{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:QIPKO7N7X2URN6W6IYCPIS62UH","short_pith_number":"pith:QIPKO7N7","canonical_record":{"source":{"id":"0911.2687","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-11-13T20:24:20Z","cross_cats_sorted":["math.GT","math.SG"],"title_canon_sha256":"c922df9de2adfc15cf1befd3dec86c4cb07afd7d55c8f26e943527465297ece0","abstract_canon_sha256":"6ad97dbffe613819177aea653463ff3cba542934a92718d3b9bf700661584ec9"},"schema_version":"1.0"},"canonical_sha256":"821ea77dbfbea916fade4604f44bdaa1e26567b2372760bb59ea55d68da9b3fa","source":{"kind":"arxiv","id":"0911.2687","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2687","created_at":"2026-05-18T02:46:38Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2687v2","created_at":"2026-05-18T02:46:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2687","created_at":"2026-05-18T02:46:38Z"},{"alias_kind":"pith_short_12","alias_value":"QIPKO7N7X2UR","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QIPKO7N7X2URN6W6","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QIPKO7N7","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:QIPKO7N7X2URN6W6IYCPIS62UH","target":"record","payload":{"canonical_record":{"source":{"id":"0911.2687","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-11-13T20:24:20Z","cross_cats_sorted":["math.GT","math.SG"],"title_canon_sha256":"c922df9de2adfc15cf1befd3dec86c4cb07afd7d55c8f26e943527465297ece0","abstract_canon_sha256":"6ad97dbffe613819177aea653463ff3cba542934a92718d3b9bf700661584ec9"},"schema_version":"1.0"},"canonical_sha256":"821ea77dbfbea916fade4604f44bdaa1e26567b2372760bb59ea55d68da9b3fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:38.094023Z","signature_b64":"OKRal8lt1C3HdEIpcxvzuRlW6wofkm3ZfIFv1rA1ZMKiE/6aAuSEpZj0sFvePIcD9veMrHJpNB9k0Pn6BYahAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"821ea77dbfbea916fade4604f44bdaa1e26567b2372760bb59ea55d68da9b3fa","last_reissued_at":"2026-05-18T02:46:38.093567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:38.093567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.2687","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":"2026-05-18T02:46:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3EgkeA0h0UXU5S/ZRuqBRbM+F3jvX8WjyJhUYXr1kmBFACwhF27mMLBgC8OKFPzt6tXpoeyx4HvTJyHeH8A3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T09:42:08.812494Z"},"content_sha256":"e24a9fb2870de642355cf778d815a54f19cee50544d4eb79f1b77267f35b9e82","schema_version":"1.0","event_id":"sha256:e24a9fb2870de642355cf778d815a54f19cee50544d4eb79f1b77267f35b9e82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:QIPKO7N7X2URN6W6IYCPIS62UH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localization for Wilson Loops in Chern-Simons Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.SG"],"primary_cat":"hep-th","authors_text":"Chris Beasley","submitted_at":"2009-11-13T20:24:20Z","abstract_excerpt":"We reconsider Chern-Simons gauge theory on a Seifert manifold M, which is the total space of a nontrivial circle bundle over a Riemann surface, possibly with orbifold points. As shown in previous work with Witten, the path integral technique of non-abelian localization can be used to express the partition function of Chern-Simons theory in terms of the equivariant cohomology of the moduli space of flat connections on M. Here we extend this result to apply to the expectation values of Wilson loop operators which wrap the circle fibers of M. Under localization, such a Wilson loop operator reduce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2687","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":"2026-05-18T02:46:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ge0HX2FCB+Hqdq4F+CaiSYw7SYb3rUiuFlZFnFs7/NFuktX/JgtB3ZOVXzv8RVKz4/XADe0VMnRIvdBhvzADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T09:42:08.813190Z"},"content_sha256":"b4d2222ab2d0cbe836bee0c10284539c8a3a3ff88d3722cda95034f28730175c","schema_version":"1.0","event_id":"sha256:b4d2222ab2d0cbe836bee0c10284539c8a3a3ff88d3722cda95034f28730175c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QIPKO7N7X2URN6W6IYCPIS62UH/bundle.json","state_url":"https://pith.science