{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QQZMMO52EHC5GMBCY2HJYUL4DH","short_pith_number":"pith:QQZMMO52","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"},"canonical_sha256":"8432c63bba21c5d33022c68e9c517c19e2bb111a02167640f2216b15bd4673d0","source":{"kind":"arxiv","id":"1202.5896","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5896","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5896v2","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5896","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"QQZMMO52EHC5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QQZMMO52EHC5GMBC","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QQZMMO52","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QQZMMO52EHC5GMBCY2HJYUL4DH","target":"record","payload":{"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"},"canonical_sha256":"8432c63bba21c5d33022c68e9c517c19e2bb111a02167640f2216b15bd4673d0","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"},"source_kind":"arxiv","source_id":"1202.5896","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T9ZIWbKz6E2/RopBGKpmQHCAD7eMB/6ObajqFg2Dbn0d9LaV40/pMADbJRDl5caWznT9SnOuyAX8Mqs9bsGTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:00:15.624331Z"},"content_sha256":"57bb9d57321dd92fde9a0e1998510df781e2d2e35b67965729ab80c84cf3396b","schema_version":"1.0","event_id":"sha256:57bb9d57321dd92fde9a0e1998510df781e2d2e35b67965729ab80c84cf3396b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QQZMMO52EHC5GMBCY2HJYUL4DH","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HBaKtBwMnccTCtQr3eDgSyDRm2535GNsDaqjIiYElQJyiaWtJilpBHrnbpDhM372INTPf2bxhikUNeW27w8sCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T16:00:15.625076Z"},"content_sha256":"4ded4488985db6ef9db3bbb527aa6151b17ca6dc7fd16c4c9dbce3e857c1f41f","schema_version":"1.0","event_id":"sha256:4ded4488985db6ef9db3bbb527aa6151b17ca6dc7fd16c4c9dbce3e857c1f41f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/bundle.json","state_url":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-29T16:00:15Z","links":{"resolver":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH","bundle":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/bundle.json","state":"https://pith.science/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QQZMMO52EHC5GMBCY2HJYUL4DH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QQZMMO52EHC5GMBCY2HJYUL4DH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"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}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5896","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5896v2","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5896","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"QQZMMO52EHC5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QQZMMO52EHC5GMBC","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QQZMMO52","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:4ded4488985db6ef9db3bbb527aa6151b17ca6dc7fd16c4c9dbce3e857c1f41f","target":"graph","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":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6rA3/5ndj0663LBtmyaZQVoThhUooYVBBujQ1KM5e+tWnFNixAePo5NItBUJDzpCXFZA5zIxca01MsCXarAdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T16:00:15.629118Z","bundle_sha256":"5ed697404753ffba32a1dd403f7e9dc6a0cddbb74fd09a1cb5379611e9c47c3d"}}