{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:CEE4HH7COK45UXQT5RTA2WOMJR","short_pith_number":"pith:CEE4HH7C","schema_version":"1.0","canonical_sha256":"1109c39fe272b9da5e13ec660d59cc4c7869845e479f94a0dd14f0eaf81bff61","source":{"kind":"arxiv","id":"2411.12927","version":1},"attestation_state":"computed","paper":{"title":"Classification of Stable Surfaces with respect to Automatic Continuity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"George Domat, Kasra Rafi, Mladen Bestvina","submitted_at":"2024-11-19T23:36:24Z","abstract_excerpt":"We provide a complete classification of when the homeomorphism group of a stable surface, $\\Sigma$, has the automatic continuity property: Any homomorphism from Homeo$(\\Sigma)$ to a separable group is necessarily continuous. This result descends to a classification of when the mapping class group of $\\Sigma$ has the automatic continuity property. Towards this classification, we provide a general framework for proving automatic continuity for groups of homeomorphisms. Applying this framework, we also show that the homeomorphism group of any stable second countable Stone space has the automatic "},"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":"2411.12927","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-11-19T23:36:24Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"311b859addce2986bacde8e1d14f4c97f4d1d2da251e14f84fd3f34baa0a1561","abstract_canon_sha256":"d0a6a858fe3502d761817057d36f90d23245036f4f1ee0894ec0095ff03bdfc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T14:15:50.249106Z","signature_b64":"ybIA62Y9awiC5h1yJYcE5JisBBtsTHonTyXzSqTwR2cl5OyYMZqIyEa0USrRO3Hk+oyTlpjDa3jo9hTJUpq/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1109c39fe272b9da5e13ec660d59cc4c7869845e479f94a0dd14f0eaf81bff61","last_reissued_at":"2026-06-24T14:15:50.248578Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T14:15:50.248578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of Stable Surfaces with respect to Automatic Continuity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"George Domat, Kasra Rafi, Mladen Bestvina","submitted_at":"2024-11-19T23:36:24Z","abstract_excerpt":"We provide a complete classification of when the homeomorphism group of a stable surface, $\\Sigma$, has the automatic continuity property: Any homomorphism from Homeo$(\\Sigma)$ to a separable group is necessarily continuous. This result descends to a classification of when the mapping class group of $\\Sigma$ has the automatic continuity property. Towards this classification, we provide a general framework for proving automatic continuity for groups of homeomorphisms. Applying this framework, we also show that the homeomorphism group of any stable second countable Stone space has the automatic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12927","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.12927/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.12927","created_at":"2026-06-24T14:15:50.248637+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.12927v1","created_at":"2026-06-24T14:15:50.248637+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12927","created_at":"2026-06-24T14:15:50.248637+00:00"},{"alias_kind":"pith_short_12","alias_value":"CEE4HH7COK45","created_at":"2026-06-24T14:15:50.248637+00:00"},{"alias_kind":"pith_short_16","alias_value":"CEE4HH7COK45UXQT","created_at":"2026-06-24T14:15:50.248637+00:00"},{"alias_kind":"pith_short_8","alias_value":"CEE4HH7C","created_at":"2026-06-24T14:15:50.248637+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/CEE4HH7COK45UXQT5RTA2WOMJR","json":"https://pith.science/pith/CEE4HH7COK45UXQT5RTA2WOMJR.json","graph_json":"https://pith.science/api/pith-number/CEE4HH7COK45UXQT5RTA2WOMJR/graph.json","events_json":"https://pith.science/api/pith-number/CEE4HH7COK45UXQT5RTA2WOMJR/events.json","paper":"https://pith.science/paper/CEE4HH7C"},"agent_actions":{"view_html":"https://pith.science/pith/CEE4HH7COK45UXQT5RTA2WOMJR","download_json":"https://pith.science/pith/CEE4HH7COK45UXQT5RTA2WOMJR.json","view_paper":"https://pith.science/paper/CEE4HH7C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.12927&json=true","fetch_graph":"https://pith.science/api/pith-number/CEE4HH7COK45UXQT5RTA2WOMJR/graph.json","fetch_events":"https://pith.science/api/pith-number/CEE4HH7COK45UXQT5RTA2WOMJR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CEE4HH7COK45UXQT5RTA2WOMJR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CEE4HH7COK45UXQT5RTA2WOMJR/action/storage_attestation","attest_author":"https://pith.science/pith/CEE4HH7COK45UXQT5RTA2WOMJR/action/author_attestation","sign_citation":"https://pith.science/pith/CEE4HH7COK45UXQT5RTA2WOMJR/action/citation_signature","submit_replication":"https://pith.science/pith/CEE4HH7COK45UXQT5RTA2WOMJR/action/replication_record"}},"created_at":"2026-06-24T14:15:50.248637+00:00","updated_at":"2026-06-24T14:15:50.248637+00:00"}