{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:CGKA7BAHOKXPRI7JMSC5MLKQCY","short_pith_number":"pith:CGKA7BAH","schema_version":"1.0","canonical_sha256":"11940f840772aef8a3e96485d62d501601a9586d041fd2511771bd7414831a3e","source":{"kind":"arxiv","id":"1901.07182","version":3},"attestation_state":"computed","paper":{"title":"Surface groups are flexibly stable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Arie Levit, Nir Lazarovich, Yair Minsky","submitted_at":"2019-01-22T06:01:47Z","abstract_excerpt":"We show that surface groups are flexibly stable in permutations. This is the first non-trivial example of a non-amenable flexibly stable group. Our method is purely geometric and relies on an analysis of branched covers of hyperbolic surfaces. Along the way we establish a quantitative variant of the LERF property for surface groups which may be of independent interest."},"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":"1901.07182","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-01-22T06:01:47Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"ac6b3295244a69e129d100a43a8f737c122507904b6353b1b87b9954c4240505","abstract_canon_sha256":"b18e4a87f0771e381ee6014864d81abfd9283e4c5869ef92b8a6321b8ae78a1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:58:55.428867Z","signature_b64":"BFA7ArHNPFIyL+fXl0DGcS8eIRDvgcT7ZtFVBXXkLWjsMNsV9qpTiJimKiSiV0qJ4b25HMERyMmkhaFeknDuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11940f840772aef8a3e96485d62d501601a9586d041fd2511771bd7414831a3e","last_reissued_at":"2026-07-05T09:58:55.428439Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:58:55.428439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Surface groups are flexibly stable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Arie Levit, Nir Lazarovich, Yair Minsky","submitted_at":"2019-01-22T06:01:47Z","abstract_excerpt":"We show that surface groups are flexibly stable in permutations. This is the first non-trivial example of a non-amenable flexibly stable group. Our method is purely geometric and relies on an analysis of branched covers of hyperbolic surfaces. Along the way we establish a quantitative variant of the LERF property for surface groups which may be of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07182","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1901.07182/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":"1901.07182","created_at":"2026-07-05T09:58:55.428497+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.07182v3","created_at":"2026-07-05T09:58:55.428497+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07182","created_at":"2026-07-05T09:58:55.428497+00:00"},{"alias_kind":"pith_short_12","alias_value":"CGKA7BAHOKXP","created_at":"2026-07-05T09:58:55.428497+00:00"},{"alias_kind":"pith_short_16","alias_value":"CGKA7BAHOKXPRI7J","created_at":"2026-07-05T09:58:55.428497+00:00"},{"alias_kind":"pith_short_8","alias_value":"CGKA7BAH","created_at":"2026-07-05T09:58:55.428497+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2408.13350","citing_title":"Conditional representation stability, classification of $*$-homomorphisms, and relative eta invariants","ref_index":95,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CGKA7BAHOKXPRI7JMSC5MLKQCY","json":"https://pith.science/pith/CGKA7BAHOKXPRI7JMSC5MLKQCY.json","graph_json":"https://pith.science/api/pith-number/CGKA7BAHOKXPRI7JMSC5MLKQCY/graph.json","events_json":"https://pith.science/api/pith-number/CGKA7BAHOKXPRI7JMSC5MLKQCY/events.json","paper":"https://pith.science/paper/CGKA7BAH"},"agent_actions":{"view_html":"https://pith.science/pith/CGKA7BAHOKXPRI7JMSC5MLKQCY","download_json":"https://pith.science/pith/CGKA7BAHOKXPRI7JMSC5MLKQCY.json","view_paper":"https://pith.science/paper/CGKA7BAH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.07182&json=true","fetch_graph":"https://pith.science/api/pith-number/CGKA7BAHOKXPRI7JMSC5MLKQCY/graph.json","fetch_events":"https://pith.science/api/pith-number/CGKA7BAHOKXPRI7JMSC5MLKQCY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CGKA7BAHOKXPRI7JMSC5MLKQCY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CGKA7BAHOKXPRI7JMSC5MLKQCY/action/storage_attestation","attest_author":"https://pith.science/pith/CGKA7BAHOKXPRI7JMSC5MLKQCY/action/author_attestation","sign_citation":"https://pith.science/pith/CGKA7BAHOKXPRI7JMSC5MLKQCY/action/citation_signature","submit_replication":"https://pith.science/pith/CGKA7BAHOKXPRI7JMSC5MLKQCY/action/replication_record"}},"created_at":"2026-07-05T09:58:55.428497+00:00","updated_at":"2026-07-05T09:58:55.428497+00:00"}