{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KESBSP7HNKITBHDZJEZEOWHUVH","short_pith_number":"pith:KESBSP7H","schema_version":"1.0","canonical_sha256":"5124193fe76a91309c7949324758f4a9c7d204e6b2bc17b80629bf2594690381","source":{"kind":"arxiv","id":"1801.08381","version":2},"attestation_state":"computed","paper":{"title":"Stability and Invariant Random Subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander Lubotzky, Andreas Thom, Oren Becker","submitted_at":"2018-01-25T12:46:14Z","abstract_excerpt":"Consider $\\operatorname{Sym}(n)$, endowed with the normalized Hamming metric $d_n$. A finitely-generated group $\\Gamma$ is \\emph{P-stable} if every almost homomorphism $\\rho_{n_k}\\colon \\Gamma\\rightarrow\\operatorname{Sym}(n_k)$ (i.e., for every $g,h\\in\\Gamma$, $\\lim_{k\\rightarrow\\infty}d_{n_k}( \\rho_{n_k}(gh),\\rho_{n_k}(g)\\rho_{n_k}(h))=0$) is close to an actual homomorphism $\\varphi_{n_k} \\colon\\Gamma\\rightarrow\\operatorname{Sym}(n_k)$. Glebsky and Rivera observed that finite groups are P-stable, while Arzhantseva and P\\u{a}unescu showed the same for abelian groups and raised many questions, "},"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":"1801.08381","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-25T12:46:14Z","cross_cats_sorted":[],"title_canon_sha256":"e19ecf518193807e7ba8516e07585102d818f3ede54a5c31643345db354e4abd","abstract_canon_sha256":"62e47a6519edf0ea52e72546c396b76ee1cc64714a5a630aa945adab86cd1c0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:05:04.616575Z","signature_b64":"2gy4vnodmP7MvvoGdSyBJ4Sospy2QDEKRa9lGk9YFoniv8gxI1WJYmBcb9jOfZFwKSGSR9PrGIJySbiFebRiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5124193fe76a91309c7949324758f4a9c7d204e6b2bc17b80629bf2594690381","last_reissued_at":"2026-07-05T00:05:04.616201Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:05:04.616201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability and Invariant Random Subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander Lubotzky, Andreas Thom, Oren Becker","submitted_at":"2018-01-25T12:46:14Z","abstract_excerpt":"Consider $\\operatorname{Sym}(n)$, endowed with the normalized Hamming metric $d_n$. A finitely-generated group $\\Gamma$ is \\emph{P-stable} if every almost homomorphism $\\rho_{n_k}\\colon \\Gamma\\rightarrow\\operatorname{Sym}(n_k)$ (i.e., for every $g,h\\in\\Gamma$, $\\lim_{k\\rightarrow\\infty}d_{n_k}( \\rho_{n_k}(gh),\\rho_{n_k}(g)\\rho_{n_k}(h))=0$) is close to an actual homomorphism $\\varphi_{n_k} \\colon\\Gamma\\rightarrow\\operatorname{Sym}(n_k)$. Glebsky and Rivera observed that finite groups are P-stable, while Arzhantseva and P\\u{a}unescu showed the same for abelian groups and raised many questions, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08381","kind":"arxiv","version":2},"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/1801.08381/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":"1801.08381","created_at":"2026-07-05T00:05:04.616266+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.08381v2","created_at":"2026-07-05T00:05:04.616266+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08381","created_at":"2026-07-05T00:05:04.616266+00:00"},{"alias_kind":"pith_short_12","alias_value":"KESBSP7HNKIT","created_at":"2026-07-05T00:05:04.616266+00:00"},{"alias_kind":"pith_short_16","alias_value":"KESBSP7HNKITBHDZ","created_at":"2026-07-05T00:05:04.616266+00:00"},{"alias_kind":"pith_short_8","alias_value":"KESBSP7H","created_at":"2026-07-05T00:05:04.616266+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1909.00282","citing_title":"Stability for product groups and property $(\\tau)$","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KESBSP7HNKITBHDZJEZEOWHUVH","json":"https://pith.science/pith/KESBSP7HNKITBHDZJEZEOWHUVH.json","graph_json":"https://pith.science/api/pith-number/KESBSP7HNKITBHDZJEZEOWHUVH/graph.json","events_json":"https://pith.science/api/pith-number/KESBSP7HNKITBHDZJEZEOWHUVH/events.json","paper":"https://pith.science/paper/KESBSP7H"},"agent_actions":{"view_html":"https://pith.science/pith/KESBSP7HNKITBHDZJEZEOWHUVH","download_json":"https://pith.science/pith/KESBSP7HNKITBHDZJEZEOWHUVH.json","view_paper":"https://pith.science/paper/KESBSP7H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.08381&json=true","fetch_graph":"https://pith.science/api/pith-number/KESBSP7HNKITBHDZJEZEOWHUVH/graph.json","fetch_events":"https://pith.science/api/pith-number/KESBSP7HNKITBHDZJEZEOWHUVH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KESBSP7HNKITBHDZJEZEOWHUVH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KESBSP7HNKITBHDZJEZEOWHUVH/action/storage_attestation","attest_author":"https://pith.science/pith/KESBSP7HNKITBHDZJEZEOWHUVH/action/author_attestation","sign_citation":"https://pith.science/pith/KESBSP7HNKITBHDZJEZEOWHUVH/action/citation_signature","submit_replication":"https://pith.science/pith/KESBSP7HNKITBHDZJEZEOWHUVH/action/replication_record"}},"created_at":"2026-07-05T00:05:04.616266+00:00","updated_at":"2026-07-05T00:05:04.616266+00:00"}