{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:HFEJOXEB7SH7FKIEBP5PPHPABL","short_pith_number":"pith:HFEJOXEB","schema_version":"1.0","canonical_sha256":"3948975c81fc8ff2a9040bfaf79de00af0d748f2d958d216f0ce225b7374eb42","source":{"kind":"arxiv","id":"1109.5477","version":9},"attestation_state":"computed","paper":{"title":"A Projective Model Structure on Pro Simplicial Sheaves, and the Relative \\'Etale Homotopy Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Ilan Barnea, Tomer M. Schlank","submitted_at":"2011-09-26T08:13:26Z","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"},"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":"1109.5477","kind":"arxiv","version":9},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-26T08:13:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"81b47565686832b5a1bbd0f5d096825d78d9058a1ce7160aea36144c5c3a027a","abstract_canon_sha256":"0b4b56376bed3e552be0300da77d189d83fe0e4239a2016a0449591b52e9b359"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:31.063346Z","signature_b64":"4PNEuHkt3DhXj5hsxtcZ9Y1vzvyR8Pp8uXt2GT4Ef3mrFWltFQIgzmJc5mCacbKcIzqah+Jx3TJBkcaXqhOJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3948975c81fc8ff2a9040bfaf79de00af0d748f2d958d216f0ce225b7374eb42","last_reissued_at":"2026-05-18T01:25:31.062912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:31.062912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Projective Model Structure on Pro Simplicial Sheaves, and the Relative \\'Etale Homotopy Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Ilan Barnea, Tomer M. Schlank","submitted_at":"2011-09-26T08:13:26Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5477","kind":"arxiv","version":9},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.5477","created_at":"2026-05-18T01:25:31.062975+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5477v9","created_at":"2026-05-18T01:25:31.062975+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5477","created_at":"2026-05-18T01:25:31.062975+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFEJOXEB7SH7","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFEJOXEB7SH7FKIE","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFEJOXEB","created_at":"2026-05-18T12:26:30.835961+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HFEJOXEB7SH7FKIEBP5PPHPABL","json":"https://pith.science/pith/HFEJOXEB7SH7FKIEBP5PPHPABL.json","graph_json":"https://pith.science/api/pith-number/HFEJOXEB7SH7FKIEBP5PPHPABL/graph.json","events_json":"https://pith.science/api/pith-number/HFEJOXEB7SH7FKIEBP5PPHPABL/events.json","paper":"https://pith.science/paper/HFEJOXEB"},"agent_actions":{"view_html":"https://pith.science/pith/HFEJOXEB7SH7FKIEBP5PPHPABL","download_json":"https://pith.science/pith/HFEJOXEB7SH7FKIEBP5PPHPABL.json","view_paper":"https://pith.science/paper/HFEJOXEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5477&json=true","fetch_graph":"https://pith.science/api/pith-number/HFEJOXEB7SH7FKIEBP5PPHPABL/graph.json","fetch_events":"https://pith.science/api/pith-number/HFEJOXEB7SH7FKIEBP5PPHPABL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFEJOXEB7SH7FKIEBP5PPHPABL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFEJOXEB7SH7FKIEBP5PPHPABL/action/storage_attestation","attest_author":"https://pith.science/pith/HFEJOXEB7SH7FKIEBP5PPHPABL/action/author_attestation","sign_citation":"https://pith.science/pith/HFEJOXEB7SH7FKIEBP5PPHPABL/action/citation_signature","submit_replication":"https://pith.science/pith/HFEJOXEB7SH7FKIEBP5PPHPABL/action/replication_record"}},"created_at":"2026-05-18T01:25:31.062975+00:00","updated_at":"2026-05-18T01:25:31.062975+00:00"}