{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CZUFCRSAMNDD42TPDJ5LOYRPBS","short_pith_number":"pith:CZUFCRSA","schema_version":"1.0","canonical_sha256":"166851464063463e6a6f1a7ab7622f0c88e0cb611172e35a354278bba1d662d0","source":{"kind":"arxiv","id":"1402.5314","version":2},"attestation_state":"computed","paper":{"title":"On palindromic width of certain extensions and quotients of free nilpotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Krishnendu Gongopadhyay, Valeriy G. Bardakov","submitted_at":"2014-02-21T14:56:41Z","abstract_excerpt":"In arXiv:1303.1129, the authors provided a bound for the palindromic width of free abelian-by-nilpotent group $AN_n$ of rank $n$ and free nilpotent group ${\\rm N}_{n,r}$ of rank $n$ and step $r$. In the present paper we study palindromic widths of groups $\\widetilde{AN}_n$ and $\\widetilde{\\rm N}_{n,r}$. We denote by $\\widetilde{G}_n = G_n / \\langle \\langle x_1^2, \\ldots, x_n^2 \\rangle \\rangle$ the quotient of group $G_n = \\langle x_1, \\ldots, x_n \\rangle$, which is free in some variety by the normal subgroup generated by $x_1^2, \\ldots, x_n^2$. We prove that the palindromic width of the quotie"},"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":"1402.5314","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-21T14:56:41Z","cross_cats_sorted":[],"title_canon_sha256":"2303eb255a6bd334a34b2308e3a0e97d0dbb29f2d06fe47738dcd49e07e036b1","abstract_canon_sha256":"9e031ae8f1688b192f52ac23a89595a5136db939c51747aaf9b98fd734fd8fda"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:55.210595Z","signature_b64":"0027GzLa4r9q2bMy5zlSOZPpxDpI1eBFXJpj9MTBP66yiIwxLaQ+OpC8ntO1sc57Q96fiAhGaLOalfytOgz7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"166851464063463e6a6f1a7ab7622f0c88e0cb611172e35a354278bba1d662d0","last_reissued_at":"2026-05-18T02:28:55.210244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:55.210244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On palindromic width of certain extensions and quotients of free nilpotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Krishnendu Gongopadhyay, Valeriy G. Bardakov","submitted_at":"2014-02-21T14:56:41Z","abstract_excerpt":"In arXiv:1303.1129, the authors provided a bound for the palindromic width of free abelian-by-nilpotent group $AN_n$ of rank $n$ and free nilpotent group ${\\rm N}_{n,r}$ of rank $n$ and step $r$. In the present paper we study palindromic widths of groups $\\widetilde{AN}_n$ and $\\widetilde{\\rm N}_{n,r}$. We denote by $\\widetilde{G}_n = G_n / \\langle \\langle x_1^2, \\ldots, x_n^2 \\rangle \\rangle$ the quotient of group $G_n = \\langle x_1, \\ldots, x_n \\rangle$, which is free in some variety by the normal subgroup generated by $x_1^2, \\ldots, x_n^2$. We prove that the palindromic width of the quotie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5314","kind":"arxiv","version":2},"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":"1402.5314","created_at":"2026-05-18T02:28:55.210291+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.5314v2","created_at":"2026-05-18T02:28:55.210291+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5314","created_at":"2026-05-18T02:28:55.210291+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZUFCRSAMNDD","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZUFCRSAMNDD42TP","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZUFCRSA","created_at":"2026-05-18T12:28:25.294606+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/CZUFCRSAMNDD42TPDJ5LOYRPBS","json":"https://pith.science/pith/CZUFCRSAMNDD42TPDJ5LOYRPBS.json","graph_json":"https://pith.science/api/pith-number/CZUFCRSAMNDD42TPDJ5LOYRPBS/graph.json","events_json":"https://pith.science/api/pith-number/CZUFCRSAMNDD42TPDJ5LOYRPBS/events.json","paper":"https://pith.science/paper/CZUFCRSA"},"agent_actions":{"view_html":"https://pith.science/pith/CZUFCRSAMNDD42TPDJ5LOYRPBS","download_json":"https://pith.science/pith/CZUFCRSAMNDD42TPDJ5LOYRPBS.json","view_paper":"https://pith.science/paper/CZUFCRSA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.5314&json=true","fetch_graph":"https://pith.science/api/pith-number/CZUFCRSAMNDD42TPDJ5LOYRPBS/graph.json","fetch_events":"https://pith.science/api/pith-number/CZUFCRSAMNDD42TPDJ5LOYRPBS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZUFCRSAMNDD42TPDJ5LOYRPBS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZUFCRSAMNDD42TPDJ5LOYRPBS/action/storage_attestation","attest_author":"https://pith.science/pith/CZUFCRSAMNDD42TPDJ5LOYRPBS/action/author_attestation","sign_citation":"https://pith.science/pith/CZUFCRSAMNDD42TPDJ5LOYRPBS/action/citation_signature","submit_replication":"https://pith.science/pith/CZUFCRSAMNDD42TPDJ5LOYRPBS/action/replication_record"}},"created_at":"2026-05-18T02:28:55.210291+00:00","updated_at":"2026-05-18T02:28:55.210291+00:00"}