removed duplicates

bench_data/old_scans_math.jsonl

@@ -111,18 +111,12 @@
 {"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_06", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "x^2 + y^2 - 1 = 0"}
 {"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_07", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "y + 2\\lambda x = 0"}
 {"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_08", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "x + 2\\lambda y = 0"}
-{"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_09", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "x^2 + y^2 - 1 = 0"}
 {"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_10", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "\\xi = \\frac{1}{2} \\sqrt{2}"}
 {"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_11", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "\\eta = \\frac{1}{2} \\sqrt{2}"}
 {"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_12", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "\\xi = -\\frac{1}{2} \\sqrt{2}"}
 {"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_13", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "\\eta = -\\frac{1}{2} \\sqrt{2}"}
-{"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_14", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "\\xi = \\frac{1}{2} \\sqrt{2}"}
-{"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_15", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "\\eta = -\\frac{1}{2} \\sqrt{2}"}
-{"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_16", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "\\xi = -\\frac{1}{2} \\sqrt{2}"}
-{"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_17", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "\\eta = \\frac{1}{2} \\sqrt{2}"}
 {"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_18", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "u = \\frac{1}{2}"}
 {"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_19", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "u = -\\frac{1}{2}"}
-{"pdf": "old_scans_math/3_pg199.pdf", "page": 1, "id": "3_pg199_equation_20", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n197/mode/2up", "math": "u = xy"}
 {"pdf": "old_scans_math/3_pg634.pdf", "page": 1, "id": "3_pg634_equation_00", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n633/mode/2up", "math": "x^{2}=1"}
 {"pdf": "old_scans_math/3_pg634.pdf", "page": 1, "id": "3_pg634_equation_01", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n633/mode/2up", "math": "\\dot{x} x=0"}
 {"pdf": "old_scans_math/3_pg634.pdf", "page": 1, "id": "3_pg634_equation_02", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n633/mode/2up", "math": "(y-x) x=0"}
@@ -187,8 +181,6 @@
 {"pdf": "old_scans_math/3_pg204.pdf", "page": 1, "id": "3_pg204_equation_05", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n203/mode/2up", "math": "\\phi(x, y, z, t) = 0"}
 {"pdf": "old_scans_math/3_pg204.pdf", "page": 1, "id": "3_pg204_equation_06", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n203/mode/2up", "math": "\\psi(x, y, z, t) = 0"}
 {"pdf": "old_scans_math/3_pg204.pdf", "page": 1, "id": "3_pg204_equation_07", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n203/mode/2up", "math": "\\frac{\\partial(\\phi, \\psi)}{\\partial(z, t)}"}
-{"pdf": "old_scans_math/3_pg204.pdf", "page": 1, "id": "3_pg204_equation_08", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n203/mode/2up", "math": "f_{x} + \\lambda \\phi_{x} + \\mu \\psi_{x} = 0"}
-{"pdf": "old_scans_math/3_pg204.pdf", "page": 1, "id": "3_pg204_equation_09", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n203/mode/2up", "math": "f_{y} + \\lambda \\phi_{y} + \\mu \\psi_{y} = 0"}
 {"pdf": "old_scans_math/3_pg204.pdf", "page": 1, "id": "3_pg204_equation_10", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n203/mode/2up", "math": "f_{z} + \\lambda \\phi_{z} + \\mu \\psi_{z} = 0"}
 {"pdf": "old_scans_math/3_pg204.pdf", "page": 1, "id": "3_pg204_equation_11", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n203/mode/2up", "math": "f_{t} + \\lambda \\phi_{t} + \\mu \\psi_{t} = 0"}
 {"pdf": "old_scans_math/3_pg204.pdf", "page": 1, "id": "3_pg204_equation_12", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n203/mode/2up", "math": "\\frac{\\partial(\\phi, \\psi)}{\\partial(z, t)} \\neq 0"}
@@ -217,8 +209,6 @@
 {"pdf": "old_scans_math/3_pg148.pdf", "page": 1, "id": "3_pg148_equation_06", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n147/mode/2up", "math": "\\psi(x, y) = const"}
 {"pdf": "old_scans_math/3_pg148.pdf", "page": 1, "id": "3_pg148_equation_07", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n147/mode/2up", "math": "x = g(\\xi, \\eta)"}
 {"pdf": "old_scans_math/3_pg148.pdf", "page": 1, "id": "3_pg148_equation_08", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n147/mode/2up", "math": "y = h(\\xi, \\eta)"}
-{"pdf": "old_scans_math/3_pg148.pdf", "page": 1, "id": "3_pg148_equation_09", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n147/mode/2up", "math": "\\xi = \\phi(x, y)"}
-{"pdf": "old_scans_math/3_pg148.pdf", "page": 1, "id": "3_pg148_equation_10", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n147/mode/2up", "math": "\\eta = \\psi(x, y)"}
 {"pdf": "old_scans_math/3_pg251.pdf", "page": 1, "id": "3_pg251_equation_00", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n249/mode/2up", "math": "\\lim_{\\delta \\to 0} \\int_{\\psi_{1}(x)}^{\\overline{\\psi_{2}}(x)} f(x, y) dy = \\int_{\\psi_{1}(x)}^{\\psi_{2}(x)} f(x, y) dy"}
 {"pdf": "old_scans_math/3_pg251.pdf", "page": 1, "id": "3_pg251_equation_01", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n249/mode/2up", "math": "\\lim_{\\delta \\to 0} \\int_{x_{0}'}^{x_{1}'} dx \\int_{\\overline{\\psi_{1}}(x)}^{\\overline{\\psi_{2}}(x)} f(x, y) dx = \\int_{x_{0}}^{x_{1}} dx \\int_{\\psi_{1}(x)}^{\\psi_{2}(x)} f(x, y) dx"}
