Publish the verified benchmark: corrected answers, extra books, synthetic problems

ANSWER_AUDIT.md

@@ -94,7 +94,7 @@ because no model can be scored correct on them.
 | `algebra_core.1.198` | `algebra_core` | `-1` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.1.200` | `algebra_core` | `-\sqrt{(t+2)}/(t-2)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.1.206` | `algebra_core` | `a/(a+1)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.1.273` | `algebra_core` | `$2\sqrt2$ for $x\in[2,4)$; $2\sqrt{x-2}$ for $x\in[4,\infty)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
+| `algebra_core.1.273` | `algebra_core` | `2\sqrt2 for x\in[2,4); 2\sqrt{x-2} for x\in[4,\infty).` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.1.320` | `algebra_core` | `1)\ \frac{x+1}{x};\quad 2)\ -\frac{x+1}{x};\quad 3)\ \frac{x` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.1.336` | `algebra_core` | `\frac{4a^2+3}{9\left(a^2+1\right)}` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.2.047` | `algebra_core` | `x=8` | three independent reads agree on the statement and the printed answer |
@@ -110,7 +110,7 @@ because no model can be scored correct on them.
 | `algebra_core.2.205` | `algebra_core` | `(2;1),\ (6;-3),\ \left(6+2\sqrt{3};-2-2\sqrt{3}\right),\ \le` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.2.240` | `algebra_core` | `(10;1),\ \left(-21/2;53/12\right)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.2.243` | `algebra_core` | `(1;4),(4;1),(-1;-4),(-4;-1)` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.2.255` | `algebra_core` | `Either $x^2+3=0$ or $x^2+5x-3=0$; the two roots of $x^2+5x-3` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
+| `algebra_core.2.255` | `algebra_core` | `Either x^2+3=0 or x^2+5x-3=0; the two roots of x^2+5x-3=0 ha` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.2.285` | `algebra_core` | `x_1=-1,\ x_2=1` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.2.287` | `algebra_core` | `x_1=-1,\ x_2=1` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.2.288` | `algebra_core` | `x = 1; x = 4` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
@@ -124,7 +124,7 @@ because no model can be scored correct on them.
 | `algebra_core.4.419` | `algebra_core` | `48` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.4.458` | `algebra_core` | `11/2` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.5.002` | `algebra_core` | `x_1=35^\circ+120^\circ\cdot k,\quad x_2=55^\circ+120^\circ\c` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.5.039` | `algebra_core` | `$x_1=\frac{\pi k}{5},\ x_2=\frac{\pi}{8}(4k+3)$.` | three independent reads agree on the statement and the printed answer |
+| `algebra_core.5.039` | `algebra_core` | `x_1=\frac{\pi k}{5},\ x_2=\frac{\pi}{8}(4k+3).` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.121` | `algebra_core` | `z_1=2\arctan3+2\pi k,\quad z_2=-2\arctan7+2\pi k` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.143` | `algebra_core` | `x=\pi k/8.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.5.147` | `algebra_core` | `x=\frac{\pi}{12}(6k+1)` | three independent reads agree on the statement and the printed answer |
@@ -132,11 +132,11 @@ because no model can be scored correct on them.
 | `algebra_core.5.174` | `algebra_core` | `t=\frac{\pi}{2}(4k+1)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.176` | `algebra_core` | `x_1=\frac{\pi}{6}+\pi k;\quad x_2=(-1)^k\frac{\pi}{8}+\frac{` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.190` | `algebra_core` | `t_1=\frac{\pi k}{4}\ (k\ne4l+2),\ t_2=\pm\frac12\arccos\frac` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.5.201` | `algebra_core` | `$x=45^\circ+180^\circ\cdot k$.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.5.202` | `algebra_core` | `$x_1=\frac{\pi k}{4},\quad x_2=\frac{\pi}{12}(2k+1)$.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.5.203` | `algebra_core` | `$t=\frac{\pi}{6}(6k\pm1)$.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.5.207` | `algebra_core` | `$z=\frac{\pi}{6}(3k\pm1)$.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.5.212` | `algebra_core` | `$t_1=\frac{\pi}{4}(4k+1),\quad t_2=(-1)^{k\frac{1}{2}}\arcsi` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
