Datasets:

caiyuchen
/

OPV-Math

id string	data_source string	prompt list	ability string	reward_model dict	extra_info dict
AIME2025_0	AIME2025	[ { "content": "Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$\nPlease reason step by step, and put your final answer within \\boxed{}.", "role": "user" } ]	math	{ "ground_truth": "70", "style": "rule" }	{ "index": 0, "split": "test" }
AIME2025_1	AIME2025	[ { "content": "In $\\triangle ABC$ points $D$ and $E$ lie on $\\overline{AB}$ so that $AD < AE < AB$, while points $F$ and $G$ lie on $\\overline{AC}$ so that $AF < AG < AC$. Suppose $AD = 4$, $DE = 16$, $EB = 8$, $AF = 13$, $FG = 52$, and $GC = 26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be t...	math	{ "ground_truth": "588", "style": "rule" }	{ "index": 1, "split": "test" }
AIME2025_2	AIME2025	[ { "content": "The $9$ members of a baseball team went to an ice-cream parlor after their game. Each player had a single scoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose...	math	{ "ground_truth": "16", "style": "rule" }	{ "index": 2, "split": "test" }
AIME2025_3	AIME2025	[ { "content": "Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$ inclusive, such that $12x^2-xy-6y^2=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.", "role": "user" } ]	math	{ "ground_truth": "117", "style": "rule" }	{ "index": 3, "split": "test" }
AIME2025_4	AIME2025	[ { "content": "There are $8!= 40320$ eight-digit positive integers that use each of the digits $1, 2, 3, 4, 5, 6, 7, 8$ exactly once. Let $N$ be the number of these integers that are divisible by $22$. Find the difference between $N$ and $2025$.$\nPlease reason step by step, and put your final answer within \\bo...	math	{ "ground_truth": "279", "style": "rule" }	{ "index": 4, "split": "test" }
AIME2025_5	AIME2025	[ { "content": "An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is $3$, and the area of the trapezoid is $72$. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^2+s^2$\nPlease reason step by step, and put your fin...	math	{ "ground_truth": "504", "style": "rule" }	{ "index": 5, "split": "test" }
AIME2025_6	AIME2025	[ { "content": "The twelve letters $A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I$,$J$,$K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and then those six words are listed alphabetically. For example, a ...	math	{ "ground_truth": "821", "style": "rule" }	{ "index": 6, "split": "test" }
AIME2025_7	AIME2025	[ { "content": "Let $k$ be a real number such that the system \\begin{align} &\|25 + 20i - z\| = 5 \\ &\|z - 4 - k\| = \|z - 3i - k\| \\end{align} has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Fin...	math	{ "ground_truth": "77", "style": "rule" }	{ "index": 7, "split": "test" }
AIME2025_8	AIME2025	[ { "content": "The parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a - \\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and ...	math	{ "ground_truth": "62", "style": "rule" }	{ "index": 8, "split": "test" }
AIME2025_9	AIME2025	[ { "content": "The $27$ cells of a $3 \\times 9$ grid are filled in using the numbers $1$ through $9$ so that each row contains $9$ different numbers, and each of the three $3 \\times 3$ blocks heavily outlined in the example below contains $9$ different numbers, as in the first three rows of a Sudoku puzzle. [a...	math	{ "ground_truth": "81", "style": "rule" }	{ "index": 9, "split": "test" }
AIME2025_10	AIME2025	[ { "content": "A piecewise linear function is defined by\\[f(x) = \\begin{cases} x & \\operatorname{if} ~ -1 \\leq x < 1 \\ 2 - x & \\operatorname{if} ~ 1 \\leq x < 3\\end{cases}\\]and $f(x + 4) = f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern depicted below. The parabola $x = 34y^{...	math	{ "ground_truth": "259", "style": "rule" }	{ "index": 10, "split": "test" }
AIME2025_11	AIME2025	[ { "content": "The set of points in $3$-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities\\[x-yz<y-zx<z-xy\\]forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sq...	math	{ "ground_truth": "510", "style": "rule" }	{ "index": 11, "split": "test" }
AIME2025_12	AIME2025	[ { "content": "Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws $25$ more lines segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting these two p...	math	{ "ground_truth": "204", "style": "rule" }	{ "index": 12, "split": "test" }
AIME2025_13	AIME2025	[ { "content": "Let $ABCDE$ be a convex pentagon with $AB=14,$ $BC=7,$ $CD=24,$ $DE=13,$ $EA=26,$ and $\\angle B=\\angle E=60^{\\circ}.$ For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX.$ The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p},$ where $m$ and $n$ are positive integers and...	math	{ "ground_truth": "60", "style": "rule" }	{ "index": 13, "split": "test" }
AIME2025_14	AIME2025	[ { "content": "Let $N$ denote the number of ordered triples of positive integers $(a, b, c)$ such that $a, b, c \\leq 3^6$ and $a^3 + b^3 + c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.", "role": "user" ...	math	{ "ground_truth": "735", "style": "rule" }	{ "index": 14, "split": "test" }
AIME2025_15	AIME2025	[ { "content": "Six points $A, B, C, D, E,$ and $F$ lie in a straight line in that order. Suppose that $G$ is a point not on the line and that $AC=26, BD=22, CE=31, DF=33, AF=73, CG=40,$ and $DG=30.$ Find the area of $\\triangle BGE.$\nPlease reason step by step, and put your final answer within \\boxed{}.", ...	math	{ "ground_truth": "468", "style": "rule" }	{ "index": 15, "split": "test" }
