{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:CZCX47SCFCHLJSOIJT5DT35PV5","short_pith_number":"pith:CZCX47SC","canonical_record":{"source":{"id":"math-ph/0611084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-11-30T11:13:39Z","cross_cats_sorted":["hep-th","math.MP","math.QA"],"title_canon_sha256":"06a1daa1547bbe37764cd0aa44efc2e1b9be1bc9dcea0e3f4ce9850be6f69eb8","abstract_canon_sha256":"b8fa1bf04656d46a64950e46330239414d2b330618ddd8672135069c4c2a397d"},"schema_version":"1.0"},"canonical_sha256":"16457e7e42288eb4c9c84cfa39efafaf5ac1da3f609ed54d238253214e518881","source":{"kind":"arxiv","id":"math-ph/0611084","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0611084","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0611084v2","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0611084","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"CZCX47SCFCHL","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"CZCX47SCFCHLJSOI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"CZCX47SC","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:CZCX47SCFCHLJSOIJT5DT35PV5","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0611084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-11-30T11:13:39Z","cross_cats_sorted":["hep-th","math.MP","math.QA"],"title_canon_sha256":"06a1daa1547bbe37764cd0aa44efc2e1b9be1bc9dcea0e3f4ce9850be6f69eb8","abstract_canon_sha256":"b8fa1bf04656d46a64950e46330239414d2b330618ddd8672135069c4c2a397d"},"schema_version":"1.0"},"canonical_sha256":"16457e7e42288eb4c9c84cfa39efafaf5ac1da3f609ed54d238253214e518881","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:29.893403Z","signature_b64":"Mc3tQkjMjhpcx5SQEhLLW7ZRdLEBO8xVPWTkTfZpOSCCX2Cnf/P4VHK0IxfRrpzJujSU81VvVcFTCHNjGdsTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16457e7e42288eb4c9c84cfa39efafaf5ac1da3f609ed54d238253214e518881","last_reissued_at":"2026-05-18T03:53:29.892848Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:29.892848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0611084","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DfGlFr2sw4MN31ZEMVniEzruxA4rfh6MwQN6ABrXmZY+hvKtEp0wvA89Rup2Vn/yZb3or1/ZvS4JGgJE8Ck9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:17:57.058717Z"},"content_sha256":"81c715031799b663d9aa137f0276f3728a6f92e6c79e630a3bd9f0338ec14283","schema_version":"1.0","event_id":"sha256:81c715031799b663d9aa137f0276f3728a6f92e6c79e630a3bd9f0338ec14283"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:CZCX47SCFCHLJSOIJT5DT35PV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chern-Simons theory and the quantum Racah formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Atle Hahn, Sebastian De Haro","submitted_at":"2006-11-30T11:13:39Z","abstract_excerpt":"We generalize several results on Chern-Simons models on Sigma x S1 in the so-called \"torus gauge\" which were obtained in arXiv:math-ph/0507040 to the case of general (simply-connected simple compact) structure groups and general link colorings. In particular, we give a non-perturbative evaluation of the Wilson loop observables corresponding to a special class of simple but non-trivial links and show that their values are given by Turaev's shadow invariant. As a byproduct we obtain a heuristic path integral derivation of the quantum Racah formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0611084","kind":"arxiv","version":2},"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":"2026-05-18T03:53:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OaqrKbRQ72VZTf1ZF0PK0Fu+xYAJlp8FCyBTPwZwiZ9dxqZBHvUI+RYM7810OGBlh7G6nqT4pmkllrlxS0NnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:17:57.059218Z"},"content_sha256":"ae42c5aea8ee18810cab5ed2e3cf1fa71468f7c18333a0c9ca8e786ed1e72f0b","schema_version":"1.0","event_id":"sha256:ae42c5aea8ee18810cab5ed2e3cf1fa71468f7c18333a0c9ca8e786ed1e72f0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CZCX47SCFCHLJSOIJT5DT35PV5/bundle.json","state_url":"https://pith.science/pith/CZCX47SCFCHLJSOIJT5DT35PV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