{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NBRVNDO2ZFYTW3HC2CR7KQT74G","short_pith_number":"pith:NBRVNDO2","canonical_record":{"source":{"id":"1604.06812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-04-22T20:08:04Z","cross_cats_sorted":[],"title_canon_sha256":"295964d75399a5b98d0aac9b69317f6e3bc5ecc3f7edecfaee4a433a5a374ad3","abstract_canon_sha256":"07afa80f94c9ba29ba34ae5fd7597bb555b6824a0dc4e1691fdab6a3190bfde7"},"schema_version":"1.0"},"canonical_sha256":"6863568ddac9713b6ce2d0a3f5427fe18034973af9b9d509bc310b5e1d36f926","source":{"kind":"arxiv","id":"1604.06812","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06812","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06812v2","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06812","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"pith_short_12","alias_value":"NBRVNDO2ZFYT","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NBRVNDO2ZFYTW3HC","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NBRVNDO2","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NBRVNDO2ZFYTW3HC2CR7KQT74G","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-04-22T20:08:04Z","cross_cats_sorted":[],"title_canon_sha256":"295964d75399a5b98d0aac9b69317f6e3bc5ecc3f7edecfaee4a433a5a374ad3","abstract_canon_sha256":"07afa80f94c9ba29ba34ae5fd7597bb555b6824a0dc4e1691fdab6a3190bfde7"},"schema_version":"1.0"},"canonical_sha256":"6863568ddac9713b6ce2d0a3f5427fe18034973af9b9d509bc310b5e1d36f926","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:37.302205Z","signature_b64":"7st7X9YDImt9RXl5BCQI0uGqpPe8Iif4iUz1kvWw0a7tdPpHzXYePYLJrQBr3Sehk2GE6GMCkfz97EeydNmtCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6863568ddac9713b6ce2d0a3f5427fe18034973af9b9d509bc310b5e1d36f926","last_reissued_at":"2026-05-18T01:11:37.301750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:37.301750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06812","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eRxnMoQCEbuAsEq0yDdQQOiY/sgCiK5ttDMmYOtcVB2mvLQz+4UhD3W2+a8b47UFxwMvxJ+Hpb3+o7TVPYDRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T02:16:34.743918Z"},"content_sha256":"a0707af2aa768b89f755481266db04456fd36b0b98438c43179f607475108f93","schema_version":"1.0","event_id":"sha256:a0707af2aa768b89f755481266db04456fd36b0b98438c43179f607475108f93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NBRVNDO2ZFYTW3HC2CR7KQT74G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lifting Enhanced Factorization Systems to Functor $ 2 $-Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Peter J. Haine","submitted_at":"2016-04-22T20:08:04Z","abstract_excerpt":"In this paper we give sufficient conditions for lifting an enhanced factorization system $ (\\mathcal{E}, \\mathcal{M}) $ on a $ 2 $-category $ \\mathbf{D} $ to the functor $ 2 $-category $ \\mathbf{D}^{\\mathbf{C}} $, where $ \\mathbf{C} $ is a small $ 2 $-category. Due to previous work of Lack, our work provides coherence results for $ 2 $-monads on functor $ 2 $-categories. These coherence results are of immediate interest to an ongoing collaboration of Guillou, May, Merling, and Osorno on equivariant infinite loop space theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06812","kind":"arxiv","version":2},"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":"2026-05-18T01:11:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K6BypKMqlls7g1Wcbnk0L1e0/ocV5TRGBwSxZ2QM0RC543UPrXYmaToTNMYaeLEn7xdoiJtk46WKJdf+1QWdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T02:16:34.744262Z"},"content_sha256":"edddb7897c98d61eded40f703bf7ddfb37064b104b6ad21f2cc1339bbb17774a","schema_version":"1.0","event_id":"sha256:edddb7897c98d61eded40f703bf7ddfb37064b104b6ad21f2cc1339bbb17774a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NBRVNDO2ZFYTW3HC2CR7KQT74G/bundle.json","state_url":"https://pith.science/pith/NBRVNDO2ZFYTW3HC2CR7KQT74G