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Denote by $\\sigma_{f_{i}}, i=1,2,$ the total jump ratio given by the product over all break points $b$ of the jump ratios $\\sigma_{f_{i}}(b)$ of $f_{i}$.\n  We prove, that for circle homeomorphisms $f_{i}, i=1,2$, which ar"},"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":"1408.5732","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-25T12:27:00Z","cross_cats_sorted":[],"title_canon_sha256":"0201cb6d5d8bb71c05021ab75d30864840c3a7c95e04dc375e4d79ac4fd8942a","abstract_canon_sha256":"b97f8a3769cb842d048a10bffec762cdf30a1fd525bf67136fa7a6e508c3536c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:16.069345Z","signature_b64":"xDziEZN5CwvZVc44fq5Mxyy/yW+COS/wftkt/bbt9aYzvXUbsyeTZekWcN6vZAm/sUEfvi/sXWMxW7GZToVpBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc0dc48ac31e9bbcc78e26c38e00dabba9d6b2aa66584ae2b9583ed1b249d608","last_reissued_at":"2026-05-18T01:37:16.068551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:16.068551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conjugacies between P-homeomorphisms with several breaks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Akhtam Dzhalilov, Dieter Mayer, Utkir Safarov","submitted_at":"2014-08-25T12:27:00Z","abstract_excerpt":"Let $f_{i},i=1,2$ be orientation preserving circle homeomorphisms with a finite number of break points, at which the first derivatives $Df_{i}$ have jumps, and with identical irrational rotation number $\\rho=\\rho_{f_{1}}=\\rho_{f_{2}}.$ The jump ratio of $f_{i}$ at the break point $b$ is denoted by $\\sigma_{f_{i}}(b)$, i.e. $\\sigma_{f_{i}}(b):=\\frac{Df_{i}(b-0)}{Df_{i}(b+0)}$. Denote by $\\sigma_{f_{i}}, i=1,2,$ the total jump ratio given by the product over all break points $b$ of the jump ratios $\\sigma_{f_{i}}(b)$ of $f_{i}$.\n  We prove, that for circle homeomorphisms $f_{i}, i=1,2$, which ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5732","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":"1408.5732","created_at":"2026-05-18T01:37:16.068700+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.5732v1","created_at":"2026-05-18T01:37:16.068700+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5732","created_at":"2026-05-18T01:37:16.068700+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZQG4JCWDD2N3","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZQG4JCWDD2N3ZR4O","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZQG4JCWD","created_at":"2026-05-18T12:28:59.999130+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/ZQG4JCWDD2N3ZR4OE3BY4AG2XO","json":"https://pith.science/pith/ZQG4JCWDD2N3ZR4OE3BY4AG2XO.json","graph_json":"https://pith.science/api/pith-number/ZQG4JCWDD2N3ZR4OE3BY4AG2XO/graph.json","events_json":"https://pith.science/api/pith-number/ZQG4JCWDD2N3ZR4OE3BY4AG2XO/events.json","paper":"https://pith.science/paper/ZQG4JCWD"},"agent_actions":{"view_html":"https://pith.science/pith/ZQG4JCWDD2N3ZR4OE3BY4AG2XO","download_json":"https://pith.science/pith/ZQG4JCWDD2N3ZR4OE3BY4AG2XO.json","view_paper":"https://pith.science/paper/ZQG4JCWD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.5732&json=true","fetch_graph":"https://pith.science/api/pith-number/ZQG4JCWDD2N3ZR4OE3BY4AG2XO/graph.json","fetch_events":"https://pith.science/api/pith-number/ZQG4JCWDD2N3ZR4OE3BY4AG2XO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZQG4JCWDD2N3ZR4OE3BY4AG2XO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZQG4JCWDD2N3ZR4OE3BY4AG2XO/action/storage_attestation","attest_author":"https://pith.science/pith/ZQG4JCWDD2N3ZR4OE3BY4AG2XO/action/author_attestation","sign_citation":"https://pith.science/pith/ZQG4JCWDD2N3ZR4OE3BY4AG2XO/action/citation_signature","submit_replication":"https://pith.science/pith/ZQG4JCWDD2N3ZR4OE3BY4AG2XO/action/replication_record"}},"created_at":"2026-05-18T01:37:16.068700+00:00","updated_at":"2026-05-18T01:37:16.068700+00:00"}