{ "sector": "S3", "top_sector_label": 599551, "definition": "M_i(eps) = sum_j A_ij(eps) b_j: M = master integrals of the eta-deformed system at eta = 0 (rows), b = boundary integrals of the large-eta region (columns); Eq. (27) of the paper", "rows_master_integrals": { "note": "exponent vectors (n_1..n_22) over D_1..D_22 of the PX2 family; row index = response_matrix_row in boundary_constants_PX2.json", "index_vectors": [ [ 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, -1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, -1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, -1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, -1, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, -1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 1, -1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 1, 0, 1, -1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, -1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, -1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, -1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, -1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 0, 1, 1, -1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, -1, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, -1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 1, -1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 1, 0, 1, -1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, -1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, -1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, -1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 0, 1, 1, -1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0 ] ] }, "columns_boundary_integrals": { "note": "the solver's labels for the boundary integrals of the large-eta region (index vectors over that region's own propagator list, which is not reproduced here); ranks and left null vectors do not depend on the column labeling", "labels": [ "1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0", "1,1,1,1,0,0,-1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0", "1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0", "1,1,1,1,0,1,-1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0", "1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0", "1,1,1,1,1,0,-1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0", "1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0", "1,1,1,1,0,-1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0", 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