{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:REWZYSQEABHGVFNK2LHTBQWQEA","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":"6d7177eaf54017ef752fb1112b96be96e362e2fe8fec73699308a778e19c586a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-07T02:44:34Z","title_canon_sha256":"7c962faa20befaa2de12212408cd44e4ba257f682da5a24863ca21b97b7771de"},"schema_version":"1.0","source":{"id":"1405.1492","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1492","created_at":"2026-05-18T01:43:16Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1492v1","created_at":"2026-05-18T01:43:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1492","created_at":"2026-05-18T01:43:16Z"},{"alias_kind":"pith_short_12","alias_value":"REWZYSQEABHG","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"REWZYSQEABHGVFNK","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"REWZYSQE","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:f6006b8a95d6f489139d132b49849d60c4e7f284aab152cd3126b8133bd25891","target":"graph","created_at":"2026-05-18T01:43:16Z","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":"On the torus of dimension $2$, $3$, or $4$, we show that the subset of diffeomorphisms with trivial centralizer in the $C^1$ topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to obtain trivial centralizer for an open neighbourhood of Anosov diffeomorphisms arbitrarily near certain irreducible hyperbolic toral automorphism.","authors_text":"Lennard Bakker, Todd Fisher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-07T02:44:34Z","title":"Open sets of diffeomorphisms with trivial centralizer in the $C^1$ topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1492","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:b5a2fa86ca29b96a63d0b3c340d62d51f786ee8815fddefe56e657c437b27799","target":"record","created_at":"2026-05-18T01:43:16Z","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":"6d7177eaf54017ef752fb1112b96be96e362e2fe8fec73699308a778e19c586a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-07T02:44:34Z","title_canon_sha256":"7c962faa20befaa2de12212408cd44e4ba257f682da5a24863ca21b97b7771de"},"schema_version":"1.0","source":{"id":"1405.1492","kind":"arxiv","version":1}},"canonical_sha256":"892d9c4a04004e6a95aad2cf30c2d02005cbf2c10dca2e5350d4e9ec14da4bb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"892d9c4a04004e6a95aad2cf30c2d02005cbf2c10dca2e5350d4e9ec14da4bb5","first_computed_at":"2026-05-18T01:43:16.872452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:16.872452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xxX0bJEb7JAelTz27r7YIH6EyW8hkxnjjSRrmMbxkU4W9aLnFLb6O3fUN9QkFff0Xx1vOyuRdJ3HnCW/j5HrCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:16.873097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.1492","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5a2fa86ca29b96a63d0b3c340d62d51f786ee8815fddefe56e657c437b27799","sha256:f6006b8a95d6f489139d132b49849d60c4e7f284aab152cd3126b8133bd25891"],"state_sha256":"24019d8bc4927fa724500a7807817d78e62405051780f3c6c305b8031bd9b717"}