{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VALEARJYTDIWQKTZB2UOQLSOUA","short_pith_number":"pith:VALEARJY","schema_version":"1.0","canonical_sha256":"a81640453898d1682a790ea8e82e4ea02dda886adc48751e3697b05b1368bb17","source":{"kind":"arxiv","id":"1402.4345","version":1},"attestation_state":"computed","paper":{"title":"Palindromic Width of Wreath Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Elisabeth Fink","submitted_at":"2014-02-18T14:19:45Z","abstract_excerpt":"We show that the wreath product $G \\wr \\mathbb{Z}^n$ of any finitely generated group $G$ with $\\mathbb{Z}^n$ has finite palindromic width. We also show that $C \\wr A$ has finite palindromic width if $C$ has finite commutator width and $A$ is a finitely generated infinite abelian group. Further we prove that if $H$ is a non-abelian group with finite palindromic width and $G$ any finitely generated group, then every element of the subgroup $G' \\wr H$ can be expressed as a product of uniformly boundedly many palindromes. From this we obtain that $P \\wr H$ has finite palindromic width if $P$ is a "},"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":"1402.4345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-18T14:19:45Z","cross_cats_sorted":[],"title_canon_sha256":"d8124ebbec61d5845f860d297415a3e123b4507285312b67be2fccd5338cb608","abstract_canon_sha256":"cab2eac5c1a226366bac37889113aab18ec089e3d7b6d33cff9c5724ff82cb72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:44.147377Z","signature_b64":"g1VLbQ1ilgtqKLqwh/dTtEOxir6G17hOADcmYYNIF46c/vGbG6S/8ObKc/nYEckjfsIIp6ZrUIvgWTO/SKiMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a81640453898d1682a790ea8e82e4ea02dda886adc48751e3697b05b1368bb17","last_reissued_at":"2026-05-18T02:58:44.146638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:44.146638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Palindromic Width of Wreath Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Elisabeth Fink","submitted_at":"2014-02-18T14:19:45Z","abstract_excerpt":"We show that the wreath product $G \\wr \\mathbb{Z}^n$ of any finitely generated group $G$ with $\\mathbb{Z}^n$ has finite palindromic width. We also show that $C \\wr A$ has finite palindromic width if $C$ has finite commutator width and $A$ is a finitely generated infinite abelian group. Further we prove that if $H$ is a non-abelian group with finite palindromic width and $G$ any finitely generated group, then every element of the subgroup $G' \\wr H$ can be expressed as a product of uniformly boundedly many palindromes. From this we obtain that $P \\wr H$ has finite palindromic width if $P$ is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4345","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":"1402.4345","created_at":"2026-05-18T02:58:44.146766+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.4345v1","created_at":"2026-05-18T02:58:44.146766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4345","created_at":"2026-05-18T02:58:44.146766+00:00"},{"alias_kind":"pith_short_12","alias_value":"VALEARJYTDIW","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"VALEARJYTDIWQKTZ","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"VALEARJY","created_at":"2026-05-18T12:28:52.271510+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/VALEARJYTDIWQKTZB2UOQLSOUA","json":"https://pith.science/pith/VALEARJYTDIWQKTZB2UOQLSOUA.json","graph_json":"https://pith.science/api/pith-number/VALEARJYTDIWQKTZB2UOQLSOUA/graph.json","events_json":"https://pith.science/api/pith-number/VALEARJYTDIWQKTZB2UOQLSOUA/events.json","paper":"https://pith.science/paper/VALEARJY"},"agent_actions":{"view_html":"https://pith.science/pith/VALEARJYTDIWQKTZB2UOQLSOUA","download_json":"https://pith.science/pith/VALEARJYTDIWQKTZB2UOQLSOUA.json","view_paper":"https://pith.science/paper/VALEARJY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.4345&json=true","fetch_graph":"https://pith.science/api/pith-number/VALEARJYTDIWQKTZB2UOQLSOUA/graph.json","fetch_events":"https://pith.science/api/pith-number/VALEARJYTDIWQKTZB2UOQLSOUA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VALEARJYTDIWQKTZB2UOQLSOUA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VALEARJYTDIWQKTZB2UOQLSOUA/action/storage_attestation","attest_author":"https://pith.science/pith/VALEARJYTDIWQKTZB2UOQLSOUA/action/author_attestation","sign_citation":"https://pith.science/pith/VALEARJYTDIWQKTZB2UOQLSOUA/action/citation_signature","submit_replication":"https://pith.science/pith/VALEARJYTDIWQKTZB2UOQLSOUA/action/replication_record"}},"created_at":"2026-05-18T02:58:44.146766+00:00","updated_at":"2026-05-18T02:58:44.146766+00:00"}