{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ACP5XVBDEWYJSNIWU5IR2KOVRB","short_pith_number":"pith:ACP5XVBD","schema_version":"1.0","canonical_sha256":"009fdbd42325b0993516a7511d29d588752e0516973f708ddeecedc2d0f7739d","source":{"kind":"arxiv","id":"1804.01015","version":4},"attestation_state":"computed","paper":{"title":"The numerical algebraic geometry of bottlenecks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Eklund","submitted_at":"2018-04-03T14:57:15Z","abstract_excerpt":"This is a computational study of bottlenecks on algebraic varieties. The bottlenecks of a smooth variety $X \\subseteq \\mathbb{C}^n$ are the lines in $\\mathbb{C}^n$ which are normal to $X$ at two distinct points. The main result is a numerical homotopy that can be used to approximate all isolated bottlenecks. This homotopy has the optimal number of paths under certain genericity assumptions. In the process we prove bounds on the number of bottlenecks in terms of the Euclidean distance degree. Applications include the optimization problem of computing the distance between two real varieties. Als"},"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":"1804.01015","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-03T14:57:15Z","cross_cats_sorted":[],"title_canon_sha256":"22832a8d5d18b3768c389636212414eaba5eae08cbf6c63add057e6a2fc8b4f5","abstract_canon_sha256":"e9f1625d9b59e29536138d28c5f405203ddc8804682cbab874ac7338f527ee0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:23.635933Z","signature_b64":"Sdpuuuc33q6Kc1HwzpvDHKtq4GLukkGZW7I1lrd0BJjIrIYQOC+PA8JlbZxBIlksLl0o/E0W9zeNI+eo9dOvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"009fdbd42325b0993516a7511d29d588752e0516973f708ddeecedc2d0f7739d","last_reissued_at":"2026-05-18T00:17:23.635248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:23.635248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The numerical algebraic geometry of bottlenecks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Eklund","submitted_at":"2018-04-03T14:57:15Z","abstract_excerpt":"This is a computational study of bottlenecks on algebraic varieties. The bottlenecks of a smooth variety $X \\subseteq \\mathbb{C}^n$ are the lines in $\\mathbb{C}^n$ which are normal to $X$ at two distinct points. The main result is a numerical homotopy that can be used to approximate all isolated bottlenecks. This homotopy has the optimal number of paths under certain genericity assumptions. In the process we prove bounds on the number of bottlenecks in terms of the Euclidean distance degree. Applications include the optimization problem of computing the distance between two real varieties. Als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01015","kind":"arxiv","version":4},"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":"1804.01015","created_at":"2026-05-18T00:17:23.635339+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.01015v4","created_at":"2026-05-18T00:17:23.635339+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01015","created_at":"2026-05-18T00:17:23.635339+00:00"},{"alias_kind":"pith_short_12","alias_value":"ACP5XVBDEWYJ","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"ACP5XVBDEWYJSNIW","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"ACP5XVBD","created_at":"2026-05-18T12:32:13.499390+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/ACP5XVBDEWYJSNIWU5IR2KOVRB","json":"https://pith.science/pith/ACP5XVBDEWYJSNIWU5IR2KOVRB.json","graph_json":"https://pith.science/api/pith-number/ACP5XVBDEWYJSNIWU5IR2KOVRB/graph.json","events_json":"https://pith.science/api/pith-number/ACP5XVBDEWYJSNIWU5IR2KOVRB/events.json","paper":"https://pith.science/paper/ACP5XVBD"},"agent_actions":{"view_html":"https://pith.science/pith/ACP5XVBDEWYJSNIWU5IR2KOVRB","download_json":"https://pith.science/pith/ACP5XVBDEWYJSNIWU5IR2KOVRB.json","view_paper":"https://pith.science/paper/ACP5XVBD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.01015&json=true","fetch_graph":"https://pith.science/api/pith-number/ACP5XVBDEWYJSNIWU5IR2KOVRB/graph.json","fetch_events":"https://pith.science/api/pith-number/ACP5XVBDEWYJSNIWU5IR2KOVRB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ACP5XVBDEWYJSNIWU5IR2KOVRB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ACP5XVBDEWYJSNIWU5IR2KOVRB/action/storage_attestation","attest_author":"https://pith.science/pith/ACP5XVBDEWYJSNIWU5IR2KOVRB/action/author_attestation","sign_citation":"https://pith.science/pith/ACP5XVBDEWYJSNIWU5IR2KOVRB/action/citation_signature","submit_replication":"https://pith.science/pith/ACP5XVBDEWYJSNIWU5IR2KOVRB/action/replication_record"}},"created_at":"2026-05-18T00:17:23.635339+00:00","updated_at":"2026-05-18T00:17:23.635339+00:00"}