{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:F3ZSVJTLNGOQS4XQRLTM25PXVT","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":"9d260037e626ce1bd4e0fbd4265c4729019bc2d6a11b7bd778d3dc6cf7c8a259","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2019-12-22T10:02:06Z","title_canon_sha256":"09b54aafed408c981fd4b3337ddb6dfbb0b05bf1d39930e629e60be72b711909"},"schema_version":"1.0","source":{"id":"1912.10407","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.10407","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"arxiv_version","alias_value":"1912.10407v4","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.10407","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"pith_short_12","alias_value":"F3ZSVJTLNGOQ","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"pith_short_16","alias_value":"F3ZSVJTLNGOQS4XQ","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"pith_short_8","alias_value":"F3ZSVJTL","created_at":"2026-07-05T01:17:06Z"}],"graph_snapshots":[{"event_id":"sha256:2f35f77444118bc904a9db67f0ed90196c95f43925d23c2e86769055fe7ec0b1","target":"graph","created_at":"2026-07-05T01:17:06Z","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/1912.10407/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalise sheaf models of intuitionistic logic to univalent type theory over a small category with a Grothendieck topology. We use in a crucial way that we have constructive models of univalence, that can then be relativized to any presheaf models, and these sheaf models are obtained by localisation for a left exact modality. We provide first an abstract notion of descent data which can be thought of as a higher version of the notion of prenucleus on frames, from which can be generated a nucleus (left exact modality) by transfinite iteration. We then provide several examples.","authors_text":"Christian Sattler, Fabian Ruch, Thierry Coquand","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2019-12-22T10:02:06Z","title":"Constructive sheaf models of type theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.10407","kind":"arxiv","version":4},"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":"sha256:917b378e16c4dc7309cf04ac15332bd21f9c1e2c68fe6eeca7f254c5679a987e","target":"record","created_at":"2026-07-05T01:17:06Z","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":"9d260037e626ce1bd4e0fbd4265c4729019bc2d6a11b7bd778d3dc6cf7c8a259","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2019-12-22T10:02:06Z","title_canon_sha256":"09b54aafed408c981fd4b3337ddb6dfbb0b05bf1d39930e629e60be72b711909"},"schema_version":"1.0","source":{"id":"1912.10407","kind":"arxiv","version":4}},"canonical_sha256":"2ef32aa66b699d0972f08ae6cd75f7acc4bdc1509dbaf042e57479ae199ab46e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ef32aa66b699d0972f08ae6cd75f7acc4bdc1509dbaf042e57479ae199ab46e","first_computed_at":"2026-07-05T01:17:06.776162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:06.776162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"St6iVGmsc+BXdy6n/TFtfmgortAmasB3D8Autgy1fPNfFSKvoA7eHLmgGE5cwLD/HRtafUm17Y2dgyO1jIsTAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:06.776635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.10407","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:917b378e16c4dc7309cf04ac15332bd21f9c1e2c68fe6eeca7f254c5679a987e","sha256:2f35f77444118bc904a9db67f0ed90196c95f43925d23c2e86769055fe7ec0b1"],"state_sha256":"84e0ea2299ab005fa568c549666477eb95b657de33816df72e0fab624a73d7ab"}