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

ANSWER_AUDIT.md

@@ -6,25 +6,25 @@ and what the printed books got wrong.
 
 ## Totals
 
-- problems in the dataset: **9,229**
-- rows in the scored `verified` config: **1,827**
-- printed answers refuted by the engine (concrete counterexample): **144**
-- printed answers refuted and replaced by a re-verified recomputation: **15**
-- printed answers only *suspected* to be wrong (no concrete counterexample): **95**
-- rows set aside as `disputed` (a third read of the page disagreed): **72**
-- rows with no printed answer at all (`no-gold`): **3,164**
+- problems in the dataset: **12,557**
+- rows in the scored `verified` config: **1,989**
+- printed answers refuted by the engine (concrete counterexample): **66**
+- printed answers refuted and replaced by a re-verified recomputation: **17**
+- printed answers only *suspected* to be wrong (no concrete counterexample): **102**
+- rows set aside as `disputed` (a third read of the page disagreed): **122**
+- rows with no printed answer at all (`no-gold`): **5,849**
 
 ## By source
 
 | source | rows | verified | corrected | refuted | suspected | disputed | unverifiable | synthetic-verified | synthetic-unverified | no-gold |
 |---|---|---|---|---|---|---|---|---|---|---|
-| `algebra_core` | 3,620 | 1,153 | 15 | 101 | 75 | 64 | 1,766 | 0 | 0 | 446 |
-| `falin_algebra` | 2,071 | 459 | 0 | 29 | 12 | 7 | 1,316 | 0 | 0 | 248 |
-| `gelfand_trig` | 212 | 0 | 0 | 1 | 0 | 0 | 28 | 0 | 0 | 183 |
-| `kozko_params` | 516 | 8 | 0 | 12 | 5 | 0 | 175 | 0 | 0 | 316 |
-| `ponarin_plane` | 570 | 0 | 0 | 0 | 0 | 0 | 11 | 0 | 0 | 559 |
-| `prasolov_planimetry` | 1,337 | 1 | 0 | 0 | 1 | 0 | 147 | 0 | 0 | 1,188 |
-| `shabunin` | 383 | 0 | 0 | 1 | 2 | 1 | 155 | 0 | 0 | 224 |
+| `algebra_core` | 3,620 | 1,180 | 17 | 31 | 77 | 114 | 1,755 | 0 | 0 | 446 |
+| `falin_algebra` | 2,346 | 513 | 0 | 10 | 14 | 7 | 1,433 | 0 | 0 | 369 |
+| `gelfand_trig` | 255 | 0 | 0 | 2 | 0 | 0 | 3 | 0 | 0 | 250 |
+| `kozko_params` | 1,131 | 38 | 0 | 19 | 7 | 0 | 415 | 0 | 0 | 652 |
+| `ponarin_plane` | 879 | 0 | 0 | 0 | 0 | 0 | 10 | 0 | 0 | 869 |
+| `prasolov_planimetry` | 2,056 | 2 | 0 | 0 | 3 | 0 | 191 | 0 | 0 | 1,860 |
+| `shabunin` | 1,750 | 48 | 0 | 4 | 1 | 1 | 293 | 0 | 0 | 1,403 |
 | `synthetic` | 520 | 0 | 0 | 0 | 0 | 0 | 0 | 191 | 329 | 0 |
 
 ## What each status means
@@ -72,6 +72,8 @@ degrees-minutes-seconds (`3^\circ45'`) are parsed as 3.75 degrees.
 | `algebra_core.5.123` | see the book | `x = \operatorname{atan}{\left(\frac{1}{5} \right)}; x = \frac{\pi}{4}` |
 | `algebra_core.5.162` | see the book | `x = 0; x = \frac{2 \pi}{3}` |
 | `algebra_core.5.217` | see the book | `x = - \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}; x = - \frac{\pi}{8}; x = - \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}; x = \frac{3 \pi}{8}` |
+| `algebra_core.5.232` | see the book | `x = - \operatorname{atan}{\left(\frac{1}{5} + \frac{\sqrt{26}}{5} \right)}; x = - \frac{\pi}{8}; x = - \operatorname{atan}{\left(\frac{1}{5} - \frac{\sqrt{26}}{5} \right)}; x = \frac{3 \pi}{8}` |
+| `algebra_core.5.413` | see the book | `x = 0; x = \pi` |
 | `algebra_core.5.421` | see the book | `x = - \frac{\pi}{4}` |
 | `algebra_core.7.038` | see the book | `x = \frac{1}{100}; x = 100` |
 | `algebra_core.7.039` | see the book | `x = \frac{1}{10}; x = 1000` |
@@ -89,150 +91,72 @@ because no model can be scored correct on them.
 
