{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:OEEO2FP2L4UARZC6U7ESRAMEBD","short_pith_number":"pith:OEEO2FP2","schema_version":"1.0","canonical_sha256":"7108ed15fa5f2808e45ea7c928818408e67fe305071ee5992839db6ea6481553","source":{"kind":"arxiv","id":"1004.0214","version":2},"attestation_state":"computed","paper":{"title":"Fixed point theorems in plane continua with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.GN","authors_text":"Alexander M. Blokh, E. D. Tymchatyn, John C. Mayer, Lex G. Oversteegen, Robbert J. Fokkink","submitted_at":"2010-04-01T19:27:52Z","abstract_excerpt":"We present proofs of basic results, including those developed by Harold Bell, for the plane fixed point problem: does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by Bell but without accessible proofs. We define the concept of the variation of a map on a simple closed curve and relate it to the index of the map on that curve: Index = Variation + 1. A fixed point theorem for positively oriented, perfect maps of the plane is obtained. This generalizes results announced by Bell in 1982. A continuous map of an interval to 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":"1004.0214","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-04-01T19:27:52Z","cross_cats_sorted":["math.DS","math.GT"],"title_canon_sha256":"0ea6c325546868a5886bd4ea900060258cab4d1709eb3a9cfcef8dc47d46ae2d","abstract_canon_sha256":"afe918658400e9a1c97fa5db99ddb6ad4c33784790665a42018e41ded1178476"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:52.707594Z","signature_b64":"V9UL03ftyAJhUj7xznqNIIxwaE9WzR4LXnisvQqWsgi8HqloD63MIJ+Ucw1ZRenAETeW5b4VO8feC75tSYWXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7108ed15fa5f2808e45ea7c928818408e67fe305071ee5992839db6ea6481553","last_reissued_at":"2026-05-18T01:22:52.707082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:52.707082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fixed point theorems in plane continua with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.GN","authors_text":"Alexander M. Blokh, E. D. Tymchatyn, John C. Mayer, Lex G. Oversteegen, Robbert J. Fokkink","submitted_at":"2010-04-01T19:27:52Z","abstract_excerpt":"We present proofs of basic results, including those developed by Harold Bell, for the plane fixed point problem: does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by Bell but without accessible proofs. We define the concept of the variation of a map on a simple closed curve and relate it to the index of the map on that curve: Index = Variation + 1. A fixed point theorem for positively oriented, perfect maps of the plane is obtained. This generalizes results announced by Bell in 1982. A continuous map of an interval to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0214","kind":"arxiv","version":2},"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":"1004.0214","created_at":"2026-05-18T01:22:52.707145+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.0214v2","created_at":"2026-05-18T01:22:52.707145+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0214","created_at":"2026-05-18T01:22:52.707145+00:00"},{"alias_kind":"pith_short_12","alias_value":"OEEO2FP2L4UA","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"OEEO2FP2L4UARZC6","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"OEEO2FP2","created_at":"2026-05-18T12:26:12.377268+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/OEEO2FP2L4UARZC6U7ESRAMEBD","json":"https://pith.science/pith/OEEO2FP2L4UARZC6U7ESRAMEBD.json","graph_json":"https://pith.science/api/pith-number/OEEO2FP2L4UARZC6U7ESRAMEBD/graph.json","events_json":"https://pith.science/api/pith-number/OEEO2FP2L4UARZC6U7ESRAMEBD/events.json","paper":"https://pith.science/paper/OEEO2FP2"},"agent_actions":{"view_html":"https://pith.science/pith/OEEO2FP2L4UARZC6U7ESRAMEBD","download_json":"https://pith.science/pith/OEEO2FP2L4UARZC6U7ESRAMEBD.json","view_paper":"https://pith.science/paper/OEEO2FP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.0214&json=true","fetch_graph":"https://pith.science/api/pith-number/OEEO2FP2L4UARZC6U7ESRAMEBD/graph.json","fetch_events":"https://pith.science/api/pith-number/OEEO2FP2L4UARZC6U7ESRAMEBD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OEEO2FP2L4UARZC6U7ESRAMEBD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OEEO2FP2L4UARZC6U7ESRAMEBD/action/storage_attestation","attest_author":"https://pith.science/pith/OEEO2FP2L4UARZC6U7ESRAMEBD/action/author_attestation","sign_citation":"https://pith.science/pith/OEEO2FP2L4UARZC6U7ESRAMEBD/action/citation_signature","submit_replication":"https://pith.science/pith/OEEO2FP2L4UARZC6U7ESRAMEBD/action/replication_record"}},"created_at":"2026-05-18T01:22:52.707145+00:00","updated_at":"2026-05-18T01:22:52.707145+00:00"}