{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5JTNI77XFHERIR3BRGR26CU5ZS","short_pith_number":"pith:5JTNI77X","canonical_record":{"source":{"id":"1802.08049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-22T14:14:23Z","cross_cats_sorted":[],"title_canon_sha256":"397b5aac9484ca4d562da27b5667756adec05bc0ea99238c7b3e66fcb3a15bbd","abstract_canon_sha256":"924b3c559aee2215563c5d1f5f1bdedd874573f355e44e499a3b1338085f00b6"},"schema_version":"1.0"},"canonical_sha256":"ea66d47ff729c914476189a3af0a9dcc8c0767e46931129fd0781b7c7ddc9b71","source":{"kind":"arxiv","id":"1802.08049","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5JTNI77XFHERIR3BRGR26CU5ZS","target":"record","payload":{"canonical_record":{"source":{"id":"1802.08049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-22T14:14:23Z","cross_cats_sorted":[],"title_canon_sha256":"397b5aac9484ca4d562da27b5667756adec05bc0ea99238c7b3e66fcb3a15bbd","abstract_canon_sha256":"924b3c559aee2215563c5d1f5f1bdedd874573f355e44e499a3b1338085f00b6"},"schema_version":"1.0"},"canonical_sha256":"ea66d47ff729c914476189a3af0a9dcc8c0767e46931129fd0781b7c7ddc9b71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:45.731752Z","signature_b64":"iqaLLkuaPI4zTaXxgcpU6/PSKXZiVpc1VTOYnIff7PhyP+cTuM+E4iJLknlnCk1rq5gfsTC9PfG3lpTyWs5TAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea66d47ff729c914476189a3af0a9dcc8c0767e46931129fd0781b7c7ddc9b71","last_reissued_at":"2026-05-18T00:22:45.731183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:45.731183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.08049","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e1Uz9H6Q6gWdD8SIiN5yzjb/imFtTACWDj3a+LUp+/w22E0Q5RvF+29l0DAg+dPdTEkullrPFZ5IMqxI5tHLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:17:29.276760Z"},"content_sha256":"1bb77d38eeabc4165e5ba013b92b6cd4c42d2133987532d592194276cf88c4cc","schema_version":"1.0","event_id":"sha256:1bb77d38eeabc4165e5ba013b92b6cd4c42d2133987532d592194276cf88c4cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5JTNI77XFHERIR3BRGR26CU5ZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Seidel's conjectures in hyperbolic 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Carlos H. Grossi, Omar Chavez Cussy","submitted_at":"2018-02-22T14:14:23Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08049","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p1EebyzpW//EkT3rLeRgiyajnerfc+xpW45G7h76hp3pqLkVCj4yOnmX2LE+Dr0gtHOn+j+tYovXAKFQNcXVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:17:29.277099Z"},"content_sha256":"30e16255e0e93877158a1ffbf48da3f15dcacac239f4520ded13049525962c8e","schema_version":"1.0","event_id":"sha256:30e16255e0e93877158a1ffbf48da3f15dcacac239f4520ded13049525962c8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JTNI77XFHERIR3BRGR26CU5ZS/bundle.json","state_url":"https://pith.science/pith/5JTNI77XFHERIR3BRGR26CU5ZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JTNI77XFHERIR3BRGR26CU5ZS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T21:17:29Z","links":{"resolver":"https://pith.science/pith/5JTNI77XFHERIR3BRGR26CU5ZS","bundle":"https://pith.science/pith/5JTNI77XFHERIR3BRGR26CU5ZS/bundle.json","state":"https://pith.science/pith/5JTNI77XFHERIR3BRGR26CU5ZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JTNI77XFHERIR3BRGR26CU5ZS/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pbffWYFVV4UMQ6KT2cz2suvKzVdPwLCOQXaayrced7hTBs3QOS4zhMP8sDmU6tGZitNKGunAhoffKtvjIJUzBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:17:29.279095Z","bundle_sha256":"27fd76800e9cc3eee22a8600f5fa3b10eb607153e81153f2f2b83f0393ac5ac9"}}