{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GUPTEQTQHYEWHHI5F2JEIG7FYB","short_pith_number":"pith:GUPTEQTQ","canonical_record":{"source":{"id":"1307.2765","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-07-10T12:12:11Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"e466a7cb432a51a57ea6aa461d1ddf43aef9a059fac365f9388184940b58179d","abstract_canon_sha256":"b38a82d6dd955c51966d7770fe9f3d1feae087ce934b8fe308fdf7940e30f961"},"schema_version":"1.0"},"canonical_sha256":"351f3242703e09639d1d2e92441be5c0782bde71f3bc1ae8f030ee4f35b38ea1","source":{"kind":"arxiv","id":"1307.2765","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2765","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2765v3","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2765","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"GUPTEQTQHYEW","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GUPTEQTQHYEWHHI5","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GUPTEQTQ","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GUPTEQTQHYEWHHI5F2JEIG7FYB","target":"record","payload":{"canonical_record":{"source":{"id":"1307.2765","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-07-10T12:12:11Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"e466a7cb432a51a57ea6aa461d1ddf43aef9a059fac365f9388184940b58179d","abstract_canon_sha256":"b38a82d6dd955c51966d7770fe9f3d1feae087ce934b8fe308fdf7940e30f961"},"schema_version":"1.0"},"canonical_sha256":"351f3242703e09639d1d2e92441be5c0782bde71f3bc1ae8f030ee4f35b38ea1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:03.188674Z","signature_b64":"s4l+aUg26p0rn3bFtN/Id/OTMzirZpUjQYeScBLF9cvQrH2KZ/kffdPZ3DSIlryI+HI4GSLZ2S68m4FGp9LWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"351f3242703e09639d1d2e92441be5c0782bde71f3bc1ae8f030ee4f35b38ea1","last_reissued_at":"2026-05-18T01:26:03.188134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:03.188134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.2765","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/IvXKlpzUDLMniShUzWRiQDY/aMTI+VETwBJBszwv8cPFWLWHeHOVLA3+Ns0Uv1gylk4Hi91JJuHnzwnb3r7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:51:58.657876Z"},"content_sha256":"bb4619192b209717d49816edbe72d57587b0350eda28199b5cb50962358192c3","schema_version":"1.0","event_id":"sha256:bb4619192b209717d49816edbe72d57587b0350eda28199b5cb50962358192c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GUPTEQTQHYEWHHI5F2JEIG7FYB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"W-types in Homotopy Type Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CT","authors_text":"Benno van den Berg, Ieke Moerdijk","submitted_at":"2013-07-10T12:12:11Z","abstract_excerpt":"We will give a detailed account of why the simplicial sets model of the univalence axiom due to Voevodsky also models W-types. In addition, we will discuss W-types in categories of simplicial presheaves and an application to models of set theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2765","kind":"arxiv","version":3},"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":"2026-05-18T01:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8t+KzRNFBE6jJ+BEWewTaOjylRTgtNVWsSsM9VojtUyvhb5XdWy6wH7mliqxhTosvFkFTF3As3JfNu22/WH3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:51:58.658241Z"},"content_sha256":"be141998bc90ca0a071faf307872333a814c58345aa000da28e82e8bd37c40b3","schema_version":"1.0","event_id":"sha256:be141998bc90ca0a071faf307872333a814c58345aa000da28e82e8bd37c40b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GUPTEQTQHYEWHHI5F2JEIG7FYB/bundle.json","state_url":"https://pith.science/pith/GUPTEQTQHYEWHHI5F2JEIG7FYB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GUPTEQTQHYEWHHI5F2JEIG7FYB/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":"2026-06-05T11:51:58Z","links":{"resolver":"https://pith.science/pith/GUPTEQTQHYEWHHI5F2JEIG7FYB","bundle":"https://pith.science/pith/GUPTEQTQHYEWHHI5F2JEIG7FYB/bundle.json","state":"https://pith.science/pith/GUPTEQTQHYEWHHI5F2JEIG7FYB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GUPTEQTQHYEWHHI5F2JEIG7FYB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GUPTEQTQHYEWHHI5F2JEIG7FYB","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":"b38a82d6dd955c51966d7770fe9f3d1feae087ce934b8fe308fdf7940e30f961","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-07-10T12:12:11Z","title_canon_sha256":"e466a7cb432a51a57ea6aa461d1ddf43aef9a059fac365f9388184940b58179d"},"schema_version":"1.0","source":{"id":"1307.2765","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2765","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2765v3","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2765","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"GUPTEQTQHYEW","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GUPTEQTQHYEWHHI5","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GUPTEQTQ","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:be141998bc90ca0a071faf307872333a814c58345aa000da28e82e8bd37c40b3","target":"graph","created_at":"2026-05-18T01:26:03Z","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 will give a detailed account of why the simplicial sets model of the univalence axiom due to Voevodsky also models W-types. In addition, we will discuss W-types in categories of simplicial presheaves and an application to models of set theory.","authors_text":"Benno van den Berg, Ieke Moerdijk","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-07-10T12:12:11Z","title":"W-types in Homotopy Type Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2765","kind":"arxiv","version":3},"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:bb4619192b209717d49816edbe72d57587b0350eda28199b5cb50962358192c3","target":"record","created_at":"2026-05-18T01:26:03Z","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":"b38a82d6dd955c51966d7770fe9f3d1feae087ce934b8fe308fdf7940e30f961","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-07-10T12:12:11Z","title_canon_sha256":"e466a7cb432a51a57ea6aa461d1ddf43aef9a059fac365f9388184940b58179d"},"schema_version":"1.0","source":{"id":"1307.2765","kind":"arxiv","version":3}},"canonical_sha256":"351f3242703e09639d1d2e92441be5c0782bde71f3bc1ae8f030ee4f35b38ea1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"351f3242703e09639d1d2e92441be5c0782bde71f3bc1ae8f030ee4f35b38ea1","first_computed_at":"2026-05-18T01:26:03.188134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:03.188134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s4l+aUg26p0rn3bFtN/Id/OTMzirZpUjQYeScBLF9cvQrH2KZ/kffdPZ3DSIlryI+HI4GSLZ2S68m4FGp9LWAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:03.188674Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2765","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb4619192b209717d49816edbe72d57587b0350eda28199b5cb50962358192c3","sha256:be141998bc90ca0a071faf307872333a814c58345aa000da28e82e8bd37c40b3"],"state_sha256":"d3cda8663e3ed69915daf2c6d37a2776311162ecd2e1a6650849ccb0f58e8cff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HaqRQD4ro2sMkMbmerc37UTqFox4kYInhHUzpQTvpJKu5sbiwkxfHszpcWcu+KsWIsWRyHck6k/sY+DwF0fGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:51:58.660287Z","bundle_sha256":"674677cfdc1b6067b12d5b3b281b5445ac3753c3de92e7c28d25dfa9b1e950a2"}}