{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:7FSBSL5UISQLI4LEX3XA22KEWH","short_pith_number":"pith:7FSBSL5U","canonical_record":{"source":{"id":"gr-qc/0405060","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2004-05-11T19:29:02Z","cross_cats_sorted":["hep-th","math-ph","math.MP","nucl-th","quant-ph"],"title_canon_sha256":"0a8b4dc2bbdd9fefde00935d4a24eff968cc3a25e4d3a11c781496aaa9c3a34c","abstract_canon_sha256":"d202d28896728b29e061eb9e4e76e45660917b6520b0be63ca97e945d5f44a0a"},"schema_version":"1.0"},"canonical_sha256":"f964192fb444a0b47164beee0d6944b1d642e79ecae59295d8140781e03cb69a","source":{"kind":"arxiv","id":"gr-qc/0405060","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0405060","created_at":"2026-05-18T01:39:22Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0405060v1","created_at":"2026-05-18T01:39:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0405060","created_at":"2026-05-18T01:39:22Z"},{"alias_kind":"pith_short_12","alias_value":"7FSBSL5UISQL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"7FSBSL5UISQLI4LE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"7FSBSL5U","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:7FSBSL5UISQLI4LEX3XA22KEWH","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0405060","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2004-05-11T19:29:02Z","cross_cats_sorted":["hep-th","math-ph","math.MP","nucl-th","quant-ph"],"title_canon_sha256":"0a8b4dc2bbdd9fefde00935d4a24eff968cc3a25e4d3a11c781496aaa9c3a34c","abstract_canon_sha256":"d202d28896728b29e061eb9e4e76e45660917b6520b0be63ca97e945d5f44a0a"},"schema_version":"1.0"},"canonical_sha256":"f964192fb444a0b47164beee0d6944b1d642e79ecae59295d8140781e03cb69a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:22.577242Z","signature_b64":"VJCcmQtBy7Rag1iGS+qicIssF57TCEPpLJtLZOTPxOTitRaCvwB4U60lhTlNWPAFANd1/nRcZF+/+VirlmuMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f964192fb444a0b47164beee0d6944b1d642e79ecae59295d8140781e03cb69a","last_reissued_at":"2026-05-18T01:39:22.576616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:22.576616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0405060","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"la1xprXYDNmuvuxAlMvg8mNHwAcJXu9RBI7wFDQusqhcWtrFU82jH9skF+VMxDwoJXjocTpGP8aL07t5jWabDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:21:46.754467Z"},"content_sha256":"481532dc46b0ad6b08e0015592e459d659477cb432de3835e0fc33c8c5b62991","schema_version":"1.0","event_id":"sha256:481532dc46b0ad6b08e0015592e459d659477cb432de3835e0fc33c8c5b62991"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:7FSBSL5UISQLI4LEX3XA22KEWH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simplification of the Spectral Analysis of the Volume Operator in Loop Quantum Gravity","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP","nucl-th","quant-ph"],"primary_cat":"gr-qc","authors_text":"Johannes Brunnemann, Thomas Thiemann","submitted_at":"2004-05-11T19:29:02Z","abstract_excerpt":"The Volume Operator plays a crucial role in the definition of the quantum dynamics of Loop Quantum Gravity (LQG). Efficient calculations for dynamical problems of LQG can therefore be performed only if one has sufficient control over the volume spectrum. While closed formulas for the matrix elements are currently available in the literature, these are complicated polynomials in 6j symbols which in turn are given in terms of Racah's formula which is too complicated in order to perform even numerical calculations for the semiclassically important regime of large spins. Hence, so far not even num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0405060","kind":"arxiv","version":1},"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":"2026-05-18T01:39:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qxkcmwWt4tfCPH+F0aukYoGMT+A0GQ+Xns+P+I7f+4IlToGv0oNKf5M6NB6yp6EB4MfJSOeEz73Rszl6P3gtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:21:46.755143Z"},"content_sha256":"bc1756f1e3ff1ed235a19f4b9b8ffb824528be7eae0b8128c4462d88afc24678","schema_version":"1.0","event_id":"sha256:bc1756f1e3ff1ed235a19f4b9b8ffb824528be7eae0b8128c4462d88afc24678"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FSBSL5UISQLI4LEX3XA22KEWH/bundle.json","state_url":"https://pith.science/pith/7FSBSL5UISQLI4LEX3XA22KEWH