{"paper":{"title":"Comments on knotted 1/2 BPS Wilson loops","arxiv_id":"1204.5975","primary_cat":"hep-th","submitted_at":"2012-04-26T16:27:47+00:00","version_compiled":"v4"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13-20260917 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v4","sentences":[{"i":0,"p":0.54,"id":"s0","own":true,"role":"contribution","text":"In this paper, we show that the localization of three-dimensional N = 2 supersymmetric Chern-Simons theory on the ellipsoid-like squashed sphere is related to a nontrivial knot structure called torus knot.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.81,"quantitative":false,"quantitative_p":0.3,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.46,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.54,"interpretation":0.0}},{"i":1,"p":0.38,"id":"s1","own":true,"role":"method","text":"More precisely, we can capture the three sphere as the nontrivial so-called Seifert fibrations by regarding 1/2 BPS Wilson loops as U(1) fibers.","hedge":{"p":0.76,"label":"asserted"},"own_p":0.77,"main_claim_p":0.14,"quantitative":false,"quantitative_p":0.2,"role_probabilities":{"gap":0.0,"method":0.38,"result":0.1,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.37,"interpretation":0.15}},{"i":2,"p":0.9,"id":"s2","own":true,"role":"result","text":"The topology of knotted 1/2 BPS Wilson loops is controlled by squashing parameters.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.57,"main_claim_p":0.24,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.9,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.09}},{"i":3,"p":0.98,"id":"s3","own":true,"role":"result","text":"We calculate the 1/2 BPS condition of the Wilson loop and find perfect agreement with known results.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.42,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":4,"p":0.48,"id":"s4","own":false,"role":"contribution","text":"We also remark on the level shift and framing anomaly.","hedge":{"p":0.78,"label":"unclear"},"own_p":0.36,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.11,"background":0.01,"limitation":0.01,"future_work":0.12,"contribution":0.48,"interpretation":0.27}}]},"compiled":{"main_claim":{"p":0.99,"text":"In this paper, we show that the localization of three-dimensional N = 2 supersymmetric Chern-Simons theory on the ellipsoid-like squashed sphere is related to a nontrivial knot structure called torus knot.","location":"abstract s0","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"OpenRouter","model":"classifier-1.13","endpoint":"https://openrouter.ai/api/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":4230,"cost_usd_reported":0.000178},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13-20260917","abstract_states":{"claims_first":0.04,"states_limitation":0.09,"human_participants":0.01,"controlled_comparison":0.04,"randomized_assignment":0.01,"states_quantitative_result":0.08,"compares_with_prior_results":0.81,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.99,"value":"proof or derivation","probabilities":{"argument":0.01,"literature":0.0,"proof_or_derivation":0.99,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.86,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.86,"dataset_or_benchmark":0.0,"position_or_commentary":0.14}},"contribution_statement":{"p":0.98,"text":"In this paper, we show that the localization of three-dimensional N = 2 supersymmetric Chern-Simons theory on the ellipsoid-like squashed sphere is related to a nontrivial knot structure called torus knot.","location":"abstract s0"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v4"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":5,"sentences_in_abstract":5},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}