{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FLNB5GROEULCW2K2T57YJ4CPVK","short_pith_number":"pith:FLNB5GRO","schema_version":"1.0","canonical_sha256":"2ada1e9a2e25162b695a9f7f84f04faa9fc98f681ac91a060c0356a3b18e9bcf","source":{"kind":"arxiv","id":"1210.5761","version":1},"attestation_state":"computed","paper":{"title":"The Gorenstein conjecture fails for the tautological ring of $\\mathcal{\\bar M}_{2,n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Petersen, Orsola Tommasi","submitted_at":"2012-10-21T20:28:19Z","abstract_excerpt":"Let $N$ be the smallest integer such that there is a non-tautological cohomology class of even degree on $\\mathcal{\\bar M}_{2,N}$. We remark that there is such a non-tautological class on $\\mathcal{\\bar M}_{2,20}$, by work of Graber and Pandharipande. We show that $\\mathcal{\\bar M}_{2,N}$ has non-tautological cohomology only in one degree, which is not the middle degree. In particular, it follows that the tautological ring of $\\mathcal{\\bar M}_{2,N}$ is not Gorenstein. We present some evidence suggesting that N=20 holds."},"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":"1210.5761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-10-21T20:28:19Z","cross_cats_sorted":[],"title_canon_sha256":"7dccf1acd101d074abb750acde883a07d59f59e24f35f9867f437860b3d87015","abstract_canon_sha256":"54ad7a6b89a868faf6be3939c8c433546e89343c9d69afa91cf7baead1780172"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:45.278690Z","signature_b64":"KiFQHgP4cAivy3+5fUhlhXHVZR1DL5V4oBOvsBErMpBvVczjBybwdDJkvjTsCMDlk4IHSvY+eVskWarlRQefCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ada1e9a2e25162b695a9f7f84f04faa9fc98f681ac91a060c0356a3b18e9bcf","last_reissued_at":"2026-05-18T01:53:45.278037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:45.278037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Gorenstein conjecture fails for the tautological ring of $\\mathcal{\\bar M}_{2,n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Petersen, Orsola Tommasi","submitted_at":"2012-10-21T20:28:19Z","abstract_excerpt":"Let $N$ be the smallest integer such that there is a non-tautological cohomology class of even degree on $\\mathcal{\\bar M}_{2,N}$. We remark that there is such a non-tautological class on $\\mathcal{\\bar M}_{2,20}$, by work of Graber and Pandharipande. We show that $\\mathcal{\\bar M}_{2,N}$ has non-tautological cohomology only in one degree, which is not the middle degree. In particular, it follows that the tautological ring of $\\mathcal{\\bar M}_{2,N}$ is not Gorenstein. We present some evidence suggesting that N=20 holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5761","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":"1210.5761","created_at":"2026-05-18T01:53:45.278138+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.5761v1","created_at":"2026-05-18T01:53:45.278138+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5761","created_at":"2026-05-18T01:53:45.278138+00:00"},{"alias_kind":"pith_short_12","alias_value":"FLNB5GROEULC","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FLNB5GROEULCW2K2","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FLNB5GRO","created_at":"2026-05-18T12:27:06.952714+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/FLNB5GROEULCW2K2T57YJ4CPVK","json":"https://pith.science/pith/FLNB5GROEULCW2K2T57YJ4CPVK.json","graph_json":"https://pith.science/api/pith-number/FLNB5GROEULCW2K2T57YJ4CPVK/graph.json","events_json":"https://pith.science/api/pith-number/FLNB5GROEULCW2K2T57YJ4CPVK/events.json","paper":"https://pith.science/paper/FLNB5GRO"},"agent_actions":{"view_html":"https://pith.science/pith/FLNB5GROEULCW2K2T57YJ4CPVK","download_json":"https://pith.science/pith/FLNB5GROEULCW2K2T57YJ4CPVK.json","view_paper":"https://pith.science/paper/FLNB5GRO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.5761&json=true","fetch_graph":"https://pith.science/api/pith-number/FLNB5GROEULCW2K2T57YJ4CPVK/graph.json","fetch_events":"https://pith.science/api/pith-number/FLNB5GROEULCW2K2T57YJ4CPVK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FLNB5GROEULCW2K2T57YJ4CPVK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FLNB5GROEULCW2K2T57YJ4CPVK/action/storage_attestation","attest_author":"https://pith.science/pith/FLNB5GROEULCW2K2T57YJ4CPVK/action/author_attestation","sign_citation":"https://pith.science/pith/FLNB5GROEULCW2K2T57YJ4CPVK/action/citation_signature","submit_replication":"https://pith.science/pith/FLNB5GROEULCW2K2T57YJ4CPVK/action/replication_record"}},"created_at":"2026-05-18T01:53:45.278138+00:00","updated_at":"2026-05-18T01:53:45.278138+00:00"}