{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XT2YNQ2O54GKAIKSLDJWFASFGW","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":"be445690dc308ecd76c465a4d8053d16e75b1eceb43c36e50de837d1f2eb5a1b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-07T15:04:47Z","title_canon_sha256":"ce81f890a0473d207dc006538e2d84e09d2b18e15f97147564161dba0040f399"},"schema_version":"1.0","source":{"id":"1603.02098","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02098","created_at":"2026-05-18T01:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02098v3","created_at":"2026-05-18T01:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02098","created_at":"2026-05-18T01:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"XT2YNQ2O54GK","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XT2YNQ2O54GKAIKS","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XT2YNQ2O","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:c25a1f72fc8d98965e06246ec776675be86e29141e446bf6aeda0cecbf4a815f","target":"graph","created_at":"2026-05-18T01:02:13Z","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":"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.","authors_text":"Sang-hyun Kim, Thomas Koberda","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-07T15:04:47Z","title":"Exotic mapping class group actions on the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02098","kind":"arxiv","version":3},"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":"sha256:7a7277baa39e94f810b8e7784a27f330eca22ab366a53f7d03b73710a733e19b","target":"record","created_at":"2026-05-18T01:02:13Z","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":"be445690dc308ecd76c465a4d8053d16e75b1eceb43c36e50de837d1f2eb5a1b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-07T15:04:47Z","title_canon_sha256":"ce81f890a0473d207dc006538e2d84e09d2b18e15f97147564161dba0040f399"},"schema_version":"1.0","source":{"id":"1603.02098","kind":"arxiv","version":3}},"canonical_sha256":"bcf586c34eef0ca0215258d36282453590a57c428ab25bf49500c97f5b098530","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcf586c34eef0ca0215258d36282453590a57c428ab25bf49500c97f5b098530","first_computed_at":"2026-05-18T01:02:13.077696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:13.077696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mW0gynZ3Yv1+LcRqEKrOmD+YqIQtQiRroMZjWljDNnXvT4SlWlQUH5seI2bbwuXjwQ7Ll8+2VTABt/HbCGttAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:13.078306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02098","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a7277baa39e94f810b8e7784a27f330eca22ab366a53f7d03b73710a733e19b","sha256:c25a1f72fc8d98965e06246ec776675be86e29141e446bf6aeda0cecbf4a815f"],"state_sha256":"39b1aa55d79f5e62bb56869a9a037ef8018f5696416ee9b27890c83a9245f801"}