{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OGTNDYXKEFM6W4XZL3HBY7FKKH","short_pith_number":"pith:OGTNDYXK","canonical_record":{"source":{"id":"1705.04310","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2017-05-11T17:55:23Z","cross_cats_sorted":["cs.LO","math.CT"],"title_canon_sha256":"2d73eb7b4e1285d8025344a38869f77ab4b8194d149b3441f732a44a3d0f413d","abstract_canon_sha256":"17ec90b65dd0c4a9527f0307707d83ab74bfb6853e8d39ebf0d9434ac1fcdeba"},"schema_version":"1.0"},"canonical_sha256":"71a6d1e2ea2159eb72f95ece1c7caa51cce6e1165cc10602ffc7470b77bd947d","source":{"kind":"arxiv","id":"1705.04310","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04310","created_at":"2026-07-05T06:23:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04310v2","created_at":"2026-07-05T06:23:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04310","created_at":"2026-07-05T06:23:20Z"},{"alias_kind":"pith_short_12","alias_value":"OGTNDYXKEFM6","created_at":"2026-07-05T06:23:20Z"},{"alias_kind":"pith_short_16","alias_value":"OGTNDYXKEFM6W4XZ","created_at":"2026-07-05T06:23:20Z"},{"alias_kind":"pith_short_8","alias_value":"OGTNDYXK","created_at":"2026-07-05T06:23:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OGTNDYXKEFM6W4XZL3HBY7FKKH","target":"record","payload":{"canonical_record":{"source":{"id":"1705.04310","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2017-05-11T17:55:23Z","cross_cats_sorted":["cs.LO","math.CT"],"title_canon_sha256":"2d73eb7b4e1285d8025344a38869f77ab4b8194d149b3441f732a44a3d0f413d","abstract_canon_sha256":"17ec90b65dd0c4a9527f0307707d83ab74bfb6853e8d39ebf0d9434ac1fcdeba"},"schema_version":"1.0"},"canonical_sha256":"71a6d1e2ea2159eb72f95ece1c7caa51cce6e1165cc10602ffc7470b77bd947d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:23:20.329489Z","signature_b64":"GdAVzPWgSHURwBwmMy3KXdzRJGM776JprX979uoWg/asU7JdpBnTKNY+au3ZWzJF/tpcPGStxGsUsk9jdpWnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71a6d1e2ea2159eb72f95ece1c7caa51cce6e1165cc10602ffc7470b77bd947d","last_reissued_at":"2026-07-05T06:23:20.329078Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:23:20.329078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.04310","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":"2026-07-05T06:23:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YFQGt4qxYzwqVksOvSGHFJ/rd5cz2GXcHHX0eBOmSoJSA5AkjgUHwviWzR1do5f3LfIyTzaVl8SmPHYzOLCgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T19:34:18.584960Z"},"content_sha256":"9ea17f808c5b58d9dfcce19918c5a9f5600898291393cbb10a96b875118d39f6","schema_version":"1.0","event_id":"sha256:9ea17f808c5b58d9dfcce19918c5a9f5600898291393cbb10a96b875118d39f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OGTNDYXKEFM6W4XZL3HBY7FKKH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categorical structures for type theory in univalent foundations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO","math.CT"],"primary_cat":"math.LO","authors_text":"Benedikt Ahrens, Peter LeFanu Lumsdaine, Vladimir Voevodsky","submitted_at":"2017-05-11T17:55:23Z","abstract_excerpt":"In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. We study these in univalent type theory, where the comparisons between them can be given more elementarily than in set-theoretic foundations. Specifically, we construct maps between the various types of structures, and show that assuming the Univalence axiom, some of the comparisons are equivalences.\n  We then analyze how these structures transfer along (weak and strong) equi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04310","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1705.04310/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:23:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"To+G45AWyoAyDFILIVXkjGI1cVruthH68YofP0WzuGVClrH0twCGt7ui/R1ZG07rKke0TAuaOa4NiJf4+x1+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T19:34:18.585296Z"},"content_sha256":"4f93ef1b76d5716a493797cf6dae71076a610da07158f6a3c3dd1ba71b5fffb2","schema_version":"1.0","event_id":"sha256:4f93ef1b76d5716a493797cf6dae71076a610da07158f6a3c3dd1ba71b5fffb2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGTNDYXKEFM6W4XZL3HBY7FKKH/bundle.json","state_url":