AIME2025_16	AIME2025	[ { "content": "Find the sum of all positive integers $n$ such that $n + 2$ divides the product $3(n + 3)(n^2 + 9)$.\nPlease reason step by step, and put your final answer within \\boxed{}.", "role": "user" } ]	math	{ "ground_truth": "49", "style": "rule" }	{ "index": 16, "split": "test" }
AIME2025_17	AIME2025	[ { "content": "Four unit squares form a $2 \\times 2$ grid. Each of the $12$ unit line segments forming the sides of the squares is colored either red or blue in such a say that each unit square has $2$ red sides and $2$ blue sides. One example is shown below (red is solid, blue is dashed). Find the number of su...	math	{ "ground_truth": "82", "style": "rule" }	{ "index": 17, "split": "test" }
AIME2025_18	AIME2025	[ { "content": "The product\\[\\prod^{63}_{k=4} \frac{\\log_k (5^{k^2 - 1})}{\\log_{k + 1} (5^{k^2 - 4})} = \frac{\\log_4 (5^{15})}{\\log_5 (5^{12})} \\cdot \frac{\\log_5 (5^{24})}{\\log_6 (5^{21})}\\cdot \frac{\\log_6 (5^{35})}{\\log_7 (5^{32})} \\cdots \frac{\\log_{63} (5^{3968})}{\\log_{64} (5^{3965})}\\]is eq...	math	{ "ground_truth": "106", "style": "rule" }	{ "index": 18, "split": "test" }
AIME2025_19	AIME2025	[ { "content": "Suppose $\\triangle ABC$ has angles $\\angle BAC = 84^\\circ, \\angle ABC=60^\\circ,$ and $\\angle ACB = 36^\\circ.$ Let $D, E,$ and $F$ be the midpoints of sides $\\overline{BC}, \\overline{AC},$ and $\\overline{AB},$ respectively. The circumcircle of $\triangle DEF$ intersects $\\overline{BD}, \...	math	{ "ground_truth": "336", "style": "rule" }	{ "index": 19, "split": "test" }
AIME2025_20	AIME2025	[ { "content": "Circle $\\omega_1$ with radius $6$ centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius $15$. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and ${\\overline{BC} \\perp \\overline{AD}}$. The rectangle $EFGH$ is in...	math	{ "ground_truth": "293", "style": "rule" }	{ "index": 20, "split": "test" }
AIME2025_21	AIME2025	[ { "content": "Let $A$ be the set of positive integer divisors of $2025$. Let $B$ be a randomly selected subset of $A$. The probability that $B$ is a nonempty set with the property that the least common multiple of its element is $2025$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers....	math	{ "ground_truth": "237", "style": "rule" }	{ "index": 21, "split": "test" }
AIME2025_22	AIME2025	[ { "content": "From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $N$ cents, where $N$ is a positive integer. He uses the so-called greedy algorithm, successively choosing the coin of greatest value that does not cause t...	math	{ "ground_truth": "610", "style": "rule" }	{ "index": 22, "split": "test" }
AIME2025_23	AIME2025	[ { "content": "There are $n$ values of $x$ in the interval $0<x<2\\pi$ where $f(x)=\\sin(7\\pi\\cdot\\sin(5x))=0$. For $t$ of these $n$ values of $x$, the graph of $y=f(x)$ is tangent to the $x$-axis. Find $n+t$.\nPlease reason step by step, and put your final answer within \\boxed{}.", "role": "user" } ]	math	{ "ground_truth": "149", "style": "rule" }	{ "index": 23, "split": "test" }
AIME2025_24	AIME2025	[ { "content": "Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $N$ be the number of subsets of $16$ chairs that could be selected. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put you...	math	{ "ground_truth": "907", "style": "rule" }	{ "index": 24, "split": "test" }
AIME2025_25	AIME2025	[ { "content": "Let $S$ be the set of vertices of a regular $24$-gon. Find the number of ways to draw $12$ segments of equal lengths so that each vertex in $S$ is an endpoint of exactly one of the $12$ segments.\nPlease reason step by step, and put your final answer within \\boxed{}.", "role": "user" } ]	math	{ "ground_truth": "113", "style": "rule" }	{ "index": 25, "split": "test" }
AIME2025_26	AIME2025	[ { "content": "Let $A_1A_2\\dots A_{11}$ be a non-convex $11$-gon such that The area of $A_iA_1A_{i+1}$ is $1$ for each $2 \\le i \\le 10$, $\\cos(\\angle A_iA_1A_{i+1})=\\frac{12}{13}$ for each $2 \\le i \\le 10$, The perimeter of $A_1A_2\\dots A_{11}$ is $20$. If $A_1A_2+A_1A_{11}$ can be expressed as $\\frac{...	math	{ "ground_truth": "19", "style": "rule" }	{ "index": 26, "split": "test" }
AIME2025_27	AIME2025	[ { "content": "Let the sequence of rationals $x_1,x_2,\\dots$ be defined such that $x_1=\\frac{25}{11}$ and\\[x_{k+1}=\\frac{1}{3}\\left(x_k+\\frac{1}{x_k}-1\\right).\\]$x_{2025}$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$. Find the remainder when $m+n$ is divided by $10...	math	{ "ground_truth": "248", "style": "rule" }	{ "index": 27, "split": "test" }
AIME2025_28	AIME2025	[ { "content": "Let ${\\triangle ABC}$ be a right triangle with $\\angle A = 90^\\circ$ and $BC = 38.$ There exist points $K$ and $L$ inside the triangle such\\[AK = AL = BK = CL = KL = 14.\\]The area of the quadrilateral $BKLC$ can be expressed as $n\\sqrt3$ for some positive integer $n.$ Find $n.$\nPlease reaso...	math	{ "ground_truth": "104", "style": "rule" }	{ "index": 28, "split": "test" }
AIME2025_29	AIME2025	[ { "content": "Let\\[f(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}.\\]There exist exactly three positive real values of $k$ such that $f$ has a minimum at exactly two real values of $x$. Find the sum of these three values of $k$.\nPlease reason step by step, and put your final answer within \\boxed{}.", "role": "u...	math	{ "ground_truth": "240", "style": "rule" }	{ "index": 29, "split": "test" }

