Datasets:

YangyiH
/

m9-verifier-38k-aligned

prompt_sha256 stringlengths 64 64	solution stringlengths 1 1.62k	answer_type stringclasses 2 values	domain stringclasses 2 values	source_dataset stringclasses 2 values	source_config stringclasses 1 value	source_split stringclasses 2 values	source_shard int64 0 139	problem_type stringclasses 2 values	prompt listlengths 1 1	base_row_index int64 2 100k
d207ad4d87d0c6fe94f6e77df784e0b4ad3dc36c36ecd3a19d1216cc43ccb845	36	math	math	nvidia/OpenMathReasoning	default	cot	8	has_answer_extracted	[ { "role": "user", "content": "How many different rectangles can be formed by connecting four of the dots in a 4 x 4 square array of dots such that the sides of the rectangle are parallel to the sides of the grid?" } ]	2
2c08b7aa1d8d09a88d82b50bc99c816fb87c39e26240e59dd588c216aef1f046	$\frac{3 \sqrt{5} + 5 \sqrt{3} - 2 \sqrt{30}}{6}$	math	math	nvidia/OpenMathReasoning	default	cot	62	has_answer_extracted	[ { "role": "user", "content": "Rationalize the denominator of $\\frac{5}{2\\sqrt{2}+\\sqrt{3}+\\sqrt{5}}$." } ]	5
561c45e3558e181aa1d49fbc22e5e1f910bfe848ae97e0e7886360d78a611f25	B	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn Fake Barn County, there are 100 barn facades (which look like barns from the road but are fake) and one real barn. Sam stops at the real barn and forms the belief, \"That is a bar...	8
92a58fdade446b669d20c0984c19adf610bf4e509b8cb026b570dbf73e90217e	B	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn the context of the Paris Agreement's nationally determined contributions (NDCs), a developing country Party facing severe economic constraints and historical low emissions propose...	10
8a2ed2510e8bd6ba0122524a168918a13b7964154b57532095c07fa273de257d	E	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nConsider a time-series of remotely sensed data with evenly spaced temporal observations. When applying the Fourier Transform for periodic component analysis, which fundamental theore...	12
34dd77f52c08c12aa3c642dd329501d45608c00778accdc1329ee4f3bf686f68	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA teacher has students with varied reading levels and interests. She wants to design a differentiated reading activity that addresses both student readiness (based on current skill l...	13
73afc5f28a267f85c8fa174c1e5e13ef8d0e2d31f85efca2fb48f694165a0179	The orthogonal complement of the span of $ \{ a_n \}_{n \in \mathbb{N}} $ is the zero vector.	math	math	nvidia/OpenMathReasoning	default	cot	8	has_answer_extracted	[ { "role": "user", "content": "Let \$ H \$ be a pre-Hilbert space, and let \$ \\{ a_n \\}_{n \\in \\mathbb{N}} \$ be an orthogonal family in \$ H \$. Find a necessary and sufficient condition such that the vector space generated by \$ \\{ a_n \\}_{n \\in \\mathbb{N}} \$ is dense in \$ H \$." } ]	15
3a2fa3e74629294860abe689a8c488051da7314e03225c56d275b742b88294f4	all odd $ k \in \mathbb{N^+} $	math	math	nvidia/OpenMathReasoning	default	cot	28	has_answer_extracted	[ { "role": "user", "content": "Let \$ k \\in \\mathbb{N^+} \$, \$ S = \\left\\{ \\left( m + \\frac{1}{k}, n \\right) \\mid m, n \\in \\mathbb{Z} \\right\\} \$, and \$ T = \\left\\{ \\left( m + \\frac{2}{k}, n \\right) \\mid m, n \\in \\mathbb{Z} \\right\\} \$. Find all \$ k \\in \\mathbb{N^+} \$ such...	16
2610079494647af1915902477edb5e2b370693fee539d399f06cbf9309d81fe9	A	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nConsidering fluxional organometallic complexes, examine the haptotropic shift mechanism in the cycloheptatriene complex (C<sub>7</sub>H<sub>8</sub>)Mo(CO)<sub>3</sub>. Which statemen...	17
