{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HWUPMN7IVVTKSRX4HDHKB3LBSE","short_pith_number":"pith:HWUPMN7I","schema_version":"1.0","canonical_sha256":"3da8f637e8ad66a946fc38cea0ed619103bd188677dd9ada35cf88bb4390430d","source":{"kind":"arxiv","id":"1706.07252","version":2},"attestation_state":"computed","paper":{"title":"The vanishing cycles of curves in toric surfaces II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GT","authors_text":"Lionel Lang, R\\'emi Cr\\'etois","submitted_at":"2017-06-22T11:07:14Z","abstract_excerpt":"We resume the study initiated in \\cite{CL}. For a generic curve $C$ in an ample linear system $\\vert \\mathcal{L} \\vert$ on a toric surface $X$, a vanishing cycle of $C$ is an isotopy class of simple closed curve that can be contracted to a point along a degeneration of $C$ to a nodal curve in $\\vert \\mathcal{L} \\vert$. The obstructions that prevent a simple closed curve in $C$ from being a vanishing cycle are encoded by the adjoint line bundle $K_X \\otimes \\mathcal{L}$. In this paper, we consider the linear systems carrying the two simplest types of obstruction. Geometrically, these obstructio"},"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":"1706.07252","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-22T11:07:14Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"56f42404794423bfa98b29e94993ddd8cb501f6279acae07d767ae554167dc02","abstract_canon_sha256":"83c4c8beb2c647e5acb48b44d79945560cdb56e6fb10294b286e6778d25a3c35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:53.510528Z","signature_b64":"z5cs5BFneJVRzxmLaV1C3SwYWxfjli7Al9cRWnZdTfH1dbSmc1tbx0HgXaCZ+KgDEJc/ZKI7JmDiS0XOXfr6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3da8f637e8ad66a946fc38cea0ed619103bd188677dd9ada35cf88bb4390430d","last_reissued_at":"2026-05-17T23:45:53.510017Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:53.510017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The vanishing cycles of curves in toric surfaces II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GT","authors_text":"Lionel Lang, R\\'emi Cr\\'etois","submitted_at":"2017-06-22T11:07:14Z","abstract_excerpt":"We resume the study initiated in \\cite{CL}. For a generic curve $C$ in an ample linear system $\\vert \\mathcal{L} \\vert$ on a toric surface $X$, a vanishing cycle of $C$ is an isotopy class of simple closed curve that can be contracted to a point along a degeneration of $C$ to a nodal curve in $\\vert \\mathcal{L} \\vert$. The obstructions that prevent a simple closed curve in $C$ from being a vanishing cycle are encoded by the adjoint line bundle $K_X \\otimes \\mathcal{L}$. In this paper, we consider the linear systems carrying the two simplest types of obstruction. Geometrically, these obstructio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07252","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":"1706.07252","created_at":"2026-05-17T23:45:53.510094+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.07252v2","created_at":"2026-05-17T23:45:53.510094+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07252","created_at":"2026-05-17T23:45:53.510094+00:00"},{"alias_kind":"pith_short_12","alias_value":"HWUPMN7IVVTK","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"HWUPMN7IVVTKSRX4","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"HWUPMN7I","created_at":"2026-05-18T12:31:21.493067+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/HWUPMN7IVVTKSRX4HDHKB3LBSE","json":"https://pith.science/pith/HWUPMN7IVVTKSRX4HDHKB3LBSE.json","graph_json":"https://pith.science/api/pith-number/HWUPMN7IVVTKSRX4HDHKB3LBSE/graph.json","events_json":"https://pith.science/api/pith-number/HWUPMN7IVVTKSRX4HDHKB3LBSE/events.json","paper":"https://pith.science/paper/HWUPMN7I"},"agent_actions":{"view_html":"https://pith.science/pith/HWUPMN7IVVTKSRX4HDHKB3LBSE","download_json":"https://pith.science/pith/HWUPMN7IVVTKSRX4HDHKB3LBSE.json","view_paper":"https://pith.science/paper/HWUPMN7I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.07252&json=true","fetch_graph":"https://pith.science/api/pith-number/HWUPMN7IVVTKSRX4HDHKB3LBSE/graph.json","fetch_events":"https://pith.science/api/pith-number/HWUPMN7IVVTKSRX4HDHKB3LBSE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HWUPMN7IVVTKSRX4HDHKB3LBSE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HWUPMN7IVVTKSRX4HDHKB3LBSE/action/storage_attestation","attest_author":"https://pith.science/pith/HWUPMN7IVVTKSRX4HDHKB3LBSE/action/author_attestation","sign_citation":"https://pith.science/pith/HWUPMN7IVVTKSRX4HDHKB3LBSE/action/citation_signature","submit_replication":"https://pith.science/pith/HWUPMN7IVVTKSRX4HDHKB3LBSE/action/replication_record"}},"created_at":"2026-05-17T23:45:53.510094+00:00","updated_at":"2026-05-17T23:45:53.510094+00:00"}