d515dc754da5f08746f61a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/bundle.json","state_url":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/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":"2026-06-06T19:20:54Z","links":{"resolver":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY","bundle":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/bundle.json","state":"https://pith.science/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WO4A7XV33VEOYDRQ5XLBSBDPDY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WO4A7XV33VEOYDRQ5XLBSBDPDY","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":"66355ce230d3a4ac061b4a5dab492dfc22c69b52a9d4948ce4f689cd40f65172","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-01-30T05:47:11Z","title_canon_sha256":"10292ea620b823adda3a5ff7f82ea8d9ea4ae0a392642e62f0e252950bc462b4"},"schema_version":"1.0","source":{"id":"1401.7748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7748","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7748v1","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7748","created_at":"2026-05-18T03:00:38Z"},{"alias_kind":"pith_short_12","alias_value":"WO4A7XV33VEO","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WO4A7XV33VEOYDRQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WO4A7XV3","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:159a1ef793f6c072cefec59729c5bc0124476ed42d515dc754da5f08746f61a4","target":"graph","created_at":"2026-05-18T03:00:38Z","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 most natural notion of a simplicial nerve for a (weak) bicategory was given by Duskin, who showed that a simplicial set is isomorphic to the nerve of a $(2,1)$-category (i.e. a bicategory with invertible $2$-morphisms) if and only if it is a quasicategory which has unique fillers for inner horns of dimension $3$ and greater. Using Duskin's technique, we show how his nerve applies to $(2,1)$-category functors, making it a fully faithful inclusion of $(2,1)$-categories into simplicial sets. Then we consider analogues of this extension of Duskin's result for several different two-dimensional ","authors_text":"Nathaniel Watson","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-01-30T05:47:11Z","title":"Non-Simplicial Nerves for Two-Dimensional Categorical Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7748","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:e3608512246686cc6203e22c4a2770546234ac22ce7b522fdc32cb658d13e9e0","target":"record","created_at":"2026-05-18T03:00:38Z","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":"66355ce230d3a4ac061b4a5dab492dfc22c69b52a9d4948ce4f689cd40f65172","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-01-30T05:47:11Z","title_canon_sha256":"10292ea620b823adda3a5ff7f82ea8d9ea4ae0a392642e62f0e252950bc462b4"},"schema_version":"1.0","source":{"id":"1401.7748","kind":"arxiv","version":1}},"canonical_sha256":"b3b80fdebbdd48ec0e30edd619046f1e0a54da4919f6e43260a9a969dc355b53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3b80fdebbdd48ec0e30edd619046f1e0a54da4919f6e43260a9a969dc355b53","first_computed_at":"2026-05-18T03:00:38.564336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:38.564336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gv7dQl7elSVLDCMhOVfMNT1A/oFVuuMtYWgldGDSIWtIQLPzHX4Te5D8sneP/id+pyXwCO4gmVvAbIxbOVmkCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:38.565173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3608512246686cc6203e22c4a2770546234ac22ce7b522fdc32cb658d13e9e0","sha256:159a1ef793f6c072cefec59729c5bc0124476ed42d515dc754da5f08746f61a4"],"state_sha256":"0aa6ca82c5e9dc121858c739bc90eb9c22214f54d38883730b385bb9278f5587"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RW3m01I/wmw/fzNtOTEjznZJDDwOBWv+B2QUKugf5eMCETljqkzZB/Z4/B7N2xgetkNiF0mz0topqY6wE7ueDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:20:54.675607Z","bundle_sha256":"50105ab58edb0b492bb1db89cc5f25a833b8642bb01c5dae593803d113d3c28d"}}