1635da4dc96ebfc9f0a5f6c960dc2e71860f597373dd6c60f7b7e647dcd20457	15	math	math	nvidia/OpenMathReasoning	default	cot	139	has_answer_extracted	[ { "role": "user", "content": "Let \$ V \$ be the vector space of all polynomials in one variable with real coefficients and having degree at most 20. Define the subspaces:\n\\[ W_1 = \\{ p \\in V : p(1) = 0, p\\left(\\frac{1}{2}\\right) = 0, p(5) = 0, p(7) = 0 \\} \\]\n\\[ W_2 = \\{ p \\in V : p(3) = 0, p...	18
4b90b29c6d1ad47d6723c7f4eea6be84c8c2e41b361244cfe7f33f9a896df121	$ 2(m + n) - 4 $	math	math	nvidia/OpenMathReasoning	default	cot	139	has_answer_extracted	[ { "role": "user", "content": "What is the maximum number of bishops that can be placed on an $m \\times n$ chessboard such that each bishop attacks no more than 2 other bishops? (A bishop attacks along diagonals.)" } ]	31
ea7c4e742c05d4d9896290aadc0dc1cef6e062668fff8f61b658e831d8c4a425	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA patient with cirrhosis undergoes a contrast-enhanced MRI for a newly detected 25 mm liver lesion. The imaging shows nonrim arterial phase hyperenhancement (APHE), nonperipheral \"w...	33
40c205175ed4f84f28f99ea8869ff8840f2e786951106a996bd2ab8ced7a53b9	A	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDuring Contrast-Enhanced Ultrasound (CEUS) using gas-filled microbubbles for vascular imaging, which physical phenomenon primarily explains the increased risk of cavitation-induced b...	35
8925d1e5bcd6101b2a09503e40cff3b2f9590b1f5ffa01e633bc38e7f59202d9	$(x,y,z)=(1,k,1), (0,k,0), (k,0,1), (2^k-1,1,k), (-1,2k,1), (-2,-1,-1)$	math	math	nvidia/OpenMathReasoning	default	cot	26	has_answer_extracted	[ { "role": "user", "content": "Find all integer solutions to the equation \$ x^y = 2^z - 1 \$." } ]	37
eb92d6453222a72fd074c593f31346de5cb819f2566d1524a35820e14e23bc5a	$5$	math	math	nvidia/OpenMathReasoning	default	cot	6	has_answer_extracted	[ { "role": "user", "content": "Find all invertible elements of $\\mathbb{Z}_6$." } ]	38
89faba15f85ee9968db1d99417cc2aa879994122b788def97a4d76a697ee8607	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhich advanced MRI technique exhibits the highest sensitivity to proteoglycan loss in early osteoarthritis but suffers from significant magnetic field strength-dependent variability ...	39
bd2722ca04a3a986576c2704ca4d2b785f8094eb6e32c8fe1519ffa8f2e44bd2	A	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn a study exploring resistance mechanisms in cancer cells with hyperactive PI3K-Akt signaling, cells expressing a constitutively active PI3K mutant (p110α-H1047R) are treated with a...	41
86224cd084357e2f81ba5b9a85b8d543ea18fdc5bb8f10aa3609ba9ae5025ad1	G	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nConsider a hypothetical scenario in an endemic onchocerciasis region where large-scale environmental changes lead to significant alterations in river flow regimes and land use patter...	42
3ebff22445c1521ba78c056fbd706b900a13537e6f68a4e96da2cee244518626	$\frac{\sqrt{2}}{2}\left( \sqrt{1+\left\| x \right\|+{{x}^{2}}}+\sqrt{1-\left\| x \right\|+{{x}^{2}}} \right)$	math	math	nvidia/OpenMathReasoning	default	cot	28	has_answer_extracted	[ { "role": "user", "content": "Simplify $\\sqrt{1+x^2+\\sqrt{1+x^2+x^4}}$." } ]	48
a377637be573adc7eb2151d3052a6e7be93bd74e6e9dfae95451b4e51b273dbb	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn a crossover trial with two treatments (A and B), three periods, and two sequences (ABA and BAB), a fixed-effects model includes an intercept, sequence effect (1 df), period effect...	50
