{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:RSWXY5K2IFVR5LOKAZS56IEGJQ","short_pith_number":"pith:RSWXY5K2","schema_version":"1.0","canonical_sha256":"8cad7c755a416b1eadca0665df20864c22f393fb6d1a16dac8f0748a43a309f1","source":{"kind":"arxiv","id":"1610.08483","version":1},"attestation_state":"computed","paper":{"title":"Dynamical rigidity of non discrete representations in PSL(2,R)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Maxime Wolff","submitted_at":"2016-10-26T19:43:15Z","abstract_excerpt":"The aim of this note is to advertise on a result, not stated explicitly, but proved, in arXiv:0802.0512. Namely, if $\\Gamma$ is any group, if $\\rho_1$, $\\rho_2$ are representations of $\\Gamma$ in $\\mathrm{PSL}(2,\\mathbb{R})$, one of them being non elementary and non discrete, and if for all $\\gamma\\in\\Gamma$, $\\rho_1(\\gamma)$ and $\\rho_2(\\gamma)$ have the same rotation number, then $\\rho_1$ and $\\rho_2$ are conjugate in $\\mathrm{PSL}(2,\\mathbb{R})$. In particular, if two non discrete, non elementary representations yield semi-conjugate actions on the circle, then they are conjugate in $\\mathrm"},"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":"1610.08483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-26T19:43:15Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5944054128eb20dba50ddab2fbb3661e71080fc19e11bca3d657fe5a3576e91b","abstract_canon_sha256":"f148b301db2b1eef3c3a59729a88e56f2188d828bd18bf1871f367276b71dbbf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:09.313946Z","signature_b64":"sGO0CJNONE/LxriS2fh9qr0veU3uGDfQNqc5AojHXC9/TldKXsOFNzOK4PjUMm74J1daZ1K90SCM5D7fktu9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cad7c755a416b1eadca0665df20864c22f393fb6d1a16dac8f0748a43a309f1","last_reissued_at":"2026-05-18T01:01:09.313309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:09.313309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamical rigidity of non discrete representations in PSL(2,R)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Maxime Wolff","submitted_at":"2016-10-26T19:43:15Z","abstract_excerpt":"The aim of this note is to advertise on a result, not stated explicitly, but proved, in arXiv:0802.0512. Namely, if $\\Gamma$ is any group, if $\\rho_1$, $\\rho_2$ are representations of $\\Gamma$ in $\\mathrm{PSL}(2,\\mathbb{R})$, one of them being non elementary and non discrete, and if for all $\\gamma\\in\\Gamma$, $\\rho_1(\\gamma)$ and $\\rho_2(\\gamma)$ have the same rotation number, then $\\rho_1$ and $\\rho_2$ are conjugate in $\\mathrm{PSL}(2,\\mathbb{R})$. In particular, if two non discrete, non elementary representations yield semi-conjugate actions on the circle, then they are conjugate in $\\mathrm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08483","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":"1610.08483","created_at":"2026-05-18T01:01:09.313414+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.08483v1","created_at":"2026-05-18T01:01:09.313414+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08483","created_at":"2026-05-18T01:01:09.313414+00:00"},{"alias_kind":"pith_short_12","alias_value":"RSWXY5K2IFVR","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"RSWXY5K2IFVR5LOK","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"RSWXY5K2","created_at":"2026-05-18T12:30:41.710351+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/RSWXY5K2IFVR5LOKAZS56IEGJQ","json":"https://pith.science/pith/RSWXY5K2IFVR5LOKAZS56IEGJQ.json","graph_json":"https://pith.science/api/pith-number/RSWXY5K2IFVR5LOKAZS56IEGJQ/graph.json","events_json":"https://pith.science/api/pith-number/RSWXY5K2IFVR5LOKAZS56IEGJQ/events.json","paper":"https://pith.science/paper/RSWXY5K2"},"agent_actions":{"view_html":"https://pith.science/pith/RSWXY5K2IFVR5LOKAZS56IEGJQ","download_json":"https://pith.science/pith/RSWXY5K2IFVR5LOKAZS56IEGJQ.json","view_paper":"https://pith.science/paper/RSWXY5K2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.08483&json=true","fetch_graph":"https://pith.science/api/pith-number/RSWXY5K2IFVR5LOKAZS56IEGJQ/graph.json","fetch_events":"https://pith.science/api/pith-number/RSWXY5K2IFVR5LOKAZS56IEGJQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RSWXY5K2IFVR5LOKAZS56IEGJQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RSWXY5K2IFVR5LOKAZS56IEGJQ/action/storage_attestation","attest_author":"https://pith.science/pith/RSWXY5K2IFVR5LOKAZS56IEGJQ/action/author_attestation","sign_citation":"https://pith.science/pith/RSWXY5K2IFVR5LOKAZS56IEGJQ/action/citation_signature","submit_replication":"https://pith.science/pith/RSWXY5K2IFVR5LOKAZS56IEGJQ/action/replication_record"}},"created_at":"2026-05-18T01:01:09.313414+00:00","updated_at":"2026-05-18T01:01:09.313414+00:00"}