Datasets:

DetionDX
/

orbit-bench

+{"pdf": "arxiv_math/2503.04245_pg7.pdf", "url": "https://arxiv.org/pdf/2503.04245", "page": 1, "id": "2503.04245_pg7_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\underline{\\varepsilon} \\cdot \\underline{x} = \\sum_{i=1}^{5} \\varepsilon_i x_i \\leq 1, \\quad \\underline{x}\\in \\mathbb{H}_5"}
+{"pdf": "arxiv_math/2503.07147_pg16.pdf", "url": "https://arxiv.org/pdf/2503.07147", "page": 1, "id": "2503.07147_pg16_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "|L| = |C|\\cdot t \\le \\frac{|U|}{10r}\\cdot t"}
+{"pdf": "arxiv_math/2503.06716_pg12.pdf", "url": "https://arxiv.org/pdf/2503.06716", "page": 1, "id": "2503.06716_pg12_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mu_{s,t}^{\\frac{1}{2_s^*(t)-2}}u"}
+{"pdf": "arxiv_math/2503.05177_pg10.pdf", "url": "https://arxiv.org/pdf/2503.05177", "page": 1, "id": "2503.05177_pg10_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "\\sum_{n=1}^{\\infty}{P(N=n)} = 1"}
+{"pdf": "arxiv_math/2503.06344_pg15.pdf", "url": "https://arxiv.org/pdf/2503.06344", "page": 1, "id": "2503.06344_pg15_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "id:\\mathbb{R}^3\\rightarrow\\mathbb{R}^3"}
+{"pdf": "arxiv_math/2503.09455_pg21.pdf", "url": "https://arxiv.org/pdf/2503.09455", "page": 1, "id": "2503.09455_pg21_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "p^*i_0^*(i_1^*b_J + \\delta \\phi) = \\delta v"}
+{"pdf": "arxiv_math/2503.08634_pg6.pdf", "url": "https://arxiv.org/pdf/2503.08634", "page": 1, "id": "2503.08634_pg6_math_011", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathbb{E}[h(\\hat{x}_\\eta) + \\eta f(\\hat{x}_\\eta)] -f^*_\\eta \\leq \\texttt{Err}_{\\eta}"}
+{"pdf": "arxiv_math/2503.07022_pg75.pdf", "url": "https://arxiv.org/pdf/2503.07022", "page": 1, "id": "2503.07022_pg75_math_010", "type": "math", "max_diffs": 0, "checked": null, "math": "\\boldsymbol{\\mathcal{I}_5(\\theta)}"}
+{"pdf": "arxiv_math/2503.05610_pg5.pdf", "url": "https://arxiv.org/pdf/2503.05610", "page": 1, "id": "2503.05610_pg5_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "\\phi_\\zeta^m(x_j)\\to\\zeta, j=1,2"}
+{"pdf": "arxiv_math/2503.08419_pg6.pdf", "url": "https://arxiv.org/pdf/2503.08419", "page": 1, "id": "2503.08419_pg6_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "E\\in \\big| \\omega_X^{\\otimes k} \\otimes \\alpha \\big|"}
+{"pdf": "arxiv_math/2503.08272_pg14.pdf", "url": "https://arxiv.org/pdf/2503.08272", "page": 1, "id": "2503.08272_pg14_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Delta R^{2}(\\omega )"}
+{"pdf": "arxiv_math/2503.07398_pg15.pdf", "url": "https://arxiv.org/pdf/2503.07398", "page": 1, "id": "2503.07398_pg15_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\{i_k\\}_{k \\in \\mathbb{N}} \\subset I"}
+{"pdf": "arxiv_math/2503.08488_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08488", "page": 1, "id": "2503.08488_pg2_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "S_k=0, \\ \\text{if}\\ k \\in \\partial\\mathcal{L}"}
+{"pdf": "arxiv_math/2503.05436_pg25.pdf", "url": "https://arxiv.org/pdf/2503.05436", "page": 1, "id": "2503.05436_pg25_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Delta(x_1,x_2)=(x_1^2+x_2^2+1)^{-\\frac{1}{2}}"}
+{"pdf": "arxiv_math/2503.06658_pg1.pdf", "url": "https://arxiv.org/pdf/2503.06658", "page": 1, "id": "2503.06658_pg1_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\tilde{\\mathbb{F}}^r := \\{\\tilde{\\mathscr F}_t^r\\}_{t\\geq 0}"}
+{"pdf": "arxiv_math/2503.09208_pg18.pdf", "url": "https://arxiv.org/pdf/2503.09208", "page": 1, "id": "2503.09208_pg18_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "h = h_1 + \\lambda h_2"}
+{"pdf": "arxiv_math/2503.04033_pg9.pdf", "url": "https://arxiv.org/pdf/2503.04033", "page": 1, "id": "2503.04033_pg9_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathbf{\\tilde{u}}_1, \\mathbf{\\tilde{u}}_2"}
+{"pdf": "arxiv_math/2503.05437_pg6.pdf", "url": "https://arxiv.org/pdf/2503.05437", "page": 1, "id": "2503.05437_pg6_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "(y,p)\\in L^2(\\Omega)\\times P'"}
+{"pdf": "arxiv_math/2503.07247_pg2.pdf", "url": "https://arxiv.org/pdf/2503.07247", "page": 1, "id": "2503.07247_pg2_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\operatorname{Tr} g \\neq 0"}
+{"pdf": "arxiv_math/2503.05572_pg22.pdf", "url": "https://arxiv.org/pdf/2503.05572", "page": 1, "id": "2503.05572_pg22_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "b_k = \\Theta(e^{k^\\beta})"}
+{"pdf": "arxiv_math/2503.08614_pg8.pdf", "url": "https://arxiv.org/pdf/2503.08614", "page": 1, "id": "2503.08614_pg8_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Phi \\in \\mathfrak{k}"}
+{"pdf": "arxiv_math/2503.06020_pg21.pdf", "url": "https://arxiv.org/pdf/2503.06020", "page": 1, "id": "2503.06020_pg21_math_010", "type": "math", "max_diffs": 0, "checked": "verified", "math": "\\underline{u}(0, x) \\leq u_0(x) \\quad \\text{for } x \\in [-h_0, h_0]"}
+{"pdf": "arxiv_math/2503.05068_pg47.pdf", "url": "https://arxiv.org/pdf/2503.05068", "page": 1, "id": "2503.05068_pg47_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "U(\\bm{x}, 0)=\\hat{U}(\\bm{x}, 0)"}
+{"pdf": "arxiv_math/2503.09034_pg7.pdf", "url": "https://arxiv.org/pdf/2503.09034", "page": 1, "id": "2503.09034_pg7_math_006", "type": "math", "max_diffs": 0, "checked": "verified", "math": "E[p^{\\infty}]^{G_{K_{\\infty, p}}}=0"}
+{"pdf": "arxiv_math/2503.04488_pg9.pdf", "url": "https://arxiv.org/pdf/2503.04488", "page": 1, "id": "2503.04488_pg9_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "\\alpha [x,y]=[\\alpha x, y]-[f,y]x"}
+{"pdf": "arxiv_math/2503.04649_pg14.pdf", "url": "https://arxiv.org/pdf/2503.04649", "page": 1, "id": "2503.04649_pg14_math_011", "type": "math", "max_diffs": 0, "checked": null, "math": "0.7 \\leq r(\\theta, \\phi) \\leq 1.3"}
