{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2LPIIP7UB5FWQB2R7B3WH5U2FT","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":"dd45deac49244dbc80abcdf8e7b06dd84f1fe63f1a19817f7bc997d0df86249c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-11-21T17:40:13Z","title_canon_sha256":"24e93a3ce6f180b6c2e79e6b4c6980bcdb4e88c1c239cc2bee400dd7f19e89b7"},"schema_version":"1.0","source":{"id":"2311.12746","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.12746","created_at":"2026-07-05T07:15:10Z"},{"alias_kind":"arxiv_version","alias_value":"2311.12746v1","created_at":"2026-07-05T07:15:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.12746","created_at":"2026-07-05T07:15:10Z"},{"alias_kind":"pith_short_12","alias_value":"2LPIIP7UB5FW","created_at":"2026-07-05T07:15:10Z"},{"alias_kind":"pith_short_16","alias_value":"2LPIIP7UB5FWQB2R","created_at":"2026-07-05T07:15:10Z"},{"alias_kind":"pith_short_8","alias_value":"2LPIIP7U","created_at":"2026-07-05T07:15:10Z"}],"graph_snapshots":[{"event_id":"sha256:e806e3c5646d2f06f25f442298aa6b0aeb7d15632b76230453a62a18f2d8fd35","target":"graph","created_at":"2026-07-05T07:15:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.12746/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we study oplax normalised functors of $(\\infty,2)$-categories. Our main theorem is a comparison between the notion of oplax normalised functor of scaled simplicial sets due to Gagna-Harpaz-Lanari and the corresponding notion in the setting of complete Segal objects in $(\\infty,1)$-categories studied by Gaitsgory and Rozenblyum. As a corollary, we derive that the Gray tensor product of $(\\infty,2)$-categories as defined by Gaitsgory-Rozenblyum is equivalent to that of Gagna-Harpaz-Lanari.\n  Moreover, we construct an $(\\infty,2)$-categorical variant of the quintet functor of Ehresm","authors_text":"Fernando Abell\\'an","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-11-21T17:40:13Z","title":"Comparing lax functors of $(\\infty,2)$-categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.12746","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:eccbfc99ad01a239c0a0e7df7c3a883b84ba12db852298fa4bf5bb4a024ba59e","target":"record","created_at":"2026-07-05T07:15:10Z","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":"dd45deac49244dbc80abcdf8e7b06dd84f1fe63f1a19817f7bc997d0df86249c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-11-21T17:40:13Z","title_canon_sha256":"24e93a3ce6f180b6c2e79e6b4c6980bcdb4e88c1c239cc2bee400dd7f19e89b7"},"schema_version":"1.0","source":{"id":"2311.12746","kind":"arxiv","version":1}},"canonical_sha256":"d2de843ff40f4b680751f87763f69a2ce0fd09fc38696116786b8ffbe8724646","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2de843ff40f4b680751f87763f69a2ce0fd09fc38696116786b8ffbe8724646","first_computed_at":"2026-07-05T07:15:10.305444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:15:10.305444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q7KynmkB8qfRGvmOxXbdwcPwba1mOA4k9OT3+yqdmdcB4ht+RZdK++N6f0/StbK0sG3nAjg8H5wtRaqVCiuHDA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:15:10.305877Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.12746","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eccbfc99ad01a239c0a0e7df7c3a883b84ba12db852298fa4bf5bb4a024ba59e","sha256:e806e3c5646d2f06f25f442298aa6b0aeb7d15632b76230453a62a18f2d8fd35"],"state_sha256":"29ef945d6d5b2cecdfd906a3f9c3df2df8f524a583ab589f96d776ee9b21e3df"}