{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OB52EJQUNPYBUVUQHQ5B55PKSX","short_pith_number":"pith:OB52EJQU","schema_version":"1.0","canonical_sha256":"707ba226146bf01a56903c3a1ef5ea95dad934c4954c4e1235b23378a863e5de","source":{"kind":"arxiv","id":"1507.08841","version":1},"attestation_state":"computed","paper":{"title":"A probabilistic Tits alternative and probabilistic identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Aner Shalev, Michael Larsen","submitted_at":"2015-07-31T11:51:09Z","abstract_excerpt":"We introduce the notion of a probabilistic identity of a residually finite group. We prove that a finitely generated linear group satisfies a probabilistic identity if and only if it is virtually solvable.\n  As an application, we prove a probabilistic variant of the Tits alternative: let G be the profinite completion of a finitely generated linear group. Then either G is virtually solvable, or for any positive integer n, with probability one, n independent, uniformly distributed elements of G freely generate a free subgroup of G of rank n."},"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":"1507.08841","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-07-31T11:51:09Z","cross_cats_sorted":[],"title_canon_sha256":"fef12fa7762bf8590060fa994f9bd130f7cf3d72d833bd139b0881fddaa0d81c","abstract_canon_sha256":"69decd7a61c18767e3b8c278ce434d43d766005e42a4b751f28eae75cff115c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:46.115219Z","signature_b64":"OFHSmQXIe0OZtWcjPY6QrWm/WQA4mSnb5lAaTwPRBGs9rIUrM12BXWT4TKs0jY3fJHp0PBeLgdUlxFmaiiB6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"707ba226146bf01a56903c3a1ef5ea95dad934c4954c4e1235b23378a863e5de","last_reissued_at":"2026-05-18T01:05:46.114562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:46.114562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A probabilistic Tits alternative and probabilistic identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Aner Shalev, Michael Larsen","submitted_at":"2015-07-31T11:51:09Z","abstract_excerpt":"We introduce the notion of a probabilistic identity of a residually finite group. We prove that a finitely generated linear group satisfies a probabilistic identity if and only if it is virtually solvable.\n  As an application, we prove a probabilistic variant of the Tits alternative: let G be the profinite completion of a finitely generated linear group. Then either G is virtually solvable, or for any positive integer n, with probability one, n independent, uniformly distributed elements of G freely generate a free subgroup of G of rank n."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08841","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":""},"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":"1507.08841","created_at":"2026-05-18T01:05:46.114666+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.08841v1","created_at":"2026-05-18T01:05:46.114666+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08841","created_at":"2026-05-18T01:05:46.114666+00:00"},{"alias_kind":"pith_short_12","alias_value":"OB52EJQUNPYB","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OB52EJQUNPYBUVUQ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OB52EJQU","created_at":"2026-05-18T12:29:34.919912+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/OB52EJQUNPYBUVUQHQ5B55PKSX","json":"https://pith.science/pith/OB52EJQUNPYBUVUQHQ5B55PKSX.json","graph_json":"https://pith.science/api/pith-number/OB52EJQUNPYBUVUQHQ5B55PKSX/graph.json","events_json":"https://pith.science/api/pith-number/OB52EJQUNPYBUVUQHQ5B55PKSX/events.json","paper":"https://pith.science/paper/OB52EJQU"},"agent_actions":{"view_html":"https://pith.science/pith/OB52EJQUNPYBUVUQHQ5B55PKSX","download_json":"https://pith.science/pith/OB52EJQUNPYBUVUQHQ5B55PKSX.json","view_paper":"https://pith.science/paper/OB52EJQU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.08841&json=true","fetch_graph":"https://pith.science/api/pith-number/OB52EJQUNPYBUVUQHQ5B55PKSX/graph.json","fetch_events":"https://pith.science/api/pith-number/OB52EJQUNPYBUVUQHQ5B55PKSX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OB52EJQUNPYBUVUQHQ5B55PKSX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OB52EJQUNPYBUVUQHQ5B55PKSX/action/storage_attestation","attest_author":"https://pith.science/pith/OB52EJQUNPYBUVUQHQ5B55PKSX/action/author_attestation","sign_citation":"https://pith.science/pith/OB52EJQUNPYBUVUQHQ5B55PKSX/action/citation_signature","submit_replication":"https://pith.science/pith/OB52EJQUNPYBUVUQHQ5B55PKSX/action/replication_record"}},"created_at":"2026-05-18T01:05:46.114666+00:00","updated_at":"2026-05-18T01:05:46.114666+00:00"}