{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZRSJ6JOIFMUY5VDQTLRLYLN3G7","short_pith_number":"pith:ZRSJ6JOI","schema_version":"1.0","canonical_sha256":"cc649f25c82b298ed4709ae2bc2dbb37e0a97995e9f7c61e3866ab63f4385d0f","source":{"kind":"arxiv","id":"1505.03576","version":2},"attestation_state":"computed","paper":{"title":"On the roots of an extended lens equation and an application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mutsuo Oka","submitted_at":"2015-05-13T23:50:27Z","abstract_excerpt":"We consider a certain mixed polynomial which is an extended Lens equation $L_{n,m}=\\bar z^m-p(z)/q(z)$ with $\\text{degree}\\, q=n$, $\\text{degree}\\, p<n$ whose numerator is a mixed polynomial of degree $(n+m;n,m)$. Then we consider its deformation of type $L_{n,m}+\\epsilon/z^m$ to construct a special mixed polynomial of degree $(n+2m;n+m,m)$ with $5n$ zeros. This generalizes an example of Rhie. We give an application to the number of connected components of the moduli space of strongly mixed weighted homogeneous polynomials of two variables with isolated singularity at 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":"1505.03576","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-13T23:50:27Z","cross_cats_sorted":[],"title_canon_sha256":"9915703ae7e5b20ea2701cc4c336e3d9191afbc1a5b5448010b958ccb8500958","abstract_canon_sha256":"9cbf1420100575eb0e5ac659d1e0b9a6afebcff5759cc59420fb2cfbdd871c39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:46.016898Z","signature_b64":"PgWolYpMwaU64t1dWkzdGkNChJarntHieCNdhxnGlUaA3+O3dMtEYTC7xuzVy61z/c8qBh6mwdGGGuYllYk5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc649f25c82b298ed4709ae2bc2dbb37e0a97995e9f7c61e3866ab63f4385d0f","last_reissued_at":"2026-05-18T01:29:46.016439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:46.016439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the roots of an extended lens equation and an application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mutsuo Oka","submitted_at":"2015-05-13T23:50:27Z","abstract_excerpt":"We consider a certain mixed polynomial which is an extended Lens equation $L_{n,m}=\\bar z^m-p(z)/q(z)$ with $\\text{degree}\\, q=n$, $\\text{degree}\\, p<n$ whose numerator is a mixed polynomial of degree $(n+m;n,m)$. Then we consider its deformation of type $L_{n,m}+\\epsilon/z^m$ to construct a special mixed polynomial of degree $(n+2m;n+m,m)$ with $5n$ zeros. This generalizes an example of Rhie. We give an application to the number of connected components of the moduli space of strongly mixed weighted homogeneous polynomials of two variables with isolated singularity at the origin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03576","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":"1505.03576","created_at":"2026-05-18T01:29:46.016513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.03576v2","created_at":"2026-05-18T01:29:46.016513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03576","created_at":"2026-05-18T01:29:46.016513+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZRSJ6JOIFMUY","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZRSJ6JOIFMUY5VDQ","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZRSJ6JOI","created_at":"2026-05-18T12:29:52.810259+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/ZRSJ6JOIFMUY5VDQTLRLYLN3G7","json":"https://pith.science/pith/ZRSJ6JOIFMUY5VDQTLRLYLN3G7.json","graph_json":"https://pith.science/api/pith-number/ZRSJ6JOIFMUY5VDQTLRLYLN3G7/graph.json","events_json":"https://pith.science/api/pith-number/ZRSJ6JOIFMUY5VDQTLRLYLN3G7/events.json","paper":"https://pith.science/paper/ZRSJ6JOI"},"agent_actions":{"view_html":"https://pith.science/pith/ZRSJ6JOIFMUY5VDQTLRLYLN3G7","download_json":"https://pith.science/pith/ZRSJ6JOIFMUY5VDQTLRLYLN3G7.json","view_paper":"https://pith.science/paper/ZRSJ6JOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.03576&json=true","fetch_graph":"https://pith.science/api/pith-number/ZRSJ6JOIFMUY5VDQTLRLYLN3G7/graph.json","fetch_events":"https://pith.science/api/pith-number/ZRSJ6JOIFMUY5VDQTLRLYLN3G7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZRSJ6JOIFMUY5VDQTLRLYLN3G7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZRSJ6JOIFMUY5VDQTLRLYLN3G7/action/storage_attestation","attest_author":"https://pith.science/pith/ZRSJ6JOIFMUY5VDQTLRLYLN3G7/action/author_attestation","sign_citation":"https://pith.science/pith/ZRSJ6JOIFMUY5VDQTLRLYLN3G7/action/citation_signature","submit_replication":"https://pith.science/pith/ZRSJ6JOIFMUY5VDQTLRLYLN3G7/action/replication_record"}},"created_at":"2026-05-18T01:29:46.016513+00:00","updated_at":"2026-05-18T01:29:46.016513+00:00"}