{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:L4GYUW3PWMPP7QGLI3WOYUQGIF","short_pith_number":"pith:L4GYUW3P","schema_version":"1.0","canonical_sha256":"5f0d8a5b6fb31effc0cb46ecec5206417152088505cb5b67fe46bca52b6ababf","source":{"kind":"arxiv","id":"2004.00586","version":1},"attestation_state":"computed","paper":{"title":"Arithmeticity of groups $\\mathbb Z^n\\rtimes\\mathbb Z$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bena Tshishiku","submitted_at":"2020-04-01T17:14:27Z","abstract_excerpt":"We study when the group $\\mathbb Z^n\\rtimes_A\\mathbb Z$ is arithmetic where $A\\in GL_n(\\mathbb Z)$ is hyperbolic and semisimple. We begin by giving a characterization of arithmeticity phrased in the language of algebraic tori, building on work of Grunewald-Platonov. We use this to prove several more concrete results that relate the arithmeticity of $\\mathbb Z^n\\rtimes_A\\mathbb Z$ to the reducibility properties of the characteristic polynomial of $A$. Our tools include algebraic tori, representation theory of finite groups, Galois theory, and the inverse Galois problem."},"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":"2004.00586","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2020-04-01T17:14:27Z","cross_cats_sorted":[],"title_canon_sha256":"3603540946118441c72ab013cf0c90e77056b26a1e82c664a20c95d398a3d5b6","abstract_canon_sha256":"eb50d183c23fbe63b3e4d94660cfdd9d16935d0ec87c2e473b69e5bf1d0bd00d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:52:12.078668Z","signature_b64":"zxi4CGQNl4xOwKFqAYb8UDnKWB20xXHMwoYDakqGf1cCaK+bYl20qCDlmNjoYqXL9k6qSHV7v9a/boym/4I1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f0d8a5b6fb31effc0cb46ecec5206417152088505cb5b67fe46bca52b6ababf","last_reissued_at":"2026-07-05T00:52:12.078265Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:52:12.078265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmeticity of groups $\\mathbb Z^n\\rtimes\\mathbb Z$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bena Tshishiku","submitted_at":"2020-04-01T17:14:27Z","abstract_excerpt":"We study when the group $\\mathbb Z^n\\rtimes_A\\mathbb Z$ is arithmetic where $A\\in GL_n(\\mathbb Z)$ is hyperbolic and semisimple. We begin by giving a characterization of arithmeticity phrased in the language of algebraic tori, building on work of Grunewald-Platonov. We use this to prove several more concrete results that relate the arithmeticity of $\\mathbb Z^n\\rtimes_A\\mathbb Z$ to the reducibility properties of the characteristic polynomial of $A$. Our tools include algebraic tori, representation theory of finite groups, Galois theory, and the inverse Galois problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.00586","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.00586/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2004.00586","created_at":"2026-07-05T00:52:12.078323+00:00"},{"alias_kind":"arxiv_version","alias_value":"2004.00586v1","created_at":"2026-07-05T00:52:12.078323+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.00586","created_at":"2026-07-05T00:52:12.078323+00:00"},{"alias_kind":"pith_short_12","alias_value":"L4GYUW3PWMPP","created_at":"2026-07-05T00:52:12.078323+00:00"},{"alias_kind":"pith_short_16","alias_value":"L4GYUW3PWMPP7QGL","created_at":"2026-07-05T00:52:12.078323+00:00"},{"alias_kind":"pith_short_8","alias_value":"L4GYUW3P","created_at":"2026-07-05T00:52:12.078323+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/L4GYUW3PWMPP7QGLI3WOYUQGIF","json":"https://pith.science/pith/L4GYUW3PWMPP7QGLI3WOYUQGIF.json","graph_json":"https://pith.science/api/pith-number/L4GYUW3PWMPP7QGLI3WOYUQGIF/graph.json","events_json":"https://pith.science/api/pith-number/L4GYUW3PWMPP7QGLI3WOYUQGIF/events.json","paper":"https://pith.science/paper/L4GYUW3P"},"agent_actions":{"view_html":"https://pith.science/pith/L4GYUW3PWMPP7QGLI3WOYUQGIF","download_json":"https://pith.science/pith/L4GYUW3PWMPP7QGLI3WOYUQGIF.json","view_paper":"https://pith.science/paper/L4GYUW3P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2004.00586&json=true","fetch_graph":"https://pith.science/api/pith-number/L4GYUW3PWMPP7QGLI3WOYUQGIF/graph.json","fetch_events":"https://pith.science/api/pith-number/L4GYUW3PWMPP7QGLI3WOYUQGIF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L4GYUW3PWMPP7QGLI3WOYUQGIF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L4GYUW3PWMPP7QGLI3WOYUQGIF/action/storage_attestation","attest_author":"https://pith.science/pith/L4GYUW3PWMPP7QGLI3WOYUQGIF/action/author_attestation","sign_citation":"https://pith.science/pith/L4GYUW3PWMPP7QGLI3WOYUQGIF/action/citation_signature","submit_replication":"https://pith.science/pith/L4GYUW3PWMPP7QGLI3WOYUQGIF/action/replication_record"}},"created_at":"2026-07-05T00:52:12.078323+00:00","updated_at":"2026-07-05T00:52:12.078323+00:00"}