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FSBSL5UISQLI4LEX3XA22KEWH/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":"2026-05-25T15:21:46Z","links":{"resolver":"https://pith.science/pith/7FSBSL5UISQLI4LEX3XA22KEWH","bundle":"https://pith.science/pith/7FSBSL5UISQLI4LEX3XA22KEWH/bundle.json","state":"https://pith.science/pith/7FSBSL5UISQLI4LEX3XA22KEWH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FSBSL5UISQLI4LEX3XA22KEWH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:7FSBSL5UISQLI4LEX3XA22KEWH","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":"d202d28896728b29e061eb9e4e76e45660917b6520b0be63ca97e945d5f44a0a","cross_cats_sorted":["hep-th","math-ph","math.MP","nucl-th","quant-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"2004-05-11T19:29:02Z","title_canon_sha256":"0a8b4dc2bbdd9fefde00935d4a24eff968cc3a25e4d3a11c781496aaa9c3a34c"},"schema_version":"1.0","source":{"id":"gr-qc/0405060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0405060","created_at":"2026-05-18T01:39:22Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0405060v1","created_at":"2026-05-18T01:39:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0405060","created_at":"2026-05-18T01:39:22Z"},{"alias_kind":"pith_short_12","alias_value":"7FSBSL5UISQL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"7FSBSL5UISQLI4LE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"7FSBSL5U","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:bc1756f1e3ff1ed235a19f4b9b8ffb824528be7eae0b8128c4462d88afc24678","target":"graph","created_at":"2026-05-18T01:39:22Z","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":"The Volume Operator plays a crucial role in the definition of the quantum dynamics of Loop Quantum Gravity (LQG). Efficient calculations for dynamical problems of LQG can therefore be performed only if one has sufficient control over the volume spectrum. While closed formulas for the matrix elements are currently available in the literature, these are complicated polynomials in 6j symbols which in turn are given in terms of Racah's formula which is too complicated in order to perform even numerical calculations for the semiclassically important regime of large spins. Hence, so far not even num","authors_text":"Johannes Brunnemann, Thomas Thiemann","cross_cats":["hep-th","math-ph","math.MP","nucl-th","quant-ph"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2004-05-11T19:29:02Z","title":"Simplification of the Spectral Analysis of the Volume Operator in Loop Quantum Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0405060","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":"sha256:481532dc46b0ad6b08e0015592e459d659477cb432de3835e0fc33c8c5b62991","target":"record","created_at":"2026-05-18T01:39:22Z","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":"d202d28896728b29e061eb9e4e76e45660917b6520b0be63ca97e945d5f44a0a","cross_cats_sorted":["hep-th","math-ph","math.MP","nucl-th","quant-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"2004-05-11T19:29:02Z","title_canon_sha256":"0a8b4dc2bbdd9fefde00935d4a24eff968cc3a25e4d3a11c781496aaa9c3a34c"},"schema_version":"1.0","source":{"id":"gr-qc/0405060","kind":"arxiv","version":1}},"canonical_sha256":"f964192fb444a0b47164beee0d6944b1d642e79ecae59295d8140781e03cb69a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f964192fb444a0b47164beee0d6944b1d642e79ecae59295d8140781e03cb69a","first_computed_at":"2026-05-18T01:39:22.576616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:22.576616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VJCcmQtBy7Rag1iGS+qicIssF57TCEPpLJtLZOTPxOTitRaCvwB4U60lhTlNWPAFANd1/nRcZF+/+VirlmuMBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:22.577242Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0405060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:481532dc46b0ad6b08e0015592e459d659477cb432de3835e0fc33c8c5b62991","sha256:bc1756f1e3ff1ed235a19f4b9b8ffb824528be7eae0b8128c4462d88afc24678"],"state_sha256":"1f63d492482e1785dadd793ad5ffd31f9c6fe54917e4e6ba94e4ce17790d0ce8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gwJC+PYoedDoRcFXD/duJaBdxH2cewvJ8y42wDZnHJyMKpJF7G84rKjb4qZLKXwbBTQu8tA4VkNORzanmhsuCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:21:46.759017Z","bundle_sha256":"d7ce81b1cb583d70c1b1a27487091e4914c49592329ef1d51ba0e47ec1b623eb"}}