{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KCQIYTDPW7J2WU3HYTZ6OYYTPW","short_pith_number":"pith:KCQIYTDP","schema_version":"1.0","canonical_sha256":"50a08c4c6fb7d3ab5367c4f3e763137d8ef53354bc79190e781bb825bb7fc19e","source":{"kind":"arxiv","id":"1811.01189","version":1},"attestation_state":"computed","paper":{"title":"On the number of cusps of deformations of complex polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GT"],"primary_cat":"math.AG","authors_text":"Kazumasa Inaba","submitted_at":"2018-11-03T10:31:21Z","abstract_excerpt":"Let f be a 1-variable complex polynomial such that f has a singularity at the origin. In the present paper, we show that there exists a deformation of f which has only fold singularities and cusps as singularities of a real polynomial map from the plane to the plane. We then calculate the number of cusps of a deformation in a sufficiently small neighborhood of the origin."},"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":"1811.01189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-03T10:31:21Z","cross_cats_sorted":["math.CV","math.GT"],"title_canon_sha256":"464a77a97c1a122fd75bfc750588bea51e06aa9f31f7b906b6396026f605f182","abstract_canon_sha256":"5ad25b11e1ef4c87e7402fc0b01c745145eb7d64353bc8553bcd5d4e3a546140"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:35.096901Z","signature_b64":"sFc42lOG4NU8OuRdcFdqxrPniBws1ZlxrIQf1EOFVJnRVsH2fa6/xow3uwzxGYIFI084pGuWpQF8X0tLbRDuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50a08c4c6fb7d3ab5367c4f3e763137d8ef53354bc79190e781bb825bb7fc19e","last_reissued_at":"2026-05-18T00:01:35.096289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:35.096289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the number of cusps of deformations of complex polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GT"],"primary_cat":"math.AG","authors_text":"Kazumasa Inaba","submitted_at":"2018-11-03T10:31:21Z","abstract_excerpt":"Let f be a 1-variable complex polynomial such that f has a singularity at the origin. In the present paper, we show that there exists a deformation of f which has only fold singularities and cusps as singularities of a real polynomial map from the plane to the plane. We then calculate the number of cusps of a deformation in a sufficiently small neighborhood of the origin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01189","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":"1811.01189","created_at":"2026-05-18T00:01:35.096411+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.01189v1","created_at":"2026-05-18T00:01:35.096411+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01189","created_at":"2026-05-18T00:01:35.096411+00:00"},{"alias_kind":"pith_short_12","alias_value":"KCQIYTDPW7J2","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"KCQIYTDPW7J2WU3H","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"KCQIYTDP","created_at":"2026-05-18T12:32:33.847187+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/KCQIYTDPW7J2WU3HYTZ6OYYTPW","json":"https://pith.science/pith/KCQIYTDPW7J2WU3HYTZ6OYYTPW.json","graph_json":"https://pith.science/api/pith-number/KCQIYTDPW7J2WU3HYTZ6OYYTPW/graph.json","events_json":"https://pith.science/api/pith-number/KCQIYTDPW7J2WU3HYTZ6OYYTPW/events.json","paper":"https://pith.science/paper/KCQIYTDP"},"agent_actions":{"view_html":"https://pith.science/pith/KCQIYTDPW7J2WU3HYTZ6OYYTPW","download_json":"https://pith.science/pith/KCQIYTDPW7J2WU3HYTZ6OYYTPW.json","view_paper":"https://pith.science/paper/KCQIYTDP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.01189&json=true","fetch_graph":"https://pith.science/api/pith-number/KCQIYTDPW7J2WU3HYTZ6OYYTPW/graph.json","fetch_events":"https://pith.science/api/pith-number/KCQIYTDPW7J2WU3HYTZ6OYYTPW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KCQIYTDPW7J2WU3HYTZ6OYYTPW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KCQIYTDPW7J2WU3HYTZ6OYYTPW/action/storage_attestation","attest_author":"https://pith.science/pith/KCQIYTDPW7J2WU3HYTZ6OYYTPW/action/author_attestation","sign_citation":"https://pith.science/pith/KCQIYTDPW7J2WU3HYTZ6OYYTPW/action/citation_signature","submit_replication":"https://pith.science/pith/KCQIYTDPW7J2WU3HYTZ6OYYTPW/action/replication_record"}},"created_at":"2026-05-18T00:01:35.096411+00:00","updated_at":"2026-05-18T00:01:35.096411+00:00"}