{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:345DFJTPPHMVPZCIQNXCQXZ6SP","short_pith_number":"pith:345DFJTP","schema_version":"1.0","canonical_sha256":"df3a32a66f79d957e448836e285f3e93d3994618a2fb90ce8a390b2ce66519a8","source":{"kind":"arxiv","id":"1507.03896","version":1},"attestation_state":"computed","paper":{"title":"Condition length and complexity for the solution of polynomial systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carlos Beltr\\'an, Diego Armentano, Felipe Cucker, Michael Shub, Peter B\\\"urgisser","submitted_at":"2015-07-14T15:42:16Z","abstract_excerpt":"Smale's 17th problem asks for an algorithm which finds an approximate zero of polynomial systems in average polynomial time (see Smale 2000). The main progress on Smale's problem is Beltr\\'an-Pardo (2011) and B\\\"urgisser-Cucker (2010). In this paper we will improve on both approaches and we prove an important intermediate result. Our main results are Theorem 1 on the complexity of a randomized algorithm which improves the result of Beltr\\'an-Pardo (2011), Theorem 2 on the average of the condition number of polynomial systems which improves the estimate found in B\\\"urgisser-Cucker (2010), and T"},"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":"1507.03896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-14T15:42:16Z","cross_cats_sorted":[],"title_canon_sha256":"05df285b9d036c713ad2d7a6f43d111d23f9d7b0c35f3fe5e40db1c1732232e2","abstract_canon_sha256":"fa8b26875319a2968282b86273a5257ad67611c9ff8468c92b8f8ec8a7b49a35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:52.274894Z","signature_b64":"xDcg/kkhsUVSmPY9559IC2QNhKeUQHjd/uXq5zhF6UMZJNUzHOpgJW46Y0E2EEGtX9P0+CEHf2ohvRylm1bgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df3a32a66f79d957e448836e285f3e93d3994618a2fb90ce8a390b2ce66519a8","last_reissued_at":"2026-05-18T01:36:52.274189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:52.274189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Condition length and complexity for the solution of polynomial systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carlos Beltr\\'an, Diego Armentano, Felipe Cucker, Michael Shub, Peter B\\\"urgisser","submitted_at":"2015-07-14T15:42:16Z","abstract_excerpt":"Smale's 17th problem asks for an algorithm which finds an approximate zero of polynomial systems in average polynomial time (see Smale 2000). The main progress on Smale's problem is Beltr\\'an-Pardo (2011) and B\\\"urgisser-Cucker (2010). In this paper we will improve on both approaches and we prove an important intermediate result. Our main results are Theorem 1 on the complexity of a randomized algorithm which improves the result of Beltr\\'an-Pardo (2011), Theorem 2 on the average of the condition number of polynomial systems which improves the estimate found in B\\\"urgisser-Cucker (2010), and T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03896","kind":"arxiv","version":1},"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":"1507.03896","created_at":"2026-05-18T01:36:52.274292+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.03896v1","created_at":"2026-05-18T01:36:52.274292+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03896","created_at":"2026-05-18T01:36:52.274292+00:00"},{"alias_kind":"pith_short_12","alias_value":"345DFJTPPHMV","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"345DFJTPPHMVPZCI","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"345DFJTP","created_at":"2026-05-18T12:29:02.477457+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/345DFJTPPHMVPZCIQNXCQXZ6SP","json":"https://pith.science/pith/345DFJTPPHMVPZCIQNXCQXZ6SP.json","graph_json":"https://pith.science/api/pith-number/345DFJTPPHMVPZCIQNXCQXZ6SP/graph.json","events_json":"https://pith.science/api/pith-number/345DFJTPPHMVPZCIQNXCQXZ6SP/events.json","paper":"https://pith.science/paper/345DFJTP"},"agent_actions":{"view_html":"https://pith.science/pith/345DFJTPPHMVPZCIQNXCQXZ6SP","download_json":"https://pith.science/pith/345DFJTPPHMVPZCIQNXCQXZ6SP.json","view_paper":"https://pith.science/paper/345DFJTP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.03896&json=true","fetch_graph":"https://pith.science/api/pith-number/345DFJTPPHMVPZCIQNXCQXZ6SP/graph.json","fetch_events":"https://pith.science/api/pith-number/345DFJTPPHMVPZCIQNXCQXZ6SP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/345DFJTPPHMVPZCIQNXCQXZ6SP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/345DFJTPPHMVPZCIQNXCQXZ6SP/action/storage_attestation","attest_author":"https://pith.science/pith/345DFJTPPHMVPZCIQNXCQXZ6SP/action/author_attestation","sign_citation":"https://pith.science/pith/345DFJTPPHMVPZCIQNXCQXZ6SP/action/citation_signature","submit_replication":"https://pith.science/pith/345DFJTPPHMVPZCIQNXCQXZ6SP/action/replication_record"}},"created_at":"2026-05-18T01:36:52.274292+00:00","updated_at":"2026-05-18T01:36:52.274292+00:00"}