{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:36DYHVR7FUTKVJQJ7EUA6AMUB3","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":"b946bdec21890c8941208b7492a87b57fb77cb61516455b16973205a6924a2cd","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-19T12:42:05Z","title_canon_sha256":"19891bd2035d7a237eaef9269d6071b37ad33fa6b75f58b6a7f940cf60ac862a"},"schema_version":"1.0","source":{"id":"1101.3678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3678","created_at":"2026-05-18T04:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3678v1","created_at":"2026-05-18T04:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3678","created_at":"2026-05-18T04:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"36DYHVR7FUTK","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"36DYHVR7FUTKVJQJ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"36DYHVR7","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:da7fcb3b07581be2abc915ceccc51fbe82057390ac2cb9835c6cd28a23596df1","target":"graph","created_at":"2026-05-18T04:14:27Z","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":"We initiate a classification of complex polynomials f of degree d having the top Betti number of the general fibre close to the maximum. We find a range in which the polynomial must have isolated singularities and another range where it may have at most a line singularity of Morse transversal type, besides controlled singularities at infinity. Our method uses deformations into particular pencils with non-isolated singularities.","authors_text":"Dirk Siersma, Mihai Tibar","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-19T12:42:05Z","title":"Betti Bounds of Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3678","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:c21cf4ee296d8789059d5c43ba8c5135aca8bea501e54fed56fbb59a68f713c8","target":"record","created_at":"2026-05-18T04:14:27Z","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":"b946bdec21890c8941208b7492a87b57fb77cb61516455b16973205a6924a2cd","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-19T12:42:05Z","title_canon_sha256":"19891bd2035d7a237eaef9269d6071b37ad33fa6b75f58b6a7f940cf60ac862a"},"schema_version":"1.0","source":{"id":"1101.3678","kind":"arxiv","version":1}},"canonical_sha256":"df8783d63f2d26aaa609f9280f01940ec3a32d7144508a5844023926d719839d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df8783d63f2d26aaa609f9280f01940ec3a32d7144508a5844023926d719839d","first_computed_at":"2026-05-18T04:14:27.558665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:27.558665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HB/31BPMFU7PddtkdUvgKN7NOZDyzbwA26wKGDiugC+m3KreTBudMylr3h9zufQLcSFohgqpAVvfzgeTOu7oCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:27.559231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c21cf4ee296d8789059d5c43ba8c5135aca8bea501e54fed56fbb59a68f713c8","sha256:da7fcb3b07581be2abc915ceccc51fbe82057390ac2cb9835c6cd28a23596df1"],"state_sha256":"159ef79ae9246bd49f26c3fed64dda0e3be031c7572f2bf6b554079162ea0755"}