{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:V52NYI7ASCQHU4KJ6MO5VIO2QG","short_pith_number":"pith:V52NYI7A","canonical_record":{"source":{"id":"1409.3355","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-11T08:41:41Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"8018b2d4917dc8f2138b2c25e9ff08333929fe831abfd7be9e0440b87957f18d","abstract_canon_sha256":"d19fe7bee71e4413d8a4efe6e822aad0ce4541d980bc36f9aa5f2767c5930846"},"schema_version":"1.0"},"canonical_sha256":"af74dc23e090a07a7149f31ddaa1da81806ccae5e794fd316274ef4faeaf7b0b","source":{"kind":"arxiv","id":"1409.3355","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3355","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3355v5","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3355","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"V52NYI7ASCQH","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V52NYI7ASCQHU4KJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V52NYI7A","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:V52NYI7ASCQHU4KJ6MO5VIO2QG","target":"record","payload":{"canonical_record":{"source":{"id":"1409.3355","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-11T08:41:41Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"8018b2d4917dc8f2138b2c25e9ff08333929fe831abfd7be9e0440b87957f18d","abstract_canon_sha256":"d19fe7bee71e4413d8a4efe6e822aad0ce4541d980bc36f9aa5f2767c5930846"},"schema_version":"1.0"},"canonical_sha256":"af74dc23e090a07a7149f31ddaa1da81806ccae5e794fd316274ef4faeaf7b0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:00.426606Z","signature_b64":"xr5ru701mKV2JfRMj8TRl+jVzXGRYvRutbzi5GMRNKX91i+LXNyUT2QCdtOVxIaSZQBPQw6ajh/lxr1o2GWVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af74dc23e090a07a7149f31ddaa1da81806ccae5e794fd316274ef4faeaf7b0b","last_reissued_at":"2026-05-18T01:13:00.426210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:00.426210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.3355","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qZWznr0CHcuvsmK2mavvvmrCiDgbeFCqHDBI9FjgLDusf09UN26F7kw6lOup0YuCHvivJXi/ALCdLIOCRt20Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:39:58.123848Z"},"content_sha256":"9ff80cad3a4aaecac865a0d95559999fdb00f52862741fb918c37ab761d9a39c","schema_version":"1.0","event_id":"sha256:9ff80cad3a4aaecac865a0d95559999fdb00f52862741fb918c37ab761d9a39c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:V52NYI7ASCQHU4KJ6MO5VIO2QG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The dual Jacobian of a generalised tetrahedron, and volumes of prisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.MG","authors_text":"Alexander Kolpakov, Jun Murakami","submitted_at":"2014-09-11T08:41:41Z","abstract_excerpt":"We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron. The Jacobian for the latter arises as an analytic continuation of the former, that falls in line with a similar behaviour of the corresponding volume formulae.\n  Also, we obtain a volume formula for a hyperbolic $n$-gonal prism: the proof requires the above mentioned Jacobian, employed in the analysis of the edge lengths behaviour of such a prism, needed later for the Schl\\\"afli formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3355","kind":"arxiv","version":5},"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":"2026-05-18T01:13:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+eIpVO0wEwtdeCM1k6MTm85wnnS1+TToZgofpCyZyhSGaohX4D1A2QZvd323pbFqUqspC0RNGtbYmZHxJ7XhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:39:58.124625Z"},"content_sha256":"55baa5b968ecf6cf4441b72dc23ec0b31a26091558fbe498fbdef4d508607c66","schema_version":"1.0","event_id":"sha256:55baa5b968ecf6cf4441b72dc23ec0b31a26091558fbe498fbdef4d508607c66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V52NYI7ASCQHU4KJ6MO5VIO2QG/bundle.json","state_url":"https://pith.science/pith/V52NYI7ASCQHU4KJ6MO5VIO2QG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V52NYI7ASCQHU4KJ6MO5VIO2QG/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":"2026-06-09T02:39:58Z","links":{"resolver":"https://pith.science/pith/V52NYI7ASCQHU4KJ6MO5VIO2QG","bundle":"https://pith.science/pith/V52NYI7ASCQHU4KJ6MO5VIO2QG/bundle.json","state":"https://pith.science/pith/V52NYI7ASCQHU4KJ6MO5VIO2QG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V52NYI7ASCQHU4KJ6MO5VIO2QG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:V52NYI7ASCQHU4KJ6MO5VIO2QG","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":"d19fe7bee71e4413d8a4efe6e822aad0ce4541d980bc36f9aa5f2767c5930846","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-11T08:41:41Z","title_canon_sha256":"8018b2d4917dc8f2138b2c25e9ff08333929fe831abfd7be9e0440b87957f18d"},"schema_version":"1.0","source":{"id":"1409.3355","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3355","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3355v5","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3355","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"V52NYI7ASCQH","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V52NYI7ASCQHU4KJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V52NYI7A","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:55baa5b968ecf6cf4441b72dc23ec0b31a26091558fbe498fbdef4d508607c66","target":"graph","created_at":"2026-05-18T01:13:00Z","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":"We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron. The Jacobian for the latter arises as an analytic continuation of the former, that falls in line with a similar behaviour of the corresponding volume formulae.\n  Also, we obtain a volume formula for a hyperbolic $n$-gonal prism: the proof requires the above mentioned Jacobian, employed in the analysis of the edge lengths behaviour of such a prism, needed later for the Schl\\\"afli formula.","authors_text":"Alexander Kolpakov, Jun Murakami","cross_cats":["math.CV","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-11T08:41:41Z","title":"The dual Jacobian of a generalised tetrahedron, and volumes of prisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3355","kind":"arxiv","version":5},"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":"sha256:9ff80cad3a4aaecac865a0d95559999fdb00f52862741fb918c37ab761d9a39c","target":"record","created_at":"2026-05-18T01:13:00Z","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":"d19fe7bee71e4413d8a4efe6e822aad0ce4541d980bc36f9aa5f2767c5930846","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-11T08:41:41Z","title_canon_sha256":"8018b2d4917dc8f2138b2c25e9ff08333929fe831abfd7be9e0440b87957f18d"},"schema_version":"1.0","source":{"id":"1409.3355","kind":"arxiv","version":5}},"canonical_sha256":"af74dc23e090a07a7149f31ddaa1da81806ccae5e794fd316274ef4faeaf7b0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af74dc23e090a07a7149f31ddaa1da81806ccae5e794fd316274ef4faeaf7b0b","first_computed_at":"2026-05-18T01:13:00.426210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:00.426210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xr5ru701mKV2JfRMj8TRl+jVzXGRYvRutbzi5GMRNKX91i+LXNyUT2QCdtOVxIaSZQBPQw6ajh/lxr1o2GWVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:00.426606Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3355","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ff80cad3a4aaecac865a0d95559999fdb00f52862741fb918c37ab761d9a39c","sha256:55baa5b968ecf6cf4441b72dc23ec0b31a26091558fbe498fbdef4d508607c66"],"state_sha256":"42cb1ff61ef3b21bf7cf325c77037ff631460fa36b051545e3e9938917e5d142"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hXq5SDfUDUhb7pohf0q+AFVN/g4Q8M1fLZqpjhrcFZN0ZSXYJSAPl4znA9J1zoxMqPr5/inaB2fo5/Fkx2Y1CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:39:58.128442Z","bundle_sha256":"f5fc8f662de24b4a41cf01adf8b4e81d91c195453576c0d64048c00af6a2ce47"}}