/pith/QIPKO7N7X2URN6W6IYCPIS62UH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QIPKO7N7X2URN6W6IYCPIS62UH/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":"2026-05-22T09:42:08Z","links":{"resolver":"https://pith.science/pith/QIPKO7N7X2URN6W6IYCPIS62UH","bundle":"https://pith.science/pith/QIPKO7N7X2URN6W6IYCPIS62UH/bundle.json","state":"https://pith.science/pith/QIPKO7N7X2URN6W6IYCPIS62UH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QIPKO7N7X2URN6W6IYCPIS62UH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QIPKO7N7X2URN6W6IYCPIS62UH","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":"6ad97dbffe613819177aea653463ff3cba542934a92718d3b9bf700661584ec9","cross_cats_sorted":["math.GT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-11-13T20:24:20Z","title_canon_sha256":"c922df9de2adfc15cf1befd3dec86c4cb07afd7d55c8f26e943527465297ece0"},"schema_version":"1.0","source":{"id":"0911.2687","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2687","created_at":"2026-05-18T02:46:38Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2687v2","created_at":"2026-05-18T02:46:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2687","created_at":"2026-05-18T02:46:38Z"},{"alias_kind":"pith_short_12","alias_value":"QIPKO7N7X2UR","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QIPKO7N7X2URN6W6","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QIPKO7N7","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:b4d2222ab2d0cbe836bee0c10284539c8a3a3ff88d3722cda95034f28730175c","target":"graph","created_at":"2026-05-18T02:46:38Z","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 reconsider Chern-Simons gauge theory on a Seifert manifold M, which is the total space of a nontrivial circle bundle over a Riemann surface, possibly with orbifold points. As shown in previous work with Witten, the path integral technique of non-abelian localization can be used to express the partition function of Chern-Simons theory in terms of the equivariant cohomology of the moduli space of flat connections on M. Here we extend this result to apply to the expectation values of Wilson loop operators which wrap the circle fibers of M. Under localization, such a Wilson loop operator reduce","authors_text":"Chris Beasley","cross_cats":["math.GT","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-11-13T20:24:20Z","title":"Localization for Wilson Loops in Chern-Simons Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2687","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:e24a9fb2870de642355cf778d815a54f19cee50544d4eb79f1b77267f35b9e82","target":"record","created_at":"2026-05-18T02:46:38Z","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":"6ad97dbffe613819177aea653463ff3cba542934a92718d3b9bf700661584ec9","cross_cats_sorted":["math.GT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-11-13T20:24:20Z","title_canon_sha256":"c922df9de2adfc15cf1befd3dec86c4cb07afd7d55c8f26e943527465297ece0"},"schema_version":"1.0","source":{"id":"0911.2687","kind":"arxiv","version":2}},"canonical_sha256":"821ea77dbfbea916fade4604f44bdaa1e26567b2372760bb59ea55d68da9b3fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"821ea77dbfbea916fade4604f44bdaa1e26567b2372760bb59ea55d68da9b3fa","first_computed_at":"2026-05-18T02:46:38.093567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:38.093567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OKRal8lt1C3HdEIpcxvzuRlW6wofkm3ZfIFv1rA1ZMKiE/6aAuSEpZj0sFvePIcD9veMrHJpNB9k0Pn6BYahAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:38.094023Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.2687","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e24a9fb2870de642355cf778d815a54f19cee50544d4eb79f1b77267f35b9e82","sha256:b4d2222ab2d0cbe836bee0c10284539c8a3a3ff88d3722cda95034f28730175c"],"state_sha256":"e14b6accc872f82698dc0cc45f88da31106476b53257289d7d1038eaee8a3218"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5LJFelJlwbiaeGhhEpa2vtRl9yQTRY00NoWFN7mHY9ef0NT4mvUXvMvDEpiyyZUkg6DwpRcKsayE1K3Zlwi6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T09:42:08.817061Z","bundle_sha256":"836d3f801940597e2a6b3522b41b241f87a6d7a6bcb36dc5353cce941f7b5887"}}