+{"pdf": "arxiv_math/2503.03855_pg5.pdf", "url": "https://arxiv.org/pdf/2503.03855", "page": 1, "id": "2503.03855_pg5_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "C^+\\coloneqq \\R_{\\geq 0}\\cdot C"}
+{"pdf": "arxiv_math/2503.07122_pg4.pdf", "url": "https://arxiv.org/pdf/2503.07122", "page": 1, "id": "2503.07122_pg4_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Theta(r) = r^{1/\\alpha}"}
+{"pdf": "arxiv_math/2503.07692_pg35.pdf", "url": "https://arxiv.org/pdf/2503.07692", "page": 1, "id": "2503.07692_pg35_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "n^{m+1,0}=\\max{\\left(2n^{m}-n^{m-1},\\epsilon\\right)}"}
+{"pdf": "arxiv_math/2503.07632_pg11.pdf", "url": "https://arxiv.org/pdf/2503.07632", "page": 1, "id": "2503.07632_pg11_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\sum_{n=1}^N \\sum_{m=1}^N \\int_0^T a_n a_m w(nf,t) w(mf,t)\\,dt"}
+{"pdf": "arxiv_math/2503.04950_pg23.pdf", "url": "https://arxiv.org/pdf/2503.04950", "page": 1, "id": "2503.04950_pg23_math_010", "type": "math", "max_diffs": 0, "checked": null, "math": "\\sigma:\\nu\\rightarrow \\{1,\\cdots,|\\nu|\\}"}
+{"pdf": "arxiv_math/2503.05717_pg14.pdf", "url": "https://arxiv.org/pdf/2503.05717", "page": 1, "id": "2503.05717_pg14_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\sqrt{2 \\pi r} T_{22}"}
+{"pdf": "arxiv_math/2503.07617_pg27.pdf", "url": "https://arxiv.org/pdf/2503.07617", "page": 1, "id": "2503.07617_pg27_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Delta{t}_{\\text{Filter}} = T/ Nt_{\\text{Filter}}"}
+{"pdf": "arxiv_math/2503.07708_pg3.pdf", "url": "https://arxiv.org/pdf/2503.07708", "page": 1, "id": "2503.07708_pg3_math_011", "type": "math", "max_diffs": 0, "checked": null, "math": "\\hat S_{1,K}(\\textbf{k}) = \\cos K\\ \\tau^z + \\sin K\\ \\tau^x"}
+{"pdf": "arxiv_math/2503.08488_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08488", "page": 1, "id": "2503.08488_pg2_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "k\\in \\partial \\mathcal{L}"}
+{"pdf": "arxiv_math/2503.06856_pg9.pdf", "url": "https://arxiv.org/pdf/2503.06856", "page": 1, "id": "2503.06856_pg9_math_010", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Pi^\\pi = \\{\\Pi^\\pi(t), 0 \\le t < \\infty \\}"}
+{"pdf": "arxiv_math/2503.04950_pg23.pdf", "url": "https://arxiv.org/pdf/2503.04950", "page": 1, "id": "2503.04950_pg23_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "\\text{st}(\\sigma)(u),\\text{st}(\\sigma)(w),\\text{st}(\\sigma)(v)"}
+{"pdf": "arxiv_math/2503.08868_pg80.pdf", "url": "https://arxiv.org/pdf/2503.08868", "page": 1, "id": "2503.08868_pg80_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "\\widehat\\gamma=\\beta'"}
+{"pdf": "arxiv_math/2503.08991_pg14.pdf", "url": "https://arxiv.org/pdf/2503.08991", "page": 1, "id": "2503.08991_pg14_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "h(g_A)=h(f_A)=h_\\eta(f_A)=h_\\mu(g_A)"}
+{"pdf": "arxiv_math/2503.05034_pg12.pdf", "url": "https://arxiv.org/pdf/2503.05034", "page": 1, "id": "2503.05034_pg12_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "d_{n,k} = [t^n]d(t)h(t)^k,\\nonumber"}
+{"pdf": "arxiv_math/2503.07022_pg75.pdf", "url": "https://arxiv.org/pdf/2503.07022", "page": 1, "id": "2503.07022_pg75_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathcal{I}_2(\\theta)"}
+{"pdf": "arxiv_math/2503.09208_pg18.pdf", "url": "https://arxiv.org/pdf/2503.09208", "page": 1, "id": "2503.09208_pg18_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "|\\langle L_I,h\\rangle| \\leq \\alpha \\int_0^T \\int_{\\mathbb{R}^N} |\\xi(t,x)|dx dt + 2\\beta \\|I\\|_{L^\\infty}\\|h\\|_{L^\\infty}T + \\gamma \\int_{\\mathbb{R}^N} |\\xi(T,x)|dx \\leq C_1 \\|h\\|_{L^\\infty(0,T)}"}
+{"pdf": "arxiv_math/2503.05672_pg9.pdf", "url": "https://arxiv.org/pdf/2503.05672", "page": 1, "id": "2503.05672_pg9_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "K = \\big\\{ u \\in V \\mid u \\cdot \\tilde{n} \\leq \\phi_1 \\text{ on } \\Gamma_\\mathrm{T} \\big\\} \\,"}
+{"pdf": "arxiv_math/2502.15977_pg21.pdf", "url": "https://arxiv.org/pdf/2502.15977", "page": 1, "id": "2502.15977_pg21_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "\\theta_1 + ... + \\theta_n"}
+{"pdf": "arxiv_math/2503.07092_pg4.pdf", "url": "https://arxiv.org/pdf/2503.07092", "page": 1, "id": "2503.07092_pg4_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "H \\in \\mathbb{R}^{f \\times p}[x]"}
+{"pdf": "arxiv_math/2503.08453_pg23.pdf", "url": "https://arxiv.org/pdf/2503.08453", "page": 1, "id": "2503.08453_pg23_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "\\alpha = \\frac{1}{2} (1\\pm i )"}
+{"pdf": "arxiv_math/2503.09352_pg5.pdf", "url": "https://arxiv.org/pdf/2503.09352", "page": 1, "id": "2503.09352_pg5_math_013", "type": "math", "max_diffs": 0, "checked": null, "math": "s=\\sum_{l=0}^\\infty a_{i,l}(x_{i}-x_{i,n})^l"}
+{"pdf": "arxiv_math/2503.04465_pg3.pdf", "url": "https://arxiv.org/pdf/2503.04465", "page": 1, "id": "2503.04465_pg3_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "u\\in L^2((0,T)\\times G_0)"}
+{"pdf": "arxiv_math/2503.04536_pg9.pdf", "url": "https://arxiv.org/pdf/2503.04536", "page": 1, "id": "2503.04536_pg9_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "T\\circ (\\sigma_t)^{-1}:(\\Omega_0,\\rho_0)\\to (\\Omega_1,\\rho_1)"}
+{"pdf": "arxiv_math/2503.05442_pg14.pdf", "url": "https://arxiv.org/pdf/2503.05442", "page": 1, "id": "2503.05442_pg14_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "BS_n\\backslash (BS_{n-1}^1\\oplus BS_{n-1}^2\\oplus BS_{n-1}^3)"}
+{"pdf": "arxiv_math/2503.04226_pg3.pdf", "url": "https://arxiv.org/pdf/2503.04226", "page": 1, "id": "2503.04226_pg3_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\left\\{ \\left( 0_{X},0_{Y},-1\\right) \\right\\}"}
