{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:VA4NDHWNRTWTRQEQX2UE2WXT42","short_pith_number":"pith:VA4NDHWN","schema_version":"1.0","canonical_sha256":"a838d19ecd8ced38c090bea84d5af3e6a10ae9eb52ca1784724d2e9b0c19e15c","source":{"kind":"arxiv","id":"1012.5064","version":1},"attestation_state":"computed","paper":{"title":"Remarks on Wilson Loops and Seifert Loops in Chern-Simons Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Chris Beasley","submitted_at":"2010-12-22T18:16:56Z","abstract_excerpt":"As noted long ago by Atiyah and Bott, the classical Yang-Mills action on a Riemann surface admits a beautiful symplectic interpretation as the norm-square of a moment map associated to the Hamiltonian action by gauge transformations on the affine space of connections. Here I explain how certain Wilson loop observables in Chern-Simons gauge theory on a Seifert three-manifold can be given an analogous symplectic description. Among other results, this symplectic description implies that the stationary-phase approximation to the Wilson loop path integral is exact for torus knots, an empirical obse"},"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":"1012.5064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-22T18:16:56Z","cross_cats_sorted":[],"title_canon_sha256":"b03a91f9ded9a4b778ac8122b69ab349948b71ac3fac2b7993fe039331c5c0dd","abstract_canon_sha256":"66cea4d49f21f4f5ee6fa5ed5051ba437cf2c5565f74ba54397e2183069d014a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:44.562867Z","signature_b64":"LPAhNhZKIT5ZHTRD3ekgJB5DZ1a9spjQP6zMvKR0FYG5pRYEY5yW2MqeNMF3A1IWvDvjtBX3mGrd01slWpjKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a838d19ecd8ced38c090bea84d5af3e6a10ae9eb52ca1784724d2e9b0c19e15c","last_reissued_at":"2026-05-18T04:32:44.562146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:44.562146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on Wilson Loops and Seifert Loops in Chern-Simons Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Chris Beasley","submitted_at":"2010-12-22T18:16:56Z","abstract_excerpt":"As noted long ago by Atiyah and Bott, the classical Yang-Mills action on a Riemann surface admits a beautiful symplectic interpretation as the norm-square of a moment map associated to the Hamiltonian action by gauge transformations on the affine space of connections. Here I explain how certain Wilson loop observables in Chern-Simons gauge theory on a Seifert three-manifold can be given an analogous symplectic description. Among other results, this symplectic description implies that the stationary-phase approximation to the Wilson loop path integral is exact for torus knots, an empirical obse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5064","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.5064","created_at":"2026-05-18T04:32:44.562265+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.5064v1","created_at":"2026-05-18T04:32:44.562265+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5064","created_at":"2026-05-18T04:32:44.562265+00:00"},{"alias_kind":"pith_short_12","alias_value":"VA4NDHWNRTWT","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"VA4NDHWNRTWTRQEQ","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"VA4NDHWN","created_at":"2026-05-18T12:26:15.391820+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/VA4NDHWNRTWTRQEQX2UE2WXT42","json":"https://pith.science/pith/VA4NDHWNRTWTRQEQX2UE2WXT42.json","graph_json":"https://pith.science/api/pith-number/VA4NDHWNRTWTRQEQX2UE2WXT42/graph.json","events_json":"https://pith.science/api/pith-number/VA4NDHWNRTWTRQEQX2UE2WXT42/events.json","paper":"https://pith.science/paper/VA4NDHWN"},"agent_actions":{"view_html":"https://pith.science/pith/VA4NDHWNRTWTRQEQX2UE2WXT42","download_json":"https://pith.science/pith/VA4NDHWNRTWTRQEQX2UE2WXT42.json","view_paper":"https://pith.science/paper/VA4NDHWN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.5064&json=true","fetch_graph":"https://pith.science/api/pith-number/VA4NDHWNRTWTRQEQX2UE2WXT42/graph.json","fetch_events":"https://pith.science/api/pith-number/VA4NDHWNRTWTRQEQX2UE2WXT42/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VA4NDHWNRTWTRQEQX2UE2WXT42/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VA4NDHWNRTWTRQEQX2UE2WXT42/action/storage_attestation","attest_author":"https://pith.science/pith/VA4NDHWNRTWTRQEQX2UE2WXT42/action/author_attestation","sign_citation":"https://pith.science/pith/VA4NDHWNRTWTRQEQX2UE2WXT42/action/citation_signature","submit_replication":"https://pith.science/pith/VA4NDHWNRTWTRQEQX2UE2WXT42/action/replication_record"}},"created_at":"2026-05-18T04:32:44.562265+00:00","updated_at":"2026-05-18T04:32:44.562265+00:00"}