{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:RD27GTTWD7TWAL5677RD2XVOQO","short_pith_number":"pith:RD27GTTW","schema_version":"1.0","canonical_sha256":"88f5f34e761fe7602fbeffe23d5eae83826ebf5a42fa9fefeeeb8ad3a420183a","source":{"kind":"arxiv","id":"1306.3443","version":1},"attestation_state":"computed","paper":{"title":"Growth rates of cocompact hyperbolic Coxeter groups and 2-Salem numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Yuriko Umemoto","submitted_at":"2013-06-14T16:26:36Z","abstract_excerpt":"By the results of Cannon, Wagreich and Parry, it is known that the growth rate of a cocompact Coxeter group in 2-dimensional hyperbolic space $H^2$ and 3-dimensional hyperbolic space $H^3$ is a Salem number. Kerada defined a j-Salem number, which is a generalization of a Salem number. In this paper, we realize infinitely many 2-Salem numbers as the growth rates of cocompact Coxeter groups in 4-dimensional hyperbolic space $H ^4$. Our Coxeter polytopes are constructed by successive gluing of Coxeter polytopes which we call Coxeter dominoes."},"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":"1306.3443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-06-14T16:26:36Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0fd406946a52fcab283772b9c7b8b84248444f8f5ce6c93f54c9f6c25ca3ee3b","abstract_canon_sha256":"f75042bbb5bfd16492b6f03bdcf03850f56d88f5f01b54e370c7e32c5d1be1eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:54.479517Z","signature_b64":"X7Vx3QputiTs4lgStZOjFsM8XtbwPDKW+FmIremAzmNCtIFgCHQVfyey9MGPh3x5NK+dnDUBVE0Ie6T14MMYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88f5f34e761fe7602fbeffe23d5eae83826ebf5a42fa9fefeeeb8ad3a420183a","last_reissued_at":"2026-05-18T02:32:54.479121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:54.479121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Growth rates of cocompact hyperbolic Coxeter groups and 2-Salem numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Yuriko Umemoto","submitted_at":"2013-06-14T16:26:36Z","abstract_excerpt":"By the results of Cannon, Wagreich and Parry, it is known that the growth rate of a cocompact Coxeter group in 2-dimensional hyperbolic space $H^2$ and 3-dimensional hyperbolic space $H^3$ is a Salem number. Kerada defined a j-Salem number, which is a generalization of a Salem number. In this paper, we realize infinitely many 2-Salem numbers as the growth rates of cocompact Coxeter groups in 4-dimensional hyperbolic space $H ^4$. Our Coxeter polytopes are constructed by successive gluing of Coxeter polytopes which we call Coxeter dominoes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3443","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":"1306.3443","created_at":"2026-05-18T02:32:54.479178+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.3443v1","created_at":"2026-05-18T02:32:54.479178+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3443","created_at":"2026-05-18T02:32:54.479178+00:00"},{"alias_kind":"pith_short_12","alias_value":"RD27GTTWD7TW","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"RD27GTTWD7TWAL56","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"RD27GTTW","created_at":"2026-05-18T12:27:57.521954+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/RD27GTTWD7TWAL5677RD2XVOQO","json":"https://pith.science/pith/RD27GTTWD7TWAL5677RD2XVOQO.json","graph_json":"https://pith.science/api/pith-number/RD27GTTWD7TWAL5677RD2XVOQO/graph.json","events_json":"https://pith.science/api/pith-number/RD27GTTWD7TWAL5677RD2XVOQO/events.json","paper":"https://pith.science/paper/RD27GTTW"},"agent_actions":{"view_html":"https://pith.science/pith/RD27GTTWD7TWAL5677RD2XVOQO","download_json":"https://pith.science/pith/RD27GTTWD7TWAL5677RD2XVOQO.json","view_paper":"https://pith.science/paper/RD27GTTW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.3443&json=true","fetch_graph":"https://pith.science/api/pith-number/RD27GTTWD7TWAL5677RD2XVOQO/graph.json","fetch_events":"https://pith.science/api/pith-number/RD27GTTWD7TWAL5677RD2XVOQO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RD27GTTWD7TWAL5677RD2XVOQO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RD27GTTWD7TWAL5677RD2XVOQO/action/storage_attestation","attest_author":"https://pith.science/pith/RD27GTTWD7TWAL5677RD2XVOQO/action/author_attestation","sign_citation":"https://pith.science/pith/RD27GTTWD7TWAL5677RD2XVOQO/action/citation_signature","submit_replication":"https://pith.science/pith/RD27GTTWD7TWAL5677RD2XVOQO/action/replication_record"}},"created_at":"2026-05-18T02:32:54.479178+00:00","updated_at":"2026-05-18T02:32:54.479178+00:00"}