removed duplicates

bench_data/arxiv_math.jsonl

@@ -773,7 +773,6 @@
 {"pdf": "arxiv_math/2503.08395_pg5.pdf", "url": "https://arxiv.org/pdf/2503.08395", "page": 1, "id": "2503.08395_pg5_math_013", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Upsilon^t=(\\rho^t)^{-1}(X^{sing})"}
 {"pdf": "arxiv_math/2503.05686_pg11.pdf", "url": "https://arxiv.org/pdf/2503.05686", "page": 1, "id": "2503.05686_pg11_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "f_1\\,f_2 -\\tilde{f}_1\\,\\tilde{f}_2 = (f_1 - \\tilde{f}_1)f_2 + (f_2-\\tilde{f}_2) \\tilde{f}_1"}
 {"pdf": "arxiv_math/2503.05686_pg11.pdf", "url": "https://arxiv.org/pdf/2503.05686", "page": 1, "id": "2503.05686_pg11_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "(M_1^\\infty, M_2^\\infty)"}
-{"pdf": "arxiv_math/2503.05686_pg11.pdf", "url": "https://arxiv.org/pdf/2503.05686", "page": 1, "id": "2503.05686_pg11_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\varepsilon \\rightarrow 0"}
 {"pdf": "arxiv_math/2503.06662_pg5.pdf", "url": "https://arxiv.org/pdf/2503.06662", "page": 1, "id": "2503.06662_pg5_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\nabla\\ell_i(x_i^t,\\lambda_i^t)"}
 {"pdf": "arxiv_math/2503.06662_pg5.pdf", "url": "https://arxiv.org/pdf/2503.06662", "page": 1, "id": "2503.06662_pg5_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "I \\in \\R^{n \\times n}"}
 {"pdf": "arxiv_math/2503.03766_pg12.pdf", "url": "https://arxiv.org/pdf/2503.03766", "page": 1, "id": "2503.03766_pg12_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\{ (0,m) : m \\ge c \\}"}
@@ -921,8 +920,6 @@
 {"pdf": "arxiv_math/2503.09440_pg14.pdf", "url": "https://arxiv.org/pdf/2503.09440", "page": 1, "id": "2503.09440_pg14_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "V(T_1)\\cap V(T_j)\\neq \\emptyset"}
 {"pdf": "arxiv_math/2503.09440_pg14.pdf", "url": "https://arxiv.org/pdf/2503.09440", "page": 1, "id": "2503.09440_pg14_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "N_G(v_j)\\subseteq N_G(v_i)"}
 {"pdf": "arxiv_math/2503.09440_pg14.pdf", "url": "https://arxiv.org/pdf/2503.09440", "page": 1, "id": "2503.09440_pg14_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "V(T_i)\\cap V(T_j)\\neq \\emptyset"}
-{"pdf": "arxiv_math/2503.09440_pg14.pdf", "url": "https://arxiv.org/pdf/2503.09440", "page": 1, "id": "2503.09440_pg14_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "d_T(w_1,r)\\geq d_T(w_j,r)"}
-{"pdf": "arxiv_math/2503.09440_pg14.pdf", "url": "https://arxiv.org/pdf/2503.09440", "page": 1, "id": "2503.09440_pg14_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "V(T_i)\\cap V(T_k)\\neq \\emptyset"}
 {"pdf": "arxiv_math/2503.09440_pg14.pdf", "url": "https://arxiv.org/pdf/2503.09440", "page": 1, "id": "2503.09440_pg14_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "d_T(r,w_k)\\leq d_T(r,w_1)"}
 {"pdf": "arxiv_math/2503.09440_pg14.pdf", "url": "https://arxiv.org/pdf/2503.09440", "page": 1, "id": "2503.09440_pg14_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "V(T_j)\\cap V(T_k)\\neq \\emptyset"}
 {"pdf": "arxiv_math/2503.09549_pg3.pdf", "url": "https://arxiv.org/pdf/2503.09549", "page": 1, "id": "2503.09549_pg3_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\bar{x}\\in \\mathbb{R}^d"}
@@ -2407,7 +2404,6 @@
 {"pdf": "arxiv_math/2503.08494_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08494", "page": 1, "id": "2503.08494_pg2_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "J_i(\\mathbf{u}), u \\in \\Omega"}
 {"pdf": "arxiv_math/2503.08494_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08494", "page": 1, "id": "2503.08494_pg2_math_005", "type": "math", "max_diffs": 0, "checked": "verified", "math": "\\mathbf{x}^*=\\mathrm{col}(x_1^*,x_2^*,...,x_N^*) \\in \\Omega \\cap \\Upsilon"}
 {"pdf": "arxiv_math/2503.08494_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08494", "page": 1, "id": "2503.08494_pg2_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "J_i(x_i^*,h(\\mathbf{x}^*)) \\leq J_i(x_i,\\frac{1}{N}x_i+\\sum_{j \\neq i} \\frac{1}{N}x_j^*), \\nonumber"}
-{"pdf": "arxiv_math/2503.08494_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08494", "page": 1, "id": "2503.08494_pg2_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "\\langle \\cdot, \\cdot \\rangle"}
 {"pdf": "arxiv_math/2503.08494_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08494", "page": 1, "id": "2503.08494_pg2_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathbf{u}, \\mathbf{v} \\in \\Omega"}
 {"pdf": "arxiv_math/2503.08494_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08494", "page": 1, "id": "2503.08494_pg2_math_010", "type": "math", "max_diffs": 0, "checked": null, "math": "\\nabla_i f(\\mathbf{x})"}
 {"pdf": "arxiv_math/2503.04068_pg2.pdf", "url": "https://arxiv.org/pdf/2503.04068", "page": 1, "id": "2503.04068_pg2_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\sum_{i=1}^mA_i\\Sigma(W_ix+b_i)"}