 | id | source | printed answer | what the engine found |
 |---|---|---|---|
-| `algebra_core.1.170` | `algebra_core` | `\frac{(a-2)\sqrt{a+1}}{(a+2)\sqrt{a-1}}` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.1.183` | `algebra_core` | `\sqrt{2}` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.1.191` | `algebra_core` | `\sqrt[3]{\frac{1-x}{3x}}` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `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.1.320` | `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 |
-| `algebra_core.2.050` | `algebra_core` | `x=64` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.2.059` | `algebra_core` | `x=2` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.2.064` | `algebra_core` | `x_1=8,\quad x_2=27` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.2.068` | `algebra_core` | `(-4;24);\ (-6;-2)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.2.070` | `algebra_core` | `(x_1;y_1)=(0,6;0,3),\quad (x_2;y_2)=(0,4;0,5)` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.2.085` | `algebra_core` | `(1/2; 4)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.2.164` | `algebra_core` | `x = -2` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.2.176` | `algebra_core` | `x=2` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.2.177` | `algebra_core` | `x=0` | three independent reads agree on the statement and the printed answer |
-| `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.2.205` | `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 - error of the book: 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=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 |
-| `algebra_core.2.295` | `algebra_core` | `x=65` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.2.321` | `algebra_core` | `(2;\,-1),\ (-1;\,2),\ (-2;\,1),\ (1;\,-2)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.2.332` | `algebra_core` | `(4;4), (4,5;3,5)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.2.335` | `algebra_core` | `(5;3), (5;4)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.2.342` | `algebra_core` | `x_1=1.5,\,x_2=0.5+\sqrt{3},\,x_3=0.5-\sqrt{3}` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.3.234` | `algebra_core` | `\sqrt[k-1]{k}` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.4.211` | `algebra_core` | `3\tan^2\alpha\cos^{-2}\alpha+1` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `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.5.121` | `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 |
-| `algebra_core.5.167` | `algebra_core` | `x=\frac{\pi k}{2}+\frac12\arctan\left(-\frac34\right)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `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}}\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 |
 | `algebra_core.5.269` | `algebra_core` | `x=-\frac{\pi}{4}(4k+1)` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.5.274` | `algebra_core` | `x=25^{\circ}+90^{\circ}\cdot k.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.5.280` | `algebra_core` | `x = - \operatorname{atan}{\left(3 + \sqrt{10} \right)}; x = ` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
 | `algebra_core.5.334` | `algebra_core` | `t=-\frac{\pi}{4}(4k+1)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.348` | `algebra_core` | `t=(-1)^k\frac{k\pi}{6}+\pi k` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.445` | `algebra_core` | `t=-\frac{\pi}{4}(4k+1)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.5.472` | `algebra_core` | `t_1=\frac{\pi}{4}(8k+1),\quad t_2=-\arctan3+\pi(2k+1)` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.5.493` | `algebra_core` | `The original equation has no solutions.` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `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.7.089` | `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.7.144` | `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.7.151` | `algebra_core` | `(9; 16)` | no assignment of the printed tuple (9;  16) satisfies the system |
 | `algebra_core.7.160` | `algebra_core` | `(3; 27)` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.7.174` | `algebra_core` | `x=4` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.7.213` | `algebra_core` | `x = \frac{3^{\frac{2}{3}}}{3}` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.7.228` | `algebra_core` | `x = 1` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.7.232` | `algebra_core` | `x = \sqrt[6]{7}` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.7.252` | `algebra_core` | `x=4` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.7.264` | `algebra_core` | `x=-2\sqrt[3]{2}` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.7.301` | `algebra_core` | `(3; 9)` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.7.329` | `algebra_core` | `x_1=1,\ x_2=4` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.7.332` | `algebra_core` | `x=64` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.7.333` | `algebra_core` | `x=3` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.7.334` | `algebra_core` | `x=7` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.7.337` | `algebra_core` | `x=4` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.8.026` | `algebra_core` | `(-1,\infty)` | three independent reads agree on the statement and the printed answer |
-| `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.8.151` | `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 |
+| `algebra_core.8.073` | `algebra_core` | `(1,\infty)` | claimed point x=11 gives F=-0.522879, which violates the inequality |
+| `algebra_core.8.087` | `algebra_core` | `x<1-\log_2 3` | claimed point x=-1000.58 gives F=-5, which violates the inequality |
 | `algebra_core.8.183` | `algebra_core` | `(-\sqrt2,-1)\cup(1,\sqrt2)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.8.187` | `algebra_core` | `(1,1+2^{-5/4})\cup(3;\infty)` | three independent reads agree on the statement and the printed answer |
