{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"critpt","formal_name":"CritPt","introduction":"CritPt evaluates scientific understanding and multi-step reasoning and computation on research-level physics problems. Its public dataset contains 70 challenges with problem descriptions and code templates.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://critpt.com/","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"f5aef08f-3cf1-51cb-a156-01306d31122a","task_key":"train--Challenge~5f13~5fmain","task_revision_id":"3","upstream_id":"Challenge_13_main","short_description":"Consider a (1+1)-D CFT on a torus that consists of right- and left-moving edges…","config":"","split":"train","body":"{\"code_template\":\"import sympy as sp\\n\\ndef answer():\\n    r\\\"\\\"\\\"\\n    Return the expectation values of Verlinde lines and corresponding labels.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    values: set[tuple[float, int, float, int, complex]], a set of tuples $(j_L,n_L,j_R,n_R,\\\\lambda_{(j_L,n_L,j_R,n_R)})$\\n        where $\\\\lambda_{(j_L,n_L,j_R,n_R)}$ is the expectation value of the Verlinde line operator.\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    values = ...\\n    # ---------------------------------------------------------------\\n\\n    return values\",\"problem_description\":\"# Problem setup:\\nConsider a (1+1)-D CFT on a torus that consists of right- and left-moving edges of a Moore-Read state at filling fraction $\\\\nu=1/k$. The primary fields are labeled by $(j_L,n_L,j_R,n_R)$, where $j_{L/R}=0,1/2,1$, $n_{L/R}\\\\in Z_{2k}$  and the electron operators in the theory are $(1,2k,0,0)$ and $(0,0,1,2k)$.\\n\\n# Main problem:\\nGiven $k=2$, find the expectation values of Verlinde lines assuming the identity operator has expectation value 1. Return your answer as a tuple $(j_L,n_L,j_R,n_R,\\\\lambda_{(j_L,n_L,j_R,n_R)})$, where $\\\\lambda_{(j_L,n_L,j_R,n_R)}$ is the expectation value.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}