{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LUDD6VZJX2PFQ6YTDVXBS4EBNW","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":"48af89d8e67c9bf44badb425cd878be9ac8d9241b4748c27eb7c3fac766d54e2","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-25T16:25:18Z","title_canon_sha256":"a4a61020f89799ae66f2f52eecfc035f6d0a63dbb4902b2eff1aca50ae089ef1"},"schema_version":"1.0","source":{"id":"0905.4044","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4044","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4044v4","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4044","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"pith_short_12","alias_value":"LUDD6VZJX2PF","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LUDD6VZJX2PFQ6YT","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LUDD6VZJ","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:d971c3667502c2414cde85c189bdfb7ecd1c675c8e07bceda9621e10052353bc","target":"graph","created_at":"2026-05-18T01:26:58Z","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":"We show that an n-geometric stack may be regarded as a special kind of simplicial scheme, namely a Duskin n-hypergroupoid in affine schemes, where surjectivity is defined in terms of covering maps, yielding Artin n-stacks, Deligne-Mumford n-stacks and n-schemes as the notion of covering varies. This formulation adapts to all HAG contexts, so in particular works for derived n-stacks (replacing rings with simplicial rings). We exploit this to describe quasi-coherent sheaves and complexes on these stacks, and to draw comparisons with Kontsevich's dg-schemes. As an application, we show how the cot","authors_text":"J.P.Pridham","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-25T16:25:18Z","title":"Presenting higher stacks as simplicial schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4044","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:df372cc4ff2679cc540e1ff906c3783044bffd2294f9848171c07398f84527ab","target":"record","created_at":"2026-05-18T01:26:58Z","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":"48af89d8e67c9bf44badb425cd878be9ac8d9241b4748c27eb7c3fac766d54e2","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-25T16:25:18Z","title_canon_sha256":"a4a61020f89799ae66f2f52eecfc035f6d0a63dbb4902b2eff1aca50ae089ef1"},"schema_version":"1.0","source":{"id":"0905.4044","kind":"arxiv","version":4}},"canonical_sha256":"5d063f5729be9e587b131d6e1970816db0bd5b7bf8a7ff79f2a7360f990f4b8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d063f5729be9e587b131d6e1970816db0bd5b7bf8a7ff79f2a7360f990f4b8d","first_computed_at":"2026-05-18T01:26:58.862273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:58.862273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8WqCFEaa091hrncsqdljIU+2EDq+lKxZqYLxVCvfrsXuVTr/AlRO6r8AtK9K1pqW9t8QsZvpljPiuCuh7ntCBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:58.862822Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.4044","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df372cc4ff2679cc540e1ff906c3783044bffd2294f9848171c07398f84527ab","sha256:d971c3667502c2414cde85c189bdfb7ecd1c675c8e07bceda9621e10052353bc"],"state_sha256":"cc6e8e168805d8ac85c4a29b6f8ac7fd3b9cf056c30a8c139b620ebd8aa601fe"}