+| `algebra_core.5.201` | `algebra_core` | `x=45^\circ+180^\circ\cdot k.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
+| `algebra_core.5.202` | `algebra_core` | `x_1=\frac{\pi k}{4},\quad x_2=\frac{\pi}{12}(2k+1).` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
+| `algebra_core.5.203` | `algebra_core` | `t=\frac{\pi}{6}(6k\pm1).` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
+| `algebra_core.5.207` | `algebra_core` | `z=\frac{\pi}{6}(3k\pm1).` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
+| `algebra_core.5.212` | `algebra_core` | `t_1=\frac{\pi}{4}(4k+1),\quad t_2=(-1)^{k\frac{1}{2}}\arcsin` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.5.221` | `algebra_core` | `x_1=-\frac{\pi}{16}(4k+1),\quad x_2=-\frac{1}{4}\arctan\frac` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.227` | `algebra_core` | `t=\arctan\frac{4}{5}+2\pi k` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.259` | `algebra_core` | `x=-\frac{\pi}{8}(4k+1)` | three independent reads agree on the statement and the printed answer |
@@ -151,9 +151,9 @@ because no model can be scored correct on them.
 | `algebra_core.7.006` | `algebra_core` | `x=\frac{5}{3}` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.7.029` | `algebra_core` | `x_1=-\frac13,\quad x_2=0` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.7.037` | `algebra_core` | `x_1=1/\sqrt3,\quad x_2=3` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.7.081` | `algebra_core` | `x_1=3$, $x_2=3+\sqrt{2}` | three independent reads agree on the statement and the printed answer |
+| `algebra_core.7.081` | `algebra_core` | `x_1=3, x_2=3+\sqrt{2}` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.7.089` | `algebra_core` | `x=5` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.7.091` | `algebra_core` | `x_1=33/8$, $x_2=17/4$, $x_3=8$, $x_4=12` | three independent reads agree on the statement and the printed answer |
+| `algebra_core.7.091` | `algebra_core` | `x_1=33/8, x_2=17/4, x_3=8, x_4=12` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.7.144` | `algebra_core` | `x=-2` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.7.147` | `algebra_core` | `\left(2^{\sqrt[3]{\sqrt{4}}};2^{\sqrt[3]{\sqrt{2}}}\right)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.7.160` | `algebra_core` | `(3; 27)` | three independent reads agree on the statement and the printed answer |
@@ -173,8 +173,8 @@ because no model can be scored correct on them.
 | `algebra_core.8.049` | `algebra_core` | `0 < x < 1` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.8.053` | `algebra_core` | `(3; \infty).` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.8.138` | `algebra_core` | `(1,2\sqrt{3}]` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.8.145` | `algebra_core` | `$(2,\infty)$.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.8.146` | `algebra_core` | `$(1,2)\cup(64,\infty)$.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
+| `algebra_core.8.145` | `algebra_core` | `(2,\infty).` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
+| `algebra_core.8.146` | `algebra_core` | `(1,2)\cup(64,\infty).` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.8.151` | `algebra_core` | `(-1/3, \infty)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.8.170` | `algebra_core` | `(1, 3) ∪ (3^9, \infty)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.8.175` | `algebra_core` | `(0, 1/3) ∪ (243, \infty)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
@@ -189,48 +189,48 @@ because no model can be scored correct on them.
 | `algebra_core.10.097` | `algebra_core` | `The equation has no roots.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.10.166` | `algebra_core` | `(-4,0)\cup(0,4)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.10.310` | `algebra_core` | `\tan\alpha=2\tan\beta` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `falin_algebra.241` | `falin_algebra` | `$x_1 = 4; x_2 = -2$.` | claimed solution 'x=4' fails the equation |
-| `falin_algebra.392` | `falin_algebra` | `$x=3\pm\sqrt{5}$.` | claimed solution 'x=3 - \\sqrt{5}' fails the equation |
-| `falin_algebra.401` | `falin_algebra` | `$x=\log_{\frac{2}{3}}\log_3 2$.` | claimed solution 'x=\\log_{\\frac{2}{3}} \\log_3 2' fails the equation |
