{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:52EFPJEDFUPNHA5DUBDPU2OKBH","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":"df93e1155f33861cfcc5d27cc1ad8c818f2a6fa450183d024d1f083483ba2417","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-13T09:43:16Z","title_canon_sha256":"92cb93153cd6b1ef2f10e81edc8d6e3bb0c617cd1ddb6df8c739ec8d618ae75c"},"schema_version":"1.0","source":{"id":"0908.1853","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1853","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1853v2","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1853","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"52EFPJEDFUPN","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"52EFPJEDFUPNHA5D","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"52EFPJED","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:f634194bf05abb21f0017db068b5608108a3f282db25d40c1a2247dd24712a07","target":"graph","created_at":"2026-05-18T04:30:03Z","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 investigate low degree rational cohomology groups of smooth compactifications of moduli spaces of curves with level structures. In particular, we determine $H^k(\\sgbar, \\Q)$ for $g \\ge 2$ and $k \\le 3$, where $\\sgbar$ denotes the moduli space of spin curves of genus $g$.","authors_text":"Claudio Fontanari, Gilberto Bini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-13T09:43:16Z","title":"On the rational cohomology of moduli spaces of curves with level structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1853","kind":"arxiv","version":2},"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":"sha256:8696c94ab6ece086a9b76e7a1c890835def4164b6f3be49579f28d34817f6228","target":"record","created_at":"2026-05-18T04:30:03Z","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":"df93e1155f33861cfcc5d27cc1ad8c818f2a6fa450183d024d1f083483ba2417","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-08-13T09:43:16Z","title_canon_sha256":"92cb93153cd6b1ef2f10e81edc8d6e3bb0c617cd1ddb6df8c739ec8d618ae75c"},"schema_version":"1.0","source":{"id":"0908.1853","kind":"arxiv","version":2}},"canonical_sha256":"ee8857a4832d1ed383a3a046fa69ca09cbbe85594aea7a6a97d017866edccb7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee8857a4832d1ed383a3a046fa69ca09cbbe85594aea7a6a97d017866edccb7d","first_computed_at":"2026-05-18T04:30:03.886262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:03.886262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hsOuDcGsKBJDoboalo0epG74vHaccfrXZUq4Q094E6zfWcT152g8UUeeZ58ny4Y26GGEpXMkIg5vRsDMdkeBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:03.886803Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1853","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8696c94ab6ece086a9b76e7a1c890835def4164b6f3be49579f28d34817f6228","sha256:f634194bf05abb21f0017db068b5608108a3f282db25d40c1a2247dd24712a07"],"state_sha256":"9088537267e1413d195a568613c77c22ed196df24c2e02edb998dbc1d041a16a"}