{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XT2YNQ2O54GKAIKSLDJWFASFGW","short_pith_number":"pith:XT2YNQ2O","schema_version":"1.0","canonical_sha256":"bcf586c34eef0ca0215258d36282453590a57c428ab25bf49500c97f5b098530","source":{"kind":"arxiv","id":"1603.02098","version":3},"attestation_state":"computed","paper":{"title":"Exotic mapping class group actions on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Sang-hyun Kim, Thomas Koberda","submitted_at":"2016-03-07T15:04:47Z","abstract_excerpt":"It has been known since the time of Nielsen that the mapping class group $\\text{Mod}_{g,1}$ of a surface of genus $g$ and one puncture acts faithfully by homeomorphisms on the circle. In this note, we show that this standard representation of the mapping class group is not rigid, precisely, if $G<\\text{Mod}_{g,1}$ is a finite index subgroup then there exist infinitely many non--conjugate faithful representations $G\\to \\text{Homeo}^+(S^1)$. We thus answer a question of B. Farb."},"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":"1603.02098","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-07T15:04:47Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ce81f890a0473d207dc006538e2d84e09d2b18e15f97147564161dba0040f399","abstract_canon_sha256":"be445690dc308ecd76c465a4d8053d16e75b1eceb43c36e50de837d1f2eb5a1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:13.078306Z","signature_b64":"mW0gynZ3Yv1+LcRqEKrOmD+YqIQtQiRroMZjWljDNnXvT4SlWlQUH5seI2bbwuXjwQ7Ll8+2VTABt/HbCGttAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcf586c34eef0ca0215258d36282453590a57c428ab25bf49500c97f5b098530","last_reissued_at":"2026-05-18T01:02:13.077696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:13.077696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exotic mapping class group actions on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Sang-hyun Kim, Thomas Koberda","submitted_at":"2016-03-07T15:04:47Z","abstract_excerpt":"It has been known since the time of Nielsen that the mapping class group $\\text{Mod}_{g,1}$ of a surface of genus $g$ and one puncture acts faithfully by homeomorphisms on the circle. In this note, we show that this standard representation of the mapping class group is not rigid, precisely, if $G<\\text{Mod}_{g,1}$ is a finite index subgroup then there exist infinitely many non--conjugate faithful representations $G\\to \\text{Homeo}^+(S^1)$. We thus answer a question of B. Farb."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02098","kind":"arxiv","version":3},"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":"1603.02098","created_at":"2026-05-18T01:02:13.077795+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.02098v3","created_at":"2026-05-18T01:02:13.077795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02098","created_at":"2026-05-18T01:02:13.077795+00:00"},{"alias_kind":"pith_short_12","alias_value":"XT2YNQ2O54GK","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XT2YNQ2O54GKAIKS","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XT2YNQ2O","created_at":"2026-05-18T12:30:51.357362+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/XT2YNQ2O54GKAIKSLDJWFASFGW","json":"https://pith.science/pith/XT2YNQ2O54GKAIKSLDJWFASFGW.json","graph_json":"https://pith.science/api/pith-number/XT2YNQ2O54GKAIKSLDJWFASFGW/graph.json","events_json":"https://pith.science/api/pith-number/XT2YNQ2O54GKAIKSLDJWFASFGW/events.json","paper":"https://pith.science/paper/XT2YNQ2O"},"agent_actions":{"view_html":"https://pith.science/pith/XT2YNQ2O54GKAIKSLDJWFASFGW","download_json":"https://pith.science/pith/XT2YNQ2O54GKAIKSLDJWFASFGW.json","view_paper":"https://pith.science/paper/XT2YNQ2O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.02098&json=true","fetch_graph":"https://pith.science/api/pith-number/XT2YNQ2O54GKAIKSLDJWFASFGW/graph.json","fetch_events":"https://pith.science/api/pith-number/XT2YNQ2O54GKAIKSLDJWFASFGW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XT2YNQ2O54GKAIKSLDJWFASFGW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XT2YNQ2O54GKAIKSLDJWFASFGW/action/storage_attestation","attest_author":"https://pith.science/pith/XT2YNQ2O54GKAIKSLDJWFASFGW/action/author_attestation","sign_citation":"https://pith.science/pith/XT2YNQ2O54GKAIKSLDJWFASFGW/action/citation_signature","submit_replication":"https://pith.science/pith/XT2YNQ2O54GKAIKSLDJWFASFGW/action/replication_record"}},"created_at":"2026-05-18T01:02:13.077795+00:00","updated_at":"2026-05-18T01:02:13.077795+00:00"}