-| `falin_algebra.402` | `falin_algebra` | `$x=\log_{\frac{7}{5}}(\log_5 7)$.` | claimed solution 'x=\\log_{\\frac{7}{5}} (\\log_5 7)' fails the equation |
-| `falin_algebra.423` | `falin_algebra` | `$x_1 = 2$, $x_2 = \frac{1}{2}\log_2(12 - \sqrt{112})$.` | claimed solution 'x=\\frac{1}{2} \\log_2 (12 - \\sqrt{112})' fails the equation |
+| `falin_algebra.241` | `falin_algebra` | `x_1 = 4; x_2 = -2.` | claimed solution 'x=4' fails the equation |
+| `falin_algebra.392` | `falin_algebra` | `x=3\pm\sqrt{5}.` | claimed solution 'x=3 - \\sqrt{5}' fails the equation |
+| `falin_algebra.401` | `falin_algebra` | `x=\log_{\frac{2}{3}}\log_3 2.` | claimed solution 'x=\\log_{\\frac{2}{3}} \\log_3 2' fails the equation |
+| `falin_algebra.402` | `falin_algebra` | `x=\log_{\frac{7}{5}}(\log_5 7).` | claimed solution 'x=\\log_{\\frac{7}{5}} (\\log_5 7)' fails the equation |
+| `falin_algebra.423` | `falin_algebra` | `x_1 = 2, x_2 = \frac{1}{2}\log_2(12 - \sqrt{112}).` | claimed solution 'x=\\frac{1}{2} \\log_2 (12 - \\sqrt{112})' fails the equation |
 | `falin_algebra.452` | `falin_algebra` | `x = \log_{\frac{7}{10}} 2` | claimed solution 'x=\\log_{\\frac{7}{10}} 2' fails the equation |
 | `falin_algebra.453` | `falin_algebra` | `x = \log_{\frac{3}{2}} 2` | claimed solution 'x=\\log_{\\frac{3}{2}} 2' fails the equation |
 | `falin_algebra.454` | `falin_algebra` | `x_1 = \frac{1}{2\sqrt{3}(\log_3 5 - 1)}; \; x_2 = \frac{4\lo` | claimed solution 'x=\\frac{1}{2\\sqrt{3}(\\log_3 5 - 1)}' fails the equation |
 | `falin_algebra.456` | `falin_algebra` | `x_1 = 0; \; x_2 = \log_3 2` | claimed solution 'x=\\log_3 2' fails the equation |
 | `falin_algebra.457` | `falin_algebra` | `x_1 = \log_2 9; \; x_2 = \log_3 2` | claimed solution 'x=\\log_2 9' fails the equation |
 | `falin_algebra.501` | `falin_algebra` | `x = 3\sqrt{3}.` | claimed solution 'x=3\\sqrt{3}' fails the equation |
-| `falin_algebra.528` | `falin_algebra` | `$x=\frac{1+\sqrt{17}}{2}$.` | claimed solution 'x=\\frac{1+\\sqrt{17}}{2}' fails the equation |
+| `falin_algebra.528` | `falin_algebra` | `x=\frac{1+\sqrt{17}}{2}.` | claimed solution 'x=\\frac{1+\\sqrt{17}}{2}' fails the equation |
 | `falin_algebra.550` | `falin_algebra` | `x_1=(\sqrt{2}+\sqrt{3}+\sqrt{5})^2;\ x_2=(\sqrt{2}+\sqrt{3}+` | claimed solution 'x=(\\sqrt{2}+\\sqrt{3}+\\sqrt{5})^2' fails the equation |
 | `falin_algebra.566` | `falin_algebra` | `x = 1 \pm \sqrt{11 + 4\sqrt{3}}` | claimed solution 'x=1 + \\sqrt{11+4\\sqrt{3}}' fails the equation |
 | `falin_algebra.900` | `falin_algebra` | `(-\infty;-2]\cup[-1;0)\cup(0;1]\cup[2;+\infty)` | x=-1.505 satisfies the inequality but is missing from the book's answer |
 | `falin_algebra.914` | `falin_algebra` | `x\leq 0` | x=0.275 satisfies the inequality but is missing from the book's answer |
 | `falin_algebra.1069` | `falin_algebra` | `\left(\frac{5}{3};-\frac{7}{3}\right)` | no assignment of the printed tuple (\dfrac{5}{3};  -\dfrac{7}{3}\right) satisfies the system |
 | `falin_algebra.1123` | `falin_algebra` | `\{(8\log_5 2-6\log_2 5;\,8\log_2 5-12\log_5 2)\}` | no assignment of the printed tuple (8\log_5 2 - 6\log_2 5;  8\log_2 5 - 12\log_5 2) satisfies the system |
-| `falin_algebra.1287` | `falin_algebra` | `$x=2, y=1$.` | claimed solution 'x=2' fails the equation |
+| `falin_algebra.1287` | `falin_algebra` | `x=2, y=1.` | claimed solution 'x=2' fails the equation |
 | `falin_algebra.1306` | `falin_algebra` | `x = 0,\ y = 0` | claimed solution 'x=0' fails the equation |
-| `falin_algebra.1432` | `falin_algebra` | `$x = 0$; $y = -1$.` | claimed solution 'x=0' fails the equation |
-| `falin_algebra.1437` | `falin_algebra` | `$k = 6$; $l = 5$.` | claimed solution 'k=6' fails the equation |
+| `falin_algebra.1432` | `falin_algebra` | `x = 0; y = -1.` | claimed solution 'x=0' fails the equation |
+| `falin_algebra.1437` | `falin_algebra` | `k = 6; l = 5.` | claimed solution 'k=6' fails the equation |
 | `falin_algebra.1555` | `falin_algebra` | `x = \frac{-99 \pm \sqrt{9405}}{2}` | claimed solution 'x=\\frac{-99 + \\sqrt{9405}}{2}' fails the equation |
 | `falin_algebra.1556` | `falin_algebra` | `x = 1` | claimed solution 'x=1' fails the equation |
