{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KTVG4YBEEPN36VRCI75UJUCL7L","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":"c2c955f6a314cd50aef827fa1b379d8032b67e7f8abdb92f60a8ec51f705bea0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-12T17:57:31Z","title_canon_sha256":"8201f1289cead8ce80f780abb0218f59af3303ca7b9ddd0bdbe521b4480ce7ea"},"schema_version":"1.0","source":{"id":"1108.2676","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2676","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2676v2","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2676","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"KTVG4YBEEPN3","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KTVG4YBEEPN36VRC","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KTVG4YBE","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:05f45325ac9ef22de22ebced600b2d765134daad3fa05de5c514368f75b94da3","target":"graph","created_at":"2026-05-18T02:58:00Z","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 hypersurface in the complex projective $n$-space we prove several known formulas for the degree of its polar map by purely algebro-geometric methods. Furthermore, we give formulas for the degree of its polar map in terms of the degrees of the polar maps of its components. As an application, we classify the plane curves with polar map of low degree, including a very simple proof of I. Dolgachev's classification of homaloidal plane curves.","authors_text":"Nivaldo Medeiros, Thiago Fassarella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-12T17:57:31Z","title":"On the polar degree of projective hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2676","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":"sha256:0c260d7690c971507d71060e69ffe4a20ae3b33cbd3d9b8b779e79a65c8ea3f3","target":"record","created_at":"2026-05-18T02:58:00Z","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":"c2c955f6a314cd50aef827fa1b379d8032b67e7f8abdb92f60a8ec51f705bea0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-12T17:57:31Z","title_canon_sha256":"8201f1289cead8ce80f780abb0218f59af3303ca7b9ddd0bdbe521b4480ce7ea"},"schema_version":"1.0","source":{"id":"1108.2676","kind":"arxiv","version":2}},"canonical_sha256":"54ea6e602423dbbf562247fb44d04bfae5960255be2f814efe421dbdd4f2b345","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54ea6e602423dbbf562247fb44d04bfae5960255be2f814efe421dbdd4f2b345","first_computed_at":"2026-05-18T02:58:00.617657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:00.617657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GSQVNXtKwmcRwG+dBlOx+/sETb8sCLJC9Rcmwx3IXJRM268RpfSntv3MGHXUTq0ku6PdOjebPubkDKkrHD/HAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:00.618332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2676","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c260d7690c971507d71060e69ffe4a20ae3b33cbd3d9b8b779e79a65c8ea3f3","sha256:05f45325ac9ef22de22ebced600b2d765134daad3fa05de5c514368f75b94da3"],"state_sha256":"c90968d6256fc47c92b4fa5344550e6b82dab64e4372ef56ade70e2327beae58"}