+{"pdf": "arxiv_math/2503.06570_pg6.pdf", "url": "https://arxiv.org/pdf/2503.06570", "page": 1, "id": "2503.06570_pg6_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "\\langle \\tau , d \\rangle \\to -\\infty"}
+{"pdf": "arxiv_math/2503.05672_pg9.pdf", "url": "https://arxiv.org/pdf/2503.05672", "page": 1, "id": "2503.05672_pg9_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "B = -\\gamma(\\cdot) \\cdot \\tilde{n}"}
+{"pdf": "arxiv_math/2503.07156_pg35.pdf", "url": "https://arxiv.org/pdf/2503.07156", "page": 1, "id": "2503.07156_pg35_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "E:=\\{U\\in C([0,\\infty),X_p) : \\|U\\|_E=\\sup_{t\\ge0}e^{-(\\omega_p+\\theta)t}\\|U(t)\\|_{p}<\\infty\\}"}
+{"pdf": "arxiv_math/2503.05270_pg21.pdf", "url": "https://arxiv.org/pdf/2503.05270", "page": 1, "id": "2503.05270_pg21_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\left({n^{1/3}}\\middle/{\\log^{{1}/{3}}}\\right)\\exp\\left\\{-g_n\\right\\}\\to\\infty"}
+{"pdf": "arxiv_math/2503.07145_pg13.pdf", "url": "https://arxiv.org/pdf/2503.07145", "page": 1, "id": "2503.07145_pg13_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "\\argmin_{L\\in C_2} D(L,M) = \\left(\\frac{m_{ij}}{\\sum_{k=1}^n m_{kj}}\\right)_{1\\le i, j\\le n}"}
+{"pdf": "arxiv_math/2503.05873_pg4.pdf", "url": "https://arxiv.org/pdf/2503.05873", "page": 1, "id": "2503.05873_pg4_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "\\hat{\\underline{V}}_{\\mathcal{L}}(\\underline{Y}_{\\mathcal{L}})"}
+{"pdf": "arxiv_math/2503.08800_pg9.pdf", "url": "https://arxiv.org/pdf/2503.08800", "page": 1, "id": "2503.08800_pg9_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "\\prod_{j = 1}^{P_{\\Delta_n}} F_{i, j} \\leq b_{i, \\Delta_n}^{P_{\\Delta_n}}"}
+{"pdf": "arxiv_math/2503.06476_pg11.pdf", "url": "https://arxiv.org/pdf/2503.06476", "page": 1, "id": "2503.06476_pg11_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\sum_{k=0}^{\\infty}\\alpha_k\\bigg( |\\Theta(x^k)|+\\frac{\\|t^k\\|^2}{2}\\bigg)<\\infty"}
+{"pdf": "arxiv_math/2503.08151_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08151", "page": 1, "id": "2503.08151_pg2_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathcal{H}_p\\otimes\\mathcal{H}_c"}
+{"pdf": "arxiv_math/2503.03994_pg108.pdf", "url": "https://arxiv.org/pdf/2503.03994", "page": 1, "id": "2503.03994_pg108_math_019", "type": "math", "max_diffs": 0, "checked": null, "math": "\\max\\{-1,-1-v_p(x_1)\\}\\leq v_p(\\Theta_0)=1-v_p(\\Theta_1)\\leq \\min\\{0,v_p(x_0)\\}"}
+{"pdf": "arxiv_math/2503.07843_pg3.pdf", "url": "https://arxiv.org/pdf/2503.07843", "page": 1, "id": "2503.07843_pg3_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\widetilde{M}=\\widehat{\\Omega}\\times Y"}
+{"pdf": "arxiv_math/2503.06804_pg14.pdf", "url": "https://arxiv.org/pdf/2503.06804", "page": 1, "id": "2503.06804_pg14_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "X^{\\text{Test}}= N-(I^{+}+R^{+}+ H)"}
+{"pdf": "arxiv_math/2503.04407_pg3.pdf", "url": "https://arxiv.org/pdf/2503.04407", "page": 1, "id": "2503.04407_pg3_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "(\\hat{\\tau},\\hat{v},\\theta)"}
+{"pdf": "arxiv_math/2503.09115_pg3.pdf", "url": "https://arxiv.org/pdf/2503.09115", "page": 1, "id": "2503.09115_pg3_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "v_1 <_x v_2 <_x \\ldots <_x v_k"}
+{"pdf": "arxiv_math/2503.07537_pg4.pdf", "url": "https://arxiv.org/pdf/2503.07537", "page": 1, "id": "2503.07537_pg4_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "0<|r_0|<(2\\vartheta)^{-1/2}"}
+{"pdf": "arxiv_math/2503.08711_pg7.pdf", "url": "https://arxiv.org/pdf/2503.08711", "page": 1, "id": "2503.08711_pg7_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\text{BSPA}_{0.1,30,30,90}"}
+{"pdf": "arxiv_math/2503.09190_pg4.pdf", "url": "https://arxiv.org/pdf/2503.09190", "page": 1, "id": "2503.09190_pg4_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "\\hat v_h \\in \\mathbb P_k(\\hat T)"}
+{"pdf": "arxiv_math/2503.05437_pg6.pdf", "url": "https://arxiv.org/pdf/2503.05437", "page": 1, "id": "2503.05437_pg6_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "(u,p)\\in H^1(\\Omega)\\times L^2_0(\\Omega)"}
+{"pdf": "arxiv_math/2503.05588_pg16.pdf", "url": "https://arxiv.org/pdf/2503.05588", "page": 1, "id": "2503.05588_pg16_math_021", "type": "math", "max_diffs": 0, "checked": null, "math": "\\widehat\\Sigma(0,-1):=\\mathrm{Cov}(X(0))"}
+{"pdf": "arxiv_math/2503.06509_pg11.pdf", "url": "https://arxiv.org/pdf/2503.06509", "page": 1, "id": "2503.06509_pg11_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "Conv\\bigg\\{\\displaystyle \\bigcup_{j\\in \\Lambda}\\partial H_j(x^*)\\bigg\\}"}
+{"pdf": "arxiv_math/2503.04147_pg3.pdf", "url": "https://arxiv.org/pdf/2503.04147", "page": 1, "id": "2503.04147_pg3_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "\\tau=\\frac{W\\lambda}{u}\\frac{|i-j|}{N-1}"}
+{"pdf": "arxiv_math/2503.07072_pg1.pdf", "url": "https://arxiv.org/pdf/2503.07072", "page": 1, "id": "2503.07072_pg1_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\operatorname{ex}\\left(n, H\\right)"}
+{"pdf": "arxiv_math/2503.04430_pg9.pdf", "url": "https://arxiv.org/pdf/2503.04430", "page": 1, "id": "2503.04430_pg9_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "(e^n_i, e^n_j) \\in \\theta"}
+{"pdf": "arxiv_math/2503.08630_pg15.pdf", "url": "https://arxiv.org/pdf/2503.08630", "page": 1, "id": "2503.08630_pg15_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Psi\\Phi=\\operatorname{id}"}
+{"pdf": "arxiv_math/2503.07322_pg9.pdf", "url": "https://arxiv.org/pdf/2503.07322", "page": 1, "id": "2503.07322_pg9_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "D^1(V_2)\\subset B_{d+1}\\otimes V_2"}
+{"pdf": "arxiv_math/2503.08345_pg8.pdf", "url": "https://arxiv.org/pdf/2503.08345", "page": 1, "id": "2503.08345_pg8_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathcal J_F(\\mathbf 0)"}
