{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:QR62CNZKD5PEN2TYJ3IV5V53UF","short_pith_number":"pith:QR62CNZK","schema_version":"1.0","canonical_sha256":"847da1372a1f5e46ea784ed15ed7bba148c8ec59629c7d240ada02c408d01b2f","source":{"kind":"arxiv","id":"0806.0991","version":1},"attestation_state":"computed","paper":{"title":"Trivial centralizers for codimension-one attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Todd Fisher","submitted_at":"2008-06-05T15:42:09Z","abstract_excerpt":"We show that if $\\Lambda$ is a codimension-one hyperbolic attractor for a $C^r$ diffeomorphism $f$, where $2\\leq r\\leq \\infty$, and $f$ is not Anosov, then there is a neighborhood $\\mathcal{U}$ of $f$ in $\\mathrm{Diff}^r(M)$ and an open and dense set $\\mathcal{V}$ of $\\mathcal{U}$ such that any $g\\in\\mathcal{V}$ has a trivial centralizer on the basin of attraction for $\\Lambda$."},"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":"0806.0991","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-06-05T15:42:09Z","cross_cats_sorted":[],"title_canon_sha256":"09ece26cc7d1ee7597ea9ee0abfd2874a37165c95c8df387ef3f68e9ce2d5972","abstract_canon_sha256":"a50b7ffa7d9a771786014158d8833e497c4c6011cf2e73189fd3a0327e3c9262"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:11.449888Z","signature_b64":"8LIkUbQTtWpgANtd3Ja+STbMPto77TUkJWADoRS9U6uSEvJfJqNlqxv7DhgEa72QX1oapeKVXGU+XT+v2Yh4Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"847da1372a1f5e46ea784ed15ed7bba148c8ec59629c7d240ada02c408d01b2f","last_reissued_at":"2026-05-18T02:58:11.449405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:11.449405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trivial centralizers for codimension-one attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Todd Fisher","submitted_at":"2008-06-05T15:42:09Z","abstract_excerpt":"We show that if $\\Lambda$ is a codimension-one hyperbolic attractor for a $C^r$ diffeomorphism $f$, where $2\\leq r\\leq \\infty$, and $f$ is not Anosov, then there is a neighborhood $\\mathcal{U}$ of $f$ in $\\mathrm{Diff}^r(M)$ and an open and dense set $\\mathcal{V}$ of $\\mathcal{U}$ such that any $g\\in\\mathcal{V}$ has a trivial centralizer on the basin of attraction for $\\Lambda$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.0991","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":"0806.0991","created_at":"2026-05-18T02:58:11.449479+00:00"},{"alias_kind":"arxiv_version","alias_value":"0806.0991v1","created_at":"2026-05-18T02:58:11.449479+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.0991","created_at":"2026-05-18T02:58:11.449479+00:00"},{"alias_kind":"pith_short_12","alias_value":"QR62CNZKD5PE","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"QR62CNZKD5PEN2TY","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"QR62CNZK","created_at":"2026-05-18T12:25:58.018023+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/QR62CNZKD5PEN2TYJ3IV5V53UF","json":"https://pith.science/pith/QR62CNZKD5PEN2TYJ3IV5V53UF.json","graph_json":"https://pith.science/api/pith-number/QR62CNZKD5PEN2TYJ3IV5V53UF/graph.json","events_json":"https://pith.science/api/pith-number/QR62CNZKD5PEN2TYJ3IV5V53UF/events.json","paper":"https://pith.science/paper/QR62CNZK"},"agent_actions":{"view_html":"https://pith.science/pith/QR62CNZKD5PEN2TYJ3IV5V53UF","download_json":"https://pith.science/pith/QR62CNZKD5PEN2TYJ3IV5V53UF.json","view_paper":"https://pith.science/paper/QR62CNZK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0806.0991&json=true","fetch_graph":"https://pith.science/api/pith-number/QR62CNZKD5PEN2TYJ3IV5V53UF/graph.json","fetch_events":"https://pith.science/api/pith-number/QR62CNZKD5PEN2TYJ3IV5V53UF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QR62CNZKD5PEN2TYJ3IV5V53UF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QR62CNZKD5PEN2TYJ3IV5V53UF/action/storage_attestation","attest_author":"https://pith.science/pith/QR62CNZKD5PEN2TYJ3IV5V53UF/action/author_attestation","sign_citation":"https://pith.science/pith/QR62CNZKD5PEN2TYJ3IV5V53UF/action/citation_signature","submit_replication":"https://pith.science/pith/QR62CNZKD5PEN2TYJ3IV5V53UF/action/replication_record"}},"created_at":"2026-05-18T02:58:11.449479+00:00","updated_at":"2026-05-18T02:58:11.449479+00:00"}