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The action on $S^1 = \\RR \\cup {\\infty}$ generated by these two affine maps $f_0$ and $h_0 $ is called the standard affine one. We prove that any representation of BS(1,n) into $Diff^1(S^1)$ is (up to a finite index subgroup) semiconjugated to the standard affine action."},"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":"1010.4133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-20T08:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"f729079956b818b6efed602d8cb228a08680dfef09be2a03b47a665d94c654de","abstract_canon_sha256":"33e2a81f7d9a900df7cd0230f2c79564362a48f862fa1ffb217a4651c71bf05c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:29.216214Z","signature_b64":"d8DTvwkIzjGHXFliYCugo9VSjNQhTxTD17z+u5yicftNWi4OW/2UGpuUkdthO5qousUhxrGEbr5wdXHDdYmECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"786665c142faa88b843ebc3b63764de75946b7081227f74e524182014ade9dd0","last_reissued_at":"2026-05-18T01:22:29.215737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:29.215737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$C^1$-actions of Baumslag-Solitar groups on $S^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Isabelle Liousse, Nancy Guelman","submitted_at":"2010-10-20T08:49:10Z","abstract_excerpt":"Let $BS(1, n)=< a, b | aba^{-1} = b^n >$ be the solvable Baumslag-Solitar group, where $ n\\geq 2$. It is known that B(1, n) is isomorphic to the group generated by the two affine maps of the line : $f_0(x) = x + 1$ and $h_0(x) = nx $. The action on $S^1 = \\RR \\cup {\\infty}$ generated by these two affine maps $f_0$ and $h_0 $ is called the standard affine one. We prove that any representation of BS(1,n) into $Diff^1(S^1)$ is (up to a finite index subgroup) semiconjugated to the standard affine action."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4133","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":"1010.4133","created_at":"2026-05-18T01:22:29.215807+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.4133v1","created_at":"2026-05-18T01:22:29.215807+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4133","created_at":"2026-05-18T01:22:29.215807+00:00"},{"alias_kind":"pith_short_12","alias_value":"PBTGLQKC7KUI","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"PBTGLQKC7KUIXBB6","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"PBTGLQKC","created_at":"2026-05-18T12:26:12.377268+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/PBTGLQKC7KUIXBB6XQ5WG5SN45","json":"https://pith.science/pith/PBTGLQKC7KUIXBB6XQ5WG5SN45.json","graph_json":"https://pith.science/api/pith-number/PBTGLQKC7KUIXBB6XQ5WG5SN45/graph.json","events_json":"https://pith.science/api/pith-number/PBTGLQKC7KUIXBB6XQ5WG5SN45/events.json","paper":"https://pith.science/paper/PBTGLQKC"},"agent_actions":{"view_html":"https://pith.science/pith/PBTGLQKC7KUIXBB6XQ5WG5SN45","download_json":"https://pith.science/pith/PBTGLQKC7KUIXBB6XQ5WG5SN45.json","view_paper":"https://pith.science/paper/PBTGLQKC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.4133&json=true","fetch_graph":"https://pith.science/api/pith-number/PBTGLQKC7KUIXBB6XQ5WG5SN45/graph.json","fetch_events":"https://pith.science/api/pith-number/PBTGLQKC7KUIXBB6XQ5WG5SN45/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PBTGLQKC7KUIXBB6XQ5WG5SN45/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PBTGLQKC7KUIXBB6XQ5WG5SN45/action/storage_attestation","attest_author":"https://pith.science/pith/PBTGLQKC7KUIXBB6XQ5WG5SN45/action/author_attestation","sign_citation":"https://pith.science/pith/PBTGLQKC7KUIXBB6XQ5WG5SN45/action/citation_signature","submit_replication":"https://pith.science/pith/PBTGLQKC7KUIXBB6XQ5WG5SN45/action/replication_record"}},"created_at":"2026-05-18T01:22:29.215807+00:00","updated_at":"2026-05-18T01:22:29.215807+00:00"}