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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","authors_text":"Amelia \\'Alvarez S\\'anchez, Jos\\'e Luis Bravo Trinidad, Pavao Mardesi\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-27T11:33:05Z","title":"Inductive Solution of the Tangential Center Problem on Zero-Cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5896","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:57bb9d57321dd92fde9a0e1998510df781e2d2e35b67965729ab80c84cf3396b","target":"record","created_at":"2026-05-18T03:32:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1329c9484b4b7078c234253a3c3699e0fc381eef62a3ddd180dd67f5dd05c34e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-27T11:33:05Z","title_canon_sha256":"57d4007ef16d3750674b0ba55e01663f04412b0c56d29f35f7b658d9c06fe5fb"},"schema_version":"1.0","source":{"id":"1202.5896","kind":"arxiv","version":2}},"canonical_sha256":"8432c63bba21c5d33022c68e9c517c19e2bb111a02167640f2216b15bd4673d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8432c63bba21c5d33022c68e9c517c19e2bb111a02167640f2216b15bd4673d0","first_computed_at":"2026-05-18T03:32:05.707138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:05.707138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lE0F2I8l/HrAPaH213j3wu/0JXOeb3qM3Ny5DQnFZgHw+WDgqAJwaZT6UvFqD7xlhE6KQWRqVrxWgsCqVby9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:05.707689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5896","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57bb9d57321dd92fde9a0e1998510df781e2d2e35b67965729ab80c84cf3396b","sha256:4ded4488985db6ef9db3bbb527aa6151b17ca6dc7fd16c4c9dbce3e857c1f41f"],"state_sha256":"dddfe5f204199c909e1d82a2758346d15056e44a6752a05b1232bba23dd510a6"}