{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:5ZSO4BUQUBQGUTGRJNKA47BZCF","short_pith_number":"pith:5ZSO4BUQ","schema_version":"1.0","canonical_sha256":"ee64ee0690a0606a4cd14b540e7c391148f845ec66f156538aaf6f8b3db02afa","source":{"kind":"arxiv","id":"1903.01795","version":1},"attestation_state":"computed","paper":{"title":"Tips of Tongues in the Double Standard Family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Epstein, Jordi Canela, Kuntal Banerjee, Xavier Buff","submitted_at":"2019-03-05T12:51:27Z","abstract_excerpt":"We answer a question raised by Misiurewicz and Rodrigues concerning the family of degree 2 circle maps $F_\\lambda:\\mathbb{R}/\\mathbb{Z}\\to \\mathbb{R}/\\mathbb{Z}$ defined by \\[F_\\lambda(x) := 2x + a+ \\frac{b}{\\pi} \\sin(2\\pi x){\\quad\\text{with}\\quad} \\lambda:=(a,b)\\in \\mathbb{R}/\\mathbb{Z}\\times (0,1).\\] We prove that if $F_\\lambda^{\\circ n}-{\\rm id}$ has a zero of multiplicity $3$ in $\\mathbb{R}/\\mathbb{Z}$, then there is a system of local coordinates $(\\alpha,\\beta):W\\to \\mathbb{R}^2$ defined in a neighborhood $W$ of $\\lambda$, such that $\\alpha(\\lambda) =\\beta(\\lambda)=0$ and $F_\\mu^{\\circ n}"},"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":"1903.01795","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-05T12:51:27Z","cross_cats_sorted":[],"title_canon_sha256":"a752a8b4e959c58dc86b9b90012220f6a312e2c4af33a33d6d3731994726b9db","abstract_canon_sha256":"23274cfbd64d7765a1c1871ac1c5861d9ed22e9d58d3d681e9d4bfc63c2ee995"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:59.739621Z","signature_b64":"hJAy+GTcR3ayPJnThSBFA9dj+hxMA8naBQZGW6Rp3ZQh7LFWM4pbT/z6XGo0vf3Wbz2CfLGNyMVbQmgW00PMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee64ee0690a0606a4cd14b540e7c391148f845ec66f156538aaf6f8b3db02afa","last_reissued_at":"2026-05-17T23:51:59.739240Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:59.739240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tips of Tongues in the Double Standard Family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Epstein, Jordi Canela, Kuntal Banerjee, Xavier Buff","submitted_at":"2019-03-05T12:51:27Z","abstract_excerpt":"We answer a question raised by Misiurewicz and Rodrigues concerning the family of degree 2 circle maps $F_\\lambda:\\mathbb{R}/\\mathbb{Z}\\to \\mathbb{R}/\\mathbb{Z}$ defined by \\[F_\\lambda(x) := 2x + a+ \\frac{b}{\\pi} \\sin(2\\pi x){\\quad\\text{with}\\quad} \\lambda:=(a,b)\\in \\mathbb{R}/\\mathbb{Z}\\times (0,1).\\] We prove that if $F_\\lambda^{\\circ n}-{\\rm id}$ has a zero of multiplicity $3$ in $\\mathbb{R}/\\mathbb{Z}$, then there is a system of local coordinates $(\\alpha,\\beta):W\\to \\mathbb{R}^2$ defined in a neighborhood $W$ of $\\lambda$, such that $\\alpha(\\lambda) =\\beta(\\lambda)=0$ and $F_\\mu^{\\circ n}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01795","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":"1903.01795","created_at":"2026-05-17T23:51:59.739298+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.01795v1","created_at":"2026-05-17T23:51:59.739298+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01795","created_at":"2026-05-17T23:51:59.739298+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ZSO4BUQUBQG","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ZSO4BUQUBQGUTGR","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ZSO4BUQ","created_at":"2026-05-18T12:33:10.108867+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/5ZSO4BUQUBQGUTGRJNKA47BZCF","json":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF.json","graph_json":"https://pith.science/api/pith-number/5ZSO4BUQUBQGUTGRJNKA47BZCF/graph.json","events_json":"https://pith.science/api/pith-number/5ZSO4BUQUBQGUTGRJNKA47BZCF/events.json","paper":"https://pith.science/paper/5ZSO4BUQ"},"agent_actions":{"view_html":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF","download_json":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF.json","view_paper":"https://pith.science/paper/5ZSO4BUQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.01795&json=true","fetch_graph":"https://pith.science/api/pith-number/5ZSO4BUQUBQGUTGRJNKA47BZCF/graph.json","fetch_events":"https://pith.science/api/pith-number/5ZSO4BUQUBQGUTGRJNKA47BZCF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/action/storage_attestation","attest_author":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/action/author_attestation","sign_citation":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/action/citation_signature","submit_replication":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/action/replication_record"}},"created_at":"2026-05-17T23:51:59.739298+00:00","updated_at":"2026-05-17T23:51:59.739298+00:00"}