+{"pdf": "arxiv_math/2503.08554_pg1.pdf", "url": "https://arxiv.org/pdf/2503.08554", "page": 1, "id": "2503.08554_pg1_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\eta = \\frac{c^2}{16\\pi^2 f_c^2 }"}
+{"pdf": "arxiv_math/2503.04923_pg9.pdf", "url": "https://arxiv.org/pdf/2503.04923", "page": 1, "id": "2503.04923_pg9_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "I_{i-1} = (I_{i} \\setminus \\{i\\})\\cup\\{j\\}"}
+{"pdf": "arxiv_math/2503.04488_pg9.pdf", "url": "https://arxiv.org/pdf/2503.04488", "page": 1, "id": "2503.04488_pg9_math_011", "type": "math", "max_diffs": 0, "checked": null, "math": "(X^{2}, \\cdot)=(X,\\cdot)"}
+{"pdf": "arxiv_math/2503.07910_pg7.pdf", "url": "https://arxiv.org/pdf/2503.07910", "page": 1, "id": "2503.07910_pg7_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "\\text{Frob}_p: \\, a \\mapsto a^p"}
+{"pdf": "arxiv_math/2503.06958_pg1.pdf", "url": "https://arxiv.org/pdf/2503.06958", "page": 1, "id": "2503.06958_pg1_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathcal{M}_{{\\rm max}}(\\varphi)"}
+{"pdf": "arxiv_math/2503.08411_pg18.pdf", "url": "https://arxiv.org/pdf/2503.08411", "page": 1, "id": "2503.08411_pg18_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "x\\in Y\\cap \\bigcap_{i=1}^n N(J_i)"}
+{"pdf": "arxiv_math/2503.06230_pg7.pdf", "url": "https://arxiv.org/pdf/2503.06230", "page": 1, "id": "2503.06230_pg7_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "Z_{i+1}(L')\\leq Z_{k+m}(L)"}
+{"pdf": "arxiv_math/2503.04147_pg3.pdf", "url": "https://arxiv.org/pdf/2503.04147", "page": 1, "id": "2503.04147_pg3_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathcal{N}_t=\\left\\{1,\\cdots,N_t\\right\\}"}
+{"pdf": "arxiv_math/2503.03948_pg3.pdf", "url": "https://arxiv.org/pdf/2503.03948", "page": 1, "id": "2503.03948_pg3_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mu_{(x,y,E)} \\approx 0"}
+{"pdf": "arxiv_math/2503.06739_pg8.pdf", "url": "https://arxiv.org/pdf/2503.06739", "page": 1, "id": "2503.06739_pg8_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "0\\neq(a_1 \\wedge a_2) \\wedge n_i = (a_1 \\wedge a_2) \\wedge (n_i^1 \\wedge n_i^2) =(a_1 \\wedge n_i^1) \\wedge (a_2 \\wedge n_i^2)"}
+{"pdf": "arxiv_math/2503.06344_pg15.pdf", "url": "https://arxiv.org/pdf/2503.06344", "page": 1, "id": "2503.06344_pg15_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "X, Y\\in\\mathfrak{L}(\\mathcal{F}^M)"}
+{"pdf": "arxiv_math/2503.08618_pg9.pdf", "url": "https://arxiv.org/pdf/2503.08618", "page": 1, "id": "2503.08618_pg9_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\beta_{n_j}=0,~~ j=0, 1, \\ldots, n"}
+{"pdf": "arxiv_math/2503.07400_pg11.pdf", "url": "https://arxiv.org/pdf/2503.07400", "page": 1, "id": "2503.07400_pg11_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "|G| \\ge b_2(k, g, (k - 2)g)+1"}
+{"pdf": "arxiv_math/2503.05672_pg9.pdf", "url": "https://arxiv.org/pdf/2503.05672", "page": 1, "id": "2503.05672_pg9_math_005", "type": "math", "max_diffs": 0, "checked": "verified", "math": "\\epsilon : H^1(\\Omega,\\mathbb{R}^3) \\to L^2(\\Omega,\\mathbb{R}^{3\\times 3}_{\\mathrm{sym}})"}
+{"pdf": "arxiv_math/2503.09195_pg13.pdf", "url": "https://arxiv.org/pdf/2503.09195", "page": 1, "id": "2503.09195_pg13_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "(\\mathcal{S},D_{\\mathcal{S}})"}
+{"pdf": "arxiv_math/2503.04245_pg7.pdf", "url": "https://arxiv.org/pdf/2503.04245", "page": 1, "id": "2503.04245_pg7_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "h_x = % (1-\\norm{x}^2)^{-1} g_x"}
+{"pdf": "arxiv_math/2503.07509_pg2.pdf", "url": "https://arxiv.org/pdf/2503.07509", "page": 1, "id": "2503.07509_pg2_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\bar \\alpha \\triangleq 1 - \\alpha"}
+{"pdf": "arxiv_math/2503.09121_pg4.pdf", "url": "https://arxiv.org/pdf/2503.09121", "page": 1, "id": "2503.09121_pg4_math_014", "type": "math", "max_diffs": 0, "checked": null, "math": "|A| + |B| \\ge p-k+\\lfloor \\frac{p-k-1}{2k-1} \\rfloor + 4 > \\frac{2k}{2k-1} p - k + 2"}
+{"pdf": "arxiv_math/2503.07122_pg4.pdf", "url": "https://arxiv.org/pdf/2503.07122", "page": 1, "id": "2503.07122_pg4_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "1 \\le \\alpha < +\\infty"}
+{"pdf": "arxiv_math/2503.08553_pg25.pdf", "url": "https://arxiv.org/pdf/2503.08553", "page": 1, "id": "2503.08553_pg25_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "S^2\\setminus B(p_+, r_1)"}
+{"pdf": "arxiv_math/2503.02004_pg9.pdf", "url": "https://arxiv.org/pdf/2503.02004", "page": 1, "id": "2503.02004_pg9_math_007", "type": "math", "max_diffs": 0, "checked": "verified", "math": "\\mathbf{G}, N_r, N_{\\text{init}}, \\Delta n"}
+{"pdf": "arxiv_math/2503.07128_pg28.pdf", "url": "https://arxiv.org/pdf/2503.07128", "page": 1, "id": "2503.07128_pg28_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "x_n/t_n\\in \\partial\\widetilde{W}"}
+{"pdf": "arxiv_math/2503.07537_pg4.pdf", "url": "https://arxiv.org/pdf/2503.07537", "page": 1, "id": "2503.07537_pg4_math_010", "type": "math", "max_diffs": 0, "checked": null, "math": "\\varkappa\\in\\mathbb Z_+"}
+{"pdf": "arxiv_math/2503.05436_pg25.pdf", "url": "https://arxiv.org/pdf/2503.05436", "page": 1, "id": "2503.05436_pg25_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "\\operatorname{Fix}(Q)\\subset\\mathbb{R}^m"}
+{"pdf": "arxiv_math/2503.05922_pg8.pdf", "url": "https://arxiv.org/pdf/2503.05922", "page": 1, "id": "2503.05922_pg8_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "1\\leq q_1 < q_2\\leq \\infty"}
+{"pdf": "arxiv_math/2503.06710_pg5.pdf", "url": "https://arxiv.org/pdf/2503.06710", "page": 1, "id": "2503.06710_pg5_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "\\psi=\\left[\\psi^{+},\\psi^{-}\\right]^\\top"}
+{"pdf": "arxiv_math/2503.04923_pg9.pdf", "url": "https://arxiv.org/pdf/2503.04923", "page": 1, "id": "2503.04923_pg9_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "\\bar{f}^{-1}_{\\mathcal{I}}(i) = j"}
