{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5DV7VX5DP5MUSSEKDTT6NISQNY","short_pith_number":"pith:5DV7VX5D","schema_version":"1.0","canonical_sha256":"e8ebfadfa37f5949488a1ce7e6a2506e1242b329cca2bd44b9c020e86ab4797c","source":{"kind":"arxiv","id":"1404.1302","version":1},"attestation_state":"computed","paper":{"title":"Persistence of fixed points under rigid perturbations of maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pedro A. S. Salom\\~ao, Salvador Addas-Zanata","submitted_at":"2014-04-04T16:26:21Z","abstract_excerpt":"Let $f:S^1\\times [0,1]\\to S^1\\times [0,1]$ be a real-analytic annulus diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift $\\tilde {f}:\\mathbb{R}\\times [0,1]\\rightarrow \\mathbb{R}\\times [0,1]$ we have ${\\rm Fix}(\\tilde{f})=\\mathbb{R}\\times \\{0\\}$ and that $\\tilde{f}$ positively translates points in $\\mathbb{R}\\times \\{1\\}$. Let $\\tilde{f}_\\epsilon $ be the perturbation of $\\tilde{f}$ by the rigid horizontal translation $(x,y)\\mapsto (x+\\epsilon,y)$. We show that for all $\\epsilon >0$ sufficiently small we have ${\\rm Fix} (\\tilde{f}_\\epsilo"},"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":"1404.1302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-04T16:26:21Z","cross_cats_sorted":[],"title_canon_sha256":"6e8ebe4163068d45690c4ae71b5b4a1bdc681ec95e36c82c70b2a5bca77faeeb","abstract_canon_sha256":"05224357799803316d8a34744b5f8a7a4a452caee58f0f3a69a985dc0333027c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:47.796754Z","signature_b64":"uBh8jMM+coEDccfJKIqXMd/qw+EeBhO/qCgkaK4wFynfY9iVH+88i7X1h/Qr7PfwOb7dpjumQBi4Jos1bWZ3Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8ebfadfa37f5949488a1ce7e6a2506e1242b329cca2bd44b9c020e86ab4797c","last_reissued_at":"2026-05-18T02:54:47.796396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:47.796396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Persistence of fixed points under rigid perturbations of maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pedro A. S. Salom\\~ao, Salvador Addas-Zanata","submitted_at":"2014-04-04T16:26:21Z","abstract_excerpt":"Let $f:S^1\\times [0,1]\\to S^1\\times [0,1]$ be a real-analytic annulus diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift $\\tilde {f}:\\mathbb{R}\\times [0,1]\\rightarrow \\mathbb{R}\\times [0,1]$ we have ${\\rm Fix}(\\tilde{f})=\\mathbb{R}\\times \\{0\\}$ and that $\\tilde{f}$ positively translates points in $\\mathbb{R}\\times \\{1\\}$. Let $\\tilde{f}_\\epsilon $ be the perturbation of $\\tilde{f}$ by the rigid horizontal translation $(x,y)\\mapsto (x+\\epsilon,y)$. We show that for all $\\epsilon >0$ sufficiently small we have ${\\rm Fix} (\\tilde{f}_\\epsilo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1302","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":"1404.1302","created_at":"2026-05-18T02:54:47.796453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.1302v1","created_at":"2026-05-18T02:54:47.796453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1302","created_at":"2026-05-18T02:54:47.796453+00:00"},{"alias_kind":"pith_short_12","alias_value":"5DV7VX5DP5MU","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5DV7VX5DP5MUSSEK","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5DV7VX5D","created_at":"2026-05-18T12:28:14.216126+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/5DV7VX5DP5MUSSEKDTT6NISQNY","json":"https://pith.science/pith/5DV7VX5DP5MUSSEKDTT6NISQNY.json","graph_json":"https://pith.science/api/pith-number/5DV7VX5DP5MUSSEKDTT6NISQNY/graph.json","events_json":"https://pith.science/api/pith-number/5DV7VX5DP5MUSSEKDTT6NISQNY/events.json","paper":"https://pith.science/paper/5DV7VX5D"},"agent_actions":{"view_html":"https://pith.science/pith/5DV7VX5DP5MUSSEKDTT6NISQNY","download_json":"https://pith.science/pith/5DV7VX5DP5MUSSEKDTT6NISQNY.json","view_paper":"https://pith.science/paper/5DV7VX5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.1302&json=true","fetch_graph":"https://pith.science/api/pith-number/5DV7VX5DP5MUSSEKDTT6NISQNY/graph.json","fetch_events":"https://pith.science/api/pith-number/5DV7VX5DP5MUSSEKDTT6NISQNY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5DV7VX5DP5MUSSEKDTT6NISQNY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5DV7VX5DP5MUSSEKDTT6NISQNY/action/storage_attestation","attest_author":"https://pith.science/pith/5DV7VX5DP5MUSSEKDTT6NISQNY/action/author_attestation","sign_citation":"https://pith.science/pith/5DV7VX5DP5MUSSEKDTT6NISQNY/action/citation_signature","submit_replication":"https://pith.science/pith/5DV7VX5DP5MUSSEKDTT6NISQNY/action/replication_record"}},"created_at":"2026-05-18T02:54:47.796453+00:00","updated_at":"2026-05-18T02:54:47.796453+00:00"}