{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:KGRYAXJIAZRVAKMFOY7K2T3SE5","short_pith_number":"pith:KGRYAXJI","schema_version":"1.0","canonical_sha256":"51a3805d280663502985763ead4f72274257af3a72d6ec21066780ac819bf860","source":{"kind":"arxiv","id":"1103.5486","version":1},"attestation_state":"computed","paper":{"title":"Classification of p-adic 6-dimensional filiform Leibniz algebras by solution of x^q=a","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RA","authors_text":"B.A. Omirov, M. Ladra, U.A. Rozikov","submitted_at":"2011-03-28T21:00:20Z","abstract_excerpt":"In this paper we study the $p$-adic equation $x^q=a$ over the field of $p$-adic numbers. We construct an algorithm of calculation of criteria of solvability in the case of $q=p^m$ and present a computer program to compute the criteria for fixed value of $m \\leq p-1$. Moreover, using this solvability criteria for $q=2,3,4,5,6$, we classify $p$-adic 6-dimensional filiform Leibniz algebras."},"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":"1103.5486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-03-28T21:00:20Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"a5f5d648c1d766ba52c0438e30c6d6876ff14fd66e6857fe48da3d36d7649738","abstract_canon_sha256":"b397b123b9889f58c8c8d8676ad33d6bbc1bc089e55b166f63580d6d58b281ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:37.473151Z","signature_b64":"px5EJxKupSSyr1FbFqUCpk+2UNA/OPa80eKiOwcIdwwICRNCdtvvZ5a7OL1cmPJx26bEAgtBScS+E57D0xchAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51a3805d280663502985763ead4f72274257af3a72d6ec21066780ac819bf860","last_reissued_at":"2026-05-18T04:25:37.472697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:37.472697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of p-adic 6-dimensional filiform Leibniz algebras by solution of x^q=a","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RA","authors_text":"B.A. Omirov, M. Ladra, U.A. Rozikov","submitted_at":"2011-03-28T21:00:20Z","abstract_excerpt":"In this paper we study the $p$-adic equation $x^q=a$ over the field of $p$-adic numbers. We construct an algorithm of calculation of criteria of solvability in the case of $q=p^m$ and present a computer program to compute the criteria for fixed value of $m \\leq p-1$. Moreover, using this solvability criteria for $q=2,3,4,5,6$, we classify $p$-adic 6-dimensional filiform Leibniz algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5486","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":"1103.5486","created_at":"2026-05-18T04:25:37.472763+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.5486v1","created_at":"2026-05-18T04:25:37.472763+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5486","created_at":"2026-05-18T04:25:37.472763+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGRYAXJIAZRV","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGRYAXJIAZRVAKMF","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGRYAXJI","created_at":"2026-05-18T12:26:32.869790+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/KGRYAXJIAZRVAKMFOY7K2T3SE5","json":"https://pith.science/pith/KGRYAXJIAZRVAKMFOY7K2T3SE5.json","graph_json":"https://pith.science/api/pith-number/KGRYAXJIAZRVAKMFOY7K2T3SE5/graph.json","events_json":"https://pith.science/api/pith-number/KGRYAXJIAZRVAKMFOY7K2T3SE5/events.json","paper":"https://pith.science/paper/KGRYAXJI"},"agent_actions":{"view_html":"https://pith.science/pith/KGRYAXJIAZRVAKMFOY7K2T3SE5","download_json":"https://pith.science/pith/KGRYAXJIAZRVAKMFOY7K2T3SE5.json","view_paper":"https://pith.science/paper/KGRYAXJI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.5486&json=true","fetch_graph":"https://pith.science/api/pith-number/KGRYAXJIAZRVAKMFOY7K2T3SE5/graph.json","fetch_events":"https://pith.science/api/pith-number/KGRYAXJIAZRVAKMFOY7K2T3SE5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGRYAXJIAZRVAKMFOY7K2T3SE5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGRYAXJIAZRVAKMFOY7K2T3SE5/action/storage_attestation","attest_author":"https://pith.science/pith/KGRYAXJIAZRVAKMFOY7K2T3SE5/action/author_attestation","sign_citation":"https://pith.science/pith/KGRYAXJIAZRVAKMFOY7K2T3SE5/action/citation_signature","submit_replication":"https://pith.science/pith/KGRYAXJIAZRVAKMFOY7K2T3SE5/action/replication_record"}},"created_at":"2026-05-18T04:25:37.472763+00:00","updated_at":"2026-05-18T04:25:37.472763+00:00"}