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NBRVNDO2ZFYTW3HC2CR7KQT74G/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":"2026-07-01T02:16:34Z","links":{"resolver":"https://pith.science/pith/NBRVNDO2ZFYTW3HC2CR7KQT74G","bundle":"https://pith.science/pith/NBRVNDO2ZFYTW3HC2CR7KQT74G/bundle.json","state":"https://pith.science/pith/NBRVNDO2ZFYTW3HC2CR7KQT74G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NBRVNDO2ZFYTW3HC2CR7KQT74G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NBRVNDO2ZFYTW3HC2CR7KQT74G","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":"07afa80f94c9ba29ba34ae5fd7597bb555b6824a0dc4e1691fdab6a3190bfde7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-04-22T20:08:04Z","title_canon_sha256":"295964d75399a5b98d0aac9b69317f6e3bc5ecc3f7edecfaee4a433a5a374ad3"},"schema_version":"1.0","source":{"id":"1604.06812","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06812","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06812v2","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06812","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"pith_short_12","alias_value":"NBRVNDO2ZFYT","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NBRVNDO2ZFYTW3HC","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NBRVNDO2","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:edddb7897c98d61eded40f703bf7ddfb37064b104b6ad21f2cc1339bbb17774a","target":"graph","created_at":"2026-05-18T01:11:37Z","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":"In this paper we give sufficient conditions for lifting an enhanced factorization system $ (\\mathcal{E}, \\mathcal{M}) $ on a $ 2 $-category $ \\mathbf{D} $ to the functor $ 2 $-category $ \\mathbf{D}^{\\mathbf{C}} $, where $ \\mathbf{C} $ is a small $ 2 $-category. Due to previous work of Lack, our work provides coherence results for $ 2 $-monads on functor $ 2 $-categories. These coherence results are of immediate interest to an ongoing collaboration of Guillou, May, Merling, and Osorno on equivariant infinite loop space theory.","authors_text":"Peter J. Haine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-04-22T20:08:04Z","title":"Lifting Enhanced Factorization Systems to Functor $ 2 $-Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06812","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:a0707af2aa768b89f755481266db04456fd36b0b98438c43179f607475108f93","target":"record","created_at":"2026-05-18T01:11:37Z","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":"07afa80f94c9ba29ba34ae5fd7597bb555b6824a0dc4e1691fdab6a3190bfde7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-04-22T20:08:04Z","title_canon_sha256":"295964d75399a5b98d0aac9b69317f6e3bc5ecc3f7edecfaee4a433a5a374ad3"},"schema_version":"1.0","source":{"id":"1604.06812","kind":"arxiv","version":2}},"canonical_sha256":"6863568ddac9713b6ce2d0a3f5427fe18034973af9b9d509bc310b5e1d36f926","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6863568ddac9713b6ce2d0a3f5427fe18034973af9b9d509bc310b5e1d36f926","first_computed_at":"2026-05-18T01:11:37.301750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:37.301750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7st7X9YDImt9RXl5BCQI0uGqpPe8Iif4iUz1kvWw0a7tdPpHzXYePYLJrQBr3Sehk2GE6GMCkfz97EeydNmtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:37.302205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06812","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0707af2aa768b89f755481266db04456fd36b0b98438c43179f607475108f93","sha256:edddb7897c98d61eded40f703bf7ddfb37064b104b6ad21f2cc1339bbb17774a"],"state_sha256":"ac815afa61c14072ae5a5b9efaff38d49d5e6a2bffe25f80d86b21a53cfa7c91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AlnI8wjEKaOSUZ8H4/bYaGQDoCPLAcOJgaxod4OYJ6O623qEu0yuPbiDj92smNF3c+Jo/MDvcH4i7C8z0dw3Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T02:16:34.746509Z","bundle_sha256":"fbe848fdaafe346a2986840cffec2dcea6165ba5e086644bb3beaf2e8ecd779d"}}