{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XFJSKLO2CMJG7VNAD7IKOXBPH2","short_pith_number":"pith:XFJSKLO2","schema_version":"1.0","canonical_sha256":"b953252dda13126fd5a01fd0a75c2f3ea36b066d08421634cf0fe14de6880048","source":{"kind":"arxiv","id":"1702.05016","version":1},"attestation_state":"computed","paper":{"title":"Fixed points of n-valued maps, the fixed point property and the case of surfaces -- a braid approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daciberg Lima Gon\\c{c}alves (IME, John Guaschi (NU, LMNO), UNICAEN, USP)","submitted_at":"2017-02-16T15:35:36Z","abstract_excerpt":"We study the fixed point theory of n-valued maps of a space X using the fixed point theory of maps between X and its configuration spaces. We give some general results to decide whether an n-valued map can be deformed to a fixed point free n-valued map. In the case of surfaces, we provide an algebraic criterion in terms of the braid groups of X to study this problem. If X is either the k-dimensional ball or an even-dimensional real or complex projective space, we show that the fixed point property holds for n-valued maps for all n $\\ge$ 1, and we prove the same result for even-dimensional sphe"},"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":"1702.05016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-16T15:35:36Z","cross_cats_sorted":[],"title_canon_sha256":"4a5b8062ddec5e5d2cf18b2f90a2f9b80e59c8cc5e6c62b3ed5489d036ddbf07","abstract_canon_sha256":"741c83af03340695c0b9752c9aaf3bf807bab503cc14a36c2c05a8f21f506595"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:36.444083Z","signature_b64":"LOrAbtaIpyM2xvoSmJK7bks1PiwLrXFKvJDS5/FCuU4udHz9Cm5d0YBWkWHPV5eYI4m6keZVsvaNndzb+078CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b953252dda13126fd5a01fd0a75c2f3ea36b066d08421634cf0fe14de6880048","last_reissued_at":"2026-05-18T00:50:36.443373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:36.443373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fixed points of n-valued maps, the fixed point property and the case of surfaces -- a braid approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Daciberg Lima Gon\\c{c}alves (IME, John Guaschi (NU, LMNO), UNICAEN, USP)","submitted_at":"2017-02-16T15:35:36Z","abstract_excerpt":"We study the fixed point theory of n-valued maps of a space X using the fixed point theory of maps between X and its configuration spaces. We give some general results to decide whether an n-valued map can be deformed to a fixed point free n-valued map. In the case of surfaces, we provide an algebraic criterion in terms of the braid groups of X to study this problem. If X is either the k-dimensional ball or an even-dimensional real or complex projective space, we show that the fixed point property holds for n-valued maps for all n $\\ge$ 1, and we prove the same result for even-dimensional sphe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05016","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":"1702.05016","created_at":"2026-05-18T00:50:36.443500+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.05016v1","created_at":"2026-05-18T00:50:36.443500+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05016","created_at":"2026-05-18T00:50:36.443500+00:00"},{"alias_kind":"pith_short_12","alias_value":"XFJSKLO2CMJG","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"XFJSKLO2CMJG7VNA","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"XFJSKLO2","created_at":"2026-05-18T12:31:53.515858+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/XFJSKLO2CMJG7VNAD7IKOXBPH2","json":"https://pith.science/pith/XFJSKLO2CMJG7VNAD7IKOXBPH2.json","graph_json":"https://pith.science/api/pith-number/XFJSKLO2CMJG7VNAD7IKOXBPH2/graph.json","events_json":"https://pith.science/api/pith-number/XFJSKLO2CMJG7VNAD7IKOXBPH2/events.json","paper":"https://pith.science/paper/XFJSKLO2"},"agent_actions":{"view_html":"https://pith.science/pith/XFJSKLO2CMJG7VNAD7IKOXBPH2","download_json":"https://pith.science/pith/XFJSKLO2CMJG7VNAD7IKOXBPH2.json","view_paper":"https://pith.science/paper/XFJSKLO2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.05016&json=true","fetch_graph":"https://pith.science/api/pith-number/XFJSKLO2CMJG7VNAD7IKOXBPH2/graph.json","fetch_events":"https://pith.science/api/pith-number/XFJSKLO2CMJG7VNAD7IKOXBPH2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XFJSKLO2CMJG7VNAD7IKOXBPH2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XFJSKLO2CMJG7VNAD7IKOXBPH2/action/storage_attestation","attest_author":"https://pith.science/pith/XFJSKLO2CMJG7VNAD7IKOXBPH2/action/author_attestation","sign_citation":"https://pith.science/pith/XFJSKLO2CMJG7VNAD7IKOXBPH2/action/citation_signature","submit_replication":"https://pith.science/pith/XFJSKLO2CMJG7VNAD7IKOXBPH2/action/replication_record"}},"created_at":"2026-05-18T00:50:36.443500+00:00","updated_at":"2026-05-18T00:50:36.443500+00:00"}