{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YWGUXLQX5YBYQZQXWGTN6EFWJC","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":"ac39f69747bc70dddced6a8ff288a7124bf25d0c232f281247a7dc74272ab2b5","cross_cats_sorted":["math.CT","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-12-22T13:33:05Z","title_canon_sha256":"22493d0a61ae00dc747200155cc5d7bc147a2d919600d6cfb704c19eab6b4367"},"schema_version":"1.0","source":{"id":"2212.11693","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.11693","created_at":"2026-07-05T05:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"2212.11693v1","created_at":"2026-07-05T05:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.11693","created_at":"2026-07-05T05:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"YWGUXLQX5YBY","created_at":"2026-07-05T05:27:41Z"},{"alias_kind":"pith_short_16","alias_value":"YWGUXLQX5YBYQZQX","created_at":"2026-07-05T05:27:41Z"},{"alias_kind":"pith_short_8","alias_value":"YWGUXLQX","created_at":"2026-07-05T05:27:41Z"}],"graph_snapshots":[{"event_id":"sha256:21c2019670178cb359199099907df6e8e2fe46a7803d179de0c7e82b3377dc49","target":"graph","created_at":"2026-07-05T05:27:41Z","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/2212.11693/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the context of relative topos theory via stacks, we introduce the notion of existential fibred site and of existential topos of such a site. These notions allow us to develop relative topos theory in a way which naturally generalizes the construction of toposes of sheaves on locales, and also provides a framework for investigating the connections between Grothendieck toposes as built from sites and elementary toposes as built from triposes. Then we focus on fibred preorder sites and establish a fibred generalisation of the ideal-completion of a preorder site. Lastly, we provide an explicit ","authors_text":"Olivia Caramello","cross_cats":["math.CT","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-12-22T13:33:05Z","title":"Fibred sites and existential toposes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11693","kind":"arxiv","version":1},"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:ad8152595fa7833d49c16e6ee87aa0f8dbaa4a4c2d51ad7f973afbe31a08c6ea","target":"record","created_at":"2026-07-05T05:27:41Z","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":"ac39f69747bc70dddced6a8ff288a7124bf25d0c232f281247a7dc74272ab2b5","cross_cats_sorted":["math.CT","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-12-22T13:33:05Z","title_canon_sha256":"22493d0a61ae00dc747200155cc5d7bc147a2d919600d6cfb704c19eab6b4367"},"schema_version":"1.0","source":{"id":"2212.11693","kind":"arxiv","version":1}},"canonical_sha256":"c58d4bae17ee03886617b1a6df10b6488f75aaf9aabbd76915d83c1eaa0b48e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c58d4bae17ee03886617b1a6df10b6488f75aaf9aabbd76915d83c1eaa0b48e5","first_computed_at":"2026-07-05T05:27:41.756175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:27:41.756175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q5uI3+SmIyD3lJt1EIlx8kQ1MDY9pZrEbcfzmkx88brGME1qUPEavqbh46EcFMFDi92Dkm18ho3h1qdf8oSQAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:27:41.756675Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.11693","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad8152595fa7833d49c16e6ee87aa0f8dbaa4a4c2d51ad7f973afbe31a08c6ea","sha256:21c2019670178cb359199099907df6e8e2fe46a7803d179de0c7e82b3377dc49"],"state_sha256":"1429f957510c5773a9be344c520c8d23112f3c7df99216ac01143daac79b0a90"}