CZCX47SCFCHLJSOIJT5DT35PV5/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":"2026-05-30T10:17:57Z","links":{"resolver":"https://pith.science/pith/CZCX47SCFCHLJSOIJT5DT35PV5","bundle":"https://pith.science/pith/CZCX47SCFCHLJSOIJT5DT35PV5/bundle.json","state":"https://pith.science/pith/CZCX47SCFCHLJSOIJT5DT35PV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CZCX47SCFCHLJSOIJT5DT35PV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:CZCX47SCFCHLJSOIJT5DT35PV5","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":"b8fa1bf04656d46a64950e46330239414d2b330618ddd8672135069c4c2a397d","cross_cats_sorted":["hep-th","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-11-30T11:13:39Z","title_canon_sha256":"06a1daa1547bbe37764cd0aa44efc2e1b9be1bc9dcea0e3f4ce9850be6f69eb8"},"schema_version":"1.0","source":{"id":"math-ph/0611084","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0611084","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0611084v2","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0611084","created_at":"2026-05-18T03:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"CZCX47SCFCHL","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"CZCX47SCFCHLJSOI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"CZCX47SC","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:ae42c5aea8ee18810cab5ed2e3cf1fa71468f7c18333a0c9ca8e786ed1e72f0b","target":"graph","created_at":"2026-05-18T03:53:29Z","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 generalize several results on Chern-Simons models on Sigma x S1 in the so-called \"torus gauge\" which were obtained in arXiv:math-ph/0507040 to the case of general (simply-connected simple compact) structure groups and general link colorings. In particular, we give a non-perturbative evaluation of the Wilson loop observables corresponding to a special class of simple but non-trivial links and show that their values are given by Turaev's shadow invariant. As a byproduct we obtain a heuristic path integral derivation of the quantum Racah formula.","authors_text":"Atle Hahn, Sebastian De Haro","cross_cats":["hep-th","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-11-30T11:13:39Z","title":"Chern-Simons theory and the quantum Racah formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0611084","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":"sha256:81c715031799b663d9aa137f0276f3728a6f92e6c79e630a3bd9f0338ec14283","target":"record","created_at":"2026-05-18T03:53:29Z","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":"b8fa1bf04656d46a64950e46330239414d2b330618ddd8672135069c4c2a397d","cross_cats_sorted":["hep-th","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-11-30T11:13:39Z","title_canon_sha256":"06a1daa1547bbe37764cd0aa44efc2e1b9be1bc9dcea0e3f4ce9850be6f69eb8"},"schema_version":"1.0","source":{"id":"math-ph/0611084","kind":"arxiv","version":2}},"canonical_sha256":"16457e7e42288eb4c9c84cfa39efafaf5ac1da3f609ed54d238253214e518881","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16457e7e42288eb4c9c84cfa39efafaf5ac1da3f609ed54d238253214e518881","first_computed_at":"2026-05-18T03:53:29.892848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:29.892848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mc3tQkjMjhpcx5SQEhLLW7ZRdLEBO8xVPWTkTfZpOSCCX2Cnf/P4VHK0IxfRrpzJujSU81VvVcFTCHNjGdsTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:29.893403Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0611084","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81c715031799b663d9aa137f0276f3728a6f92e6c79e630a3bd9f0338ec14283","sha256:ae42c5aea8ee18810cab5ed2e3cf1fa71468f7c18333a0c9ca8e786ed1e72f0b"],"state_sha256":"5b08924d63bd8024c882730f9d88f4f1988011d97d81e63d30d2f4c4caa00012"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JB0nxifx3LzsA2p2+Vu4xosPY7n6QSKnOpPfl+eEmQHvjxFKktgxJX0XvCcdVv8JH6DYbUBQLbSiw+1lQgD/Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:17:57.062472Z","bundle_sha256":"bc132250219b4f7c41b6414e8acd66c6cfb0bf5ae240f9358733d3f47c782013"}}