-| `falin_algebra.1927` | `falin_algebra` | `a_1 = 1 + \log_5 \frac{8+\sqrt{55}}{3}$, $a_2 = 1 + \log_5 \` | claimed solution 'a=1 + \\log_5 \\frac{8 + \\sqrt{55}}{3}; a=1 + \\log_5 \\frac{8 -' fails the equation |
+| `falin_algebra.1927` | `falin_algebra` | `a_1 = 1 + \log_5 \frac{8+\sqrt{55}}{3}, a_2 = 1 + \log_5 \fr` | claimed solution 'a=1 + \\log_5 \\frac{8 + \\sqrt{55}}{3}; a=1 + \\log_5 \\frac{8 -' fails the equation |
 | `falin_algebra.2000` | `falin_algebra` | `a_1=-1,\ a_2=-3,\ a_3=-\frac{5}{7}` | claimed solution 'a=-1; a=-3; a=-\\dfrac{5}{7}' fails the equation |
 | `falin_algebra.2010` | `falin_algebra` | `p=-\frac{1}{2}` | claimed solution 'p=-\\frac{1}{2}' fails the equation |
-| `falin_algebra.2068` | `falin_algebra` | `$a = -\frac{9}{82}$.` | claimed solution 'a=-\\frac{9}{82}' fails the equation |
-| `falin_algebra.2069` | `falin_algebra` | `$p = 114,\ p = -6$.` | claimed solution 'p=114; p=-6' fails the equation |
-| `shabunin.Пример 8` | `shabunin` | `$(2;\sqrt[3]{3}; \sqrt[3]{9}),\ \left(\frac{1}{\sqrt[3]{2}};` | no assignment of the printed tuple (2; \sqrt[3]{3};  \sqrt[3]{9}) satisfies the system |
-| `kozko_params.50` | `kozko_params` | `$a = \pm 1$, $b = 0$; $a = 0$, $b = 0$.` | claimed solution 'a=+ 1; a=0' fails the equation |
+| `falin_algebra.2068` | `falin_algebra` | `a = -\frac{9}{82}.` | claimed solution 'a=-\\frac{9}{82}' fails the equation |
+| `falin_algebra.2069` | `falin_algebra` | `p = 114,\ p = -6.` | claimed solution 'p=114; p=-6' fails the equation |
+| `shabunin.Пример 8` | `shabunin` | `(2;\sqrt[3]{3}; \sqrt[3]{9}),\ \left(\frac{1}{\sqrt[3]{2}}; ` | no assignment of the printed tuple (2; \sqrt[3]{3};  \sqrt[3]{9}) satisfies the system |
+| `kozko_params.50` | `kozko_params` | `a = \pm 1, b = 0; a = 0, b = 0.` | claimed solution 'a=+ 1; a=0' fails the equation |
 | `kozko_params.121` | `kozko_params` | `a = \pm 1/6, \, a = \pm \sqrt{2}/6` | claimed solution 'a=+ 1/6; a=+ \\sqrt{2}/6' fails the equation |
-| `kozko_params.214` | `kozko_params` | `m=0$, $x=3$; $m=\pm 1$, $x=\pm(3 \pm 2\sqrt{2})/2$; $m=\pm 2` | claimed solution 'm=0; m=+ 1; m=+ 2; m=+ 3' fails the equation |
-| `kozko_params.215` | `kozko_params` | `m=1$, $n=-1$ and $m=-1$, $n=1` | claimed solution 'm=1' fails the equation |
-| `kozko_params.222` | `kozko_params` | `m=4$, $n=9$; $m=5$, $n=8` | claimed solution 'm=4; m=5' fails the equation |
-| `kozko_params.224` | `kozko_params` | `m=0$, $n=0` | claimed solution 'm=0' fails the equation |
-| `kozko_params.225` | `kozko_params` | `x=2$, $y=1` | claimed solution 'x=2' fails the equation |
+| `kozko_params.214` | `kozko_params` | `m=0, x=3; m=\pm 1, x=\pm(3 \pm 2\sqrt{2})/2; m=\pm 2, x=(3 \` | claimed solution 'm=0; m=+ 1; m=+ 2; m=+ 3' fails the equation |
+| `kozko_params.215` | `kozko_params` | `m=1, n=-1 and m=-1, n=1` | claimed solution 'm=1' fails the equation |
+| `kozko_params.222` | `kozko_params` | `m=4, n=9; m=5, n=8` | claimed solution 'm=4; m=5' fails the equation |
+| `kozko_params.224` | `kozko_params` | `m=0, n=0` | claimed solution 'm=0' fails the equation |
+| `kozko_params.225` | `kozko_params` | `x=2, y=1` | claimed solution 'x=2' fails the equation |
 | `kozko_params.260` | `kozko_params` | `a = -2` | claimed solution 'a=-2' fails the equation |
 | `kozko_params.271` | `kozko_params` | `x = y = 0` | claimed solution 'x=y = 0' fails the equation |
 | `kozko_params.2003-2-3` | `kozko_params` | `[3/7; 1) \cup (3; +\infty)` | claimed endpoint 0.428571 gives F=-1.1818182, which violates the inequality |
 | `kozko_params.Задача 1 (Вариант 2006, апрель)` | `kozko_params` | `[-2; (7+\sqrt{21})/21)` | claimed point x=6.14955 gives F=-0.294805, which violates the inequality |
-| `kozko_params.ВАРИАНТ 2004 (июль), социологический факультет, 1` | `kozko_params` | `$[-5; -3]$.` | claimed endpoint -5 gives F=0.66666667, which violates the inequality |
+| `kozko_params.ВАРИАНТ 2004 (июль), социологический факультет, 1` | `kozko_params` | `[-5; -3].` | claimed endpoint -5 gives F=0.66666667, which violates the inequality |
 | `gelfand_trig.24.14` | `gelfand_trig` | `(x;y) = \left(\frac{\pi}{2} + \pi(k+n); -\frac{\pi}{2} + \pi` | no assignment of the printed tuple (x;  y) satisfies the system |
 