"https://pith.science/pith/OGTNDYXKEFM6W4XZL3HBY7FKKH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGTNDYXKEFM6W4XZL3HBY7FKKH/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":"2026-08-11T19:34:18Z","links":{"resolver":"https://pith.science/pith/OGTNDYXKEFM6W4XZL3HBY7FKKH","bundle":"https://pith.science/pith/OGTNDYXKEFM6W4XZL3HBY7FKKH/bundle.json","state":"https://pith.science/pith/OGTNDYXKEFM6W4XZL3HBY7FKKH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGTNDYXKEFM6W4XZL3HBY7FKKH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OGTNDYXKEFM6W4XZL3HBY7FKKH","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":"17ec90b65dd0c4a9527f0307707d83ab74bfb6853e8d39ebf0d9434ac1fcdeba","cross_cats_sorted":["cs.LO","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2017-05-11T17:55:23Z","title_canon_sha256":"2d73eb7b4e1285d8025344a38869f77ab4b8194d149b3441f732a44a3d0f413d"},"schema_version":"1.0","source":{"id":"1705.04310","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04310","created_at":"2026-07-05T06:23:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04310v2","created_at":"2026-07-05T06:23:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04310","created_at":"2026-07-05T06:23:20Z"},{"alias_kind":"pith_short_12","alias_value":"OGTNDYXKEFM6","created_at":"2026-07-05T06:23:20Z"},{"alias_kind":"pith_short_16","alias_value":"OGTNDYXKEFM6W4XZ","created_at":"2026-07-05T06:23:20Z"},{"alias_kind":"pith_short_8","alias_value":"OGTNDYXK","created_at":"2026-07-05T06:23:20Z"}],"graph_snapshots":[{"event_id":"sha256:4f93ef1b76d5716a493797cf6dae71076a610da07158f6a3c3dd1ba71b5fffb2","target":"graph","created_at":"2026-07-05T06:23:20Z","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/1705.04310/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. We study these in univalent type theory, where the comparisons between them can be given more elementarily than in set-theoretic foundations. Specifically, we construct maps between the various types of structures, and show that assuming the Univalence axiom, some of the comparisons are equivalences.\n  We then analyze how these structures transfer along (weak and strong) equi","authors_text":"Benedikt Ahrens, Peter LeFanu Lumsdaine, Vladimir Voevodsky","cross_cats":["cs.LO","math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2017-05-11T17:55:23Z","title":"Categorical structures for type theory in univalent foundations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04310","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":"sha256:9ea17f808c5b58d9dfcce19918c5a9f5600898291393cbb10a96b875118d39f6","target":"record","created_at":"2026-07-05T06:23:20Z","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":"17ec90b65dd0c4a9527f0307707d83ab74bfb6853e8d39ebf0d9434ac1fcdeba","cross_cats_sorted":["cs.LO","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2017-05-11T17:55:23Z","title_canon_sha256":"2d73eb7b4e1285d8025344a38869f77ab4b8194d149b3441f732a44a3d0f413d"},"schema_version":"1.0","source":{"id":"1705.04310","kind":"arxiv","version":2}},"canonical_sha256":"71a6d1e2ea2159eb72f95ece1c7caa51cce6e1165cc10602ffc7470b77bd947d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71a6d1e2ea2159eb72f95ece1c7caa51cce6e1165cc10602ffc7470b77bd947d","first_computed_at":"2026-07-05T06:23:20.329078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:23:20.329078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GdAVzPWgSHURwBwmMy3KXdzRJGM776JprX979uoWg/asU7JdpBnTKNY+au3ZWzJF/tpcPGStxGsUsk9jdpWnCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:23:20.329489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04310","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ea17f808c5b58d9dfcce19918c5a9f5600898291393cbb10a96b875118d39f6","sha256:4f93ef1b76d5716a493797cf6dae71076a610da07158f6a3c3dd1ba71b5fffb2"],"state_sha256":"6e660124ca821090d8a5e665cc1ff62d6bcae32956692316d9901cb8c6906bf7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IEPcCl/kBzTicIo8X/l2+VBanrIYVMIrugUuvGc9EShK6OmsYytzEQ9b2xGuD+JJ2jplXXpS1OeKrfvz4KnEDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T19:34:18.588352Z","bundle_sha256":"9a3e61dfdeb65e8f21ba34be76b8457cf13e1697be77e62968f71527a53d4df6"}}