{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DVMIGSSGHSXOXDW52LVOHONQF5","short_pith_number":"pith:DVMIGSSG","schema_version":"1.0","canonical_sha256":"1d58834a463caeeb8eddd2eae3b9b02f5aea3afd04d266fdf1e98593122868b6","source":{"kind":"arxiv","id":"1505.05165","version":1},"attestation_state":"computed","paper":{"title":"On state-closed representations of restricted wreath product of groups of type G_{p,d}=C_{p}wrC^{d}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alex C. Dantas, Said N. Sidki","submitted_at":"2015-05-19T20:13:02Z","abstract_excerpt":"Let $G_{p,d}$ be the restricted wreath product $C_{p} wr C^{d}$ where $C_{p}$ is a cyclic group of order a prime $p$ and $C^{d}$ a free abelian group of finite rank $d$. We study the existence of faithful state-closed (fsc) representations of $G_{p,d}$ on the $1$-rooted $m$-ary tree for some finite $m$. The group $G_{2,1}$, known as the lamplighter group, admits an fsc representation on the binary tree. We prove that for $d \\geq 2$ there are no fsc representations of $G_{p,d}$ on the $p$ -adic tree. We characterize all fsc representations of $G=G_{p,1}$ on the $p$-adic tree where the first lev"},"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":"1505.05165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-05-19T20:13:02Z","cross_cats_sorted":[],"title_canon_sha256":"abb162d003f1d3ce51faf39f4582027e1014d2c00d556d26af43e1fbbcd9b606","abstract_canon_sha256":"f7e1212d40f8cf87f777e851aa9b0075718f2158636270cb3eb55f11d602590d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:59.282887Z","signature_b64":"K/1EXxCdiho35GpWFwHbjhcouflZd2xj+60iHDEDFypIxOxvU8dhm4Uk1sNhNBCeLh6rL5C5Nsewo72yZnyxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d58834a463caeeb8eddd2eae3b9b02f5aea3afd04d266fdf1e98593122868b6","last_reissued_at":"2026-05-18T02:03:59.282142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:59.282142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On state-closed representations of restricted wreath product of groups of type G_{p,d}=C_{p}wrC^{d}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alex C. Dantas, Said N. Sidki","submitted_at":"2015-05-19T20:13:02Z","abstract_excerpt":"Let $G_{p,d}$ be the restricted wreath product $C_{p} wr C^{d}$ where $C_{p}$ is a cyclic group of order a prime $p$ and $C^{d}$ a free abelian group of finite rank $d$. We study the existence of faithful state-closed (fsc) representations of $G_{p,d}$ on the $1$-rooted $m$-ary tree for some finite $m$. The group $G_{2,1}$, known as the lamplighter group, admits an fsc representation on the binary tree. We prove that for $d \\geq 2$ there are no fsc representations of $G_{p,d}$ on the $p$ -adic tree. We characterize all fsc representations of $G=G_{p,1}$ on the $p$-adic tree where the first lev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05165","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":"1505.05165","created_at":"2026-05-18T02:03:59.282268+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.05165v1","created_at":"2026-05-18T02:03:59.282268+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05165","created_at":"2026-05-18T02:03:59.282268+00:00"},{"alias_kind":"pith_short_12","alias_value":"DVMIGSSGHSXO","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DVMIGSSGHSXOXDW5","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DVMIGSSG","created_at":"2026-05-18T12:29:17.054201+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/DVMIGSSGHSXOXDW52LVOHONQF5","json":"https://pith.science/pith/DVMIGSSGHSXOXDW52LVOHONQF5.json","graph_json":"https://pith.science/api/pith-number/DVMIGSSGHSXOXDW52LVOHONQF5/graph.json","events_json":"https://pith.science/api/pith-number/DVMIGSSGHSXOXDW52LVOHONQF5/events.json","paper":"https://pith.science/paper/DVMIGSSG"},"agent_actions":{"view_html":"https://pith.science/pith/DVMIGSSGHSXOXDW52LVOHONQF5","download_json":"https://pith.science/pith/DVMIGSSGHSXOXDW52LVOHONQF5.json","view_paper":"https://pith.science/paper/DVMIGSSG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.05165&json=true","fetch_graph":"https://pith.science/api/pith-number/DVMIGSSGHSXOXDW52LVOHONQF5/graph.json","fetch_events":"https://pith.science/api/pith-number/DVMIGSSGHSXOXDW52LVOHONQF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DVMIGSSGHSXOXDW52LVOHONQF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DVMIGSSGHSXOXDW52LVOHONQF5/action/storage_attestation","attest_author":"https://pith.science/pith/DVMIGSSGHSXOXDW52LVOHONQF5/action/author_attestation","sign_citation":"https://pith.science/pith/DVMIGSSGHSXOXDW52LVOHONQF5/action/citation_signature","submit_replication":"https://pith.science/pith/DVMIGSSGHSXOXDW52LVOHONQF5/action/replication_record"}},"created_at":"2026-05-18T02:03:59.282268+00:00","updated_at":"2026-05-18T02:03:59.282268+00:00"}