{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UP3NA4NTYWRXU7HCEVBUYZLDOI","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":"96eeb531abc3ab6f08ffd8f0caa36f2d9cbeb1d1463a869d19c717d0ee74c76d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-29T18:34:10Z","title_canon_sha256":"227985b504d4fd77edbec5bb175046179d28d544292aaef76e404e7e39df0525"},"schema_version":"1.0","source":{"id":"1511.09056","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09056","created_at":"2026-05-18T01:25:41Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09056v1","created_at":"2026-05-18T01:25:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09056","created_at":"2026-05-18T01:25:41Z"},{"alias_kind":"pith_short_12","alias_value":"UP3NA4NTYWRX","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UP3NA4NTYWRXU7HC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UP3NA4NT","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:53810578a5d287462e4c2fea1ecab49d9f7f9d5bb454a238f29c0297313e7c82","target":"graph","created_at":"2026-05-18T01:25:41Z","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":"Let $f, g:S^1\\to S^1$ be two $C^3$ critical homeomorphisms of the circle with the same irrational rotation number and the same (finite) number of critical points, all of which are assumed to be non-flat, of power-law type. In this paper we prove that if $h:S^1\\to S^1$ is a topological conjugacy between $f$ and $g$ and $h$ maps the critical points of $f$ to the critical points of $g$, then $h$ is quasisymmetric. When the power-law exponents at all critical points are integers, this result is a special case of a general theorem recently proved by T.~Clark and S.~van Strien \\cite{CS}. However, un","authors_text":"Edson de Faria, Gabriela Estevez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-29T18:34:10Z","title":"Real bounds and quasisymmetric rigidity of multicritical circle maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09056","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":"sha256:20ad7fcc77e4e516be6f77b135d86959fccc83d5c777a552026152f5697625df","target":"record","created_at":"2026-05-18T01:25:41Z","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":"96eeb531abc3ab6f08ffd8f0caa36f2d9cbeb1d1463a869d19c717d0ee74c76d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-29T18:34:10Z","title_canon_sha256":"227985b504d4fd77edbec5bb175046179d28d544292aaef76e404e7e39df0525"},"schema_version":"1.0","source":{"id":"1511.09056","kind":"arxiv","version":1}},"canonical_sha256":"a3f6d071b3c5a37a7ce225434c656372324cdbecf2efca870d90cb84698ccb66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3f6d071b3c5a37a7ce225434c656372324cdbecf2efca870d90cb84698ccb66","first_computed_at":"2026-05-18T01:25:41.345938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:41.345938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U2gHgFwZ54maIQjaWGo+9qPU7nlo9S4fUNsGD3qwGbEMx2ZV/DnQ9L1LF1Z/qHMAxfPSKZXni63hH7q1MKScAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:41.346684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.09056","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20ad7fcc77e4e516be6f77b135d86959fccc83d5c777a552026152f5697625df","sha256:53810578a5d287462e4c2fea1ecab49d9f7f9d5bb454a238f29c0297313e7c82"],"state_sha256":"1336fcfb054417f2367b7a610d2a24baa9d443b880ed4ba1856af178a3fef334"}