{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:EIIQNW2A2QAB4NRUVBZJCUBJRT","short_pith_number":"pith:EIIQNW2A","schema_version":"1.0","canonical_sha256":"221106db40d4001e3634a8729150298cf9aea687289849fe1175eed9505a8f16","source":{"kind":"arxiv","id":"1904.07716","version":2},"attestation_state":"computed","paper":{"title":"On the Hilbert scheme of linearly normal curves in $\\mathbb{P}^r$ of relatively high degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Changho Keem, Claudio Fontanari, Edoardo Ballico","submitted_at":"2019-04-15T16:41:27Z","abstract_excerpt":"Let $\\mathcal{H}_{d,g,r}$ be the Hilbert scheme parametrizing smooth irreducible and non-degenerate curves of degree $d$ and genus $g$ in $\\PP^r$. We denote by $\\mathcal{H}^\\mathcal{L}_{d,g,r}$ the union of those components of $\\mathcal{H}_{d,g,r}$ whose general element is linearly normal and we show that any non-empty $\\mathcal{H}^\\mathcal{L}_{d,g,r}$ ($d\\ge g+r-3$) is irreducible for an extensive range of triples $(d,g,r)$ beyond the Brill-Noether range. This establishes the validity of a suitably modified assertion of Severi regarding the irreducibility of the Hilbert scheme $\\mathcal{H}^\\m"},"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":"1904.07716","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-15T16:41:27Z","cross_cats_sorted":[],"title_canon_sha256":"6cb23808c5a8d0a36611897744074a71542a1d405b930b8392c64d0058127e31","abstract_canon_sha256":"3145e6825dcf81fdb0c3b5389e8692472a6668a8523b42181aeebe64214c9d98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:42.376067Z","signature_b64":"Pes9X/a5ruXWcBq1EngD76mkmei+9xsofpzlViw2ZVX2GgEua2thYkVJlhX/sMEkPeRrzmfIn021mDaFEoXABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"221106db40d4001e3634a8729150298cf9aea687289849fe1175eed9505a8f16","last_reissued_at":"2026-05-17T23:41:42.375625Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:42.375625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Hilbert scheme of linearly normal curves in $\\mathbb{P}^r$ of relatively high degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Changho Keem, Claudio Fontanari, Edoardo Ballico","submitted_at":"2019-04-15T16:41:27Z","abstract_excerpt":"Let $\\mathcal{H}_{d,g,r}$ be the Hilbert scheme parametrizing smooth irreducible and non-degenerate curves of degree $d$ and genus $g$ in $\\PP^r$. We denote by $\\mathcal{H}^\\mathcal{L}_{d,g,r}$ the union of those components of $\\mathcal{H}_{d,g,r}$ whose general element is linearly normal and we show that any non-empty $\\mathcal{H}^\\mathcal{L}_{d,g,r}$ ($d\\ge g+r-3$) is irreducible for an extensive range of triples $(d,g,r)$ beyond the Brill-Noether range. This establishes the validity of a suitably modified assertion of Severi regarding the irreducibility of the Hilbert scheme $\\mathcal{H}^\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07716","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":"1904.07716","created_at":"2026-05-17T23:41:42.375690+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.07716v2","created_at":"2026-05-17T23:41:42.375690+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07716","created_at":"2026-05-17T23:41:42.375690+00:00"},{"alias_kind":"pith_short_12","alias_value":"EIIQNW2A2QAB","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"EIIQNW2A2QAB4NRU","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"EIIQNW2A","created_at":"2026-05-18T12:33:15.570797+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/EIIQNW2A2QAB4NRUVBZJCUBJRT","json":"https://pith.science/pith/EIIQNW2A2QAB4NRUVBZJCUBJRT.json","graph_json":"https://pith.science/api/pith-number/EIIQNW2A2QAB4NRUVBZJCUBJRT/graph.json","events_json":"https://pith.science/api/pith-number/EIIQNW2A2QAB4NRUVBZJCUBJRT/events.json","paper":"https://pith.science/paper/EIIQNW2A"},"agent_actions":{"view_html":"https://pith.science/pith/EIIQNW2A2QAB4NRUVBZJCUBJRT","download_json":"https://pith.science/pith/EIIQNW2A2QAB4NRUVBZJCUBJRT.json","view_paper":"https://pith.science/paper/EIIQNW2A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.07716&json=true","fetch_graph":"https://pith.science/api/pith-number/EIIQNW2A2QAB4NRUVBZJCUBJRT/graph.json","fetch_events":"https://pith.science/api/pith-number/EIIQNW2A2QAB4NRUVBZJCUBJRT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EIIQNW2A2QAB4NRUVBZJCUBJRT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EIIQNW2A2QAB4NRUVBZJCUBJRT/action/storage_attestation","attest_author":"https://pith.science/pith/EIIQNW2A2QAB4NRUVBZJCUBJRT/action/author_attestation","sign_citation":"https://pith.science/pith/EIIQNW2A2QAB4NRUVBZJCUBJRT/action/citation_signature","submit_replication":"https://pith.science/pith/EIIQNW2A2QAB4NRUVBZJCUBJRT/action/replication_record"}},"created_at":"2026-05-17T23:41:42.375690+00:00","updated_at":"2026-05-17T23:41:42.375690+00:00"}