 | `algebra_core.8.238` | `algebra_core` | `(-\infty,-2]\cup[-1,(\sqrt{13}-1)/6)` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.9.031` | `algebra_core` | `x=10` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.9.032` | `algebra_core` | `x=7` | three independent reads agree on the statement and the printed answer |
+| `algebra_core.8.283` | `algebra_core` | `x=3` | claimed integer 3 gives F=-1.2910247, which violates the inequality |
 | `algebra_core.10.012` | `algebra_core` | `(-3,2)\cup(2,3)` | three independent reads agree on the statement and the printed answer |
-| `algebra_core.10.070` | `algebra_core` | `x=-1` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `algebra_core.10.072` | `algebra_core` | `x=2,\ y=9` | third read of the answer page confirms a different printed answer, and the engine still refutes it |
-| `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.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.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 |
+| `algebra_core.11.246` | `algebra_core` | `-\frac{1}{3}` | third read of the page corrected the row |
+| `falin_algebra.p88.677` | `falin_algebra` | `(-\infty; -1] \cup \{1\} \cup [2; \infty)` | claimed point x=-2 gives F=0.333333, which violates the inequality |
 | `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.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.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 \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 |
-| `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, 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 |
+| `falin_algebra.p114.914` | `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 (\frac{5}{3}; -\frac{7}{3}\right) satisfies the system |
+| `falin_algebra.p137.1083` | `falin_algebra` | `\left(\frac{1}{5}; \frac{1}{81}\right)` | no assignment of the printed tuple (\frac{1}{5};  \frac{1}{81}\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.p370.598` | `falin_algebra` | `(-\infty;\, -\tfrac{5+\sqrt{21}}{2}) \cup (\tfrac{-5+\sqrt{2` | claimed point x=-5.79129 gives F=961.17, which violates the inequality |
+| `falin_algebra.p382.914` | `falin_algebra` | `x\leq 0` | x=0.275 satisfies the inequality but is missing from the book's answer |
+| `falin_algebra.p383.957` | `falin_algebra` | `x \leq 0` | claimed point t=-10 gives F=2.99024, which violates the inequality |
+| `falin_algebra.p390.1020` | `falin_algebra` | `(-1; 2]` | claimed point x=-0.85 gives F=-2.2992, which violates the inequality |
+| `shabunin.p183.Example 3` | `shabunin` | `(1;2), (-1;0)` | no assignment of the printed tuple (1; 2) satisfies the system |
+| `shabunin.p190.Example 2` | `shabunin` | `(1;2;3),\ (-1;-2;-3)` | no assignment of the printed tuple (1; 2; 3) satisfies the system |
+| `shabunin.p194.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 |
+| `shabunin.p222.Пример 2` | `shabunin` | `(1; 3); \left(\frac{9}{4}; 4\right)` | no assignment of the printed tuple (1;  3) satisfies the system |
+| `kozko_params.p163.3` | `kozko_params` | `0 < x \leqslant 1/2;\ x \geqslant \log_2 3` | claimed point x=2.58496 gives F=-24.8292, which violates the inequality |
 | `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.p172.6` | `kozko_params` | `(1; 18 - 12\sqrt{2}]` | a=500.545 satisfies the inequality but is missing from the book's answer |
+| `kozko_params.p173.6` | `kozko_params` | `(1; 8 - 4\sqrt{3}]` | a=500.565 satisfies the inequality but is missing from the book's answer |
+| `kozko_params.p176.Задача 3` | `kozko_params` | `[(-1-2\sqrt{29})/5;\,2]` | claimed point x=-2.81962 gives F=0.68419, which violates the inequality |
+| `kozko_params.p188.4` | `kozko_params` | `(x; y) = (0; \sqrt{3}); (0; -\sqrt{3}); \left(\sqrt{\frac{3}` | no assignment of the printed tuple (x;  y) satisfies the system |
+| `kozko_params.p189.4` | `kozko_params` | `(x;y) = (0;\sqrt{2});\ (0;-\sqrt{2});\ \left(\sqrt{\frac{2}{` | no assignment of the printed tuple (x; y) satisfies the system |
+| `kozko_params.p195.3` | `kozko_params` | `\left\{\left(-\frac{1}{2}; \log_9 \frac{9}{2}\right); \left(` | no assignment of the printed tuple (-\frac{1}{2};  \log_9 \frac{9}{2}\right) satisfies the system |
+| `kozko_params.p237.7` | `kozko_params` | `\left(\dfrac{\pi}{4}+2\pi m;\ \dfrac{3\pi}{4}+2\pi k\right);` | no assignment of the printed tuple (\dfrac{\pi}{4}+2\pi m; \ \dfrac{3\pi}{4}+2\pi k\right) satisfies the syste |
 | `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 |
+| `kozko_params.p271.2` | `kozko_params` | `(-\infty; 1/4]` | claimed point x=-0.75 gives F=0.275412, which violates the inequality |
+| `kozko_params.p274.1` | `kozko_params` | `2` | claimed integer 2 gives F=9, which violates the inequality |
+| `kozko_params.ВАРИАНТ 2005 (июль), географический факультет, 1` | `kozko_params` | `1. (x;y) = (-\pi/2 \pm \pi/3 + 2\pi k;\ 2\pi m),\ k,m \in \m` | no assignment of the printed tuple (x; y) satisfies the system |
+| `kozko_params.p280.4` | `kozko_params` | `(-\infty;\, 1-\sqrt{14}] \cup [-\sqrt{17}/3;\, -2) \cup (1;\` | x=-2.19 satisfies the inequality but is missing from the book's answer |
+| `kozko_params.p281.1` | `kozko_params` | `x=-2` | claimed solution 'x=-2' fails the equation |
+| `kozko_params.p289.2` | `kozko_params` | `(-\infty;2]` | claimed endpoint 2 gives F=-0.17157288, which violates the inequality |
+| `kozko_params.p290.2` | `kozko_params` | `(-\infty; 0]` | claimed point x=-10 gives F=0.00537474, 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.p293.Задача 2` | `kozko_params` | `[-3; (5+\sqrt{21})/2)` | claimed endpoint -3 gives F=-5, which violates the inequality |
+| `gelfand_trig.p146.24.14` | `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 |
+| `gelfand_trig.p147.24.14` | `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
 