OPV Math: original experiment data

Prepared for Learning to Steer, Steering to See. train is filtered DeepMath (distillation); teacher_train is the original DAPO teacher corpus. validation is AIME2024. These corpora are not interchangeable.

Split	Rows
train	57,046
teacher_train	14,116
validation	30
aime2025	30

Provenance and terms

The data is derived from the following sources; their original terms and attribution obligations continue to apply. No new blanket license is asserted over the collection. Source-file and uploaded-file hashes are in manifest.json.

Format and evaluation

These are byte-for-byte copies of the original Parquet files. All columns, Arrow schemas, nested verifier metadata, row order, prompts and answers are unchanged. Use the existing verl reward functions directly. Each file has a separate Hub configuration because original train/evaluation schemas differ.

Use the full evaluation split and four independently sampled responses per prompt; report mean@4, not pass@4. No training responses or model weights are included. Exact normalized-chat train/evaluation overlap: 0 prompts. Original splits are preserved, including any disclosed overlap, to match existing teacher provenance. This is not a semantic contamination audit.

from datasets import load_dataset
train = load_dataset("caiyuchen/OPV-Math", "train", split="train")
validation = load_dataset("caiyuchen/OPV-Math", "validation", split="validation")

The available artifacts differ from several manuscript descriptions. The accompanying repository records these differences instead of relabeling datasets or inventing results.

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