1f62dffffef0dd73f35ab5e2b80c3281380f2dfb7c9fff2d1fbd0f6cd2e2895d	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nThe Spring and Autumn Annals records an event in the 3rd year of Duke Xi: \"楚人伐鄭\" (The men of Chu attacked Zheng). Later, in the 28th year of Duke Xiang, it records: \"楚子昭伐吳\" (Zhao...	54
211a6a4129bac20cacd3a602659fb3050fb37346d967815a7badb445426a4eff	B	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDuring a left-sided medial visceral rotation (Mattox maneuver) for trauma exposure, the surgical team encounters unexpected bleeding at the level of the left renal vein. Which of the...	56
4d0409b888fe1260a9601098d2826ebc39b335d8dfe378934a67cd899c991732	E	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn the Drude model, a metal has two types of charge carriers: electrons with density \$2n\$, effective mass \$m\$, and relaxation time \$\\tau\$; and holes with density \$n\$...	58
630e0a564da5cfe9f754cb0bf6c8d3a0899b3d0d11f49bab12c683b920573bb5	J	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDuring corneal wound healing, which of the following statements accurately describes a key mechanism or outcome?\n\nA: Fibroblast proliferation dominates the initial epithelial heali...	60
9a611f21ace1a88066c75423673529f074ba5713155038f886ef04859d772eff	$x = 2, y = 1$	math	math	nvidia/OpenMathReasoning	default	cot	6	has_answer_extracted	[ { "role": "user", "content": "Solve the equation $3^x - 2^y = 7$ in natural numbers $x$ and $y$." } ]	63
112f00269bf0252ca36d0371629e20797fbc95a0c27d989c4ac95449baec8007	360	math	math	nvidia/OpenMathReasoning	default	cot	8	has_answer_extracted	[ { "role": "user", "content": "What is the largest integer that divides \$ n^2 \\cdot (n^2 - 1) \\cdot (n^2 - 4) \$ for all integers \$ n \$?" } ]	64
c85bbda31cc4b34ef3c29c367d1167f0257d41e443204527b2a2dba7366184dd	$\frac{a(b-a)}{2b}$	math	math	nvidia/OpenMathReasoning	default	cot	139	has_answer_extracted	[ { "role": "user", "content": "Determine whether the function \$ f(x) \$ is differentiable on the right at \$ x = 0 \$. The function is defined as:\n\\[ f(x) = \\begin{cases} \n\\frac{\\ln(1+ax)}{\\ln(1+bx)} & \\text{if } x \\neq 0 \\\\\n\\frac{a}{b} & \\text{if } x = 0 \n\\end{cases} \\]\nFind the limit...	69
4ea1f91253f98cca6e6b75e2927e8b39b82e5385b2cf28dc703d62c5ed0c7528	$ y = 2019^{2019} $	math	math	nvidia/OpenMathReasoning	default	cot	6	has_answer_extracted	[ { "role": "user", "content": "Find \$ y \$ if \$ y^y = 2019^{2019^{2020}} \$." } ]	70
b50d5c60354acdd2bc90a115c39da70cf9c7afc5a11c6796e893141be948b80b	12	math	math	nvidia/OpenMathReasoning	default	cot	7	has_answer_extracted	[ { "role": "user", "content": "Find the smallest natural number \$ n \$ such that \$ n^5 + 5^n \$ is divisible by 13." } ]	74
25a38c4eb55bdd165381e6907f2d86fabe17ad3be67082b8c9eb2312d08b3833	$\frac{13}{4}$	math	math	nvidia/OpenMathReasoning	default	cot	62	has_answer_extracted	[ { "role": "user", "content": "What is the sum of the reciprocals of the divisors of 360?" } ]	75
68b0206c6605109e059a403870f034dc89615cc533d8c9ea7cf0a2f36ee37050	$ x \in [0, \pi/4) \cup (\pi/3, 3\pi/4) \cup (5\pi/4, 5\pi/3) \cup (7\pi/4, 2\pi] $	math	math	nvidia/OpenMathReasoning	default	cot	62	has_answer_extracted	[ { "role": "user", "content": "Solve the inequality: $(1-\\cos{x})(1+\\cos{2x})(1-\\cos{3x}) < \\frac{1}{2}$." } ]	78
