{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:32BSZFRFWMIJSZRCGAGFEHNU45","short_pith_number":"pith:32BSZFRF","schema_version":"1.0","canonical_sha256":"de832c9625b310996622300c521db4e748462f0f6ef02318dffe58f02a8e3ae3","source":{"kind":"arxiv","id":"0805.1069","version":2},"attestation_state":"computed","paper":{"title":"Fixed points in non-invariant plane continua","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"AL, Alexander Blokh, Birmingham, Lex Oversteegen (UAB, USA)","submitted_at":"2008-05-08T15:56:06Z","abstract_excerpt":"If $f:[a,b]\\to \\mathbb{R}$, with $a<b$, is continuous and such that $a$ and $b$ are mapped in opposite directions by $f$, then $f$ has a fixed point in $I$. Suppose that $f:\\mathbb{C}\\to\\mathbb{C}$ is map and $X$ is a continuum. We extend the above for certain continuous maps of dendrites $X\\to D, X\\subset D$ and for positively oriented maps $f:X\\to \\mathbb{C}, X\\subset \\mathbb{C}$ with the continuum $X$ not necessarily invariant. Then we show that in certain cases a holomorphic map $f:\\mathbb{C}\\to\\mathbb{C}$ must have a fixed point $a$ in a continuum $X$ so that either $a\\in \\mathrm{Int}(X)$"},"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":"0805.1069","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2008-05-08T15:56:06Z","cross_cats_sorted":[],"title_canon_sha256":"4e6d0fde85fe5600f7c1d2f7506c73f69b1db78c935d0d9909905670874d126a","abstract_canon_sha256":"8292cce2e6234aa6816bc64dace73e9501401761fb6198856fb83a1b37307677"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:10.811439Z","signature_b64":"cu2MEFHFBJlrlFifRpP1XqWLbqCF1Gfl8UZnMxQKKkdAHLRRBh61kqfkJ/DzP3JyA8E3Su8nqYm7BlcUl50KCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de832c9625b310996622300c521db4e748462f0f6ef02318dffe58f02a8e3ae3","last_reissued_at":"2026-05-18T01:22:10.810878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:10.810878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fixed points in non-invariant plane continua","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"AL, Alexander Blokh, Birmingham, Lex Oversteegen (UAB, USA)","submitted_at":"2008-05-08T15:56:06Z","abstract_excerpt":"If $f:[a,b]\\to \\mathbb{R}$, with $a<b$, is continuous and such that $a$ and $b$ are mapped in opposite directions by $f$, then $f$ has a fixed point in $I$. Suppose that $f:\\mathbb{C}\\to\\mathbb{C}$ is map and $X$ is a continuum. We extend the above for certain continuous maps of dendrites $X\\to D, X\\subset D$ and for positively oriented maps $f:X\\to \\mathbb{C}, X\\subset \\mathbb{C}$ with the continuum $X$ not necessarily invariant. Then we show that in certain cases a holomorphic map $f:\\mathbb{C}\\to\\mathbb{C}$ must have a fixed point $a$ in a continuum $X$ so that either $a\\in \\mathrm{Int}(X)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1069","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":"0805.1069","created_at":"2026-05-18T01:22:10.810954+00:00"},{"alias_kind":"arxiv_version","alias_value":"0805.1069v2","created_at":"2026-05-18T01:22:10.810954+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.1069","created_at":"2026-05-18T01:22:10.810954+00:00"},{"alias_kind":"pith_short_12","alias_value":"32BSZFRFWMIJ","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"32BSZFRFWMIJSZRC","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"32BSZFRF","created_at":"2026-05-18T12:25:56.245647+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/32BSZFRFWMIJSZRCGAGFEHNU45","json":"https://pith.science/pith/32BSZFRFWMIJSZRCGAGFEHNU45.json","graph_json":"https://pith.science/api/pith-number/32BSZFRFWMIJSZRCGAGFEHNU45/graph.json","events_json":"https://pith.science/api/pith-number/32BSZFRFWMIJSZRCGAGFEHNU45/events.json","paper":"https://pith.science/paper/32BSZFRF"},"agent_actions":{"view_html":"https://pith.science/pith/32BSZFRFWMIJSZRCGAGFEHNU45","download_json":"https://pith.science/pith/32BSZFRFWMIJSZRCGAGFEHNU45.json","view_paper":"https://pith.science/paper/32BSZFRF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0805.1069&json=true","fetch_graph":"https://pith.science/api/pith-number/32BSZFRFWMIJSZRCGAGFEHNU45/graph.json","fetch_events":"https://pith.science/api/pith-number/32BSZFRFWMIJSZRCGAGFEHNU45/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/32BSZFRFWMIJSZRCGAGFEHNU45/action/timestamp_anchor","attest_storage":"https://pith.science/pith/32BSZFRFWMIJSZRCGAGFEHNU45/action/storage_attestation","attest_author":"https://pith.science/pith/32BSZFRFWMIJSZRCGAGFEHNU45/action/author_attestation","sign_citation":"https://pith.science/pith/32BSZFRFWMIJSZRCGAGFEHNU45/action/citation_signature","submit_replication":"https://pith.science/pith/32BSZFRFWMIJSZRCGAGFEHNU45/action/replication_record"}},"created_at":"2026-05-18T01:22:10.810954+00:00","updated_at":"2026-05-18T01:22:10.810954+00:00"}