 ## Printed answers only suspected to be wrong
@@ -273,7 +273,7 @@ out of the scored split as well.
 | `algebra_core.1.136` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.137` | `algebra_core` | `\frac{a+b}{ab}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.142` | `algebra_core` | `-\frac{\sqrt{6}}{2}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.161` | `algebra_core` | `1) $\frac{x^2+5x-3}{x^4}$; 2) $\frac{(x+2)(x+3)}{x^4}$; 3) $` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
+| `algebra_core.1.161` | `algebra_core` | `1) \frac{x^2+5x-3}{x^4}; 2) \frac{(x+2)(x+3)}{x^4}; 3) \frac` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.184` | `algebra_core` | `\frac{1}{x-\sqrt{2x+1}}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.213` | `algebra_core` | `\frac{z^2}{z^2+z+1}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.217` | `algebra_core` | `\sqrt{a^2-1}` | numeric difference over 4 point(s) - reported as suspected, not as a refutation: the difference can come from  |
@@ -282,22 +282,22 @@ out of the scored split as well.
 | `algebra_core.1.237` | `algebra_core` | `2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.241` | `algebra_core` | `1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.286` | `algebra_core` | `m/2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.322` | `algebra_core` | `1) $m-n$; 2) $n-m$; 3) $m-n$` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.323` | `algebra_core` | `2x^2-a^2$ if $x<-\|a\|$; $-a^2$ if $x>\|a\|` | branch '2x^2-a^2' differs numerically - reported as suspected, not as a refutation: the difference can come fr |
-| `algebra_core.1.324` | `algebra_core` | `b-4a$ if $a\in[0,\sqrt{2})$; $2(a-1)^2$ if $a\in[\sqrt{2},+\` | branch '2(a-1)^2' differs numerically - reported as suspected, not as a refutation: the difference can come fr |
-| `algebra_core.1.325` | `algebra_core` | `5/(2\sqrt{x})$ if $x\in(0,4)$; $(2x-3)/(2\sqrt{x})$ if $x\in` | branch '5/(2\\sqrt{x})' differs numerically - reported as suspected, not as a refutation: the difference can c |
-| `algebra_core.1.328` | `algebra_core` | `\frac{2-x}{2}$ if $x\in(-\infty,-2)$; $-\frac{x^2+2x+8}{2x}$` | branch '\\frac{2-x}{2}' differs numerically - reported as suspected, not as a refutation: the difference can c |
-| `algebra_core.1.329` | `algebra_core` | `-x$ if $x\in(0,1)$; $x$ if $x\in(1,\infty)` | branch '-x' differs numerically - reported as suspected, not as a refutation: the difference can come from the |
-| `algebra_core.1.330` | `algebra_core` | `\frac{x-1}{x}$ if $x\in(-\infty,0)\cup[1,\infty)$; $\frac{1-` | branch '\\frac{x-1}{x}' differs numerically - reported as suspected, not as a refutation: the difference can c |
-| `algebra_core.1.331` | `algebra_core` | `-\frac{z+1}{z}$ if $z\in(-\infty,-1)\cup(0,1)$; $\frac{z+1}{` | branch '-\\frac{z+1}{z}' differs numerically - reported as suspected, not as a refutation: the difference can  |
+| `algebra_core.1.322` | `algebra_core` | `1) m-n; 2) n-m; 3) m-n` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
+| `algebra_core.1.323` | `algebra_core` | `2x^2-a^2 if x<-\|a\|; -a^2 if x>\|a\|` | branch '2x^2-a^2' differs numerically - reported as suspected, not as a refutation: the difference can come fr |
+| `algebra_core.1.324` | `algebra_core` | `b-4a if a\in[0,\sqrt{2}); 2(a-1)^2 if a\in[\sqrt{2},+\infty)` | branch '2(a-1)^2' differs numerically - reported as suspected, not as a refutation: the difference can come fr |
+| `algebra_core.1.325` | `algebra_core` | `5/(2\sqrt{x}) if x\in(0,4); (2x-3)/(2\sqrt{x}) if x\in[4,+\i` | branch '5/(2\\sqrt{x})' differs numerically - reported as suspected, not as a refutation: the difference can c |
+| `algebra_core.1.328` | `algebra_core` | `\frac{2-x}{2} if x\in(-\infty,-2); -\frac{x^2+2x+8}{2x} if x` | branch '\\frac{2-x}{2}' differs numerically - reported as suspected, not as a refutation: the difference can c |
+| `algebra_core.1.329` | `algebra_core` | `-x if x\in(0,1); x if x\in(1,\infty)` | branch '-x' differs numerically - reported as suspected, not as a refutation: the difference can come from the |
