{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BO7JZCQIQ2YMKL2X4DU7X2DFTT","short_pith_number":"pith:BO7JZCQI","schema_version":"1.0","canonical_sha256":"0bbe9c8a0886b0c52f57e0e9fbe8659cdd47abc0383046fb33d116cd8a369464","source":{"kind":"arxiv","id":"1712.03406","version":3},"attestation_state":"computed","paper":{"title":"Virtually free finite-normal-subgroup-free groups are strongly verbally closed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrey M. Mazhuga, Anton A. Klyachko, Veronika Yu. Miroshnichenko","submitted_at":"2017-12-09T16:03:12Z","abstract_excerpt":"Any virtually free group $H$ containing no non-trivial finite normal subgroup (e.g., the infinite dihedral group) is a retract of any finitely generated group containing $H$ as a verbally closed subgroup."},"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":"1712.03406","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-12-09T16:03:12Z","cross_cats_sorted":[],"title_canon_sha256":"d09f4559acd7536e654a1c7010934bc877e08a6f79ec0dbbd8897b57280abd56","abstract_canon_sha256":"ee2547d98f9743f2862f6a7e3773ed94619ce189167ea9d93e22d93181d9642c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:32.585512Z","signature_b64":"WHw1Mk+SmcEAkWN0fqVkiu9nQxDs40GiqHciSUBhU11CQF9C4UYTbkZ95Rv+icwGkX6XCliSluHV3BSJYhymAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bbe9c8a0886b0c52f57e0e9fbe8659cdd47abc0383046fb33d116cd8a369464","last_reissued_at":"2026-05-18T00:12:32.584865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:32.584865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Virtually free finite-normal-subgroup-free groups are strongly verbally closed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrey M. Mazhuga, Anton A. Klyachko, Veronika Yu. Miroshnichenko","submitted_at":"2017-12-09T16:03:12Z","abstract_excerpt":"Any virtually free group $H$ containing no non-trivial finite normal subgroup (e.g., the infinite dihedral group) is a retract of any finitely generated group containing $H$ as a verbally closed subgroup."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03406","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":""},"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":"1712.03406","created_at":"2026-05-18T00:12:32.584972+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.03406v3","created_at":"2026-05-18T00:12:32.584972+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03406","created_at":"2026-05-18T00:12:32.584972+00:00"},{"alias_kind":"pith_short_12","alias_value":"BO7JZCQIQ2YM","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BO7JZCQIQ2YMKL2X","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BO7JZCQI","created_at":"2026-05-18T12:31:08.081275+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/BO7JZCQIQ2YMKL2X4DU7X2DFTT","json":"https://pith.science/pith/BO7JZCQIQ2YMKL2X4DU7X2DFTT.json","graph_json":"https://pith.science/api/pith-number/BO7JZCQIQ2YMKL2X4DU7X2DFTT/graph.json","events_json":"https://pith.science/api/pith-number/BO7JZCQIQ2YMKL2X4DU7X2DFTT/events.json","paper":"https://pith.science/paper/BO7JZCQI"},"agent_actions":{"view_html":"https://pith.science/pith/BO7JZCQIQ2YMKL2X4DU7X2DFTT","download_json":"https://pith.science/pith/BO7JZCQIQ2YMKL2X4DU7X2DFTT.json","view_paper":"https://pith.science/paper/BO7JZCQI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.03406&json=true","fetch_graph":"https://pith.science/api/pith-number/BO7JZCQIQ2YMKL2X4DU7X2DFTT/graph.json","fetch_events":"https://pith.science/api/pith-number/BO7JZCQIQ2YMKL2X4DU7X2DFTT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BO7JZCQIQ2YMKL2X4DU7X2DFTT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BO7JZCQIQ2YMKL2X4DU7X2DFTT/action/storage_attestation","attest_author":"https://pith.science/pith/BO7JZCQIQ2YMKL2X4DU7X2DFTT/action/author_attestation","sign_citation":"https://pith.science/pith/BO7JZCQIQ2YMKL2X4DU7X2DFTT/action/citation_signature","submit_replication":"https://pith.science/pith/BO7JZCQIQ2YMKL2X4DU7X2DFTT/action/replication_record"}},"created_at":"2026-05-18T00:12:32.584972+00:00","updated_at":"2026-05-18T00:12:32.584972+00:00"}