3297fc178053758f2dc34d0152a54200beedd308f0b54a8bec75e9113c651313	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn a 45-year-old male kidney transplant recipient 6 months post-operation, managed on maintenance immunosuppression with tacrolimus and mycophenolate mofetil, which of the following ...	86
808abd5185e60012428c2e683f98b3959a04143295ec1f8c4db09a48cd1c4b58	20	math	math	nvidia/OpenMathReasoning	default	cot	70	has_answer_extracted	[ { "role": "user", "content": "Let \$ABCD\$ be a square and let \$P\$ be a point inside it. The area of triangle \$PAB\$ is \$10\$, the area of triangle \$PBC\$ is \$30\$, and the area of triangle \$PCD\$ is \$40\$. Find the area of triangle \$PDA\$." } ]	87
c35ef824e18c9798b724613e63cada8ca3ab17ea3af0db5414b0f531338c3c4e	A circle passing through $ A $ and $ B $ and coaxial with $ w_1 $ and $ w_2 $.	math	math	nvidia/OpenMathReasoning	default	cot	8	has_answer_extracted	[ { "role": "user", "content": "Let the circles \$ w_1 \$ and \$ w_2 \$ intersect at points \$ A \$ and \$ B \$. Find the locus of the point \$ S \$ such that \$\\frac{\\text{Pow}(S, w_1)}{\\text{Pow}(S, w_2)} = k\$ where \$ k \$ is a constant and \$ k \\neq 1 \$." } ]	91
69c939316e50545b3c76634332667467a34756829550fe941f97df70a6ff4e92	F	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA 68-year-old man with idiopathic pulmonary fibrosis (IPF) develops elevated transaminases (ALT/AST >5× ULN) after 8 weeks of anti-fibrotic therapy. According to FDA-approved prescri...	92
d58107a3c3bf0f67c0707800df38fbbd8cc9f5260e4f6fd39226329d031a1f66	$ x^2 - y^2 = y $	math	math	nvidia/OpenMathReasoning	default	cot	6	has_answer_extracted	[ { "role": "user", "content": "Draw the trajectory of \$ R(\\theta) = \\frac{\\sin(\\theta)}{\\cos(2\\theta)} \$." } ]	94
8f66950f6eacccf846913a59d9ed829af0922e13acf1222479193c9f7ac58f5d	376	math	math	nvidia/OpenMathReasoning	default	cot	139	has_answer_extracted	[ { "role": "user", "content": "Given eight distinguishable rings, let $n$ be the number of possible five-ring arrangements on the four fingers (not the thumb) of one hand. The order of rings on each finger is significant, but it is not required that each finger have a ring. Find the leftmost three nonzero di...	98
832428621e835d75d24f7c77d8eb04f79f08a6c1dfb57bafd669f58755c7ea79	$\mathbb{Q}$	math	math	nvidia/OpenMathReasoning	default	cot	22	has_answer_extracted	[ { "role": "user", "content": "Find the splitting field of the polynomial $x^3 - 2x^2 + x^2 - x + 1$." } ]	99
3f9681505988789556c0b6939dcc381153bccb5fa2c22a0899f227f940cbb44a	B	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn Jacques Derrida's deconstruction, how does the undecidability of the signifier operate in Emily Dickinson's poem \"My Life had stood - a Loaded Gun -\", particularly in the lines ...	100
d52ec30d16b6b399c7f2c94d3e39ef7fdf02acaa919b8a39d4a1426c5b5374fa	J	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nConsider the triple-alpha process in stellar nucleosynthesis, where three helium-4 nuclei (\$ ^4\\text{He} \$) fuse to form carbon-12 (\$ ^{12}\\text{C} \$) in the presence of a ...	110
0a9a54a5e0b7097553dcdd7ca94d864074c2b22ad2d58f2cc5b1f589ae2807e7	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhich mode of heat transfer can occur through a perfect vacuum?\n\nA: Conduction only \nB: Convection only \nC: Radiation only \nD: Conduction and convection \nE: Conduction and ...	113
