{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:N6KETHKIQEFWKPOQ2HH3EOWZET","short_pith_number":"pith:N6KETHKI","canonical_record":{"source":{"id":"1101.3524","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-01-18T19:19:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"909c831e55b99a1ae04fc40a696ee28936cca55fdc6c3592ba10a9d5d7a6f804","abstract_canon_sha256":"db3cc573bc6d76d30c3640b8179af1f53209dd78ce0fb09621c4294a2ac75936"},"schema_version":"1.0"},"canonical_sha256":"6f94499d48810b653dd0d1cfb23ad924c27d51b47de27ea75faf9b34637d1b9c","source":{"kind":"arxiv","id":"1101.3524","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3524","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3524v3","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3524","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"pith_short_12","alias_value":"N6KETHKIQEFW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N6KETHKIQEFWKPOQ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N6KETHKI","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:N6KETHKIQEFWKPOQ2HH3EOWZET","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3524","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-01-18T19:19:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"909c831e55b99a1ae04fc40a696ee28936cca55fdc6c3592ba10a9d5d7a6f804","abstract_canon_sha256":"db3cc573bc6d76d30c3640b8179af1f53209dd78ce0fb09621c4294a2ac75936"},"schema_version":"1.0"},"canonical_sha256":"6f94499d48810b653dd0d1cfb23ad924c27d51b47de27ea75faf9b34637d1b9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:47.057148Z","signature_b64":"8pNphHMaV4SjQhC73wdHUPYPlz5a/Pey+hZKz7zvNKg62V29MkjhovZWM7vNV+R56e29AJyt+7+wgmbyB+hTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f94499d48810b653dd0d1cfb23ad924c27d51b47de27ea75faf9b34637d1b9c","last_reissued_at":"2026-05-18T04:13:47.056685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:47.056685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3524","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":"2026-05-18T04:13:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lYODGlUL7rwvH6IG4qg5g6hQIuEdiXaFFMZTWtTrTKa9xv6q5ziqSGWSPHEjdzKcfpqzST2nEwl94GbRWxa5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:51:12.402803Z"},"content_sha256":"124d4fda753cd48fac3e93b1851d1e431d202d88f89f917c717161bd960eb461","schema_version":"1.0","event_id":"sha256:124d4fda753cd48fac3e93b1851d1e431d202d88f89f917c717161bd960eb461"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:N6KETHKIQEFWKPOQ2HH3EOWZET","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hamiltonian constraint in 3d Riemannian loop quantum gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Laurent Freidel, Valentin Bonzom","submitted_at":"2011-01-18T19:19:58Z","abstract_excerpt":"We discretize the Hamiltonian scalar constraint of three-dimensional Riemannian gravity on a graph of the loop quantum gravity phase space. This Hamiltonian has a clear interpretation in terms of discrete geometries: it computes the extrinsic curvature from dihedral angles. The Wheeler-DeWitt equation takes the form of difference equations, which are actually recursion relations satisfied by Wigner symbols. On the boundary of a tetrahedron, the Hamiltonian generates the exact recursion relation on the 6j-symbol which comes from the Biedenharn-Elliott (pentagon) identity. This fills the gap bet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3524","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":"2026-05-18T04:13:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p57Zgz6y+YdZnxITyLVh8w0ve+lTe4WpFn2FRkgzH0SKIqFzzqdniYeXFWS48wf1nmCANRkULc9Sm4C9KOP3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:51:12.403168Z"},"content_sha256":"3aada0a2b84e62a5e76e70f14881e0fea978867fa7c171b5bfb10ec4f0d4b523","schema_version":"1.0","event_id":"sha256:3aada0a2b84e62a5e76e70f14881e0fea978867fa7c171b5bfb10ec4f0d4b523"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/bundle.json","state_url":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/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":"2026-05-27T01:51:12Z","links":{"resolver":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET","bundle":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/bundle.json","state":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N6KETHKIQEFWKPOQ2HH3EOWZET","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":"db3cc573bc6d76d30c3640b8179af1f53209dd78ce0fb09621c4294a2ac75936","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-01-18T19:19:58Z","title_canon_sha256":"909c831e55b99a1ae04fc40a696ee28936cca55fdc6c3592ba10a9d5d7a6f804"},"schema_version":"1.0","source":{"id":"1101.3524","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3524","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3524v3","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3524","created_at":"2026-05-18T04:13:47Z"},{"alias_kind":"pith_short_12","alias_value":"N6KETHKIQEFW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N6KETHKIQEFWKPOQ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N6KETHKI","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:3aada0a2b84e62a5e76e70f14881e0fea978867fa7c171b5bfb10ec4f0d4b523","target":"graph","created_at":"2026-05-18T04:13:47Z","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 discretize the Hamiltonian scalar constraint of three-dimensional Riemannian gravity on a graph of the loop quantum gravity phase space. This Hamiltonian has a clear interpretation in terms of discrete geometries: it computes the extrinsic curvature from dihedral angles. The Wheeler-DeWitt equation takes the form of difference equations, which are actually recursion relations satisfied by Wigner symbols. On the boundary of a tetrahedron, the Hamiltonian generates the exact recursion relation on the 6j-symbol which comes from the Biedenharn-Elliott (pentagon) identity. This fills the gap bet","authors_text":"Laurent Freidel, Valentin Bonzom","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-01-18T19:19:58Z","title":"The Hamiltonian constraint in 3d Riemannian loop quantum gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3524","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":"sha256:124d4fda753cd48fac3e93b1851d1e431d202d88f89f917c717161bd960eb461","target":"record","created_at":"2026-05-18T04:13:47Z","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":"db3cc573bc6d76d30c3640b8179af1f53209dd78ce0fb09621c4294a2ac75936","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-01-18T19:19:58Z","title_canon_sha256":"909c831e55b99a1ae04fc40a696ee28936cca55fdc6c3592ba10a9d5d7a6f804"},"schema_version":"1.0","source":{"id":"1101.3524","kind":"arxiv","version":3}},"canonical_sha256":"6f94499d48810b653dd0d1cfb23ad924c27d51b47de27ea75faf9b34637d1b9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f94499d48810b653dd0d1cfb23ad924c27d51b47de27ea75faf9b34637d1b9c","first_computed_at":"2026-05-18T04:13:47.056685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:47.056685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8pNphHMaV4SjQhC73wdHUPYPlz5a/Pey+hZKz7zvNKg62V29MkjhovZWM7vNV+R56e29AJyt+7+wgmbyB+hTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:47.057148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3524","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:124d4fda753cd48fac3e93b1851d1e431d202d88f89f917c717161bd960eb461","sha256:3aada0a2b84e62a5e76e70f14881e0fea978867fa7c171b5bfb10ec4f0d4b523"],"state_sha256":"e362d907a3ebfa0a548550441b808338928262acce907eec42a80c17280cfc3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4YXF+ZC+0RQFiXtCWP8LRiJHp4EuaMd5GT8sF/fD8Oz93b/G3RL56lQ4TgPrzweV9tH/NGTaEPgZ+d++aVMBBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:51:12.406438Z","bundle_sha256":"d05c2dc6c76c4317c1accc4a249a9c5b164e76aeb849beae137905b394e7ebbc"}}