{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MBPBBTB6YEHRKNXYF5IE2K7PA4","short_pith_number":"pith:MBPBBTB6","schema_version":"1.0","canonical_sha256":"605e10cc3ec10f1536f82f504d2bef0707d5695146d60bbc1774542f67352be1","source":{"kind":"arxiv","id":"1201.1401","version":3},"attestation_state":"computed","paper":{"title":"Rigidity for piecewise smooth homeomorphisms on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daniel Smania, Kleyber Cunha","submitted_at":"2012-01-06T12:21:50Z","abstract_excerpt":"We find conditions for two piecewise C^{2+\\nu} homeomorphisms f and g of the circle to be C^1 conjugate. Besides the restrictions on the combinatorics of the maps (we assume that the maps have bounded combinatorics), and necessary conditions on the one-side derivatives of points where f and g are not differentiable, we also assume zero mean nonlinearity for f and g."},"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":"1201.1401","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-06T12:21:50Z","cross_cats_sorted":[],"title_canon_sha256":"f08392335dab42a0603013ebf239a6a8ba2c288d2bd2e8be20f147296dcef7f6","abstract_canon_sha256":"28a27f9a5aa34b4b4e0de77d0faf97d86e1970dd36779a823312df54a4ab6cf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:54.942931Z","signature_b64":"tYDtGriN6f9uaGRB1KqZ6c3nTW17egpcvS1MLAxI58XLlUuKAB9u727scc6C/45q5LLD8H4phZLIcYlKpD5yDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"605e10cc3ec10f1536f82f504d2bef0707d5695146d60bbc1774542f67352be1","last_reissued_at":"2026-05-18T01:58:54.942133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:54.942133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity for piecewise smooth homeomorphisms on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daniel Smania, Kleyber Cunha","submitted_at":"2012-01-06T12:21:50Z","abstract_excerpt":"We find conditions for two piecewise C^{2+\\nu} homeomorphisms f and g of the circle to be C^1 conjugate. Besides the restrictions on the combinatorics of the maps (we assume that the maps have bounded combinatorics), and necessary conditions on the one-side derivatives of points where f and g are not differentiable, we also assume zero mean nonlinearity for f and g."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1401","kind":"arxiv","version":3},"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":"1201.1401","created_at":"2026-05-18T01:58:54.942252+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.1401v3","created_at":"2026-05-18T01:58:54.942252+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1401","created_at":"2026-05-18T01:58:54.942252+00:00"},{"alias_kind":"pith_short_12","alias_value":"MBPBBTB6YEHR","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MBPBBTB6YEHRKNXY","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MBPBBTB6","created_at":"2026-05-18T12:27:14.488303+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/MBPBBTB6YEHRKNXYF5IE2K7PA4","json":"https://pith.science/pith/MBPBBTB6YEHRKNXYF5IE2K7PA4.json","graph_json":"https://pith.science/api/pith-number/MBPBBTB6YEHRKNXYF5IE2K7PA4/graph.json","events_json":"https://pith.science/api/pith-number/MBPBBTB6YEHRKNXYF5IE2K7PA4/events.json","paper":"https://pith.science/paper/MBPBBTB6"},"agent_actions":{"view_html":"https://pith.science/pith/MBPBBTB6YEHRKNXYF5IE2K7PA4","download_json":"https://pith.science/pith/MBPBBTB6YEHRKNXYF5IE2K7PA4.json","view_paper":"https://pith.science/paper/MBPBBTB6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.1401&json=true","fetch_graph":"https://pith.science/api/pith-number/MBPBBTB6YEHRKNXYF5IE2K7PA4/graph.json","fetch_events":"https://pith.science/api/pith-number/MBPBBTB6YEHRKNXYF5IE2K7PA4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MBPBBTB6YEHRKNXYF5IE2K7PA4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MBPBBTB6YEHRKNXYF5IE2K7PA4/action/storage_attestation","attest_author":"https://pith.science/pith/MBPBBTB6YEHRKNXYF5IE2K7PA4/action/author_attestation","sign_citation":"https://pith.science/pith/MBPBBTB6YEHRKNXYF5IE2K7PA4/action/citation_signature","submit_replication":"https://pith.science/pith/MBPBBTB6YEHRKNXYF5IE2K7PA4/action/replication_record"}},"created_at":"2026-05-18T01:58:54.942252+00:00","updated_at":"2026-05-18T01:58:54.942252+00:00"}