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Given integers $n_1...,n_m$ such that $n_1+...+n_m=0$, the tangential center problem on zero-cycles asks to find all polynomials $g\\in\\C[z]$ such that $n_1g(z_1(t))+...+n_mg(z_m(t))\\equiv 0$. The classical Center-Focus Problem, or rather its tangential version in important non-trivial planar systems lead to the above problem.\n  The tangential center problem on zero-cycles was recently solved in a preprint by Gavrilov and Pakovich.\n  Here we give an alternative solution"},"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":"1202.5896","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-27T11:33:05Z","cross_cats_sorted":[],"title_canon_sha256":"57d4007ef16d3750674b0ba55e01663f04412b0c56d29f35f7b658d9c06fe5fb","abstract_canon_sha256":"1329c9484b4b7078c234253a3c3699e0fc381eef62a3ddd180dd67f5dd05c34e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:05.707689Z","signature_b64":"lE0F2I8l/HrAPaH213j3wu/0JXOeb3qM3Ny5DQnFZgHw+WDgqAJwaZT6UvFqD7xlhE6KQWRqVrxWgsCqVby9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8432c63bba21c5d33022c68e9c517c19e2bb111a02167640f2216b15bd4673d0","last_reissued_at":"2026-05-18T03:32:05.707138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:05.707138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inductive Solution of the Tangential Center Problem on Zero-Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Amelia \\'Alvarez S\\'anchez, Jos\\'e Luis Bravo Trinidad, Pavao Mardesi\\'c","submitted_at":"2012-02-27T11:33:05Z","abstract_excerpt":"Given a polynomial $f\\in\\C[z]$ of degree $m$, let $z_1(t),...,z_m(t)$ denote all algebraic functions defined by $f(z_k(t))=t$. Given integers $n_1...,n_m$ such that $n_1+...+n_m=0$, the tangential center problem on zero-cycles asks to find all polynomials $g\\in\\C[z]$ such that $n_1g(z_1(t))+...+n_mg(z_m(t))\\equiv 0$. The classical Center-Focus Problem, or rather its tangential version in important non-trivial planar systems lead to the above problem.\n  The tangential center problem on zero-cycles was recently solved in a preprint by Gavrilov and Pakovich.\n  Here we give an alternative solution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5896","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":"1202.5896","created_at":"2026-05-18T03:32:05.707240+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.5896v2","created_at":"2026-05-18T03:32:05.707240+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5896","created_at":"2026-05-18T03:32:05.707240+00:00"},{"alias_kind":"pith_short_12","alias_value":"QQZMMO52EHC5","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QQZMMO52EHC5GMBC","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QQZMMO52","created_at":"2026-05-18T12:27:18.751474+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/QQZMMO52EHC5GMBCY2HJYUL4DH","json":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH.json","graph_json":"https://pith.science/api/pith-number/QQZMMO52EHC5GMBCY2HJYUL4DH/graph.json","events_json":"https://pith.science/api/pith-number/QQZMMO52EHC5GMBCY2HJYUL4DH/events.json","paper":"https://pith.science/paper/QQZMMO52"},"agent_actions":{"view_html":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH","download_json":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH.json","view_paper":"https://pith.science/paper/QQZMMO52","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.5896&json=true","fetch_graph":"https://pith.science/api/pith-number/QQZMMO52EHC5GMBCY2HJYUL4DH/graph.json","fetch_events":"https://pith.science/api/pith-number/QQZMMO52EHC5GMBCY2HJYUL4DH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/action/storage_attestation","attest_author":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/action/author_attestation","sign_citation":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/action/citation_signature","submit_replication":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/action/replication_record"}},"created_at":"2026-05-18T03:32:05.707240+00:00","updated_at":"2026-05-18T03:32:05.707240+00:00"}