{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FHRKTM3UIHTU3HO3XOGHJPP6OX","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":"efabce1683a9a56e0935181d8a43fcf31eee22f4b5584865c51528148699d18d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-26T15:26:43Z","title_canon_sha256":"6a41aa921ef3b0a2b69f42f0f3acfcc5fede9d1199aac8fbff08d882ca09db6e"},"schema_version":"1.0","source":{"id":"1501.06443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06443","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06443v1","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06443","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"pith_short_12","alias_value":"FHRKTM3UIHTU","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FHRKTM3UIHTU3HO3","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FHRKTM3U","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:f8a3a50622bc767679af28334465c90e68cd89633e2322de509c6e7be423672f","target":"graph","created_at":"2026-05-18T02:28:41Z","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":"We study the covolumes of arithmetic lattices in $PSL_2(\\mathbb R)^n$ for $n\\geq 2$ and identify uniform and non-uniform irreducible lattices of minimal covolume. More precisely, let $\\mu$ be the Euler-Poincar\\'e measure on $PSL_2(\\mathbb R)^n$ and $\\chi=\\mu/2^n$. We show that the Hilbert modular group $PSL_2(\\mathfrak o_{k_{49}})\\subset PSL_2(\\mathbb R)^3$, with $k_{49}$ the totally real cubic field of discriminant $49$ has the minimal covolume with respect to $\\chi$ among all irreducible lattices in $PSL_2(\\mathbb R)^n$ for $n\\geq 2$ and is unique such lattice up to conjugation. The uniform ","authors_text":"Amir D\\v{z}ambi\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-26T15:26:43Z","title":"Lower bounds for covolumes of arithmetic lattices in $PSL_2(\\mathbb R)^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06443","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":"sha256:224c859aa9dd53a59c42bb9a5167a26607cdc0f3279bf111f85021fe504af124","target":"record","created_at":"2026-05-18T02:28:41Z","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":"efabce1683a9a56e0935181d8a43fcf31eee22f4b5584865c51528148699d18d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-01-26T15:26:43Z","title_canon_sha256":"6a41aa921ef3b0a2b69f42f0f3acfcc5fede9d1199aac8fbff08d882ca09db6e"},"schema_version":"1.0","source":{"id":"1501.06443","kind":"arxiv","version":1}},"canonical_sha256":"29e2a9b37441e74d9ddbbb8c74bdfe75c53c4c662123997ba1de45862753365e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29e2a9b37441e74d9ddbbb8c74bdfe75c53c4c662123997ba1de45862753365e","first_computed_at":"2026-05-18T02:28:41.455108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:41.455108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sn+h6+49BM5QL/E+GTGQoko5m+8vSqnMHyQbaBB1a5TgyA1Kouuj6cTkxr5A/96ObSQLdt2agwTJDjT89qayCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:41.455640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:224c859aa9dd53a59c42bb9a5167a26607cdc0f3279bf111f85021fe504af124","sha256:f8a3a50622bc767679af28334465c90e68cd89633e2322de509c6e7be423672f"],"state_sha256":"5eb1504a03bd7218cbc5692a1eae60fd12b928240fd6081cf0c3d70754f4fa1c"}