{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:3XWV7KEKEKVALZWW67TCEOGEE2","short_pith_number":"pith:3XWV7KEK","schema_version":"1.0","canonical_sha256":"dded5fa88a22aa05e6d6f7e62238c4269eba9f5c38706618d3205907f8cbed71","source":{"kind":"arxiv","id":"2110.14576","version":2},"attestation_state":"computed","paper":{"title":"Kripke-Joyal forcing for type theory and uniform fibrations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.LO","authors_text":"N. Gambino, S. Awodey, S. Hazratpour","submitted_at":"2021-10-27T16:44:21Z","abstract_excerpt":"We introduce a new method for precisely relating certain kinds of algebraic structures in a presheaf category and judgements of its internal type theory. The method provides a systematic way to organise complex diagrammatic reasoning and generalises the well-known Kripke-Joyal forcing for logic. As an application, we prove several properties of algebraic weak factorisation systems considered in Homotopy Type Theory."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2110.14576","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2021-10-27T16:44:21Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"dbdf549836476af17928354b2ca8f3f15ece83b65cd9f5ac6e6911d4658cdb01","abstract_canon_sha256":"f4b45d90e99d2c55fffc7fd8ed5dacfb3f478e2fc4ca227b7b79032a5615c04f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:17:07.809371Z","signature_b64":"6j2Yo1OXNHkPdC3pSrIAfcy9pJYDGpkVYX7d9Zy1PE5WqrJhwmJfZitXe2a54OS9ZlRKu/sZ5Nn6zZlC0ueRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dded5fa88a22aa05e6d6f7e62238c4269eba9f5c38706618d3205907f8cbed71","last_reissued_at":"2026-07-05T08:17:07.808898Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:17:07.808898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kripke-Joyal forcing for type theory and uniform fibrations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.LO","authors_text":"N. Gambino, S. Awodey, S. Hazratpour","submitted_at":"2021-10-27T16:44:21Z","abstract_excerpt":"We introduce a new method for precisely relating certain kinds of algebraic structures in a presheaf category and judgements of its internal type theory. The method provides a systematic way to organise complex diagrammatic reasoning and generalises the well-known Kripke-Joyal forcing for logic. As an application, we prove several properties of algebraic weak factorisation systems considered in Homotopy Type Theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14576","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/2110.14576/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2110.14576","created_at":"2026-07-05T08:17:07.808961+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.14576v2","created_at":"2026-07-05T08:17:07.808961+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14576","created_at":"2026-07-05T08:17:07.808961+00:00"},{"alias_kind":"pith_short_12","alias_value":"3XWV7KEKEKVA","created_at":"2026-07-05T08:17:07.808961+00:00"},{"alias_kind":"pith_short_16","alias_value":"3XWV7KEKEKVALZWW","created_at":"2026-07-05T08:17:07.808961+00:00"},{"alias_kind":"pith_short_8","alias_value":"3XWV7KEK","created_at":"2026-07-05T08:17:07.808961+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2307.05938","citing_title":"Decalf: A Directed, Effectful Cost-Aware Logical Framework","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3XWV7KEKEKVALZWW67TCEOGEE2","json":"https://pith.science/pith/3XWV7KEKEKVALZWW67TCEOGEE2.json","graph_json":"https://pith.science/api/pith-number/3XWV7KEKEKVALZWW67TCEOGEE2/graph.json","events_json":"https://pith.science/api/pith-number/3XWV7KEKEKVALZWW67TCEOGEE2/events.json","paper":"https://pith.science/paper/3XWV7KEK"},"agent_actions":{"view_html":"https://pith.science/pith/3XWV7KEKEKVALZWW67TCEOGEE2","download_json":"https://pith.science/pith/3XWV7KEKEKVALZWW67TCEOGEE2.json","view_paper":"https://pith.science/paper/3XWV7KEK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.14576&json=true","fetch_graph":"https://pith.science/api/pith-number/3XWV7KEKEKVALZWW67TCEOGEE2/graph.json","fetch_events":"https://pith.science/api/pith-number/3XWV7KEKEKVALZWW67TCEOGEE2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3XWV7KEKEKVALZWW67TCEOGEE2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3XWV7KEKEKVALZWW67TCEOGEE2/action/storage_attestation","attest_author":"https://pith.science/pith/3XWV7KEKEKVALZWW67TCEOGEE2/action/author_attestation","sign_citation":"https://pith.science/pith/3XWV7KEKEKVALZWW67TCEOGEE2/action/citation_signature","submit_replication":"https://pith.science/pith/3XWV7KEKEKVALZWW67TCEOGEE2/action/replication_record"}},"created_at":"2026-07-05T08:17:07.808961+00:00","updated_at":"2026-07-05T08:17:07.808961+00:00"}