{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:UJJ3IT6ZDSLDAG4J3HCIATI2S5","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":"b9dbcdb314fc9cea1df50eb7b44c3d09a9550b4e3aeecce890a1e6004ca939e7","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2002-10-13T18:27:36Z","title_canon_sha256":"73f2ada678c11afe22eadf6c29a4cc80b384ab183bca0fb63b96ff77608a6602"},"schema_version":"1.0","source":{"id":"math/0210192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0210192","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0210192v1","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0210192","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"UJJ3IT6ZDSLD","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_16","alias_value":"UJJ3IT6ZDSLDAG4J","created_at":"2026-07-04T14:36:37Z"},{"alias_kind":"pith_short_8","alias_value":"UJJ3IT6Z","created_at":"2026-07-04T14:36:37Z"}],"graph_snapshots":[{"event_id":"sha256:53da8e6739d754e5d8b5c94582efed9bf93dcc2e097467a361952ff10b0ebaa7","target":"graph","created_at":"2026-07-04T14:36:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0210192/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the quasivariety of groups generated by finite and locally indicable groups does not contain the class of periodic groups. This result is related to (and inspired by) the solvability of equations over groups. The proof uses the Feit-Thompson theorem on the solvability of finite groups of odd order, Kostrikin-Zelmanov results on the restricted Burnside problem and applies techninal details of a recent construction of weakly finitely presented periodic groups.","authors_text":"S.V. Ivanov","cross_cats":[],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2002-10-13T18:27:36Z","title":"On quasivarities of groups and equations over groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210192","kind":"arxiv","version":1},"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":"sha256:346ce0d0d1bdd415eb1e8914761e2cf8909ad1cc8f6e15af57833fe77af8a847","target":"record","created_at":"2026-07-04T14:36:37Z","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":"b9dbcdb314fc9cea1df50eb7b44c3d09a9550b4e3aeecce890a1e6004ca939e7","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2002-10-13T18:27:36Z","title_canon_sha256":"73f2ada678c11afe22eadf6c29a4cc80b384ab183bca0fb63b96ff77608a6602"},"schema_version":"1.0","source":{"id":"math/0210192","kind":"arxiv","version":1}},"canonical_sha256":"a253b44fd91c96301b89d9c4804d1a9766265dc3b89de9b097904009a95bc70c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a253b44fd91c96301b89d9c4804d1a9766265dc3b89de9b097904009a95bc70c","first_computed_at":"2026-07-04T14:36:37.958949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:37.958949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ApUGknpq3Oxyazp95mTd2foRYwup0gUuhpNTTnavhhVcztsLMupEXc/BtB5DRxWHWxZxlmCSGWHrXZraVFKDg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:37.959354Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0210192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:346ce0d0d1bdd415eb1e8914761e2cf8909ad1cc8f6e15af57833fe77af8a847","sha256:53da8e6739d754e5d8b5c94582efed9bf93dcc2e097467a361952ff10b0ebaa7"],"state_sha256":"308c6f5f80a4c46cdf6c6f55001b3f4ddeb15e217bb5e3350d67119928a15438"}