{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XO6ISPJJAYKV3IE7WLHH3NCUJE","short_pith_number":"pith:XO6ISPJJ","schema_version":"1.0","canonical_sha256":"bbbc893d2906155da09fb2ce7db4544917eee40762115a41357bc98ef71f6b60","source":{"kind":"arxiv","id":"1512.07499","version":3},"attestation_state":"computed","paper":{"title":"Bifurcation set of multi-parameter families of complex curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CV"],"primary_cat":"math.AG","authors_text":"Cezar Joita, Mihai Tibar","submitted_at":"2015-12-23T14:46:49Z","abstract_excerpt":"The problem of detecting the bifurcation set of polynomial mappings $\\mathbb{ C}^m \\to \\mathbb{ C}^k$, $m\\ge 2$, $m\\ge k\\ge 1$, has been solved in the case $m=2$, $k=1$ only. Its solution, which goes back to the 1970s, involves the non-constancy of the Euler characteristic of fibres. We provide a complete answer to the general case $m= k+1 \\ge 3$ in terms of the Betti numbers of fibres and of a vanishing phenomenon discovered in the late 1990s in the real setting."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.07499","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-23T14:46:49Z","cross_cats_sorted":["math.AT","math.CV"],"title_canon_sha256":"aef582dd85d4ccc71f8f71cba030f6b0b52edb4e0d6c77bfba37eef9882b3702","abstract_canon_sha256":"4488e164de81d3a27639817d09e7f192778fe6092548b5bfb1af7d381cde74f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:41.003889Z","signature_b64":"7rLs4Ee5cP2FGBCG3x0Nbl2EOydutx/tKOSIh8tS10C7nxqpzOerx0GyBo8t+s4SmTpCu0l7LB3XAuOVJX/ICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbbc893d2906155da09fb2ce7db4544917eee40762115a41357bc98ef71f6b60","last_reissued_at":"2026-05-18T00:12:41.003150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:41.003150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bifurcation set of multi-parameter families of complex curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CV"],"primary_cat":"math.AG","authors_text":"Cezar Joita, Mihai Tibar","submitted_at":"2015-12-23T14:46:49Z","abstract_excerpt":"The problem of detecting the bifurcation set of polynomial mappings $\\mathbb{ C}^m \\to \\mathbb{ C}^k$, $m\\ge 2$, $m\\ge k\\ge 1$, has been solved in the case $m=2$, $k=1$ only. Its solution, which goes back to the 1970s, involves the non-constancy of the Euler characteristic of fibres. We provide a complete answer to the general case $m= k+1 \\ge 3$ in terms of the Betti numbers of fibres and of a vanishing phenomenon discovered in the late 1990s in the real setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07499","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.07499","created_at":"2026-05-18T00:12:41.003270+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.07499v3","created_at":"2026-05-18T00:12:41.003270+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07499","created_at":"2026-05-18T00:12:41.003270+00:00"},{"alias_kind":"pith_short_12","alias_value":"XO6ISPJJAYKV","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XO6ISPJJAYKV3IE7","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XO6ISPJJ","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XO6ISPJJAYKV3IE7WLHH3NCUJE","json":"https://pith.science/pith/XO6ISPJJAYKV3IE7WLHH3NCUJE.json","graph_json":"https://pith.science/api/pith-number/XO6ISPJJAYKV3IE7WLHH3NCUJE/graph.json","events_json":"https://pith.science/api/pith-number/XO6ISPJJAYKV3IE7WLHH3NCUJE/events.json","paper":"https://pith.science/paper/XO6ISPJJ"},"agent_actions":{"view_html":"https://pith.science/pith/XO6ISPJJAYKV3IE7WLHH3NCUJE","download_json":"https://pith.science/pith/XO6ISPJJAYKV3IE7WLHH3NCUJE.json","view_paper":"https://pith.science/paper/XO6ISPJJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.07499&json=true","fetch_graph":"https://pith.science/api/pith-number/XO6ISPJJAYKV3IE7WLHH3NCUJE/graph.json","fetch_events":"https://pith.science/api/pith-number/XO6ISPJJAYKV3IE7WLHH3NCUJE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XO6ISPJJAYKV3IE7WLHH3NCUJE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XO6ISPJJAYKV3IE7WLHH3NCUJE/action/storage_attestation","attest_author":"https://pith.science/pith/XO6ISPJJAYKV3IE7WLHH3NCUJE/action/author_attestation","sign_citation":"https://pith.science/pith/XO6ISPJJAYKV3IE7WLHH3NCUJE/action/citation_signature","submit_replication":"https://pith.science/pith/XO6ISPJJAYKV3IE7WLHH3NCUJE/action/replication_record"}},"created_at":"2026-05-18T00:12:41.003270+00:00","updated_at":"2026-05-18T00:12:41.003270+00:00"}