{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JWB75HAAQWZ2QFM5EAJQMYMOKN","short_pith_number":"pith:JWB75HAA","canonical_record":{"source":{"id":"1608.03657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-08-12T01:50:39Z","cross_cats_sorted":["math.AG","math.CT"],"title_canon_sha256":"ecf04feabd3005b5fd487bc9c8ef76dd7f063ccdbc4372b8977e2cad70fa86cb","abstract_canon_sha256":"102bc1f2ac5a6f9409c11d3785c6751dfe6332b917a999e66db4e8a06296681a"},"schema_version":"1.0"},"canonical_sha256":"4d83fe9c0085b3a8159d201306618e5352205d43367dd0b11b0cccd0f6eca958","source":{"kind":"arxiv","id":"1608.03657","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03657","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03657v1","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03657","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"JWB75HAAQWZ2","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JWB75HAAQWZ2QFM5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JWB75HAA","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JWB75HAAQWZ2QFM5EAJQMYMOKN","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-08-12T01:50:39Z","cross_cats_sorted":["math.AG","math.CT"],"title_canon_sha256":"ecf04feabd3005b5fd487bc9c8ef76dd7f063ccdbc4372b8977e2cad70fa86cb","abstract_canon_sha256":"102bc1f2ac5a6f9409c11d3785c6751dfe6332b917a999e66db4e8a06296681a"},"schema_version":"1.0"},"canonical_sha256":"4d83fe9c0085b3a8159d201306618e5352205d43367dd0b11b0cccd0f6eca958","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:12.200535Z","signature_b64":"vkUfQK7mJzFUmHyAMKGZdzgSfFPtRb6xwV+PSl5mNw5Q6qEdd/qeTWC5iF0JH8rSq32dfLcf0sB0cvAI1ss8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d83fe9c0085b3a8159d201306618e5352205d43367dd0b11b0cccd0f6eca958","last_reissued_at":"2026-05-18T01:09:12.199931Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:12.199931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03657","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":"2026-05-18T01:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SuagQzh5zxIRwd2gLXHMsGZ4rbue8uev+SmfHlcbFogckC4BVH1h1ORDW+ETVNLxs4kgiwFsGBHVdJTsts3XAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:42:56.814353Z"},"content_sha256":"142656fa2f50d5f5775237c80d6bee243e7e13b73e0e1637b78781a2ed12bac1","schema_version":"1.0","event_id":"sha256:142656fa2f50d5f5775237c80d6bee243e7e13b73e0e1637b78781a2ed12bac1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JWB75HAAQWZ2QFM5EAJQMYMOKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parametrized higher category theory and higher algebra: Expos\\'e I -- Elements of parametrized higher category theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CT"],"primary_cat":"math.AT","authors_text":"Clark Barwick, Denis Nardin, Emanuele Dotto, Jay Shah, Saul Glasman","submitted_at":"2016-08-12T01:50:39Z","abstract_excerpt":"We introduce the basic elements of the theory of parametrized $\\infty$-categories and functors between them. These notions are defined as suitable fibrations of $\\infty$-categories and functors between them. We give as many examples as we are able at this stage. Simple operations, such as the formation of opposites and the formation of functor $\\infty$-categories, become slightly more involved in the parametrized setting, but we explain precisely how to perform these constructions. All of these constructions can be performed explicitly, without resorting to such acts of desperation as straight"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03657","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":"2026-05-18T01:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d2lM4WyB73KNPPFzinqIauDY1aMKc45rrAnOmZGj3wcerf8KMNWxRgy8qQb8cRA6IaemsW++hXnoVI4n5d/WBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:42:56.814733Z"},"content_sha256":"0d1d27b159135f71f2950b2db30682186e48baf5cf7d5f2c25ea71fff6c7d279","schema_version":"1.0","event_id":"sha256:0d1d27b159135f71f2950b2db30682186e48baf5cf7d5f2c25ea71fff6c7d279"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JWB75HAAQWZ2QFM5EAJQMYMOKN/bundle.json","state_url":"https://pith.science/pith/JWB75HAAQWZ2QFM5EAJQMYMOKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JWB75HAAQWZ2QFM5EAJQMYMOKN/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":"2026-06-01T10:42:56Z","links":{"resolver":"https://pith.science/pith/JWB75HAAQWZ2QFM5EAJQMYMOKN","bundle":"https://pith.science/pith/JWB75HAAQWZ2QFM5EAJQMYMOKN/bundle.json","state":"https://pith.science/pith/JWB75HAAQWZ2QFM5EAJQMYMOKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JWB75HAAQWZ2QFM5EAJQMYMOKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JWB75HAAQWZ2QFM5EAJQMYMOKN","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":"102bc1f2ac5a6f9409c11d3785c6751dfe6332b917a999e66db4e8a06296681a","cross_cats_sorted":["math.AG","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-08-12T01:50:39Z","title_canon_sha256":"ecf04feabd3005b5fd487bc9c8ef76dd7f063ccdbc4372b8977e2cad70fa86cb"},"schema_version":"1.0","source":{"id":"1608.03657","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03657","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03657v1","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03657","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"JWB75HAAQWZ2","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JWB75HAAQWZ2QFM5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JWB75HAA","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:0d1d27b159135f71f2950b2db30682186e48baf5cf7d5f2c25ea71fff6c7d279","target":"graph","created_at":"2026-05-18T01:09:12Z","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 introduce the basic elements of the theory of parametrized $\\infty$-categories and functors between them. These notions are defined as suitable fibrations of $\\infty$-categories and functors between them. We give as many examples as we are able at this stage. Simple operations, such as the formation of opposites and the formation of functor $\\infty$-categories, become slightly more involved in the parametrized setting, but we explain precisely how to perform these constructions. All of these constructions can be performed explicitly, without resorting to such acts of desperation as straight","authors_text":"Clark Barwick, Denis Nardin, Emanuele Dotto, Jay Shah, Saul Glasman","cross_cats":["math.AG","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-08-12T01:50:39Z","title":"Parametrized higher category theory and higher algebra: Expos\\'e I -- Elements of parametrized higher category theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03657","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":"sha256:142656fa2f50d5f5775237c80d6bee243e7e13b73e0e1637b78781a2ed12bac1","target":"record","created_at":"2026-05-18T01:09:12Z","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":"102bc1f2ac5a6f9409c11d3785c6751dfe6332b917a999e66db4e8a06296681a","cross_cats_sorted":["math.AG","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-08-12T01:50:39Z","title_canon_sha256":"ecf04feabd3005b5fd487bc9c8ef76dd7f063ccdbc4372b8977e2cad70fa86cb"},"schema_version":"1.0","source":{"id":"1608.03657","kind":"arxiv","version":1}},"canonical_sha256":"4d83fe9c0085b3a8159d201306618e5352205d43367dd0b11b0cccd0f6eca958","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d83fe9c0085b3a8159d201306618e5352205d43367dd0b11b0cccd0f6eca958","first_computed_at":"2026-05-18T01:09:12.199931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:12.199931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vkUfQK7mJzFUmHyAMKGZdzgSfFPtRb6xwV+PSl5mNw5Q6qEdd/qeTWC5iF0JH8rSq32dfLcf0sB0cvAI1ss8Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:12.200535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03657","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:142656fa2f50d5f5775237c80d6bee243e7e13b73e0e1637b78781a2ed12bac1","sha256:0d1d27b159135f71f2950b2db30682186e48baf5cf7d5f2c25ea71fff6c7d279"],"state_sha256":"d3975cfcfc59ce36a1555295a73a5429b39754607622d54331c2f7a92595c291"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cV8yMkTF7CSGn5iStx0aHjZ0mK2dCeRUKrqF1nUmgg6AQprjEFJ72KgLM/ZOTqAvOkDkh+GigJXR4CWtEUYGAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:42:56.816833Z","bundle_sha256":"84e0d564b9185761359d516b7617aba3117015413219d3edbf8bc087d9ce78c6"}}