{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5JTNI77XFHERIR3BRGR26CU5ZS","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":"924b3c559aee2215563c5d1f5f1bdedd874573f355e44e499a3b1338085f00b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-22T14:14:23Z","title_canon_sha256":"397b5aac9484ca4d562da27b5667756adec05bc0ea99238c7b3e66fcb3a15bbd"},"schema_version":"1.0","source":{"id":"1802.08049","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08049","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08049v1","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08049","created_at":"2026-05-18T00:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"5JTNI77XFHER","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5JTNI77XFHERIR3B","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5JTNI77X","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:30e16255e0e93877158a1ffbf48da3f15dcacac239f4520ded13049525962c8e","target":"graph","created_at":"2026-05-18T00:22:45Z","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 prove, in the case of hyperbolic 3-space, a couple of conjectures raised by J. J. Seidel in \"On the volume of a hyperbolic simplex\", Stud. Sci. Math. Hung. 21, 243-249, 1986. These conjectures concern expressing the volume of an ideal hyperbolic tetrahedron as a monotonic function of algebraic maps. More precisely, Seidel's first conjecture states that the volume of an ideal tetrahedron in hyperbolic 3-space is determined by (the permanent and the determinant of) the doubly stochastic Gram matrix $G$ of its vertices; Seidel's fourth conjecture claims that the mentioned volume is a monotonic","authors_text":"Carlos H. Grossi, Omar Chavez Cussy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-22T14:14:23Z","title":"Seidel's conjectures in hyperbolic 3-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08049","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":"sha256:1bb77d38eeabc4165e5ba013b92b6cd4c42d2133987532d592194276cf88c4cc","target":"record","created_at":"2026-05-18T00:22:45Z","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":"924b3c559aee2215563c5d1f5f1bdedd874573f355e44e499a3b1338085f00b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-22T14:14:23Z","title_canon_sha256":"397b5aac9484ca4d562da27b5667756adec05bc0ea99238c7b3e66fcb3a15bbd"},"schema_version":"1.0","source":{"id":"1802.08049","kind":"arxiv","version":1}},"canonical_sha256":"ea66d47ff729c914476189a3af0a9dcc8c0767e46931129fd0781b7c7ddc9b71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea66d47ff729c914476189a3af0a9dcc8c0767e46931129fd0781b7c7ddc9b71","first_computed_at":"2026-05-18T00:22:45.731183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:45.731183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iqaLLkuaPI4zTaXxgcpU6/PSKXZiVpc1VTOYnIff7PhyP+cTuM+E4iJLknlnCk1rq5gfsTC9PfG3lpTyWs5TAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:45.731752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bb77d38eeabc4165e5ba013b92b6cd4c42d2133987532d592194276cf88c4cc","sha256:30e16255e0e93877158a1ffbf48da3f15dcacac239f4520ded13049525962c8e"],"state_sha256":"cbe9eac005bb28dd89f4027d74c5f0d5cca326dc5e039ba1f5eae924ad6f1035"}