{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:UJJ3IT6ZDSLDAG4J3HCIATI2S5","short_pith_number":"pith:UJJ3IT6Z","canonical_record":{"source":{"id":"math/0210192","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2002-10-13T18:27:36Z","cross_cats_sorted":[],"title_canon_sha256":"73f2ada678c11afe22eadf6c29a4cc80b384ab183bca0fb63b96ff77608a6602","abstract_canon_sha256":"b9dbcdb314fc9cea1df50eb7b44c3d09a9550b4e3aeecce890a1e6004ca939e7"},"schema_version":"1.0"},"canonical_sha256":"a253b44fd91c96301b89d9c4804d1a9766265dc3b89de9b097904009a95bc70c","source":{"kind":"arxiv","id":"math/0210192","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:UJJ3IT6ZDSLDAG4J3HCIATI2S5","target":"record","payload":{"canonical_record":{"source":{"id":"math/0210192","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2002-10-13T18:27:36Z","cross_cats_sorted":[],"title_canon_sha256":"73f2ada678c11afe22eadf6c29a4cc80b384ab183bca0fb63b96ff77608a6602","abstract_canon_sha256":"b9dbcdb314fc9cea1df50eb7b44c3d09a9550b4e3aeecce890a1e6004ca939e7"},"schema_version":"1.0"},"canonical_sha256":"a253b44fd91c96301b89d9c4804d1a9766265dc3b89de9b097904009a95bc70c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:36:37.959354Z","signature_b64":"3ApUGknpq3Oxyazp95mTd2foRYwup0gUuhpNTTnavhhVcztsLMupEXc/BtB5DRxWHWxZxlmCSGWHrXZraVFKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a253b44fd91c96301b89d9c4804d1a9766265dc3b89de9b097904009a95bc70c","last_reissued_at":"2026-07-04T14:36:37.958949Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:36:37.958949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0210192","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AKrlLwq28CAXONSJm2ss6WxOmdbqtjBHS1skzPDwVZPvSlmrp1ITzI/CJwoCsJVLvjGx+C1cl7OT+1+Bm87hAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T05:39:58.433167Z"},"content_sha256":"346ce0d0d1bdd415eb1e8914761e2cf8909ad1cc8f6e15af57833fe77af8a847","schema_version":"1.0","event_id":"sha256:346ce0d0d1bdd415eb1e8914761e2cf8909ad1cc8f6e15af57833fe77af8a847"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:UJJ3IT6ZDSLDAG4J3HCIATI2S5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On quasivarities of groups and equations over groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"S.V. Ivanov","submitted_at":"2002-10-13T18:27:36Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210192","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/math/0210192/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4P7ta0szChHui28RwPqUAheX5Dlezil4FORNuAb+8qup14neC2uzENaygumYA9m/Y8lK/Yes+L4BJbBjthliAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T05:39:58.433548Z"},"content_sha256":"53da8e6739d754e5d8b5c94582efed9bf93dcc2e097467a361952ff10b0ebaa7","schema_version":"1.0","event_id":"sha256:53da8e6739d754e5d8b5c94582efed9bf93dcc2e097467a361952ff10b0ebaa7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJJ3IT6ZDSLDAG4J3HCIATI2S5/bundle.json","state_url":"https://pith.science/pith/UJJ3IT6ZDSLDAG4J3HCIATI2S5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJJ3IT6ZDSLDAG4J3HCIATI2S5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-05T05:39:58Z","links":{"resolver":"https://pith.science/pith/UJJ3IT6ZDSLDAG4J3HCIATI2S5","bundle":"https://pith.science/pith/UJJ3IT6ZDSLDAG4J3HCIATI2S5/bundle.json","state":"https://pith.science/pith/UJJ3IT6ZDSLDAG4J3HCIATI2S5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJJ3IT6ZDSLDAG4J3HCIATI2S5/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8pofQXnkTvwVjYAKAGYWCOiPNPzcv9++ESroFmqZHKBdL8SaMkF746ccaNu2TPwyQxeti5cS0glNToMP1YiDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T05:39:58.435408Z","bundle_sha256":"9f8e3f12ba4b4c094b79ec6a49943c136c57176b21693fac7100a40b5ee96191"}}