+| `algebra_core.1.330` | `algebra_core` | `\frac{x-1}{x} if x\in(-\infty,0)\cup[1,\infty); \frac{1-x}{x` | branch '\\frac{x-1}{x}' differs numerically - reported as suspected, not as a refutation: the difference can c |
+| `algebra_core.1.331` | `algebra_core` | `-\frac{z+1}{z} if z\in(-\infty,-1)\cup(0,1); \frac{z+1}{z} i` | branch '-\\frac{z+1}{z}' differs numerically - reported as suspected, not as a refutation: the difference can  |
 | `algebra_core.2.368` | `algebra_core` | `x=2` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.4.080` | `algebra_core` | `\tan\frac{m+n}{2}\alpha` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.4.107` | `algebra_core` | `\tan4\alpha` | numeric difference over 5 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.4.117` | `algebra_core` | `\tan^6\alpha` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.4.257` | `algebra_core` | `\tan^4\frac{\alpha}{2}` | numeric difference over 5 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.4.300` | `algebra_core` | `\frac{4\sin^2\left(\frac{\pi}{4}-4\alpha\right)}{\sin8\alpha` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.4.381` | `algebra_core` | `a) $(\cos 2\alpha)_1=-3/5$; b) $(\cos 2\alpha)_2=4/5$` | sides differ numerically - reported as suspected, not as a refutation: the difference can come from the readin |
-| `algebra_core.4.382` | `algebra_core` | `a) $4/5$; b) $3/5$` | sides differ numerically - reported as suspected, not as a refutation: the difference can come from the readin |
+| `algebra_core.4.381` | `algebra_core` | `a) (\cos 2\alpha)_1=-3/5; b) (\cos 2\alpha)_2=4/5` | sides differ numerically - reported as suspected, not as a refutation: the difference can come from the readin |
+| `algebra_core.4.382` | `algebra_core` | `a) 4/5; b) 3/5` | sides differ numerically - reported as suspected, not as a refutation: the difference can come from the readin |
 | `algebra_core.4.412` | `algebra_core` | `-\cos^32x` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.4.488` | `algebra_core` | `A=B=\|\cos\alpha\cos\beta\cos\gamma\|` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.5.154` | `algebra_core` | `x = \frac{2\pi}{3}(3k \pm 1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
@@ -305,39 +305,39 @@ out of the scored split as well.
 | `algebra_core.5.156` | `algebra_core` | `t_1=(-1)^k\frac{\pi}{6}+\pi k,\quad t_2=\frac{\pi}{2}(4k+1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.5.158` | `algebra_core` | `x=\frac{\pi}{6}(6k\pm1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.5.186` | `algebra_core` | `x_1=2\pi k,\ x_2=\frac{\pi}{2}(2k+1),\ x_3=\frac{\pi}{4}(4k-` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.197` | `algebra_core` | `$x_1=\frac{\pi k}{3}$; $x_2=\frac{\pi}{12}(2k+1)$.` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
+| `algebra_core.5.197` | `algebra_core` | `x_1=\frac{\pi k}{3}; x_2=\frac{\pi}{12}(2k+1).` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.5.263` | `algebra_core` | `t=\frac{\pi}{3}(3k\pm1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.5.301` | `algebra_core` | `t_1 = 360^\circ \cdot k; \quad t_2 = 90^\circ (4k+1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.5.302` | `algebra_core` | `t_1=90^\circ\cdot k;\quad t_2=\pm15^\circ+90^\circ\cdot k` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
-| `algebra_core.5.311` | `algebra_core` | `$x=2\pi k$.` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
+| `algebra_core.5.311` | `algebra_core` | `x=2\pi k.` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.5.337` | `algebra_core` | `t=\pi k` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.5.467` | `algebra_core` | `x=\frac{\pi}{2}(4k+1)` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.5.490` | `algebra_core` | `x_1=\arccos\left(\sqrt5-2\right)+2\pi k,\quad x_2=\pi(2k+1).` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.7.045` | `algebra_core` | `890` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.7.201` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.8.055` | `algebra_core` | `[0, 4).` | the book's answer excludes the upper endpoint 4, but it satisfies the inequality - reported as suspected, not  |
-| `algebra_core.10.145` | `algebra_core` | `$x$ is an integer.` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
