{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:I6O2VRMFAP5SQODI2SAGEMXWJU","short_pith_number":"pith:I6O2VRMF","schema_version":"1.0","canonical_sha256":"479daac58503fb283868d4806232f64d0dd8ca7aefa50973d0939cca1ee26c1a","source":{"kind":"arxiv","id":"1407.4887","version":1},"attestation_state":"computed","paper":{"title":"On the smoothability of certain K\\\"ahler cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ronan J. Conlon","submitted_at":"2014-07-18T05:24:54Z","abstract_excerpt":"Let $D$ be a Fano manifold that may be realised as $\\mathbb{P}(\\mathcal{E})$ for some rank $2$ holomorphic vector bundle $\\mathcal{E}\\longrightarrow Z$ over some Fano manifold $Z$. Let $k\\in\\mathbb{N}$ divide $c_{1}(D)$. We classify those K\\\"ahler cones of dimension $\\leq4$ of the form $(\\frac{1}{k}K_{D})^{\\times}$ that are smoothable. As a consequence, we find that any irregular Calabi-Yau cone of dimension $\\leq 4$ of this form does not admit a smoothing, leaving $K_{\\mathbb{P}^{2}_{(2)}}^{\\times}$ as currently the only known example of a smoothable irregular Calabi-Yau cone in these dimensi"},"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":"1407.4887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-18T05:24:54Z","cross_cats_sorted":[],"title_canon_sha256":"5035d886d0ae3d307df97e601e40c6e28e3bed2aa3e12bfbeee0020eff66f668","abstract_canon_sha256":"8ac0f406e766f3fe1bb8272c2da078b9395e8f2a667323b06a156a9df6f4f9cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:22.450874Z","signature_b64":"T1TjUdBq1J1JKbZcLCHxZ3rMUqRb3HOpZk5dJUstPldidko90OfwPHbah8eYwOV7Svjqfy8gUNal7a5PZJc3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"479daac58503fb283868d4806232f64d0dd8ca7aefa50973d0939cca1ee26c1a","last_reissued_at":"2026-05-18T02:47:22.450211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:22.450211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the smoothability of certain K\\\"ahler cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ronan J. Conlon","submitted_at":"2014-07-18T05:24:54Z","abstract_excerpt":"Let $D$ be a Fano manifold that may be realised as $\\mathbb{P}(\\mathcal{E})$ for some rank $2$ holomorphic vector bundle $\\mathcal{E}\\longrightarrow Z$ over some Fano manifold $Z$. Let $k\\in\\mathbb{N}$ divide $c_{1}(D)$. We classify those K\\\"ahler cones of dimension $\\leq4$ of the form $(\\frac{1}{k}K_{D})^{\\times}$ that are smoothable. As a consequence, we find that any irregular Calabi-Yau cone of dimension $\\leq 4$ of this form does not admit a smoothing, leaving $K_{\\mathbb{P}^{2}_{(2)}}^{\\times}$ as currently the only known example of a smoothable irregular Calabi-Yau cone in these dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4887","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":"1407.4887","created_at":"2026-05-18T02:47:22.450302+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.4887v1","created_at":"2026-05-18T02:47:22.450302+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4887","created_at":"2026-05-18T02:47:22.450302+00:00"},{"alias_kind":"pith_short_12","alias_value":"I6O2VRMFAP5S","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"I6O2VRMFAP5SQODI","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"I6O2VRMF","created_at":"2026-05-18T12:28:33.132498+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/I6O2VRMFAP5SQODI2SAGEMXWJU","json":"https://pith.science/pith/I6O2VRMFAP5SQODI2SAGEMXWJU.json","graph_json":"https://pith.science/api/pith-number/I6O2VRMFAP5SQODI2SAGEMXWJU/graph.json","events_json":"https://pith.science/api/pith-number/I6O2VRMFAP5SQODI2SAGEMXWJU/events.json","paper":"https://pith.science/paper/I6O2VRMF"},"agent_actions":{"view_html":"https://pith.science/pith/I6O2VRMFAP5SQODI2SAGEMXWJU","download_json":"https://pith.science/pith/I6O2VRMFAP5SQODI2SAGEMXWJU.json","view_paper":"https://pith.science/paper/I6O2VRMF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.4887&json=true","fetch_graph":"https://pith.science/api/pith-number/I6O2VRMFAP5SQODI2SAGEMXWJU/graph.json","fetch_events":"https://pith.science/api/pith-number/I6O2VRMFAP5SQODI2SAGEMXWJU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I6O2VRMFAP5SQODI2SAGEMXWJU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I6O2VRMFAP5SQODI2SAGEMXWJU/action/storage_attestation","attest_author":"https://pith.science/pith/I6O2VRMFAP5SQODI2SAGEMXWJU/action/author_attestation","sign_citation":"https://pith.science/pith/I6O2VRMFAP5SQODI2SAGEMXWJU/action/citation_signature","submit_replication":"https://pith.science/pith/I6O2VRMFAP5SQODI2SAGEMXWJU/action/replication_record"}},"created_at":"2026-05-18T02:47:22.450302+00:00","updated_at":"2026-05-18T02:47:22.450302+00:00"}