{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5H4SKBJGL4EGRWVRTOP6PJT32W","short_pith_number":"pith:5H4SKBJG","canonical_record":{"source":{"id":"1307.6248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-07-23T21:20:12Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"b3c3173bc960da384edc75d91a73b7aa12d33b03a5d5a42fc5ab2f5e81504898","abstract_canon_sha256":"9618966f53746e8739ed8fef02d2cb537b12086e904a39bf192725d2588cb092"},"schema_version":"1.0"},"canonical_sha256":"e9f92505265f0868dab19b9fe7a67bd5ba8390b2985473f3c020a3e0be81955f","source":{"kind":"arxiv","id":"1307.6248","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6248","created_at":"2026-05-18T02:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6248v2","created_at":"2026-05-18T02:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6248","created_at":"2026-05-18T02:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"5H4SKBJGL4EG","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5H4SKBJGL4EGRWVR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5H4SKBJG","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5H4SKBJGL4EGRWVRTOP6PJT32W","target":"record","payload":{"canonical_record":{"source":{"id":"1307.6248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-07-23T21:20:12Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"b3c3173bc960da384edc75d91a73b7aa12d33b03a5d5a42fc5ab2f5e81504898","abstract_canon_sha256":"9618966f53746e8739ed8fef02d2cb537b12086e904a39bf192725d2588cb092"},"schema_version":"1.0"},"canonical_sha256":"e9f92505265f0868dab19b9fe7a67bd5ba8390b2985473f3c020a3e0be81955f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:15.953625Z","signature_b64":"5Kmu0nfCdwUOfnNyyuVbIuClFXyeW6/K813b6Tx3hMSjSQ1LhDpmZ0vjwB5+lF1Ts/Fe17coTFzHaI7/jXxZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9f92505265f0868dab19b9fe7a67bd5ba8390b2985473f3c020a3e0be81955f","last_reissued_at":"2026-05-18T02:29:15.953217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:15.953217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.6248","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":"2026-05-18T02:29:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/IpdZWb/4Wr4jJbBXIQ/gQuESHIj01ImCQ1jQLKtDWwR89R8fEKdg1n6Z32c+ENrOfsqbAVh4bWu59bplvCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:17:30.228263Z"},"content_sha256":"4c05ef00ac4dca9052c500ece714b2718e0b43e016c33f03f8b679549a436ba5","schema_version":"1.0","event_id":"sha256:4c05ef00ac4dca9052c500ece714b2718e0b43e016c33f03f8b679549a436ba5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5H4SKBJGL4EGRWVRTOP6PJT32W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The univalence axiom for elegant Reedy presheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Michael Shulman","submitted_at":"2013-07-23T21:20:12Z","abstract_excerpt":"We show that Voevodsky's univalence axiom for intensional type theory is valid in categories of simplicial presheaves on elegant Reedy categories. In addition to diagrams on inverse categories, as considered in previous work of the author, this includes bisimplicial sets and $\\Theta_n$-spaces. This has potential applications to the study of homotopical models for higher categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6248","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":"2026-05-18T02:29:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KrmWm+/2NMX0PzkQSwDik2q+4mDOvDiOrq7k4zQvt6pbDhNxwlWJDKc+qt6K/9qDb+sbTM+tf7bIt6Mpg9cIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:17:30.228620Z"},"content_sha256":"3dc18ee5e689c6804c25de62610cec549d7e2f40eb359af575005aa359327e73","schema_version":"1.0","event_id":"sha256:3dc18ee5e689c6804c25de62610cec549d7e2f40eb359af575005aa359327e73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5H4SKBJGL4EGRWVRTOP6PJT32W/bundle.json","state_url":"https://pith.science/pith/5H4SKBJGL4EGRWVRTOP6PJT32W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5H4SKBJGL4EGRWVRTOP6PJT32W/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":"2026-07-05T09:17:30Z","links":{"resolver":"https://pith.science/pith/5H4SKBJGL4EGRWVRTOP6PJT32W","bundle":"https://pith.science/pith/5H4SKBJGL4EGRWVRTOP6PJT32W/bundle.json","state":"https://pith.science/pith/5H4SKBJGL4EGRWVRTOP6PJT32W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5H4SKBJGL4EGRWVRTOP6PJT32W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5H4SKBJGL4EGRWVRTOP6PJT32W","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":"9618966f53746e8739ed8fef02d2cb537b12086e904a39bf192725d2588cb092","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-07-23T21:20:12Z","title_canon_sha256":"b3c3173bc960da384edc75d91a73b7aa12d33b03a5d5a42fc5ab2f5e81504898"},"schema_version":"1.0","source":{"id":"1307.6248","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6248","created_at":"2026-05-18T02:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6248v2","created_at":"2026-05-18T02:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6248","created_at":"2026-05-18T02:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"5H4SKBJGL4EG","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5H4SKBJGL4EGRWVR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5H4SKBJG","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:3dc18ee5e689c6804c25de62610cec549d7e2f40eb359af575005aa359327e73","target":"graph","created_at":"2026-05-18T02:29:15Z","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 show that Voevodsky's univalence axiom for intensional type theory is valid in categories of simplicial presheaves on elegant Reedy categories. In addition to diagrams on inverse categories, as considered in previous work of the author, this includes bisimplicial sets and $\\Theta_n$-spaces. This has potential applications to the study of homotopical models for higher categories.","authors_text":"Michael Shulman","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-07-23T21:20:12Z","title":"The univalence axiom for elegant Reedy presheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6248","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":"sha256:4c05ef00ac4dca9052c500ece714b2718e0b43e016c33f03f8b679549a436ba5","target":"record","created_at":"2026-05-18T02:29:15Z","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":"9618966f53746e8739ed8fef02d2cb537b12086e904a39bf192725d2588cb092","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-07-23T21:20:12Z","title_canon_sha256":"b3c3173bc960da384edc75d91a73b7aa12d33b03a5d5a42fc5ab2f5e81504898"},"schema_version":"1.0","source":{"id":"1307.6248","kind":"arxiv","version":2}},"canonical_sha256":"e9f92505265f0868dab19b9fe7a67bd5ba8390b2985473f3c020a3e0be81955f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9f92505265f0868dab19b9fe7a67bd5ba8390b2985473f3c020a3e0be81955f","first_computed_at":"2026-05-18T02:29:15.953217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:15.953217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Kmu0nfCdwUOfnNyyuVbIuClFXyeW6/K813b6Tx3hMSjSQ1LhDpmZ0vjwB5+lF1Ts/Fe17coTFzHaI7/jXxZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:15.953625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6248","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c05ef00ac4dca9052c500ece714b2718e0b43e016c33f03f8b679549a436ba5","sha256:3dc18ee5e689c6804c25de62610cec549d7e2f40eb359af575005aa359327e73"],"state_sha256":"9230268ca5c571b4675002441280ffc4b1baef317083f32216d204f1f6f81cc9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/d61LPnF/JJodyH9LBUiDu39l4CnZgcHphmoXBwsl9SzN13vHM+i+q23QDhDIju+nLjBEXx5AApkKlz4a4ezDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T09:17:30.230871Z","bundle_sha256":"6fc1c253ab5e21ef5d2fba2104b524cfe9a67ea7cbfa9ce851b45ebc69f34b47"}}