{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:C27CKZFRDLNB24N35QDP67S3VP","short_pith_number":"pith:C27CKZFR","schema_version":"1.0","canonical_sha256":"16be2564b11ada1d71bbec06ff7e5babff2e76b4f476af00a4e84ef66cfe9ef4","source":{"kind":"arxiv","id":"1711.09371","version":1},"attestation_state":"computed","paper":{"title":"Reidemeister classes in lamplighter type groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Evgenij Troitsky","submitted_at":"2017-11-26T12:00:22Z","abstract_excerpt":"We prove that for any automorphism $\\phi$ of the restricted wreath product $\\mathbb{Z}_2 \\mathrm{wr} \\mathbb{Z}^k$ and $\\mathbb{Z}_3 \\mathrm{wr} \\mathbb{Z}^{2d}$ the Reidemeister number $R(\\phi)$ is infinite, i.e. these groups have the property $R_\\infty$.\n  For $\\mathbb{Z}_3 \\mathrm{wr} \\mathbb{Z}^{2d+1}$ and $\\mathbb{Z}_p \\mathrm{wr} \\mathbb{Z}^k$, where $p>3$ is prime, we give examples of automorphisms with finite Reidemeister numbers. So these groups do not have the property $R_\\infty$.\n  For these groups and $\\mathbb{Z}_m \\mathrm{wr} \\mathbb{Z}$, where $m$ is relatively prime to $6$, we p"},"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":"1711.09371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-26T12:00:22Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"59c67210f3aa0b31ce6db734e0af473742c294ab498838e32f47c396c9b0d30c","abstract_canon_sha256":"3bc8f2f29c929bf82e2d1f21f67cb7b64cbe6c9f2d0f78cc54724d0199fe054f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:35.833266Z","signature_b64":"j1vr83XVLyuBBqLwpSniYghNpPSV43BwVUgIWREq4F7qAozc1K4UbnpIVq1m0MUp2RodXS/n7dmza4+OnTPjCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16be2564b11ada1d71bbec06ff7e5babff2e76b4f476af00a4e84ef66cfe9ef4","last_reissued_at":"2026-05-18T00:29:35.832690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:35.832690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reidemeister classes in lamplighter type groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Evgenij Troitsky","submitted_at":"2017-11-26T12:00:22Z","abstract_excerpt":"We prove that for any automorphism $\\phi$ of the restricted wreath product $\\mathbb{Z}_2 \\mathrm{wr} \\mathbb{Z}^k$ and $\\mathbb{Z}_3 \\mathrm{wr} \\mathbb{Z}^{2d}$ the Reidemeister number $R(\\phi)$ is infinite, i.e. these groups have the property $R_\\infty$.\n  For $\\mathbb{Z}_3 \\mathrm{wr} \\mathbb{Z}^{2d+1}$ and $\\mathbb{Z}_p \\mathrm{wr} \\mathbb{Z}^k$, where $p>3$ is prime, we give examples of automorphisms with finite Reidemeister numbers. So these groups do not have the property $R_\\infty$.\n  For these groups and $\\mathbb{Z}_m \\mathrm{wr} \\mathbb{Z}$, where $m$ is relatively prime to $6$, we p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09371","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":"1711.09371","created_at":"2026-05-18T00:29:35.832786+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.09371v1","created_at":"2026-05-18T00:29:35.832786+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09371","created_at":"2026-05-18T00:29:35.832786+00:00"},{"alias_kind":"pith_short_12","alias_value":"C27CKZFRDLNB","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"C27CKZFRDLNB24N3","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"C27CKZFR","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/C27CKZFRDLNB24N35QDP67S3VP","json":"https://pith.science/pith/C27CKZFRDLNB24N35QDP67S3VP.json","graph_json":"https://pith.science/api/pith-number/C27CKZFRDLNB24N35QDP67S3VP/graph.json","events_json":"https://pith.science/api/pith-number/C27CKZFRDLNB24N35QDP67S3VP/events.json","paper":"https://pith.science/paper/C27CKZFR"},"agent_actions":{"view_html":"https://pith.science/pith/C27CKZFRDLNB24N35QDP67S3VP","download_json":"https://pith.science/pith/C27CKZFRDLNB24N35QDP67S3VP.json","view_paper":"https://pith.science/paper/C27CKZFR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.09371&json=true","fetch_graph":"https://pith.science/api/pith-number/C27CKZFRDLNB24N35QDP67S3VP/graph.json","fetch_events":"https://pith.science/api/pith-number/C27CKZFRDLNB24N35QDP67S3VP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C27CKZFRDLNB24N35QDP67S3VP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C27CKZFRDLNB24N35QDP67S3VP/action/storage_attestation","attest_author":"https://pith.science/pith/C27CKZFRDLNB24N35QDP67S3VP/action/author_attestation","sign_citation":"https://pith.science/pith/C27CKZFRDLNB24N35QDP67S3VP/action/citation_signature","submit_replication":"https://pith.science/pith/C27CKZFRDLNB24N35QDP67S3VP/action/replication_record"}},"created_at":"2026-05-18T00:29:35.832786+00:00","updated_at":"2026-05-18T00:29:35.832786+00:00"}