+{"pdf": "arxiv_math/2503.09254_pg3.pdf", "url": "https://arxiv.org/pdf/2503.09254", "page": 1, "id": "2503.09254_pg3_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "M = \\{ m_1 , ..., m_r \\}"}
+{"pdf": "arxiv_math/2503.08345_pg8.pdf", "url": "https://arxiv.org/pdf/2503.08345", "page": 1, "id": "2503.08345_pg8_math_011", "type": "math", "max_diffs": 0, "checked": null, "math": "A_F f = \\sum_{\\alpha\\in \\mathbb N^n} \\left( \\sum_{\\beta\\in\\mathbb N^n} {A_F}_{\\alpha,\\beta} f_\\beta \\right)e_\\alpha\\\\"}
+{"pdf": "arxiv_math/2503.06758_pg6.pdf", "url": "https://arxiv.org/pdf/2503.06758", "page": 1, "id": "2503.06758_pg6_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\{\\delta^i_\\eta : \\eta < \\lambda^{+k}\\}"}
+{"pdf": "arxiv_math/2503.09571_pg3.pdf", "url": "https://arxiv.org/pdf/2503.09571", "page": 1, "id": "2503.09571_pg3_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "s_{ij} = p^{(i)} \\cdot p^{(j)}"}
+{"pdf": "arxiv_math/2503.04189_pg11.pdf", "url": "https://arxiv.org/pdf/2503.04189", "page": 1, "id": "2503.04189_pg11_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\varphi(x, \\xi') - \\varphi(y, \\xi') = \\Sigma(x, y', \\xi')(x' - y')"}
+{"pdf": "arxiv_math/2503.08187_pg4.pdf", "url": "https://arxiv.org/pdf/2503.08187", "page": 1, "id": "2503.08187_pg4_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "z(\\theta)=\\min(\\max(\\theta,-\\frac{\\pi}{2}),\\frac{\\pi}{2})"}
+{"pdf": "arxiv_math/2503.05960_pg4.pdf", "url": "https://arxiv.org/pdf/2503.05960", "page": 1, "id": "2503.05960_pg4_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "G = \\bigsqcup_{A, B \\in \\mathcal{C}} \\mathrm{Hom} (A, B)"}
+{"pdf": "arxiv_math/2503.06051_pg2.pdf", "url": "https://arxiv.org/pdf/2503.06051", "page": 1, "id": "2503.06051_pg2_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "s_{i_1},s_{i_2},\\ldots,s_{i_{\\ell(\\sigma)}}"}
+{"pdf": "arxiv_math/2503.05941_pg1.pdf", "url": "https://arxiv.org/pdf/2503.05941", "page": 1, "id": "2503.05941_pg1_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathbf{l} \\in \\mathbf{R}^{m}"}
+{"pdf": "arxiv_math/2503.05442_pg14.pdf", "url": "https://arxiv.org/pdf/2503.05442", "page": 1, "id": "2503.05442_pg14_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\kappa(BS_{n-1})=4k+1"}
+{"pdf": "arxiv_math/2503.06612_pg19.pdf", "url": "https://arxiv.org/pdf/2503.06612", "page": 1, "id": "2503.06612_pg19_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "c_1x_1^\\alpha + c_2 x_2^\\beta + g(x_1,x_2)"}
+{"pdf": "arxiv_math/2503.04465_pg3.pdf", "url": "https://arxiv.org/pdf/2503.04465", "page": 1, "id": "2503.04465_pg3_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\xi\\mapsto y(T,\\cdot;\\xi;y_0;u)"}
+{"pdf": "arxiv_math/2503.08172_pg25.pdf", "url": "https://arxiv.org/pdf/2503.08172", "page": 1, "id": "2503.08172_pg25_math_000", "type": "math", "max_diffs": 0, "checked": "verified", "math": "p(\\tau, \\tau \\sqcup \\{ij\\}) = \\left\\{ \\begin{array}{cl} \\displaystyle \\frac{\\alpha_{ij} w_{i, ij}}{\\sum_{k=1}^d \\alpha_{ik} w_{i, ik}} \\alpha_i , & \\text{if } i \\in \\partial \\tau, \\\\[15pt] \\alpha_{ij}, & \\text{if } i \\notin \\partial \\tau \\text{ and } ij \\notin \\tau, \\end{array} \\right."}
+{"pdf": "arxiv_math/2503.06020_pg21.pdf", "url": "https://arxiv.org/pdf/2503.06020", "page": 1, "id": "2503.06020_pg21_math_011", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Omega_{T_m} := \\{(t, x) : t \\in (0, T_m), x \\in [g(t), h(t)]\\}"}
+{"pdf": "arxiv_math/2503.04897_pg4.pdf", "url": "https://arxiv.org/pdf/2503.04897", "page": 1, "id": "2503.04897_pg4_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\rho(m)=\\sum_{i} {m_{(0)}}_i\\otimes {m_{(1)}}_i\\in M\\otimes C"}
+{"pdf": "arxiv_math/2503.08127_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08127", "page": 1, "id": "2503.08127_pg2_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "(\\bm{u}\\cdot \\nabla)\\bm{C}"}
+{"pdf": "arxiv_math/2503.09374_pg3.pdf", "url": "https://arxiv.org/pdf/2503.09374", "page": 1, "id": "2503.09374_pg3_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathcal{F}: \\mathbb{R}^d \\to \\mathbb{R}^{n}"}
+{"pdf": "arxiv_math/2503.05661_pg16.pdf", "url": "https://arxiv.org/pdf/2503.05661", "page": 1, "id": "2503.05661_pg16_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "d_G(v,x)\\le d_G(v,z) + d_G(z,x)\\le K-1+(K-1)/2=3/2(K-1)<\\lfloor\\frac{3}{2}K\\rfloor"}
+{"pdf": "arxiv_math/2503.09155_pg16.pdf", "url": "https://arxiv.org/pdf/2503.09155", "page": 1, "id": "2503.09155_pg16_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "e\\in \\operatorname{int}\\left(\\mathcal{B}_{G} \\right )"}
+{"pdf": "arxiv_math/2503.07221_pg16.pdf", "url": "https://arxiv.org/pdf/2503.07221", "page": 1, "id": "2503.07221_pg16_math_011", "type": "math", "max_diffs": 0, "checked": null, "math": "[-\\tau,\\tau]=[-\\tau,0]\\cup [0,\\tau]"}
+{"pdf": "arxiv_math/2503.06476_pg11.pdf", "url": "https://arxiv.org/pdf/2503.06476", "page": 1, "id": "2503.06476_pg11_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "\\sum_{k=0}^{\\infty}\\|x^{k+1}-x^k\\|^2\\leq \\sum_{k=0}^{\\infty} \\alpha_k\\| t^k\\|^2<\\infty"}
+{"pdf": "arxiv_math/2503.07122_pg4.pdf", "url": "https://arxiv.org/pdf/2503.07122", "page": 1, "id": "2503.07122_pg4_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "c_{p,\\Theta;d} = e^{-\\max\\{p,d+1\\}}"}
+{"pdf": "arxiv_math/2503.08634_pg6.pdf", "url": "https://arxiv.org/pdf/2503.08634", "page": 1, "id": "2503.08634_pg6_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "\\eta\\le\\tfrac{\\alpha}{2\\|\\nabla f(x^*)\\|}"}
