{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:COIIPW77UEK3VCOHDFO75G33PY","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":"93ea3ac0658ca667ebb8897bb36372a1d61ecbd0b6b8f50e518c9dce36f719fa","cross_cats_sorted":["math.AG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-20T20:19:34Z","title_canon_sha256":"a4cbcccd814abcb0220742bbf8bad6296bf5f00775189c441a5f58c2f4f7e070"},"schema_version":"1.0","source":{"id":"1406.5523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5523","created_at":"2026-05-18T02:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5523v1","created_at":"2026-05-18T02:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5523","created_at":"2026-05-18T02:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"COIIPW77UEK3","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"COIIPW77UEK3VCOH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"COIIPW77","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:56f198f4796dac69c4c49e600f1c7bbc6ddaf1cc716e0e6ec6f28d2c26c314e7","target":"graph","created_at":"2026-05-18T02:49:11Z","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":"Motivated by Wilmshurst's conjecture, we investigate the zeros of harmonic polynomials. We utilize a certified counting approach which is a combination of two methods from numerical algebraic geometry: numerical polynomial homotopy continuation to compute a numerical approximation of each zero and Smale's alpha-theory to certify the results. Using this approach, we provide new examples of harmonic polynomials having the most extreme number of zeros known so far; we also study the mean and variance of the number of zeros of random harmonic polynomials.","authors_text":"Antonio Lerario, Dhagash Mehta, Erik Lundberg, Jonathan D. Hauenstein","cross_cats":["math.AG","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-20T20:19:34Z","title":"Experiments on the zeros of harmonic polynomials using certified counting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5523","kind":"arxiv","version":1},"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":"sha256:60677c5fd972cef1da6f385e08894c3fed61906fffbc3f93fbe23515b485913b","target":"record","created_at":"2026-05-18T02:49:11Z","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":"93ea3ac0658ca667ebb8897bb36372a1d61ecbd0b6b8f50e518c9dce36f719fa","cross_cats_sorted":["math.AG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-20T20:19:34Z","title_canon_sha256":"a4cbcccd814abcb0220742bbf8bad6296bf5f00775189c441a5f58c2f4f7e070"},"schema_version":"1.0","source":{"id":"1406.5523","kind":"arxiv","version":1}},"canonical_sha256":"139087dbffa115ba89c7195dfe9b7b7e128fe5524f94b4da1b8f04ed9bdf254f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"139087dbffa115ba89c7195dfe9b7b7e128fe5524f94b4da1b8f04ed9bdf254f","first_computed_at":"2026-05-18T02:49:11.324843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:11.324843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GImWSrHePDE1Cv80dqaO7vcJ/xQoPNx2qvVdm0E4M2JQTICDyxzW68+U3uH9grfIWozPyMQ8i8xcF3iXQAyyCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:11.325358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60677c5fd972cef1da6f385e08894c3fed61906fffbc3f93fbe23515b485913b","sha256:56f198f4796dac69c4c49e600f1c7bbc6ddaf1cc716e0e6ec6f28d2c26c314e7"],"state_sha256":"fa9d7fbc11bcb291d0478f8a1b448549fdd010d66385d055a2e2750f06d7df2b"}