{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5DV7VX5DP5MUSSEKDTT6NISQNY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"05224357799803316d8a34744b5f8a7a4a452caee58f0f3a69a985dc0333027c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-04T16:26:21Z","title_canon_sha256":"6e8ebe4163068d45690c4ae71b5b4a1bdc681ec95e36c82c70b2a5bca77faeeb"},"schema_version":"1.0","source":{"id":"1404.1302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1302","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1302v1","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1302","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"5DV7VX5DP5MU","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5DV7VX5DP5MUSSEK","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5DV7VX5D","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:d2398b9867de9e9b24b230932d503bfe57a99bb89da4284f78ce28e42dd5f4c7","target":"graph","created_at":"2026-05-18T02:54:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Pedro A. S. Salom\\~ao, Salvador Addas-Zanata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-04T16:26:21Z","title":"Persistence of fixed points under rigid perturbations of maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1302","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ff2ead96a25dfa8af1c731631cc1be39efead5ccfd59a287b3c2d6ca7c1fd207","target":"record","created_at":"2026-05-18T02:54:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"05224357799803316d8a34744b5f8a7a4a452caee58f0f3a69a985dc0333027c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-04T16:26:21Z","title_canon_sha256":"6e8ebe4163068d45690c4ae71b5b4a1bdc681ec95e36c82c70b2a5bca77faeeb"},"schema_version":"1.0","source":{"id":"1404.1302","kind":"arxiv","version":1}},"canonical_sha256":"e8ebfadfa37f5949488a1ce7e6a2506e1242b329cca2bd44b9c020e86ab4797c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8ebfadfa37f5949488a1ce7e6a2506e1242b329cca2bd44b9c020e86ab4797c","first_computed_at":"2026-05-18T02:54:47.796396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:47.796396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uBh8jMM+coEDccfJKIqXMd/qw+EeBhO/qCgkaK4wFynfY9iVH+88i7X1h/Qr7PfwOb7dpjumQBi4Jos1bWZ3Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:47.796754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff2ead96a25dfa8af1c731631cc1be39efead5ccfd59a287b3c2d6ca7c1fd207","sha256:d2398b9867de9e9b24b230932d503bfe57a99bb89da4284f78ce28e42dd5f4c7"],"state_sha256":"4a6a47828f6ef7f9537717cc31539046b72471d8260c374e2705e0f06cc174c9"}