+{"pdf": "arxiv_math/2503.09577_pg20.pdf", "url": "https://arxiv.org/pdf/2503.09577", "page": 1, "id": "2503.09577_pg20_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "I(k, n, w) = \\binom{k}{2} \\sum_{i=1}^{i_0-1}k^{i-1}\\binom{k^{(c_w)_{i}} }{2}k^{2n-2i-2(c_w)_i} = \\frac{k-1}{4}\\sum_{i=1}^{i_0-1}(k^{2n-i} - k^{2n-i-(c_w)_i})"}
+{"pdf": "arxiv_math/2503.06826_pg10.pdf", "url": "https://arxiv.org/pdf/2503.06826", "page": 1, "id": "2503.06826_pg10_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "U_i = N_\\Gamma(W_i) \\cap U"}
+{"pdf": "arxiv_math/2503.08595_pg4.pdf", "url": "https://arxiv.org/pdf/2503.08595", "page": 1, "id": "2503.08595_pg4_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "E_j(\\theta) = (1+\\mu_j) E_{\\Gamma_0}(\\theta)+\\mu_j"}
+{"pdf": "arxiv_math/2503.04407_pg3.pdf", "url": "https://arxiv.org/pdf/2503.04407", "page": 1, "id": "2503.04407_pg3_math_010", "type": "math", "max_diffs": 0, "checked": null, "math": "x_{r,m}=\\frac{\\lambda}{2}m,m\\in\\mathcal{M}_r"}
+{"pdf": "arxiv_math/2503.08374_pg13.pdf", "url": "https://arxiv.org/pdf/2503.08374", "page": 1, "id": "2503.08374_pg13_math_005", "type": "math", "max_diffs": 0, "checked": "verified", "math": "\\det A_{n;3}(x,\\sqrt{x})=\\delta_n^3+p_n(x,\\sqrt{x})\\delta_n+q_n(x,\\sqrt{x})=0"}
+{"pdf": "arxiv_math/2503.04040_pg2.pdf", "url": "https://arxiv.org/pdf/2503.04040", "page": 1, "id": "2503.04040_pg2_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "\\lVert \\mathbf{A} \\rVert_{\\rm F}"}
+{"pdf": "arxiv_math/2503.05873_pg4.pdf", "url": "https://arxiv.org/pdf/2503.05873", "page": 1, "id": "2503.05873_pg4_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathbb{P}(\\underline{\\hat{V}}_{\\mathcal{L}}(\\underline{Y}_{\\mathcal{L}}) \\neq \\underline{V}_{\\mathcal{L}}) \\leq \\epsilon_e"}
+{"pdf": "arxiv_math/2503.05993_pg15.pdf", "url": "https://arxiv.org/pdf/2503.05993", "page": 1, "id": "2503.05993_pg15_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\phi,\\dot{\\phi},\\cos \\phi"}
+{"pdf": "arxiv_math/2503.06969_pg11.pdf", "url": "https://arxiv.org/pdf/2503.06969", "page": 1, "id": "2503.06969_pg11_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "\\varphi_i(\\overline{W_i}) = 1"}
+{"pdf": "arxiv_math/2503.08488_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08488", "page": 1, "id": "2503.08488_pg2_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathcal{L}=[-L,L]^3\\bigcap \\mathbb{Z}^3"}
+{"pdf": "arxiv_math/2503.08059_pg6.pdf", "url": "https://arxiv.org/pdf/2503.08059", "page": 1, "id": "2503.08059_pg6_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "i\\bm{k}/(\\bm{k}^2+\\bm{l}^2)\\tilde{s}"}
+{"pdf": "arxiv_math/2503.05140_pg22.pdf", "url": "https://arxiv.org/pdf/2503.05140", "page": 1, "id": "2503.05140_pg22_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "\\begin{cases} \\frac{1}{q} > \\frac{2}{3p} - \\frac{1}{6}, & \\text{for } q \\geq 3p'; \\\\ \\frac{1}{q} > \\frac{1}{p} - \\frac{1}{3}, & \\text{for } p' < q < 3p'; \\\\ \\frac{1}{q} > \\frac{2}{p} - 1, & \\text{for } q \\leq p'. \\end{cases}"}
+{"pdf": "arxiv_math/2503.08105_pg5.pdf", "url": "https://arxiv.org/pdf/2503.08105", "page": 1, "id": "2503.08105_pg5_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "f^2=(h + \\overline{g})^2 = h^2 +\\overline{g}^2+ 2h\\overline{g}"}
+{"pdf": "arxiv_math/2503.06226_pg4.pdf", "url": "https://arxiv.org/pdf/2503.06226", "page": 1, "id": "2503.06226_pg4_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "{\\bar {\\mathcal{A}}}_u \\in \\mathbb{R}^{nm \\times nm}"}
+{"pdf": "arxiv_math/2503.08059_pg6.pdf", "url": "https://arxiv.org/pdf/2503.08059", "page": 1, "id": "2503.08059_pg6_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\hat{F}_1 = 0.0099s_{xx}+0.9955u"}
+{"pdf": "arxiv_math/2503.08649_pg4.pdf", "url": "https://arxiv.org/pdf/2503.08649", "page": 1, "id": "2503.08649_pg4_math_010", "type": "math", "max_diffs": 0, "checked": null, "math": "w(x):=d^\\beta(x), \\quad{\\rm \\ \\ }"}
+{"pdf": "arxiv_math/2503.08244_pg9.pdf", "url": "https://arxiv.org/pdf/2503.08244", "page": 1, "id": "2503.08244_pg9_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "\\omega \\in \\Sigma_\\vartheta"}
+{"pdf": "arxiv_math/2503.09231_pg4.pdf", "url": "https://arxiv.org/pdf/2503.09231", "page": 1, "id": "2503.09231_pg4_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\|f\\|_{C([0,T]; X)} = \\sup_{t \\in [0,T]} \\|f(t)\\|_X "}
+{"pdf": "arxiv_math/2503.06086_pg17.pdf", "url": "https://arxiv.org/pdf/2503.06086", "page": 1, "id": "2503.06086_pg17_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "d(x'_1,y)=d(x'_1,v_{i_l})"}
+{"pdf": "arxiv_math/2503.08351_pg5.pdf", "url": "https://arxiv.org/pdf/2503.08351", "page": 1, "id": "2503.08351_pg5_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "\\eta_F:[0,\\infty)\\to [0,\\infty)"}
+{"pdf": "arxiv_math/2503.06969_pg11.pdf", "url": "https://arxiv.org/pdf/2503.06969", "page": 1, "id": "2503.06969_pg11_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "x \\in \\complement \\overline{V_i} \\cap U_i"}
+{"pdf": "arxiv_math/2503.08910_pg26.pdf", "url": "https://arxiv.org/pdf/2503.08910", "page": 1, "id": "2503.08910_pg26_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Xi_1(b_{i'}^{\\sigma(i')})= \\Xi_1({\\sim}b_{i'})=0"}
+{"pdf": "arxiv_math/2503.06969_pg11.pdf", "url": "https://arxiv.org/pdf/2503.06969", "page": 1, "id": "2503.06969_pg11_math_012", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Phi(X) \\subseteq T^n(\\mu)"}
+{"pdf": "arxiv_math/2503.04226_pg3.pdf", "url": "https://arxiv.org/pdf/2503.04226", "page": 1, "id": "2503.04226_pg3_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "\\overline{U}\\cap V=U\\cap V"}
+{"pdf": "arxiv_math/2503.04238_pg26.pdf", "url": "https://arxiv.org/pdf/2503.04238", "page": 1, "id": "2503.04238_pg26_math_010", "type": "math", "max_diffs": 0, "checked": null, "math": "\\left<x, y\\right>_S = x^\\top S y"}
