{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NTZZSB324BAP5MYAG4554QORTN","short_pith_number":"pith:NTZZSB32","schema_version":"1.0","canonical_sha256":"6cf399077ae040feb300373bde41d19b7ad4f86bc11b5d5060707e8c4e0c91ae","source":{"kind":"arxiv","id":"1512.03327","version":1},"attestation_state":"computed","paper":{"title":"Nonrigidity for circle homeomorphisms with several break points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Abdelhamid Adouani, Habib Marzougui","submitted_at":"2015-12-10T17:09:08Z","abstract_excerpt":"Let $f$ and $g$ be two class $P$-homeomorphisms of the circle $S^{1}$ with break points singularities. Assume that the derivatives $\\textrm{Df}$ and $\\textrm{Dg}$ are absolutely continuous on every continuity interval of $\\textrm{Df}$ and $\\textrm{Dg}$ respectively. Denote by $C(f)$ the set of break points of $f$. For $c\\in S^{1}$, denote by $\\pi_{s, O_{f}(c)}(f)$ the product of $f-$ jumps in break points lying to the $f-$ orbit of $c$ and by $\\textrm{SO}(f) = \\{O_{f}(c):~c \\in C(f)~\\textrm{and}~\\pi_{s, O_{f}(c)}(f)\\neq 1\\}$, called the set of singular $f$-orbits. The maps $f$ and $g$ are call"},"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":"1512.03327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-10T17:09:08Z","cross_cats_sorted":[],"title_canon_sha256":"3cf23ec73da5cabaef84830d7d0201c1f69471afdf99b90b13ca2150b31a5cb3","abstract_canon_sha256":"2c5f0213e88345664c9f31f6a056d30c6c93d6efe60f1d41341f3729a1011db1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:30.501234Z","signature_b64":"HLnYPkDZs0kpA6l4MAXNvamwPfb7Nwfdc9wjjra7kdQ9qG3i+9xqcuo5F01vmv32zDxIlVO5MvXmLbN7y0rOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cf399077ae040feb300373bde41d19b7ad4f86bc11b5d5060707e8c4e0c91ae","last_reissued_at":"2026-05-17T23:56:30.500727Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:30.500727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonrigidity for circle homeomorphisms with several break points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Abdelhamid Adouani, Habib Marzougui","submitted_at":"2015-12-10T17:09:08Z","abstract_excerpt":"Let $f$ and $g$ be two class $P$-homeomorphisms of the circle $S^{1}$ with break points singularities. Assume that the derivatives $\\textrm{Df}$ and $\\textrm{Dg}$ are absolutely continuous on every continuity interval of $\\textrm{Df}$ and $\\textrm{Dg}$ respectively. Denote by $C(f)$ the set of break points of $f$. For $c\\in S^{1}$, denote by $\\pi_{s, O_{f}(c)}(f)$ the product of $f-$ jumps in break points lying to the $f-$ orbit of $c$ and by $\\textrm{SO}(f) = \\{O_{f}(c):~c \\in C(f)~\\textrm{and}~\\pi_{s, O_{f}(c)}(f)\\neq 1\\}$, called the set of singular $f$-orbits. The maps $f$ and $g$ are call"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03327","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":"1512.03327","created_at":"2026-05-17T23:56:30.500803+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.03327v1","created_at":"2026-05-17T23:56:30.500803+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03327","created_at":"2026-05-17T23:56:30.500803+00:00"},{"alias_kind":"pith_short_12","alias_value":"NTZZSB324BAP","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NTZZSB324BAP5MYA","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NTZZSB32","created_at":"2026-05-18T12:29:34.919912+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/NTZZSB324BAP5MYAG4554QORTN","json":"https://pith.science/pith/NTZZSB324BAP5MYAG4554QORTN.json","graph_json":"https://pith.science/api/pith-number/NTZZSB324BAP5MYAG4554QORTN/graph.json","events_json":"https://pith.science/api/pith-number/NTZZSB324BAP5MYAG4554QORTN/events.json","paper":"https://pith.science/paper/NTZZSB32"},"agent_actions":{"view_html":"https://pith.science/pith/NTZZSB324BAP5MYAG4554QORTN","download_json":"https://pith.science/pith/NTZZSB324BAP5MYAG4554QORTN.json","view_paper":"https://pith.science/paper/NTZZSB32","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.03327&json=true","fetch_graph":"https://pith.science/api/pith-number/NTZZSB324BAP5MYAG4554QORTN/graph.json","fetch_events":"https://pith.science/api/pith-number/NTZZSB324BAP5MYAG4554QORTN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NTZZSB324BAP5MYAG4554QORTN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NTZZSB324BAP5MYAG4554QORTN/action/storage_attestation","attest_author":"https://pith.science/pith/NTZZSB324BAP5MYAG4554QORTN/action/author_attestation","sign_citation":"https://pith.science/pith/NTZZSB324BAP5MYAG4554QORTN/action/citation_signature","submit_replication":"https://pith.science/pith/NTZZSB324BAP5MYAG4554QORTN/action/replication_record"}},"created_at":"2026-05-17T23:56:30.500803+00:00","updated_at":"2026-05-17T23:56:30.500803+00:00"}