{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DYXC4RCZENQ62G2MQLUNHZRFUO","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":"85217368dd9e1a8e2c8787e20ba84898be24abfab5bfffc4733932e93ab9f81a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-01-05T13:34:13Z","title_canon_sha256":"b2c0ad68bdceef432a4e59068807e0ecd19473dbb99abe609945c051573dbf0f"},"schema_version":"1.0","source":{"id":"1501.00855","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00855","created_at":"2026-05-18T01:29:31Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00855v1","created_at":"2026-05-18T01:29:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00855","created_at":"2026-05-18T01:29:31Z"},{"alias_kind":"pith_short_12","alias_value":"DYXC4RCZENQ6","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DYXC4RCZENQ62G2M","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DYXC4RCZ","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:309a2ae27da8b26912e8df8ba4bd5f0188454943bc8b5d247df3cb31ef290223","target":"graph","created_at":"2026-05-18T01:29:31Z","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 investigate the generalization of loop gravity's twisted geometries to a q-deformed gauge group. In the standard undeformed case, loop gravity is a formulation of general relativity as a diffeomorphism-invariant SU(2) gauge theory. Its classical states are graphs provided with algebraic data. In particular closure constraints at every node of the graph ensure their interpretation as twisted geometries. Dual to each node, one has a polyhedron embedded in flat space R^3. One then glues them allowing for both curvature and torsion. It was recently conjectured that q-deforming the gauge group S","authors_text":"Christoph Charles, Etera R. Livine","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-01-05T13:34:13Z","title":"Closure constraints for hyperbolic tetrahedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00855","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":"sha256:66ae4329a0859f18537129966c147aed50cce003b845a73cd25feb99d380690e","target":"record","created_at":"2026-05-18T01:29:31Z","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":"85217368dd9e1a8e2c8787e20ba84898be24abfab5bfffc4733932e93ab9f81a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-01-05T13:34:13Z","title_canon_sha256":"b2c0ad68bdceef432a4e59068807e0ecd19473dbb99abe609945c051573dbf0f"},"schema_version":"1.0","source":{"id":"1501.00855","kind":"arxiv","version":1}},"canonical_sha256":"1e2e2e44592361ed1b4c82e8d3e625a38401d6f1322466892e40683f58cbfca0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e2e2e44592361ed1b4c82e8d3e625a38401d6f1322466892e40683f58cbfca0","first_computed_at":"2026-05-18T01:29:31.892051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:31.892051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ccpq0iHTKfu879VOHxlGrhzw63XCQLGPVdkugZjVr9wL0hJgQh2kecvz6K52AYGb49/TuP2v1WSLWLYKNuTnBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:31.892676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.00855","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66ae4329a0859f18537129966c147aed50cce003b845a73cd25feb99d380690e","sha256:309a2ae27da8b26912e8df8ba4bd5f0188454943bc8b5d247df3cb31ef290223"],"state_sha256":"03c1baf1c1ca6900d04f7c1af97320896ba11ff7a4b81d5292d2b6a742493b36"}