+{"pdf": "arxiv_math/2503.07801_pg15.pdf", "url": "https://arxiv.org/pdf/2503.07801", "page": 1, "id": "2503.07801_pg15_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "\\ell(p) \\ge \\frac{p+1}{2}"}
+{"pdf": "arxiv_math/2503.07145_pg13.pdf", "url": "https://arxiv.org/pdf/2503.07145", "page": 1, "id": "2503.07145_pg13_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "\\argmin_{L\\in C_1} D(L,M) = \\left(\\frac{m_{ij}}{\\sum_{k=1}^n m_{ik}}\\right)_{1\\le i, j\\le n}"}
+{"pdf": "arxiv_math/2503.08062_pg10.pdf", "url": "https://arxiv.org/pdf/2503.08062", "page": 1, "id": "2503.08062_pg10_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "(1-\\frac{N_{\\tau}-N_{cp}}{N})^2"}
+{"pdf": "arxiv_math/2503.07617_pg27.pdf", "url": "https://arxiv.org/pdf/2503.07617", "page": 1, "id": "2503.07617_pg27_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\tilde{\\varepsilon}^i \\sim \\mathcal{N}(0, \\pmb{I}_l)"}
+{"pdf": "arxiv_math/2503.06509_pg11.pdf", "url": "https://arxiv.org/pdf/2503.06509", "page": 1, "id": "2503.06509_pg11_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "h_{j^0}(x,\\xi_i)\\geq h_{j^0}(x^*,\\xi_i) + \\nabla h_{j^0}(x^*,\\xi_i)^T(x-x^*),~ \\forall ~i\\in I_{j^0}(x^*)"}
+{"pdf": "arxiv_math/2503.05614_pg12.pdf", "url": "https://arxiv.org/pdf/2503.05614", "page": 1, "id": "2503.05614_pg12_math_001", "type": "math", "max_diffs": 0, "checked": "verified", "math": "C^\\bullet(E) \\simeq R\\text{Hom}(C^\\bullet(E), \\mathbb{Q}/\\mathbb{Z}(1))[1]"}
+{"pdf": "arxiv_math/2503.08127_pg2.pdf", "url": "https://arxiv.org/pdf/2503.08127", "page": 1, "id": "2503.08127_pg2_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "(\\bm{u}\\otimes\\bm{v})_{ij}=u_i v_j, ~(\\bm{C}\\otimes\\bm{u})_{ijk}= C_{ij}u_k"}
+{"pdf": "arxiv_math/2503.09421_pg9.pdf", "url": "https://arxiv.org/pdf/2503.09421", "page": 1, "id": "2503.09421_pg9_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "| \\left\\{ x \\in \\R \\, \\text{s.t. } \\|M_1 \\, (A+x)^{-1} \\, M_2 \\| > t \\right\\} | \\leq c \\, \\|M_1\\|_{HS} \\, \\|M_2\\|_{HS} \\, \\frac{1}{t}"}
+{"pdf": "arxiv_math/2503.04425_pg8.pdf", "url": "https://arxiv.org/pdf/2503.04425", "page": 1, "id": "2503.04425_pg8_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "0 < \\overline{\\epsilon} \\leq \\epsilon^*"}
+{"pdf": "arxiv_math/2503.05476_pg14.pdf", "url": "https://arxiv.org/pdf/2503.05476", "page": 1, "id": "2503.05476_pg14_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\psi_{n}(t)\\le\\psi(t)"}
+{"pdf": "arxiv_math/2503.06464_pg8.pdf", "url": "https://arxiv.org/pdf/2503.06464", "page": 1, "id": "2503.06464_pg8_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "V(H)=\\{ u,v,w_1,\\ldots,w_m \\}"}
+{"pdf": "arxiv_math/2503.06110_pg13.pdf", "url": "https://arxiv.org/pdf/2503.06110", "page": 1, "id": "2503.06110_pg13_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "d([e_1], g_t u_x H_C) = d([e_1], u_y H_{t,C}) \\asymp d([u_{-y} e_1], H_{t,C}) \\asymp \\phi_{t,C}(u_{-y} e_1)"}
+{"pdf": "arxiv_math/2503.04124_pg14.pdf", "url": "https://arxiv.org/pdf/2503.04124", "page": 1, "id": "2503.04124_pg14_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "|S_1\\cup S_2|\\le \\frac{2|V(D_1)|+2|V(D_2)|+2(k-1)}{5}= \\frac{2n}{5} "}
+{"pdf": "arxiv_math/2503.09528_pg16.pdf", "url": "https://arxiv.org/pdf/2503.09528", "page": 1, "id": "2503.09528_pg16_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "P=\\{b^{l_1}_1/b^{l_2}_2: (l_1,l_2)\\in\\mathbb{Z}^2_{>0}\\}\\subset\\mathbb{C}"}
+{"pdf": "arxiv_math/2503.06230_pg7.pdf", "url": "https://arxiv.org/pdf/2503.06230", "page": 1, "id": "2503.06230_pg7_math_004", "type": "math", "max_diffs": 0, "checked": "verified", "math": "[x+y,_{n}x]=[y,_{n}x]=0"}
+{"pdf": "arxiv_math/2503.06723_pg3.pdf", "url": "https://arxiv.org/pdf/2503.06723", "page": 1, "id": "2503.06723_pg3_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\{e_{1},\\dots,e_{d}\\}"}
+{"pdf": "arxiv_math/2503.04430_pg9.pdf", "url": "https://arxiv.org/pdf/2503.04430", "page": 1, "id": "2503.04430_pg9_math_001", "type": "math", "max_diffs": 0, "checked": "verified", "math": "Y_1 \\lor (\\cdots (Y_{n-1} \\lor Y_n)) = q^n_2(x, y_1[1], \\ldots, y_n[1])"}
+{"pdf": "arxiv_math/2503.04897_pg4.pdf", "url": "https://arxiv.org/pdf/2503.04897", "page": 1, "id": "2503.04897_pg4_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Delta\\colon H\\to H\\otimes H"}
+{"pdf": "arxiv_math/2503.08176_pg20.pdf", "url": "https://arxiv.org/pdf/2503.08176", "page": 1, "id": "2503.08176_pg20_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "(k_{1},k_{2})\\in \\mathcal{A}_{2}^{*}(3,1,2)"}
+{"pdf": "arxiv_math/2503.04993_pg18.pdf", "url": "https://arxiv.org/pdf/2503.04993", "page": 1, "id": "2503.04993_pg18_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\frac{d}{d\\epsilon} J_1(u_1 + \\epsilon v_1, u_2) \\Big|_{\\epsilon=0}"}
+{"pdf": "arxiv_math/2503.06944_pg2.pdf", "url": "https://arxiv.org/pdf/2503.06944", "page": 1, "id": "2503.06944_pg2_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\zeta \\in \\left[0, \\pi\\right)"}
+{"pdf": "arxiv_math/2503.02004_pg9.pdf", "url": "https://arxiv.org/pdf/2503.02004", "page": 1, "id": "2503.02004_pg9_math_006", "type": "math", "max_diffs": 0, "checked": null, "math": "T_{(0)} = \\{\\varnothing\\}"}
+{"pdf": "arxiv_math/2503.04077_pg1.pdf", "url": "https://arxiv.org/pdf/2503.04077", "page": 1, "id": "2503.04077_pg1_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathbb{R}\\times S^1\\times\\mathbb{C}"}
+{"pdf": "arxiv_math/2503.08646_pg17.pdf", "url": "https://arxiv.org/pdf/2503.08646", "page": 1, "id": "2503.08646_pg17_math_004", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathrm{T}_p\\mu^{-1}(0)\\simeq \\mathrm{T}_pL"}
+{"pdf": "arxiv_math/2503.07147_pg16.pdf", "url": "https://arxiv.org/pdf/2503.07147", "page": 1, "id": "2503.07147_pg16_math_009", "type": "math", "max_diffs": 0, "checked": null, "math": "|C| \\le \\frac{|U|}{10r}"}
