{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HFEJOXEB7SH7FKIEBP5PPHPABL","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":"0b4b56376bed3e552be0300da77d189d83fe0e4239a2016a0449591b52e9b359","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-26T08:13:26Z","title_canon_sha256":"81b47565686832b5a1bbd0f5d096825d78d9058a1ce7160aea36144c5c3a027a"},"schema_version":"1.0","source":{"id":"1109.5477","kind":"arxiv","version":9}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5477","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5477v9","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5477","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"pith_short_12","alias_value":"HFEJOXEB7SH7","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HFEJOXEB7SH7FKIE","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HFEJOXEB","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:6a02a8ba84eddee94eaa7816d69318cfe64d2597d984ad1e3a8541a01b66e5bc","target":"graph","created_at":"2026-05-18T01:25:31Z","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":"In this work we shall introduce a new model structure on the category of pro-simplicial sheaves, which is very convenient for the study of \\'etale homotopy. Using this model structure we define a pro-space associated to a topos, as a result of applying a derived functor. We show that our construction lifts Artin and Mazur's \\'etale homotopy type [AM] in the relevant special case. Our definition extends naturally to a relative notion, namely, a pro-object associated to a map of topoi. This relative notion lifts the relative \\'etale homotopy type that was used in [HaSc] for the study of obstruct","authors_text":"Ilan Barnea, Tomer M. Schlank","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-26T08:13:26Z","title":"A Projective Model Structure on Pro Simplicial Sheaves, and the Relative \\'Etale Homotopy Type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5477","kind":"arxiv","version":9},"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:a896a62729f9391674a7e043ce6230e160325d5aeb2b333f77422e1dcc61323d","target":"record","created_at":"2026-05-18T01:25:31Z","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":"0b4b56376bed3e552be0300da77d189d83fe0e4239a2016a0449591b52e9b359","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-26T08:13:26Z","title_canon_sha256":"81b47565686832b5a1bbd0f5d096825d78d9058a1ce7160aea36144c5c3a027a"},"schema_version":"1.0","source":{"id":"1109.5477","kind":"arxiv","version":9}},"canonical_sha256":"3948975c81fc8ff2a9040bfaf79de00af0d748f2d958d216f0ce225b7374eb42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3948975c81fc8ff2a9040bfaf79de00af0d748f2d958d216f0ce225b7374eb42","first_computed_at":"2026-05-18T01:25:31.062912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:31.062912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4PNEuHkt3DhXj5hsxtcZ9Y1vzvyR8Pp8uXt2GT4Ef3mrFWltFQIgzmJc5mCacbKcIzqah+Jx3TJBkcaXqhOJDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:31.063346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5477","source_kind":"arxiv","source_version":9}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a896a62729f9391674a7e043ce6230e160325d5aeb2b333f77422e1dcc61323d","sha256:6a02a8ba84eddee94eaa7816d69318cfe64d2597d984ad1e3a8541a01b66e5bc"],"state_sha256":"d2e2dfde126134541207a3398d5fe3ca29fb40f37c13244339a60a2a2e008614"}