{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5QOA3XRHGWZ57NUZB3MYNGZOMW","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":"513ebb93cb82de5bd867ebe9f840f72659d17c024e22811f45b92809ba33c0a3","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-06-28T17:41:00Z","title_canon_sha256":"0b930da3e1d1ba6774417cbf3c4db3ba3e86e7ee115a6336a063f8ab5c983858"},"schema_version":"1.0","source":{"id":"2206.14174","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.14174","created_at":"2026-07-05T04:35:53Z"},{"alias_kind":"arxiv_version","alias_value":"2206.14174v1","created_at":"2026-07-05T04:35:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.14174","created_at":"2026-07-05T04:35:53Z"},{"alias_kind":"pith_short_12","alias_value":"5QOA3XRHGWZ5","created_at":"2026-07-05T04:35:53Z"},{"alias_kind":"pith_short_16","alias_value":"5QOA3XRHGWZ57NUZ","created_at":"2026-07-05T04:35:53Z"},{"alias_kind":"pith_short_8","alias_value":"5QOA3XRH","created_at":"2026-07-05T04:35:53Z"}],"graph_snapshots":[{"event_id":"sha256:2ce1542d80e6dc61d5c3a7cb46d693b2938fc2a85d7c6f6e93ecd993e506fb68","target":"graph","created_at":"2026-07-05T04:35:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.14174/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We identify the finitely many arithmetic lattices $\\Gamma$ in the orientation preserving isometry group of hyperbolic $3$-space $\\mathbb{H}^3$ generated by an element of order $4$ and and element of order $p\\geq 2$. Thus $\\Gamma$ has a presentation of the form $\\Gamma\\cong\\langle f,g: f^4=g^p=w(f,g)=\\cdots=1 \\rangle$ We find that necessarily $p\\in \\{2,3,4,5,6,\\infty\\}$, where $p=\\infty$ denotes that $g$ is a parabolic element, the total degree of the invariant trace field $k\\Gamma=\\mathbb{Q}(\\{\\tr^2(h):h\\in\\Gamma\\})$ is at most $4$, and each orbifold is either a two bridge link of slope $r/s$ ","authors_text":"G.J. Martin, K. Salehi, Y. Yamashita","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-06-28T17:41:00Z","title":"The $(4,p)$-arithmetic hyperbolic lattices, $p\\geq 2$, in three dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.14174","kind":"arxiv","version":1},"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":"sha256:4a97e4bf22f4918e176a1af24afb4c4ceabac383c823a67f64805c678cef1d12","target":"record","created_at":"2026-07-05T04:35:53Z","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":"513ebb93cb82de5bd867ebe9f840f72659d17c024e22811f45b92809ba33c0a3","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-06-28T17:41:00Z","title_canon_sha256":"0b930da3e1d1ba6774417cbf3c4db3ba3e86e7ee115a6336a063f8ab5c983858"},"schema_version":"1.0","source":{"id":"2206.14174","kind":"arxiv","version":1}},"canonical_sha256":"ec1c0dde2735b3dfb6990ed9869b2e659e2631a9f708727917a25760e14fa246","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec1c0dde2735b3dfb6990ed9869b2e659e2631a9f708727917a25760e14fa246","first_computed_at":"2026-07-05T04:35:53.803365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:35:53.803365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y3apW59UfA6UlrzfdID/b+sAhWsS59ZMkhcp9wI6bDnxyTFQEhGJNVAnFkv5tzOgg8nf2RPTaNOJX3sNh/aZBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:35:53.803763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.14174","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a97e4bf22f4918e176a1af24afb4c4ceabac383c823a67f64805c678cef1d12","sha256:2ce1542d80e6dc61d5c3a7cb46d693b2938fc2a85d7c6f6e93ecd993e506fb68"],"state_sha256":"cb84969c81346c6715b9e83d3d5d103e8044a49fe697f87de1efbc2b76756b8f"}