+| `algebra_core.10.145` | `algebra_core` | `x is an integer.` | the two sides of the identity differ at every tested point - reported as suspected, not as a refutation: the d |
 | `algebra_core.11.078` | `algebra_core` | `a>4` | the book's answer excludes the lower endpoint 4, but it satisfies the inequality - reported as suspected, not  |
 | `falin_algebra.269` | `falin_algebra` | `x = \dfrac{-3 + \sqrt{17}}{2}.` | sides differ numerically |
 | `falin_algebra.387` | `falin_algebra` | `x = 2` | sides differ numerically |
-| `falin_algebra.540` | `falin_algebra` | `$\{\tfrac{2}{5};\, 10\}$.` | the two sides of the identity differ at every tested point |
-| `falin_algebra.788` | `falin_algebra` | `$-1 < x < -\frac{5}{6}$.` | the book's answer excludes the upper endpoint -0.833333, but it satisfies the inequality |
+| `falin_algebra.540` | `falin_algebra` | `\{\tfrac{2}{5};\, 10\}.` | the two sides of the identity differ at every tested point |
+| `falin_algebra.788` | `falin_algebra` | `-1 < x < -\frac{5}{6}.` | the book's answer excludes the upper endpoint -0.833333, but it satisfies the inequality |
 | `falin_algebra.907` | `falin_algebra` | `x>\sqrt{3}` | claimed point x=2.73205 gives F=-4.81664, which violates the inequality |
 | `falin_algebra.923` | `falin_algebra` | `(-\infty; -\sqrt{7}) \cup (\sqrt{7}; 9]` | the book's answer excludes the upper endpoint -2.64575, but it satisfies the inequality |
 | `falin_algebra.926` | `falin_algebra` | `[-18;-3] \cup (0;2).` | the book's answer includes the upper endpoint -3, where equality holds |
 | `falin_algebra.957` | `falin_algebra` | `(2 - \log_2^2 3; 2]` | the book's answer excludes the lower endpoint -0.512106, but it satisfies the inequality |
-| `falin_algebra.980` | `falin_algebra` | `$3$.` | integer 2 satisfies the inequality but is not listed |
+| `falin_algebra.980` | `falin_algebra` | `3.` | integer 2 satisfies the inequality but is not listed |
 | `falin_algebra.1023` | `falin_algebra` | `4017` | integer 4014 satisfies the inequality but is not listed |
-| `falin_algebra.1185` | `falin_algebra` | `$S = \frac{\pi}{8}$. The figure is the union of two sectors ` | sides differ numerically |
+| `falin_algebra.1185` | `falin_algebra` | `S = \frac{\pi}{8}. The figure is the union of two sectors in` | sides differ numerically |
 | `falin_algebra.1529` | `falin_algebra` | `k = 3` | integer 4 satisfies the inequality but is not listed |
 | `shabunin.226` | `shabunin` | `(3;9),\ (9;3)` | the book's answer excludes the lower endpoint 3, but it satisfies the inequality |
-| `shabunin.Continuation` | `shabunin` | `$x = \frac{\pi n}{8},\ n \in \mathbf{Z}$.` | sides differ numerically |
+| `shabunin.Continuation` | `shabunin` | `x = \frac{\pi n}{8},\ n \in \mathbf{Z}.` | sides differ numerically |
 | `kozko_params.216` | `kozko_params` | `72` | value differs ((2.6163733970336187+0j) vs (72+0j)) |
 | `kozko_params.217` | `kozko_params` | `-13/3 < a \leqslant -19/5` | sides differ numerically |
 | `kozko_params.198_2` | `kozko_params` | `207` | value differs ((1.063057394823077+0j) vs (207+0j)) |
-| `kozko_params.ВАРИАНТ 2003` | `kozko_params` | `1. $x = (5 - \sqrt{5})/3$; 2. $(\pm \arccos((\sqrt{5} - 1)/4` | sides differ numerically |
-| `kozko_params.ВАРИАНТ 2004 (май), факультет почвоведения, 2 — Задача 3` | `kozko_params` | `$x \in (-\infty; \log_2 3)$ (listed answer: $x \in (\log_6 2` | the book's answer excludes the upper endpoint 1.58496, but it satisfies the inequality |
-| `prasolov_planimetry.31.62` | `prasolov_planimetry` | `If $ad \neq bc$ the curve is an ellipse; if $ad = bc$ it is ` | the two sides of the identity differ at every tested point |
+| `kozko_params.ВАРИАНТ 2003` | `kozko_params` | `1. x = (5 - \sqrt{5})/3; 2. (\pm \arccos((\sqrt{5} - 1)/4) +` | sides differ numerically |
+| `kozko_params.ВАРИАНТ 2004 (май), факультет почвоведения, 2 — Задача 3` | `kozko_params` | `x \in (-\infty; \log_2 3) (listed answer: x \in (\log_6 2; +` | the book's answer excludes the upper endpoint 1.58496, but it satisfies the inequality |
+| `prasolov_planimetry.31.62` | `prasolov_planimetry` | `If ad \neq bc the curve is an ellipse; if ad = bc it is a se` | the two sides of the identity differ at every tested point |
 
