{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:D2DBGMOKL6PBAWD4ITHEF7Z2DZ","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":"0b9dff3fa55233633c37a233d31303b524b9f42d67f274f7778e0d313284ca47","cross_cats_sorted":["gr-qc"],"license":"","primary_cat":"hep-th","submitted_at":"1999-07-19T17:26:58Z","title_canon_sha256":"3e8656ea0af4a0a9a6e5487770a9b63377d77499c4960cc56eea2ff8979d611c"},"schema_version":"1.0","source":{"id":"hep-th/9907154","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9907154","created_at":"2026-07-04T16:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9907154v2","created_at":"2026-07-04T16:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9907154","created_at":"2026-07-04T16:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"D2DBGMOKL6PB","created_at":"2026-07-04T16:14:54Z"},{"alias_kind":"pith_short_16","alias_value":"D2DBGMOKL6PBAWD4","created_at":"2026-07-04T16:14:54Z"},{"alias_kind":"pith_short_8","alias_value":"D2DBGMOK","created_at":"2026-07-04T16:14:54Z"}],"graph_snapshots":[{"event_id":"sha256:50d5a29b473019e6f13e44d5781cb1563fb5741167957a8487fd24d2dcd25960","target":"graph","created_at":"2026-07-04T16:14:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/9907154/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Boulatov and Ooguri have generalized the matrix models of 2d quantum gravity to 3d and 4d, in the form of field theories over group manifolds. We show that the Barrett-Crane quantum gravity model arises naturally from a theory of this type, but restricted to the homogeneous space S^3=SO(4)/SO(3), as a term in its Feynman expansion. From such a perspective, 4d quantum spacetime emerges as a Feynman graph, in the manner of the 2d matrix models. This formalism provides a precise meaning to the ``sum over triangulations'', which is presumably necessary for a physical interpretation of a spin foam ","authors_text":"C. Rovelli, K. Krasnov, L. Freidel, R. De Pietri","cross_cats":["gr-qc"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1999-07-19T17:26:58Z","title":"Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9907154","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":"sha256:73df91d9aa6dedd35dad4556fc1c258e91aab420167fff3c67b16d3c15e954b7","target":"record","created_at":"2026-07-04T16:14:54Z","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":"0b9dff3fa55233633c37a233d31303b524b9f42d67f274f7778e0d313284ca47","cross_cats_sorted":["gr-qc"],"license":"","primary_cat":"hep-th","submitted_at":"1999-07-19T17:26:58Z","title_canon_sha256":"3e8656ea0af4a0a9a6e5487770a9b63377d77499c4960cc56eea2ff8979d611c"},"schema_version":"1.0","source":{"id":"hep-th/9907154","kind":"arxiv","version":2}},"canonical_sha256":"1e861331ca5f9e10587c44ce42ff3a1e4586833f5be0875f2c3cb7a835a0ff98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e861331ca5f9e10587c44ce42ff3a1e4586833f5be0875f2c3cb7a835a0ff98","first_computed_at":"2026-07-04T16:14:54.905354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:14:54.905354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"toXEeoJwGuGXJW0x1ENofOsuwO93Zuf4qoirKH2pG1UhMaj+M7CzgAzyn60+qJDqSmS9DnDxrcttFtFAv3IeDg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:14:54.905748Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9907154","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73df91d9aa6dedd35dad4556fc1c258e91aab420167fff3c67b16d3c15e954b7","sha256:50d5a29b473019e6f13e44d5781cb1563fb5741167957a8487fd24d2dcd25960"],"state_sha256":"8171748075fc289d47e8a67a6d840553ba880e1c3a3c02d5426cf70e56238b0c"}