{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:S5QY67EFVIJ2BAG6CJLQHUWN5O","short_pith_number":"pith:S5QY67EF","schema_version":"1.0","canonical_sha256":"97618f7c85aa13a080de125703d2cdeb8f112803618140b1c462b42ddb641da4","source":{"kind":"arxiv","id":"1101.5489","version":1},"attestation_state":"computed","paper":{"title":"Tautological and non-tautological cohomology of the moduli space of curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"C. Faber, R. Pandharipande","submitted_at":"2011-01-28T09:39:12Z","abstract_excerpt":"After a short exposition of the basic properties of the tautological ring of the moduli space of genus g Deligne-Mumford stable curves with n markings, we explain three methods of detecting non-tautological classes in cohomology. The first is via curve counting over finite fields. The second is by obtaining length bounds on the action of the symmetric group S_n on tautological classes. The third is via classical boundary geometry. Several new non-tautological classes are found."},"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":"1101.5489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-28T09:39:12Z","cross_cats_sorted":[],"title_canon_sha256":"2a8384fec4874af872073d6274546c75517f3115dc563f2fe56c7e62893f982d","abstract_canon_sha256":"02f3b5f4e57e6d5154f31d001b8d87fd6c4837ff0d01f3e13380055efe7bc371"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:34.851990Z","signature_b64":"8XQKRLLJBlAZxF4gjBJUACPA1VmtMzHATuKUjYrq/DUDPmKNYBq2nmLCaEdYB2aj5g1+jfnk60FMNfKDXYZAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97618f7c85aa13a080de125703d2cdeb8f112803618140b1c462b42ddb641da4","last_reissued_at":"2026-05-18T04:30:34.851580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:34.851580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tautological and non-tautological cohomology of the moduli space of curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"C. Faber, R. Pandharipande","submitted_at":"2011-01-28T09:39:12Z","abstract_excerpt":"After a short exposition of the basic properties of the tautological ring of the moduli space of genus g Deligne-Mumford stable curves with n markings, we explain three methods of detecting non-tautological classes in cohomology. The first is via curve counting over finite fields. The second is by obtaining length bounds on the action of the symmetric group S_n on tautological classes. The third is via classical boundary geometry. Several new non-tautological classes are found."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5489","kind":"arxiv","version":1},"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":"1101.5489","created_at":"2026-05-18T04:30:34.851639+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.5489v1","created_at":"2026-05-18T04:30:34.851639+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5489","created_at":"2026-05-18T04:30:34.851639+00:00"},{"alias_kind":"pith_short_12","alias_value":"S5QY67EFVIJ2","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"S5QY67EFVIJ2BAG6","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"S5QY67EF","created_at":"2026-05-18T12:26:41.206345+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.09714","citing_title":"Gertsch quotient living in the \"poor man's adele ring\" $\\mathcal{A}$: Kurepa-Bell-Wilson congruence","ref_index":26,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S5QY67EFVIJ2BAG6CJLQHUWN5O","json":"https://pith.science/pith/S5QY67EFVIJ2BAG6CJLQHUWN5O.json","graph_json":"https://pith.science/api/pith-number/S5QY67EFVIJ2BAG6CJLQHUWN5O/graph.json","events_json":"https://pith.science/api/pith-number/S5QY67EFVIJ2BAG6CJLQHUWN5O/events.json","paper":"https://pith.science/paper/S5QY67EF"},"agent_actions":{"view_html":"https://pith.science/pith/S5QY67EFVIJ2BAG6CJLQHUWN5O","download_json":"https://pith.science/pith/S5QY67EFVIJ2BAG6CJLQHUWN5O.json","view_paper":"https://pith.science/paper/S5QY67EF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.5489&json=true","fetch_graph":"https://pith.science/api/pith-number/S5QY67EFVIJ2BAG6CJLQHUWN5O/graph.json","fetch_events":"https://pith.science/api/pith-number/S5QY67EFVIJ2BAG6CJLQHUWN5O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S5QY67EFVIJ2BAG6CJLQHUWN5O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S5QY67EFVIJ2BAG6CJLQHUWN5O/action/storage_attestation","attest_author":"https://pith.science/pith/S5QY67EFVIJ2BAG6CJLQHUWN5O/action/author_attestation","sign_citation":"https://pith.science/pith/S5QY67EFVIJ2BAG6CJLQHUWN5O/action/citation_signature","submit_replication":"https://pith.science/pith/S5QY67EFVIJ2BAG6CJLQHUWN5O/action/replication_record"}},"created_at":"2026-05-18T04:30:34.851639+00:00","updated_at":"2026-05-18T04:30:34.851639+00:00"}