 {"pdf": "old_scans_math/3_pg251.pdf", "page": 1, "id": "3_pg251_equation_02", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/in.ernet.dli.2015.212519/page/n249/mode/2up", "math": "\\lim_{\\delta \\to 0} \\iint_{R} f(x, y) dS = \\iint_{R} f(x, y) dS"}
@@ -293,9 +283,7 @@
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_01", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "y = \\frac{a}{2} (e^{\\frac{x}{a}} + e^{-\\frac{x}{a}})"}
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_02", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "y = sin x"}
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_03", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "y^2 = 4 ax"}
-{"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_04", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "y^2 = 4 ax"}
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_05", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "y = -2 a"}
-{"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_06", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "y^2 = 4 ax"}
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_07", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "x = a (\\phi - sin \\phi)"}
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_08", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "y = a (1 - cos \\phi)"}
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_09", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "x = a cos^3 \\phi"}
@@ -305,7 +293,6 @@
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_13", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "x = -\\frac{a}{4}"}
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_14", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "x^2 + xy + y^2 = 3"}
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_15", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "y = x"}
-{"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_16", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "x^{\\frac{1}{2}} + y^{\\frac{1}{2}} = a^{\\frac{1}{2}}"}
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_17", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "x + y = a"}
 {"pdf": "old_scans_math/2_pg238.pdf", "page": 1, "id": "2_pg238_equation_18", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/integralcalculus00philrich/page/n237/mode/2up", "math": "PQR \\cdot \\Delta x = X \\Delta x"}
 {"pdf": "old_scans_math/4_pg433.pdf", "page": 1, "id": "4_pg433_equation_00", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/416/mode/2up", "math": "\\begin{vmatrix} \na_1 \\pm mb_1 & b_1 & c_1 \\\\ \na_2 \\pm mb_2 & b_2 & c_2 \\\\ \na_3 \\pm mb_3 & b_3 & c_3 \n\\end{vmatrix} = \n\\begin{vmatrix} \na_1 & b_1 & c_1 \\\\ \na_2 & b_2 & c_2 \\\\ \na_3 & b_3 & c_3 \n\\end{vmatrix} \\pm \n\\begin{vmatrix} \nmb_1 & b_1 & c_1 \\\\ \nmb_2 & b_2 & c_2 \\\\ \nmb_3 & b_3 & c_3 \n\\end{vmatrix}\n"}
@@ -328,7 +315,6 @@
 {"pdf": "old_scans_math/4_pg451.pdf", "page": 1, "id": "4_pg451_equation_07", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/435/mode/2up", "math": "2 x^3 =8x^2"}
 {"pdf": "old_scans_math/4_pg451.pdf", "page": 1, "id": "4_pg451_equation_08", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/435/mode/2up", "math": "-x^2=-4x"}
 {"pdf": "old_scans_math/4_pg451.pdf", "page": 1, "id": "4_pg451_equation_09", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/435/mode/2up", "math": "-4x=-16"}
-{"pdf": "old_scans_math/4_pg451.pdf", "page": 1, "id": "4_pg451_equation_10", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/435/mode/2up", "math": "f(4) = - 14"}
 {"pdf": "old_scans_math/4_pg48.pdf", "page": 1, "id": "4_pg48_equation_00", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/32/mode/2up", "math": "a+[b-(a - b)]"}
 {"pdf": "old_scans_math/4_pg48.pdf", "page": 1, "id": "4_pg48_equation_01", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/32/mode/2up", "math": "a+b -[(b+d) - (a - b)]"}
 {"pdf": "old_scans_math/4_pg48.pdf", "page": 1, "id": "4_pg48_equation_02", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/32/mode/2up", "math": "m-(n-p) +[3m-\\overline{3n-6 m}]"}
@@ -408,10 +394,7 @@
 {"pdf": "old_scans_math/4_pg380.pdf", "page": 1, "id": "4_pg380_equation_17", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/364/mode/2up", "math": "f(x) = 5 x^{3}-2x-3"}
 {"pdf": "old_scans_math/4_pg380.pdf", "page": 1, "id": "4_pg380_equation_18", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/364/mode/2up", "math": "f(2)"}
 {"pdf": "old_scans_math/4_pg380.pdf", "page": 1, "id": "4_pg380_equation_19", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/364/mode/2up", "math": "f(a)"}
-{"pdf": "old_scans_math/4_pg380.pdf", "page": 1, "id": "4_pg380_equation_20", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/364/mode/2up", "math": "f(0)"}
 {"pdf": "old_scans_math/4_pg380.pdf", "page": 1, "id": "4_pg380_equation_21", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/364/mode/2up", "math": "f(x) = 4^{x}"}
-{"pdf": "old_scans_math/4_pg380.pdf", "page": 1, "id": "4_pg380_equation_22", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/364/mode/2up", "math": "f(0)"}
-{"pdf": "old_scans_math/4_pg380.pdf", "page": 1, "id": "4_pg380_equation_23", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/364/mode/2up", "math": "f(-1)"}
 {"pdf": "old_scans_math/4_pg380.pdf", "page": 1, "id": "4_pg380_equation_24", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/364/mode/2up", "math": "f(\\frac{1}{2})"}
 {"pdf": "old_scans_math/4_pg512.pdf", "page": 1, "id": "4_pg512_equation_00", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/496/mode/2up", "math": "x^3-3x-2=0"}
 {"pdf": "old_scans_math/4_pg512.pdf", "page": 1, "id": "4_pg512_equation_01", "type": "math", "max_diffs": 0, "checked": "verified", "url": "https://archive.org/details/advancedalgebra00schu/page/496/mode/2up", "math": "x^3-9x + 28 = 0"}