+{"pdf": "arxiv_math/2503.07441_pg11.pdf", "url": "https://arxiv.org/pdf/2503.07441", "page": 1, "id": "2503.07441_pg11_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "i: D ^{2} \\hookrightarrow \\mathcal{D}"}
+{"pdf": "arxiv_math/2503.09574_pg27.pdf", "url": "https://arxiv.org/pdf/2503.09574", "page": 1, "id": "2503.09574_pg27_math_010", "type": "math", "max_diffs": 0, "checked": null, "math": "\\tau_+^{-A}=\\tau_-^{A}= \\lambda \\delta_B"}
+{"pdf": "arxiv_math/2503.06581_pg8.pdf", "url": "https://arxiv.org/pdf/2503.06581", "page": 1, "id": "2503.06581_pg8_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "J\\in\\left(H^1(\\mathbb R^3)\\right)^3"}
+{"pdf": "arxiv_math/2503.04329_pg7.pdf", "url": "https://arxiv.org/pdf/2503.04329", "page": 1, "id": "2503.04329_pg7_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "F\\in Stem(D)\\cap\\mathcal{C}^1(D)"}
+{"pdf": "arxiv_math/2503.06880_pg36.pdf", "url": "https://arxiv.org/pdf/2503.06880", "page": 1, "id": "2503.06880_pg36_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "E_2 = \\operatorname{Span}\\{b_1, b_2\\}"}
+{"pdf": "arxiv_math/2503.07345_pg12.pdf", "url": "https://arxiv.org/pdf/2503.07345", "page": 1, "id": "2503.07345_pg12_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "\\langle L_1 \\phi , \\chi_b(r) r^{\\frac12}\\rho_1\\rangle = \\lambda_0 \\langle \\phi, \\chi_b(r) r^{\\frac12}\\rho_1\\rangle"}
+{"pdf": "arxiv_math/2503.08186_pg7.pdf", "url": "https://arxiv.org/pdf/2503.08186", "page": 1, "id": "2503.08186_pg7_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Omega_+ := \\{ (x',x_d) \\in \\R^d : x_d > \\phi(x') \\}"}
+{"pdf": "arxiv_math/2503.06804_pg14.pdf", "url": "https://arxiv.org/pdf/2503.06804", "page": 1, "id": "2503.06804_pg14_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "C_T \\left(u^T_n X^{\\text{Test}}_n,\\overline{ \\text{x}}^{\\text{Test}}\\right)"}
+{"pdf": "arxiv_math/2503.07696_pg3.pdf", "url": "https://arxiv.org/pdf/2503.07696", "page": 1, "id": "2503.07696_pg3_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\arg(\\eta(s))\\ne\\pm\\pi/2"}
+{"pdf": "arxiv_math/2503.06570_pg6.pdf", "url": "https://arxiv.org/pdf/2503.06570", "page": 1, "id": "2503.06570_pg6_math_008", "type": "math", "max_diffs": 0, "checked": null, "math": "(\\tau,z)=(\\sum_{j=1}^{b^{2}(X)} t_j \\phi_j, z) \\in H^2(X) \\times \\mathbb{C}^\\times"}
+{"pdf": "arxiv_math/2503.05880_pg5.pdf", "url": "https://arxiv.org/pdf/2503.05880", "page": 1, "id": "2503.05880_pg5_math_000", "type": "math", "max_diffs": 0, "checked": null, "math": "x_{0}\\in \\mathbf{R}^{d}"}
+{"pdf": "arxiv_math/2503.08975_pg3.pdf", "url": "https://arxiv.org/pdf/2503.08975", "page": 1, "id": "2503.08975_pg3_math_006", "type": "math", "max_diffs": 0, "checked": "verified", "math": "N\\in\\{1-33,35-37,39-41,43,46-50,53,59,61,65,71,79,83,89,101,131\\}"}
+{"pdf": "arxiv_math/2503.06651_pg13.pdf", "url": "https://arxiv.org/pdf/2503.06651", "page": 1, "id": "2503.06651_pg13_math_005", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathrm{\\textbf{H}_\\text D}"}
+{"pdf": "arxiv_math/2503.09471_pg2.pdf", "url": "https://arxiv.org/pdf/2503.09471", "page": 1, "id": "2503.09471_pg2_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "\\delta_i\\in C([\\tau,\\infty);\\mathbb R_{>0})"}
+{"pdf": "arxiv_math/2503.08618_pg9.pdf", "url": "https://arxiv.org/pdf/2503.08618", "page": 1, "id": "2503.08618_pg9_math_007", "type": "math", "max_diffs": 0, "checked": null, "math": "p(q)=\\sum_{\\nu=0}^{k} q^{n_\\nu} a_{n_\\nu}"}
+{"pdf": "arxiv_math/2503.04465_pg3.pdf", "url": "https://arxiv.org/pdf/2503.04465", "page": 1, "id": "2503.04465_pg3_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\mathbb{P}\\left[\\omega\\;:\\; y(T,\\cdot;\\alpha(\\omega);y_0;u)=0\\right]=0"}
+{"pdf": "arxiv_math/2503.08244_pg9.pdf", "url": "https://arxiv.org/pdf/2503.08244", "page": 1, "id": "2503.08244_pg9_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "\\Theta: {\\Sigma_\\vartheta} \\times \\mathbb{T} \\to {\\Sigma_\\vartheta} \\times \\mathbb{T}"}
+{"pdf": "arxiv_math/2503.07924_pg3.pdf", "url": "https://arxiv.org/pdf/2503.07924", "page": 1, "id": "2503.07924_pg3_math_002", "type": "math", "max_diffs": 0, "checked": null, "math": "\\begin{aligned} H(\\sigma) &= \\sum_{i \\neq j} Q_{ij} \\cdot \\frac{(\\sigma_i + 1)(\\sigma_j + 1)}{4} + \\sum_i q_i \\cdot \\frac{\\sigma_i + 1}{2} \\\\ &= \\sum_{i \\neq j} \\frac{Q_{ij}}{4} \\sigma_i \\sigma_j + \\sum_i \\left( \\frac{q_i}{2} + \\frac{\\sum_{i \\neq j} (Q_{ij} + Q_{ji})}{4} \\right) \\sigma_i \\\\ &\\quad + \\left( \\frac{\\sum_i q_i}{2} + \\frac{\\sum_{i \\neq j} Q_{ij}}{4} \\right) \\end{aligned}"}
+{"pdf": "arxiv_math/2503.07567_pg6.pdf", "url": "https://arxiv.org/pdf/2503.07567", "page": 1, "id": "2503.07567_pg6_math_001", "type": "math", "max_diffs": 0, "checked": null, "math": "d_{\\text{min}}^{\\mathcal{C}} = 14"}
+{"pdf": "arxiv_math/2503.04189_pg11.pdf", "url": "https://arxiv.org/pdf/2503.04189", "page": 1, "id": "2503.04189_pg11_math_002", "type": "math", "max_diffs": 0, "checked": "verified", "math": "a_1 \\in \\widetilde{S}_s^{m-1, k}"}
+{"pdf": "arxiv_math/2503.04897_pg4.pdf", "url": "https://arxiv.org/pdf/2503.04897", "page": 1, "id": "2503.04897_pg4_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "(H, \\Delta, \\varepsilon)"}
+{"pdf": "arxiv_math/2503.04397_pg2.pdf", "url": "https://arxiv.org/pdf/2503.04397", "page": 1, "id": "2503.04397_pg2_math_001", "type": "math", "max_diffs": 0, "checked": "verified", "math": "{\\cal CN}(0,\\sigma^2)"}
+{"pdf": "arxiv_math/2503.09469_pg13.pdf", "url": "https://arxiv.org/pdf/2503.09469", "page": 1, "id": "2503.09469_pg13_math_003", "type": "math", "max_diffs": 0, "checked": null, "math": "% \\lambda_{-1}(0) &= \\lambda_{-1}(\\B) \\\\ % \\lambda^{\\prime}_{-1}(0) &= -\\vect{v}_{-1}(\\B)^T \\C \\vect{v}_{-1}(\\B) =: - \\xi %"}