 ## Reproducing the audit
 

BENCHMARKING.md

@@ -28,6 +28,13 @@ before.
 
 ---
 
+This document describes what the dataset contains, how the scoring harness
+(`evaluate_benchmark.py`) decides that an answer is correct, and how to run and
+report results. It is written for an engineer who has not seen this project
+before.
+
+---
+
 ## 1. What the dataset is
 
 `ORCHORDS/dgn-math-problems` is an **English-language mathematics benchmark**

data/books/test-00000-of-00001.parquet

@@ -1,3 +1,3 @@
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-size 213563
+oid sha256:cee65220e558344b940ae64e83c2651f1557292f3c95d312d533bc53fd029a26
+size 213135

data/books/train-00000-of-00001.parquet

@@ -1,3 +1,3 @@
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+size 1016423

data/core/test-00000-of-00001.parquet

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-size 119774
+oid sha256:1974bcc5c955a8b9c9755de901d78aac233a41947f1257ff54da4a882aab455a
+size 119592

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+size 577764

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+size 321074

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-size 1647219
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+size 1643967

data/qa/test-00000-of-00001.parquet

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+oid sha256:94f142573cd93f0f9ea68ede7d7bc63bb28ff362b84b3e0c172272c859b5dbbb
+size 1286692

data/verified/train-00000-of-00001.parquet

@@ -1,3 +1,3 @@
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-size 220106
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+size 219607

evaluate_benchmark.py

@@ -1,5 +1,5 @@
 #!/usr/bin/env python3
-"""evaluate_benchmark.py -- scoring harness for the Sklyanov math benchmark.
+"""evaluate_benchmark.py -- scoring harness for the DGN math benchmark.
 
 Usage
 -----
@@ -1368,7 +1368,7 @@ def parse_tiers(spec: str):
 def main(argv=None):
     ap = argparse.ArgumentParser(
         prog="evaluate_benchmark.py",
-        description="Score a predictions file against the Sklyanov math benchmark.",
+        description="Score a predictions file against the DGN math benchmark.",
     )
     ap.add_argument("--dataset", required=True, help="dataset file (.jsonl or .parquet)")
     ap.add_argument("--predictions", required=True, help="predictions file (.jsonl)")