@@ -249,13 +173,13 @@ out of the scored split as well.
 | `algebra_core.1.028` | `algebra_core` | `\frac{2}{\sqrt[3]{r^2}}\left(r^2-\sqrt{r^4-16}\right)` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.039` | `algebra_core` | `y^2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.041` | `algebra_core` | `-4` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.043` | `algebra_core` | `x+1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.050` | `algebra_core` | `2\sqrt[6]{a^5/a}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.053` | `algebra_core` | `\sqrt{6x}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.054` | `algebra_core` | `\sqrt[3]{20x}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.059` | `algebra_core` | `-1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.063` | `algebra_core` | `a^{1/3}+b^{1/3}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.067` | `algebra_core` | `1` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
+| `algebra_core.1.068` | `algebra_core` | `\frac{1}{a\left(\sqrt[m]{a}-\sqrt[n]{a}\right)}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.069` | `algebra_core` | `6` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.080` | `algebra_core` | `0` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.084` | `algebra_core` | `4p-\sqrt{4p^2-1}` | numeric difference over 3 point(s) - reported as suspected, not as a refutation: the difference can come from  |
@@ -263,7 +187,7 @@ out of the scored split as well.
 | `algebra_core.1.086` | `algebra_core` | `\frac{1}{\sqrt{a}+\sqrt{2}}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.089` | `algebra_core` | `(1-a)/\sqrt{a}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.098` | `algebra_core` | `\sqrt[3]{x+y}-\sqrt[3]{x-y}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
-| `algebra_core.1.100` | `algebra_core` | `x+y` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
+| `algebra_core.1.100` | `algebra_core` | `x+y` | numeric difference over 3 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.101` | `algebra_core` | `2` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.120` | `algebra_core` | `3/5` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.121` | `algebra_core` | `31/3` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
@@ -280,6 +204,7 @@ out of the scored split as well.
 | `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  |
 | `algebra_core.1.222` | `algebra_core` | `-\frac{\sqrt{x-2}}{x+2}` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `algebra_core.1.224` | `algebra_core` | `\sqrt{a}\left(\sqrt{2a+1}-\sqrt{a}\right)` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
+| `algebra_core.1.226` | `algebra_core` | `2.4` | numeric difference over 2 point(s) - reported as suspected, not as a refutation: the difference can come from  |
 | `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  |
@@ -319,35 +244,56 @@ out of the scored split as well.
 | `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.11.078` | `algebra_core` | `a>4` | the book's answer excludes the lower endpoint 4, but it satisfies the inequality - reported as suspected, not  |
+| `algebra_core.11.252` | `algebra_core` | `0.5\ln 2-1.5` | book says \(0{,}5\ln 2-1{,}5\), computed -128.0 - reported as suspected, not as a refutation: the difference c |
 | `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.p81.622` | `falin_algebra` | `(-\infty; -2] \cup (-1; 0) \cup (0; +\infty).` | the book's answer excludes the upper endpoint 0, but it satisfies the inequality |
 | `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.907` | `falin_algebra` | `x>\sqrt{3}` | the book's answer excludes the lower endpoint 1.73205, but it satisfies 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.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 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 |
-| `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 |
+| `falin_algebra.p195.1542` | `falin_algebra` | `\frac{3 - \sqrt{7}}{2}` | numeric difference over 2 point(s) |
+| `falin_algebra.p384.965` | `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.p446.1397` | `falin_algebra` | `**Answer:** \emptyset.` | the two sides of the identity differ at every tested point |
+| `shabunin.p288.23` | `shabunin` | `x > -\frac{1}{2}` | the book's answer excludes the lower endpoint -0.5, but it satisfies the inequality |
+| `kozko_params.p18.30` | `kozko_params` | `a \in (0; 1/54)` | the book's answer excludes the upper endpoint 0.0185185, but it satisfies the inequality |
+| `kozko_params.p188.1` | `kozko_params` | `[-7; -2) \cup (-2; -1].` | the book's answer excludes the upper endpoint -2, but it satisfies the inequality |
 | `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 a se` | the two sides of the identity differ at every tested point |
+| `kozko_params.p263.3` | `kozko_params` | `x \in [1; 2) \cup (2; \sqrt{5})` | the book's answer excludes the upper endpoint 2.23607, but it satisfies the inequality |
+| `kozko_params.p266.Задача 1` | `kozko_params` | `(0;\, (5 - \sqrt{17})/2)` | the book's answer excludes the upper endpoint 0.438447, but it satisfies the inequality |
+| `kozko_params.p266.Задача 5` | `kozko_params` | `a \in [\pi/2;\, 3\pi/2 - 3] \cup (5\pi/2 - 6;\, 7\pi/2 - 9]` | the book's answer excludes the lower endpoint 20.5708, but it satisfies the inequality |
+| `prasolov_planimetry.6.37` | `prasolov_planimetry` | `AB \cdot CD + AD \cdot BC = AC \cdot BD` | the two sides of the identity differ at every tested point |
+| `prasolov_planimetry.13.31` | `prasolov_planimetry` | `\boldsymbol{e}_1 \sin\alpha + \boldsymbol{e}_2 \sin\beta + \` | the two sides of the identity differ at every tested point |
+| `prasolov_planimetry.31.45` | `prasolov_planimetry` | `a + c = 0` | the two sides of the identity differ at every tested point |
 
