{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZELGYFCHD4DHXG45CHJ52QRKWS","short_pith_number":"pith:ZELGYFCH","schema_version":"1.0","canonical_sha256":"c9166c14471f067b9b9d11d3dd422ab4acbb6b3eedd759671e5438ce1496aa21","source":{"kind":"arxiv","id":"1809.01411","version":1},"attestation_state":"computed","paper":{"title":"Connected components of the space of proper gradient vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Maciej Starostka","submitted_at":"2018-09-05T09:47:16Z","abstract_excerpt":"We show that there exist two proper gradient vector fields on $\\mathbb{R}^n$ which are homotopic in the category of proper maps but not homotopic in the category of proper gradient maps."},"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":"1809.01411","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-05T09:47:16Z","cross_cats_sorted":[],"title_canon_sha256":"698fb1ee22873a157c4bbe4b9b436bde0bb7eee80bc095b9c573bd620cfca8cf","abstract_canon_sha256":"3a54a05e49da27e139fc261eb2e8dfe72b4e7715b9cd8b05a0beb98717e004d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:27.722354Z","signature_b64":"pzOrNyzGGYOJjWUeIk2cBdy3PEDJacfbGthbG6o67CsdSZng2k3c+Xf8gS0KhxDYAkLDl90mJmKGBDfjmltiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9166c14471f067b9b9d11d3dd422ab4acbb6b3eedd759671e5438ce1496aa21","last_reissued_at":"2026-05-18T00:06:27.721751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:27.721751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connected components of the space of proper gradient vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Maciej Starostka","submitted_at":"2018-09-05T09:47:16Z","abstract_excerpt":"We show that there exist two proper gradient vector fields on $\\mathbb{R}^n$ which are homotopic in the category of proper maps but not homotopic in the category of proper gradient maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01411","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":"1809.01411","created_at":"2026-05-18T00:06:27.721844+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.01411v1","created_at":"2026-05-18T00:06:27.721844+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01411","created_at":"2026-05-18T00:06:27.721844+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZELGYFCHD4DH","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZELGYFCHD4DHXG45","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZELGYFCH","created_at":"2026-05-18T12:33:07.085635+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/ZELGYFCHD4DHXG45CHJ52QRKWS","json":"https://pith.science/pith/ZELGYFCHD4DHXG45CHJ52QRKWS.json","graph_json":"https://pith.science/api/pith-number/ZELGYFCHD4DHXG45CHJ52QRKWS/graph.json","events_json":"https://pith.science/api/pith-number/ZELGYFCHD4DHXG45CHJ52QRKWS/events.json","paper":"https://pith.science/paper/ZELGYFCH"},"agent_actions":{"view_html":"https://pith.science/pith/ZELGYFCHD4DHXG45CHJ52QRKWS","download_json":"https://pith.science/pith/ZELGYFCHD4DHXG45CHJ52QRKWS.json","view_paper":"https://pith.science/paper/ZELGYFCH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.01411&json=true","fetch_graph":"https://pith.science/api/pith-number/ZELGYFCHD4DHXG45CHJ52QRKWS/graph.json","fetch_events":"https://pith.science/api/pith-number/ZELGYFCHD4DHXG45CHJ52QRKWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZELGYFCHD4DHXG45CHJ52QRKWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZELGYFCHD4DHXG45CHJ52QRKWS/action/storage_attestation","attest_author":"https://pith.science/pith/ZELGYFCHD4DHXG45CHJ52QRKWS/action/author_attestation","sign_citation":"https://pith.science/pith/ZELGYFCHD4DHXG45CHJ52QRKWS/action/citation_signature","submit_replication":"https://pith.science/pith/ZELGYFCHD4DHXG45CHJ52QRKWS/action/replication_record"}},"created_at":"2026-05-18T00:06:27.721844+00:00","updated_at":"2026-05-18T00:06:27.721844+00:00"}