{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:N6KETHKIQEFWKPOQ2HH3EOWZET","short_pith_number":"pith:N6KETHKI","schema_version":"1.0","canonical_sha256":"6f94499d48810b653dd0d1cfb23ad924c27d51b47de27ea75faf9b34637d1b9c","source":{"kind":"arxiv","id":"1101.3524","version":3},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.3524","created_at":"2026-05-18T04:13:47.056758+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.3524v3","created_at":"2026-05-18T04:13:47.056758+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3524","created_at":"2026-05-18T04:13:47.056758+00:00"},{"alias_kind":"pith_short_12","alias_value":"N6KETHKIQEFW","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"N6KETHKIQEFWKPOQ","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"N6KETHKI","created_at":"2026-05-18T12:26:37.096874+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET","json":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET.json","graph_json":"https://pith.science/api/pith-number/N6KETHKIQEFWKPOQ2HH3EOWZET/graph.json","events_json":"https://pith.science/api/pith-number/N6KETHKIQEFWKPOQ2HH3EOWZET/events.json","paper":"https://pith.science/paper/N6KETHKI"},"agent_actions":{"view_html":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET","download_json":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET.json","view_paper":"https://pith.science/paper/N6KETHKI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.3524&json=true","fetch_graph":"https://pith.science/api/pith-number/N6KETHKIQEFWKPOQ2HH3EOWZET/graph.json","fetch_events":"https://pith.science/api/pith-number/N6KETHKIQEFWKPOQ2HH3EOWZET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/action/storage_attestation","attest_author":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/action/author_attestation","sign_citation":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/action/citation_signature","submit_replication":"https://pith.science/pith/N6KETHKIQEFWKPOQ2HH3EOWZET/action/replication_record"}},"created_at":"2026-05-18T04:13:47.056758+00:00","updated_at":"2026-05-18T04:13:47.056758+00:00"}