{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CFZ5BBT2P46FGXM4IW6CRMKJFR","short_pith_number":"pith:CFZ5BBT2","canonical_record":{"source":{"id":"1803.10809","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-03-23T09:57:31Z","cross_cats_sorted":[],"title_canon_sha256":"d8bfc461b19fbcbb7a12e9ef1766cc68be6b0e5ce29f3c976c139558b38b09f9","abstract_canon_sha256":"3b38928f5cec71ea5e52caa94f8b810d08c7d55b8ed330de833bd346597b872e"},"schema_version":"1.0"},"canonical_sha256":"1173d0867a7f3c535d9c45bc28b1492c48431a775853ed9d96fa948fe1068fa4","source":{"kind":"arxiv","id":"1803.10809","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10809","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10809v3","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10809","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"pith_short_12","alias_value":"CFZ5BBT2P46F","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CFZ5BBT2P46FGXM4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CFZ5BBT2","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CFZ5BBT2P46FGXM4IW6CRMKJFR","target":"record","payload":{"canonical_record":{"source":{"id":"1803.10809","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-03-23T09:57:31Z","cross_cats_sorted":[],"title_canon_sha256":"d8bfc461b19fbcbb7a12e9ef1766cc68be6b0e5ce29f3c976c139558b38b09f9","abstract_canon_sha256":"3b38928f5cec71ea5e52caa94f8b810d08c7d55b8ed330de833bd346597b872e"},"schema_version":"1.0"},"canonical_sha256":"1173d0867a7f3c535d9c45bc28b1492c48431a775853ed9d96fa948fe1068fa4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:30.802724Z","signature_b64":"48OV3YjuiuyJRih+WkZ++Y4Eep990t1U5Jo3Twyhr2ZTtMvFUOl/W9mm8G5n1CiYcOOx5vn0LcRQVcoLmc8QCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1173d0867a7f3c535d9c45bc28b1492c48431a775853ed9d96fa948fe1068fa4","last_reissued_at":"2026-05-18T00:18:30.802338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:30.802338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.10809","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1X4wNqz9Z8iBkd/lEklmd2OW2jhGB+ymfMUypVp/NOkXfBIvYyxU4MIcYxtUAsxdxzS+PBMVpqVSBeYVTK6GCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:16:44.451201Z"},"content_sha256":"ca2759eb5994342c3ea0c903e8e64584f41c073ab25f0f5a9afea1fe6930c15a","schema_version":"1.0","event_id":"sha256:ca2759eb5994342c3ea0c903e8e64584f41c073ab25f0f5a9afea1fe6930c15a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CFZ5BBT2P46FGXM4IW6CRMKJFR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Volume and Boundary Face Area of a Regular Tetrahedron in a Constant Curvature Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Noureddine Mebarki, Omar Nemoul","submitted_at":"2018-03-23T09:57:31Z","abstract_excerpt":"An example of the volume and boundary face area of a curved polyhedron for the case of regular spherical and hyperbolic tetrahedron is discussed. An exact formula is explicitly derived as a function of the scalar curvature and the edge length. This work can be used in loop quantum gravity and Regge calculus in the context of a non-vanishing cosmological constant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10809","kind":"arxiv","version":3},"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":"2026-05-18T00:18:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Km4xp9liUiBXakB9zQVTt9kVyW93OAquh4R8cE5Ao+fGFKD7wTzbQT0DoK5IO3roJ8L1dqXL6Gn4GgpaxBFaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:16:44.451550Z"},"content_sha256":"9bd8f43da1e406a83eed4348a339b71aef7307095b197d71d3bf64a9a70bf521","schema_version":"1.0","event_id":"sha256:9bd8f43da1e406a83eed4348a339b71aef7307095b197d71d3bf64a9a70bf521"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFZ5BBT2P46FGXM4IW6CRMKJFR/bundle.json","state_url":"https://pith.science/pith/CFZ5BBT2P46FGXM4IW6CRMKJFR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFZ5BBT2P46FGXM4IW6CRMKJFR/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":"2026-06-27T20:16:44Z","links":{"resolver":"https://pith.science/pith/CFZ5BBT2P46FGXM4IW6CRMKJFR","bundle":"https://pith.science/pith/CFZ5BBT2P46FGXM4IW6CRMKJFR/bundle.json","state":"https://pith.science/pith/CFZ5BBT2P46FGXM4IW6CRMKJFR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFZ5BBT2P46FGXM4IW6CRMKJFR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CFZ5BBT2P46FGXM4IW6CRMKJFR","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":"3b38928f5cec71ea5e52caa94f8b810d08c7d55b8ed330de833bd346597b872e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-03-23T09:57:31Z","title_canon_sha256":"d8bfc461b19fbcbb7a12e9ef1766cc68be6b0e5ce29f3c976c139558b38b09f9"},"schema_version":"1.0","source":{"id":"1803.10809","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10809","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10809v3","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10809","created_at":"2026-05-18T00:18:30Z"},{"alias_kind":"pith_short_12","alias_value":"CFZ5BBT2P46F","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CFZ5BBT2P46FGXM4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CFZ5BBT2","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:9bd8f43da1e406a83eed4348a339b71aef7307095b197d71d3bf64a9a70bf521","target":"graph","created_at":"2026-05-18T00:18:30Z","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":"An example of the volume and boundary face area of a curved polyhedron for the case of regular spherical and hyperbolic tetrahedron is discussed. An exact formula is explicitly derived as a function of the scalar curvature and the edge length. This work can be used in loop quantum gravity and Regge calculus in the context of a non-vanishing cosmological constant.","authors_text":"Noureddine Mebarki, Omar Nemoul","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-03-23T09:57:31Z","title":"Volume and Boundary Face Area of a Regular Tetrahedron in a Constant Curvature Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10809","kind":"arxiv","version":3},"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:ca2759eb5994342c3ea0c903e8e64584f41c073ab25f0f5a9afea1fe6930c15a","target":"record","created_at":"2026-05-18T00:18:30Z","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":"3b38928f5cec71ea5e52caa94f8b810d08c7d55b8ed330de833bd346597b872e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-03-23T09:57:31Z","title_canon_sha256":"d8bfc461b19fbcbb7a12e9ef1766cc68be6b0e5ce29f3c976c139558b38b09f9"},"schema_version":"1.0","source":{"id":"1803.10809","kind":"arxiv","version":3}},"canonical_sha256":"1173d0867a7f3c535d9c45bc28b1492c48431a775853ed9d96fa948fe1068fa4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1173d0867a7f3c535d9c45bc28b1492c48431a775853ed9d96fa948fe1068fa4","first_computed_at":"2026-05-18T00:18:30.802338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:30.802338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"48OV3YjuiuyJRih+WkZ++Y4Eep990t1U5Jo3Twyhr2ZTtMvFUOl/W9mm8G5n1CiYcOOx5vn0LcRQVcoLmc8QCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:30.802724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10809","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca2759eb5994342c3ea0c903e8e64584f41c073ab25f0f5a9afea1fe6930c15a","sha256:9bd8f43da1e406a83eed4348a339b71aef7307095b197d71d3bf64a9a70bf521"],"state_sha256":"ba72339ec47a84ab90db489594c536e5c9dea8d4bc5b339464e237a0f20645ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eENf5wO+/vkikjejWbrnF4fuQt1qsp2MbxpPZWJ6oeJ3rlWTcw3C2hbJVcQpMrEJ43s+Vo28dXMYouHirV/CAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T20:16:44.453342Z","bundle_sha256":"a18cf3c387781ef8944bc3397a859748fa83498cff587d75679a4d69998cd1c4"}}