{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FHRLAGSO6QF2WNCOC3E7RU7KJS","short_pith_number":"pith:FHRLAGSO","schema_version":"1.0","canonical_sha256":"29e2b01a4ef40bab344e16c9f8d3ea4cb5defc8515522c9c5fe99c263515397d","source":{"kind":"arxiv","id":"1206.1424","version":2},"attestation_state":"computed","paper":{"title":"Uniruledness of some moduli spaces of stable pointed curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Benzo","submitted_at":"2012-06-07T08:50:46Z","abstract_excerpt":"We prove uniruledness of some moduli spaces $\\bar{M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points using linear systems on nonsingular projective surfaces containing the general curve of genus $g$. Precisely we show that $\\bar{M}_{g,n}$ is uniruled for $g=12$ and $n \\leq 5$, $g=13$ and $n \\leq 3$, $g=15$ and $n \\leq 2$. We then prove that the pointed hyperelliptic locus $H_{g,n}$ is uniruled for $g \\geq 2$ and $n \\leq 4g+4$. In the last part we show that a nonsingular complete intersection surface does not carry a linear system containing the general curve of genus $g \\geq 16$ an"},"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":"1206.1424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-07T08:50:46Z","cross_cats_sorted":[],"title_canon_sha256":"971fe0b5f5bdee90d3bac90c7311291ed85944fdbc2ac44d4d30e2a2d500f978","abstract_canon_sha256":"9f01082978545e15cb65cad227c99ae34c4c1fa34703adc2f33cd81d2c8efe40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:22.353943Z","signature_b64":"bfymj0ZbvyBzQck5BaSavF0dsN4UFEIWl6KfVsHQWXkn1rld6EV0f7AtOMG4LEBgWz8+h23VUyuESDwVwD6nAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29e2b01a4ef40bab344e16c9f8d3ea4cb5defc8515522c9c5fe99c263515397d","last_reissued_at":"2026-05-18T03:01:22.353344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:22.353344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniruledness of some moduli spaces of stable pointed curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Benzo","submitted_at":"2012-06-07T08:50:46Z","abstract_excerpt":"We prove uniruledness of some moduli spaces $\\bar{M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points using linear systems on nonsingular projective surfaces containing the general curve of genus $g$. Precisely we show that $\\bar{M}_{g,n}$ is uniruled for $g=12$ and $n \\leq 5$, $g=13$ and $n \\leq 3$, $g=15$ and $n \\leq 2$. We then prove that the pointed hyperelliptic locus $H_{g,n}$ is uniruled for $g \\geq 2$ and $n \\leq 4g+4$. In the last part we show that a nonsingular complete intersection surface does not carry a linear system containing the general curve of genus $g \\geq 16$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1424","kind":"arxiv","version":2},"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":"1206.1424","created_at":"2026-05-18T03:01:22.353443+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.1424v2","created_at":"2026-05-18T03:01:22.353443+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1424","created_at":"2026-05-18T03:01:22.353443+00:00"},{"alias_kind":"pith_short_12","alias_value":"FHRLAGSO6QF2","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FHRLAGSO6QF2WNCO","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FHRLAGSO","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/FHRLAGSO6QF2WNCOC3E7RU7KJS","json":"https://pith.science/pith/FHRLAGSO6QF2WNCOC3E7RU7KJS.json","graph_json":"https://pith.science/api/pith-number/FHRLAGSO6QF2WNCOC3E7RU7KJS/graph.json","events_json":"https://pith.science/api/pith-number/FHRLAGSO6QF2WNCOC3E7RU7KJS/events.json","paper":"https://pith.science/paper/FHRLAGSO"},"agent_actions":{"view_html":"https://pith.science/pith/FHRLAGSO6QF2WNCOC3E7RU7KJS","download_json":"https://pith.science/pith/FHRLAGSO6QF2WNCOC3E7RU7KJS.json","view_paper":"https://pith.science/paper/FHRLAGSO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.1424&json=true","fetch_graph":"https://pith.science/api/pith-number/FHRLAGSO6QF2WNCOC3E7RU7KJS/graph.json","fetch_events":"https://pith.science/api/pith-number/FHRLAGSO6QF2WNCOC3E7RU7KJS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FHRLAGSO6QF2WNCOC3E7RU7KJS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FHRLAGSO6QF2WNCOC3E7RU7KJS/action/storage_attestation","attest_author":"https://pith.science/pith/FHRLAGSO6QF2WNCOC3E7RU7KJS/action/author_attestation","sign_citation":"https://pith.science/pith/FHRLAGSO6QF2WNCOC3E7RU7KJS/action/citation_signature","submit_replication":"https://pith.science/pith/FHRLAGSO6QF2WNCOC3E7RU7KJS/action/replication_record"}},"created_at":"2026-05-18T03:01:22.353443+00:00","updated_at":"2026-05-18T03:01:22.353443+00:00"}