{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:6XUFSNN4DNABKBQADXCF3ERM4C","short_pith_number":"pith:6XUFSNN4","canonical_record":{"source":{"id":"gr-qc/0011006","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2000-11-02T13:19:45Z","cross_cats_sorted":[],"title_canon_sha256":"5b1a25d78bc54387e1a934b49c710a68f134ad55b6b32a1fbf047945d390d073","abstract_canon_sha256":"74f5305c587353adeb4c670a2d6d528d1b4b93e49fde9f0fb07ec2b3c6cd0574"},"schema_version":"1.0"},"canonical_sha256":"f5e85935bc1b401506001dc45d922ce0af921266929609b63130f5f5f179ad2d","source":{"kind":"arxiv","id":"gr-qc/0011006","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0011006","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0011006v2","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0011006","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"pith_short_12","alias_value":"6XUFSNN4DNAB","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"6XUFSNN4DNABKBQA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"6XUFSNN4","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:6XUFSNN4DNABKBQADXCF3ERM4C","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0011006","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2000-11-02T13:19:45Z","cross_cats_sorted":[],"title_canon_sha256":"5b1a25d78bc54387e1a934b49c710a68f134ad55b6b32a1fbf047945d390d073","abstract_canon_sha256":"74f5305c587353adeb4c670a2d6d528d1b4b93e49fde9f0fb07ec2b3c6cd0574"},"schema_version":"1.0"},"canonical_sha256":"f5e85935bc1b401506001dc45d922ce0af921266929609b63130f5f5f179ad2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:36.268702Z","signature_b64":"DtfVjxDc8zv9/2MNvXnZJ/MUJ/dF1UPZDXfEVsHNWvdU6hI/F/9IOnWpiAnVVijrHsJSdDJXsVJdFcMYu+CzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5e85935bc1b401506001dc45d922ce0af921266929609b63130f5f5f179ad2d","last_reissued_at":"2026-05-18T02:37:36.268102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:36.268102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0011006","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aOKYyhb9ZdO/lYlFVc5cokofELiURUNXhoNXqul+/LPGmsLdDA1daspCFEkX4I2wXzKD4xn1ui8lJ74m7VunCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:36:56.018578Z"},"content_sha256":"04415f5157c2c62505b156f6e6e7e8bcc0fb056856226453b6ef085086d75d08","schema_version":"1.0","event_id":"sha256:04415f5157c2c62505b156f6e6e7e8bcc0fb056856226453b6ef085086d75d08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:6XUFSNN4DNABKBQADXCF3ERM4C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constraints on Area Variables in Regge Calculus","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Jarmo Makela, Ruth M. Williams","submitted_at":"2000-11-02T13:19:45Z","abstract_excerpt":"We describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The number of independent constraints on the variations of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0011006","kind":"arxiv","version":2},"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":"2026-05-18T02:37:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZdHCp7hkeIIEoPKqEiqK3xmfi/4a3Znj6p2NuTTEnZQ1mL4gKmRUtEmwfLr1rm094n6Kai5MN1OLzzlLS8crCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:36:56.019109Z"},"content_sha256":"afd0cac299efecf64b19c60abd58924c42dbb75719d1c8c371d1263165047403","schema_version":"1.0","event_id":"sha256:afd0cac299efecf64b19c60abd58924c42dbb75719d1c8c371d1263165047403"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6XUFSNN4DNABKBQADXCF3ERM4C/bundle.json","state_url":"https://pith.science/pith/6XUFSNN4DNABKBQADXCF3ERM4C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6XUFSNN4DNABKBQADXCF3ERM4C/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":"2026-06-04T21:36:56Z","links":{"resolver":"https://pith.science/pith/6XUFSNN4DNABKBQADXCF3ERM4C","bundle":"https://pith.science/pith/6XUFSNN4DNABKBQADXCF3ERM4C/bundle.json","state":"https://pith.science/pith/6XUFSNN4DNABKBQADXCF3ERM4C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6XUFSNN4DNABKBQADXCF3ERM4C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:6XUFSNN4DNABKBQADXCF3ERM4C","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":"74f5305c587353adeb4c670a2d6d528d1b4b93e49fde9f0fb07ec2b3c6cd0574","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2000-11-02T13:19:45Z","title_canon_sha256":"5b1a25d78bc54387e1a934b49c710a68f134ad55b6b32a1fbf047945d390d073"},"schema_version":"1.0","source":{"id":"gr-qc/0011006","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0011006","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0011006v2","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0011006","created_at":"2026-05-18T02:37:36Z"},{"alias_kind":"pith_short_12","alias_value":"6XUFSNN4DNAB","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"6XUFSNN4DNABKBQA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"6XUFSNN4","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:afd0cac299efecf64b19c60abd58924c42dbb75719d1c8c371d1263165047403","target":"graph","created_at":"2026-05-18T02:37:36Z","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 describe a general method of obtaining the constraints between area variables in one approach to area Regge calculus, and illustrate it with a simple example. The simplicial complex is the simplest tessellation of the 4-sphere. The number of independent constraints on the variations of the triangle areas is shown to equal the difference between the numbers of triangles and edges, and a general method of choosing independent constraints is described. The constraints chosen by using our method are shown to imply the Regge equations of motion in our example.","authors_text":"Jarmo Makela, Ruth M. Williams","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2000-11-02T13:19:45Z","title":"Constraints on Area Variables in Regge Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0011006","kind":"arxiv","version":2},"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":"sha256:04415f5157c2c62505b156f6e6e7e8bcc0fb056856226453b6ef085086d75d08","target":"record","created_at":"2026-05-18T02:37:36Z","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":"74f5305c587353adeb4c670a2d6d528d1b4b93e49fde9f0fb07ec2b3c6cd0574","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2000-11-02T13:19:45Z","title_canon_sha256":"5b1a25d78bc54387e1a934b49c710a68f134ad55b6b32a1fbf047945d390d073"},"schema_version":"1.0","source":{"id":"gr-qc/0011006","kind":"arxiv","version":2}},"canonical_sha256":"f5e85935bc1b401506001dc45d922ce0af921266929609b63130f5f5f179ad2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5e85935bc1b401506001dc45d922ce0af921266929609b63130f5f5f179ad2d","first_computed_at":"2026-05-18T02:37:36.268102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:36.268102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DtfVjxDc8zv9/2MNvXnZJ/MUJ/dF1UPZDXfEVsHNWvdU6hI/F/9IOnWpiAnVVijrHsJSdDJXsVJdFcMYu+CzDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:36.268702Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0011006","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04415f5157c2c62505b156f6e6e7e8bcc0fb056856226453b6ef085086d75d08","sha256:afd0cac299efecf64b19c60abd58924c42dbb75719d1c8c371d1263165047403"],"state_sha256":"9862102c96418ac4306cefc41ed7cc29a79e08c8f011ba9a79438cab73aaef41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"giXJLm9vTngPLC1FboBjyX1OzVo4S6KazcCF3CKPcpG4C2yaidGyvl5odRAsoZp1Fc+iKKUa3eh03BZLmdJqAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:36:56.022273Z","bundle_sha256":"acb79d6cc070514ab2017024c6e20e5769031e95167d9a1ccf9fa2cc45207ef2"}}