 ## Reproducing the audit
 
 ```bash
-python verify_all3.py 12 dataset/skrypnyk_math_dataset_v2.jsonl v4   # the core book
-python verify_all3.py  8 books/<book>/<book>_vision_rows.jsonl v4_<book>
+python verify_all3.py 12 dataset/skrypnyk_math_dataset_v2.jsonl v15   # the core book
+python reverify_books2.py bookv15                                   # the additional books
 python build_benchmark.py                                            # assemble + split
+python audit_pairing.py hf_dataset/benchmark_full.jsonl              # question/answer integrity
 ```
 
 The verification engine is `verify3.py`; `verify.py` holds the individual
 checkers and `verify2.py` the newer ones (inequalities, limits, integrals,
 factors).
+
+## Errors of the books that the engine cannot see
+
+These are errors of the source books, found by reading the printed
+page.  Two kinds occur: a *wrong printed answer*, which the symbolic
+engine does not reach because the exercise has several parts and a list
+of answers cannot be checked as a whole, and a *misprinted statement*,
+where the book prints a statement that does not match its own printed
+answer.
+
+| id | kind | part | what the book prints | what is correct | why |
+|---|---|---|---|---|---|
+| `gelfand_trig.p158.26.6` | wrong printed answer | (d) | `\left(\dfrac{\sqrt{3}}{3}; 1\right]` | `\left(\dfrac{\sqrt{3}}{2}; 1\right]` | the exercise asks to solve arccos x < pi/6, whose solution is x in (cos(pi/6), 1] = (sqrt(3)/2, 1]; the book prints (sqrt(3)/3, 1] |
+| `algebra_core.2.205` | misprinted statement | second equation of the system | `\begin{cases}x+y+\frac{x^2}{y^2}=7,\\ \frac{(x-y)x^2}{y^2}=12.\end{cases}` | `\begin{cases}x+y+\frac{x^2}{y^2}=7,\\ \frac{(x+y)x^2}{y^2}=12.\end{cases}` | the printed answer does not satisfy the printed second equation: (2; 1) gives (x-y)x^2/y^2 = 4, not 12, and (6; -3) gives 36, not 12. All four printed answers satisfy x+y+x^2/y^2 = 7 and (x+y)x^2/y^2 = 12 exactly, so the book misprinted x+y as x-y. The printed system as written has exactly one real solution, (1.3863205; -0.5580341), whose coordinates are roots of a quintic and are therefore certainly not the intended answer. |

