{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WB6IA44UNFJSBH4IRVDDLEIU5N","short_pith_number":"pith:WB6IA44U","schema_version":"1.0","canonical_sha256":"b07c8073946953209f888d46359114eb430f74ea33a7fbf5f675d849c57d179a","source":{"kind":"arxiv","id":"1210.3556","version":1},"attestation_state":"computed","paper":{"title":"Displacement sequence of an orientation preserving circle homeomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Justyna Signerska, Wac{\\l}aw Marzantowicz","submitted_at":"2012-10-12T15:51:40Z","abstract_excerpt":"We give a complete description of the behaviour of the sequence of displacements $\\eta_n(z)=\\Phi^n(x) - \\Phi^{n-1}(x) \\ \\rmod \\ 1$, $z=\\exp(2\\pi \\rmi x)$, along a trajectory $\\{\\varphi^{n}(z)\\}$, where $\\varphi$ is an orientation preserving circle homeomorphism and $\\Phi:\\mathbb{R} \\to \\mathbb{R}$ its lift. If the rotation number $\\varrho(\\varphi)=\\frac{p}{q}$ is rational then $\\eta_n(z)$ is asymptotically periodic with semi-period $q$. This convergence to a periodic sequence is uniform in $z$ if we admit that some points are iterated backward instead of taking only forward iterations for all "},"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":"1210.3556","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-12T15:51:40Z","cross_cats_sorted":[],"title_canon_sha256":"0125d7db6f9abc2b436c2e98c78c32450000d502f381c71c6cc6e1301a644476","abstract_canon_sha256":"c7280d8a032b11f06c3a15fdbdd68430006a7025dc14e0644721bef3a8ad0739"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:19.434027Z","signature_b64":"KwYrvBnsktziDKqb+pbDzBS9H7nldEdo9ye3pvG89xlrAdnnUsUFhYVDuUb20+IMfTbUidgbixSeh6U23j0eDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b07c8073946953209f888d46359114eb430f74ea33a7fbf5f675d849c57d179a","last_reissued_at":"2026-05-18T03:43:19.433326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:19.433326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Displacement sequence of an orientation preserving circle homeomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Justyna Signerska, Wac{\\l}aw Marzantowicz","submitted_at":"2012-10-12T15:51:40Z","abstract_excerpt":"We give a complete description of the behaviour of the sequence of displacements $\\eta_n(z)=\\Phi^n(x) - \\Phi^{n-1}(x) \\ \\rmod \\ 1$, $z=\\exp(2\\pi \\rmi x)$, along a trajectory $\\{\\varphi^{n}(z)\\}$, where $\\varphi$ is an orientation preserving circle homeomorphism and $\\Phi:\\mathbb{R} \\to \\mathbb{R}$ its lift. If the rotation number $\\varrho(\\varphi)=\\frac{p}{q}$ is rational then $\\eta_n(z)$ is asymptotically periodic with semi-period $q$. This convergence to a periodic sequence is uniform in $z$ if we admit that some points are iterated backward instead of taking only forward iterations for all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3556","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":"1210.3556","created_at":"2026-05-18T03:43:19.433436+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.3556v1","created_at":"2026-05-18T03:43:19.433436+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3556","created_at":"2026-05-18T03:43:19.433436+00:00"},{"alias_kind":"pith_short_12","alias_value":"WB6IA44UNFJS","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WB6IA44UNFJSBH4I","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WB6IA44U","created_at":"2026-05-18T12:27:25.539911+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/WB6IA44UNFJSBH4IRVDDLEIU5N","json":"https://pith.science/pith/WB6IA44UNFJSBH4IRVDDLEIU5N.json","graph_json":"https://pith.science/api/pith-number/WB6IA44UNFJSBH4IRVDDLEIU5N/graph.json","events_json":"https://pith.science/api/pith-number/WB6IA44UNFJSBH4IRVDDLEIU5N/events.json","paper":"https://pith.science/paper/WB6IA44U"},"agent_actions":{"view_html":"https://pith.science/pith/WB6IA44UNFJSBH4IRVDDLEIU5N","download_json":"https://pith.science/pith/WB6IA44UNFJSBH4IRVDDLEIU5N.json","view_paper":"https://pith.science/paper/WB6IA44U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.3556&json=true","fetch_graph":"https://pith.science/api/pith-number/WB6IA44UNFJSBH4IRVDDLEIU5N/graph.json","fetch_events":"https://pith.science/api/pith-number/WB6IA44UNFJSBH4IRVDDLEIU5N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WB6IA44UNFJSBH4IRVDDLEIU5N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WB6IA44UNFJSBH4IRVDDLEIU5N/action/storage_attestation","attest_author":"https://pith.science/pith/WB6IA44UNFJSBH4IRVDDLEIU5N/action/author_attestation","sign_citation":"https://pith.science/pith/WB6IA44UNFJSBH4IRVDDLEIU5N/action/citation_signature","submit_replication":"https://pith.science/pith/WB6IA44UNFJSBH4IRVDDLEIU5N/action/replication_record"}},"created_at":"2026-05-18T03:43:19.433436+00:00","updated_at":"2026-05-18T03:43:19.433436+00:00"}