{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:5ZSO4BUQUBQGUTGRJNKA47BZCF","short_pith_number":"pith:5ZSO4BUQ","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"},"canonical_sha256":"ee64ee0690a0606a4cd14b540e7c391148f845ec66f156538aaf6f8b3db02afa","source":{"kind":"arxiv","id":"1903.01795","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01795","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01795v1","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01795","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"5ZSO4BUQUBQG","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5ZSO4BUQUBQGUTGR","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5ZSO4BUQ","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:5ZSO4BUQUBQGUTGRJNKA47BZCF","target":"record","payload":{"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"},"canonical_sha256":"ee64ee0690a0606a4cd14b540e7c391148f845ec66f156538aaf6f8b3db02afa","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"},"source_kind":"arxiv","source_id":"1903.01795","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nCJYabG6Re/s8fJikeEmzQ0Go77OfLnkwjd+tJk+Q28dXakrsJPLmw8iK98chZl5A3xOTITpArou/rdlL5xXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:47:48.673165Z"},"content_sha256":"c5ac6120ebc6773674aff0577c36f39a0b059ac15a5bd4cb09c32312ac5760f7","schema_version":"1.0","event_id":"sha256:c5ac6120ebc6773674aff0577c36f39a0b059ac15a5bd4cb09c32312ac5760f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:5ZSO4BUQUBQGUTGRJNKA47BZCF","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VNS/Zbp5xRLsU1SL/XRrrRu1c8wUSMJJC2/jkr4Jo5QziT/i4pHTDUxo4C71uG50p3DVO8Cba0ICJvd/CEmmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:47:48.673533Z"},"content_sha256":"dc949b22d3ec07c4e1a5969aa5d6198b83d0481cbe40fd7ef179a210daeff517","schema_version":"1.0","event_id":"sha256:dc949b22d3ec07c4e1a5969aa5d6198b83d0481cbe40fd7ef179a210daeff517"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/bundle.json","state_url":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T06:47:48Z","links":{"resolver":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF","bundle":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/bundle.json","state":"https://pith.science/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ZSO4BUQUBQGUTGRJNKA47BZCF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5ZSO4BUQUBQGUTGRJNKA47BZCF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"23274cfbd64d7765a1c1871ac1c5861d9ed22e9d58d3d681e9d4bfc63c2ee995","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-05T12:51:27Z","title_canon_sha256":"a752a8b4e959c58dc86b9b90012220f6a312e2c4af33a33d6d3731994726b9db"},"schema_version":"1.0","source":{"id":"1903.01795","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01795","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01795v1","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01795","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"5ZSO4BUQUBQG","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5ZSO4BUQUBQGUTGR","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5ZSO4BUQ","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:dc949b22d3ec07c4e1a5969aa5d6198b83d0481cbe40fd7ef179a210daeff517","target":"graph","created_at":"2026-05-17T23:51:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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}","authors_text":"Adam Epstein, Jordi Canela, Kuntal Banerjee, Xavier Buff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-05T12:51:27Z","title":"Tips of Tongues in the Double Standard Family"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01795","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c5ac6120ebc6773674aff0577c36f39a0b059ac15a5bd4cb09c32312ac5760f7","target":"record","created_at":"2026-05-17T23:51:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"23274cfbd64d7765a1c1871ac1c5861d9ed22e9d58d3d681e9d4bfc63c2ee995","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-05T12:51:27Z","title_canon_sha256":"a752a8b4e959c58dc86b9b90012220f6a312e2c4af33a33d6d3731994726b9db"},"schema_version":"1.0","source":{"id":"1903.01795","kind":"arxiv","version":1}},"canonical_sha256":"ee64ee0690a0606a4cd14b540e7c391148f845ec66f156538aaf6f8b3db02afa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee64ee0690a0606a4cd14b540e7c391148f845ec66f156538aaf6f8b3db02afa","first_computed_at":"2026-05-17T23:51:59.739240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:59.739240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hJAy+GTcR3ayPJnThSBFA9dj+hxMA8naBQZGW6Rp3ZQh7LFWM4pbT/z6XGo0vf3Wbz2CfLGNyMVbQmgW00PMDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:59.739621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.01795","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5ac6120ebc6773674aff0577c36f39a0b059ac15a5bd4cb09c32312ac5760f7","sha256:dc949b22d3ec07c4e1a5969aa5d6198b83d0481cbe40fd7ef179a210daeff517"],"state_sha256":"3b37aa615df26531217dc008da5c6563e4abed50d97fa5b4d090f2faf7ed9208"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kkonamoms1PmnGNvlOclz69cN3WFHPEn/ffBnTvt9FDee+6qiepRV4jsLbuFQTuy1UEp78mH3ZUovWFu+IWlCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:47:48.675527Z","bundle_sha256":"9810857dad97391dbabfaf8489c07a0da3dc4c7c900c63f3cd97131ce01c60ba"}}