BENCHMARKING.md

@@ -35,6 +35,13 @@ 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**
@@ -64,11 +71,11 @@ therefore filters on `source` if you want a single subset.
 
 | config | rows | what it is |
 |---|---|---|
-| `full` | 9,229 | every problem, every column, including the unverified ones |
-| `qa` | 9,229 | the minimal MATH-style columns: problem, answer, metadata |
-| `verified` | 1,827 | **the scored split** - only rows whose answer the engine confirmed |
+| `full` | 12,557 | every problem, every column, including the unverified ones |
+| `qa` | 12,557 | the minimal MATH-style columns: problem, answer, metadata |
+| `verified` | 1,989 | **the scored split** - only rows whose answer the engine confirmed |
 | `core` | 3,620 | the scanned algebra book |
-| `books` | 5,089 | the additional problem books |
+| `books` | 8,417 | the additional problem books |
 | `synthetic` | 520 | the generated problems |
 
 The published repository splits the rows **85 % train / 15 % test, stratified by
@@ -101,12 +108,12 @@ a test score and a train score are not comparable.
 
 | | count |
 |---|---|
-| rows | 9,229 |
-| rows with a gold answer | 6,065 |
-| rows with **no** gold answer | 3,164 |
-| rows in the `verified` config (the scored split) | 1,827 |
-| rows by source | `algebra_core` 3,620, `falin_algebra` 2,071, `gelfand_trig` 212, `kozko_params` 516, `ponarin_plane` 570, `prasolov_planimetry` 1,337, `shabunin` 383, `synthetic` 520 |
-| rows by `answer_status` | `corrected` 15, `disputed` 72, `no-gold` 3,164, `refuted` 144, `suspected` 95, `synthetic-unverified` 329, `synthetic-verified` 191, `unverifiable` 3,598, `verified` 1,621 |
+| rows | 12,557 |
+| rows with a gold answer | 6,708 |
+| rows with **no** gold answer | 5,849 |
+| rows in the `verified` config (the scored split) | 1,989 |
+| rows by source | `algebra_core` 3,620, `falin_algebra` 2,346, `gelfand_trig` 255, `kozko_params` 1,131, `ponarin_plane` 879, `prasolov_planimetry` 2,056, `shabunin` 1,750, `synthetic` 520 |
+| rows by `answer_status` | `corrected` 17, `disputed` 122, `no-gold` 5,849, `refuted` 66, `suspected` 102, `synthetic-unverified` 329, `synthetic-verified` 191, `unverifiable` 4,100, `verified` 1,781 |
 
