{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CVKBG3CUJLZZPOJSY24XW6RJBI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6b164b17380b95d3bf172be0471111706b28321fa3938199d858306fe2991d10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-16T08:21:33Z","title_canon_sha256":"422d8d671f2dcfd2b3479658f3496a9e90d71acb8f333c8237a9aac433eb6114"},"schema_version":"1.0","source":{"id":"1603.04987","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04987","created_at":"2026-05-17T23:51:00Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04987v4","created_at":"2026-05-17T23:51:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04987","created_at":"2026-05-17T23:51:00Z"},{"alias_kind":"pith_short_12","alias_value":"CVKBG3CUJLZZ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CVKBG3CUJLZZPOJS","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CVKBG3CU","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:e93054d34b0fcc0b47a5f2be0508baa650f7fdff153b63b82d219c140ac9b832","target":"graph","created_at":"2026-05-17T23:51:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra some of its dihedral angles are $\\frac{\\pi}{m}$ for $m\\geq{7}$. By combining with the classical result by Parry \\cite{Pa} and the main result of \\cite{Y}, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers.","authors_text":"Tomoshige Yukita","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-16T08:21:33Z","title":"Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04987","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8d30642f33123e7ffd45364eaa54e9b5cb7461e0c32faaf4f16f0f4f48f5f398","target":"record","created_at":"2026-05-17T23:51:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6b164b17380b95d3bf172be0471111706b28321fa3938199d858306fe2991d10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-16T08:21:33Z","title_canon_sha256":"422d8d671f2dcfd2b3479658f3496a9e90d71acb8f333c8237a9aac433eb6114"},"schema_version":"1.0","source":{"id":"1603.04987","kind":"arxiv","version":4}},"canonical_sha256":"1554136c544af397b932c6b97b7a290a105d5dc8ff8d4bbb630f88672502b0e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1554136c544af397b932c6b97b7a290a105d5dc8ff8d4bbb630f88672502b0e2","first_computed_at":"2026-05-17T23:51:00.577825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:00.577825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E4NkZRPSVqUUTpcBxJ7dvKKtKGD3ICQilTFVC3RqL3Onhl0Pfsus6hcxjJbWU7cXrHDHp5HS9fyH3zHtjh9jBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:00.578609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04987","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d30642f33123e7ffd45364eaa54e9b5cb7461e0c32faaf4f16f0f4f48f5f398","sha256:e93054d34b0fcc0b47a5f2be0508baa650f7fdff153b63b82d219c140ac9b832"],"state_sha256":"9dbb296b1c03e33cd6ee264d6323b7df15b2e72b647c4ca24f1d424ae104deb3"}