 Rows without a gold answer are rows where the source page prints the result only
 inside the worked solution, or not at all (`answer_status = "no-gold"`). They are

README.md

@@ -30,7 +30,7 @@ task_categories:
 language:
 - en
 size_categories:
-- 1K<n<10K
+- 10K<n<100K
 library_name: datasets
 library:
 - datasets
@@ -77,9 +77,9 @@ configs:
 
 # DGN Math Benchmark
 
-**9,229 question-answer pairs** - 1,827 of them with an engine-verified answer and
+**12,557 question-answer pairs** - 1,989 of them with an engine-verified answer and
 therefore usable as a scored benchmark. 3,620 problems come from scanned books,
-5,089 from additional problem books, 520 are generated and machine-checked.
+8,417 from additional problem books, 520 are generated and machine-checked.
 
 > Every printed answer in this dataset was checked with a real symbolic engine (SymPy).
 > Where the engine produced a concrete counterexample, the answer was either replaced by a
@@ -99,11 +99,11 @@ solution, and the final answer is stored in the standard MATH convention
 
 | config | rows | what it is |
 |---|---|---|
-| `full` | 9,229 | every problem, every column, including the unverified ones |
-| `qa` | 9,229 | the minimal MATH-style columns: problem, answer, metadata |
-| `verified` | 1,827 | **the scored split** - only rows whose answer the engine confirmed |
+| `full` | 12,557 | every problem, every column, including the unverified ones |
+| `qa` | 12,557 | the minimal MATH-style columns: problem, answer, metadata |
+| `verified` | 1,989 | **the scored split** - only rows whose answer the engine confirmed |
 | `core` | 3,620 | the scanned algebra book (11 chapters) |
-| `books` | 5,089 | the additional problem books |
+| `books` | 8,417 | the additional problem books |
 | `synthetic` | 520 | generated problems with computed, re-checked answers |
 
 Each config has a deterministic 85/15 train/test split (seed 42), stratified by
@@ -133,13 +133,13 @@ source and chapter.
 
 | status | count | meaning |
 |---|---|---|
-| `verified` | 1,621 | the engine substituted the answer back into the problem and it held |
-| `corrected` | 15 | the printed answer was refuted and replaced by a re-verified recomputation |
-| `refuted` | 144 | the engine found a concrete counterexample: the printed answer does not hold |
-| `suspected` | 95 | the recomputed answer differs from the printed one, but no counterexample was found - **not** counted as a book error |
-| `disputed` | 72 | a third read of the scanned page disagreed with the bulk transcription |
-| `unverifiable` | 3,598 | outside the reach of automatic checking |
-| `no-gold` | 3,164 | the source page carries no printed answer for this problem |
+| `verified` | 1,781 | the engine substituted the answer back into the problem and it held |
+| `corrected` | 17 | the printed answer was refuted and replaced by a re-verified recomputation |
+| `refuted` | 66 | the engine found a concrete counterexample: the printed answer does not hold |
+| `suspected` | 102 | the recomputed answer differs from the printed one, but no counterexample was found - **not** counted as a book error |
+| `disputed` | 122 | a third read of the scanned page disagreed with the bulk transcription |
+| `unverifiable` | 4,100 | outside the reach of automatic checking |
+| `no-gold` | 5,849 | the source page carries no printed answer for this problem |
 | `synthetic-verified` | 191 | generated template; the printed statement was parsed, solved and compared with the printed answer |
 | `synthetic-unverified` | 329 | generated template; the answer is a derived quantity no engine could re-check - not scored |
 

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