17a78e360e0d975d40d28c66eee1d42c9ac96085c888337d3e6883661b983400	A	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDuring simultaneous large-scale natural disasters in resource-limited regions, a rehabilitation team must prioritize patients for prosthetic/orthotic services amidst extreme scarcity...	115
c62d58429a82365aaf68bb72fe3694609bde5e221e0e5f1dd782889425815656	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn the context of U.S. labor history, which event demonstrated a successful application of industrial unionism by leveraging newly established federal protections, while also trigger...	123
69e82659989eefabdabfec7bd3135361a124ab1408e2149f152394dd57c812c1	112	math	math	nvidia/OpenMathReasoning	default	cot	26	has_answer_extracted	[ { "role": "user", "content": "Let \$f(n, b)\$ be a function that expresses a positive integer \$n > 2\$ in base \$b > 1\$ and then returns that expression as if it was written in base \$n + 1\$. For example, \$4 = 100_2\$ so \$f(4, 2) = 100_5 = 25\$. We say a number \$n\$ is optimal if \$n\$...	124
a88574cfa1136ba991e8b3927512531bbd1ec8a8378e3e4708ffe52a9d1b5ea1	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA comprehensive urban high school implements a dropout prevention program featuring: (1) need-based scholarship funds, (2) mandatory after-school tutoring for students below grade le...	128
3984e0dd1d23f2a2338b10a4bf709daec2d23b65ed366f7557dfc8bbae9068ba	$\left(\sqrt[8]{2}\cos{\pi\over 16},\sqrt[8]{2}\sin{\pi\over 16}\right), \left(-\sqrt[8]{2}\sin{\pi\over 16},\sqrt[8]{2}\cos{\pi\over 16}\right), \left(-\sqrt[8]{2}\cos{\pi\over 16},-\sqrt[8]{2}\sin{\pi\over 16}\right), \left(\sqrt[8]{2}\sin{\pi\over 16},-\sqrt[8]{2}\cos{\pi\over 16}\right)$	math	math	nvidia/OpenMathReasoning	default	cot	6	has_answer_extracted	[ { "role": "user", "content": "Find all solutions to the system of equations:\n\\[\n\\left\\{\\begin{matrix} \nx^{4}-6x^{2}y^{2}+y^{4}=1 \\\\ \n4x^{3}y-4xy^{3}=1 \n\\end{matrix}\\right.\n\\]" } ]	129
ca9416b127110f119c39dfa50cfc151a6c8761d9f00409e42a1c7860e94d74a3	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn integrating palliative care within skilled nursing facilities, a quality improvement initiative aims to address systemic barriers. According to evidence-based frameworks, which ba...	131
b12469811ed82386126b7262819e9c026ba4033e77e3d7d0176a8597b8960253	28	math	math	nvidia/OpenMathReasoning	default	cot	28	has_answer_extracted	[ { "role": "user", "content": "Let \$ p \$ and \$ q \$ be prime numbers such that \$ n^{3pq} - n \$ is a multiple of \$ 3pq \$ for all positive integers \$ n \$. Find the least value of \$ p + q \$." } ]	132
51347218343edd62a0070ebbb0df711b6b3fb5cfaee3136bff1813e260c9669a	A	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA homodimeric protein has a denaturation midpoint (\$T_m\$) of 65°C (338.15 K) at a total monomer concentration of 200 μM. The enthalpy change (\$\\Delta H\$) upon unfolding is 1...	134
c68a5d90bb641fc8726b1a1c0390909e22157129a51fece831dd7d48307850d7	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn the context of epistemic autonomy, which approach to forming a belief about climate change best demonstrates an epistemically autonomous stance? \nA: Adopting a prominent scienti...	135
aa0dab03832518f4fd0c14e5254a64c210e527b493befdf49f64a5c8b6edc9d3	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nAt Çatalhöyük, a large Neolithic site in Turkey, archaeologists identified several rooms containing dense concentrations of bull horns (bucrania) embedded in platforms or walls, alon...	136
4f7fada4e5917b108842bc271dc8329f5ee04d93173c7e9e41eed37ef2268a72	$ k + 2 \leq m $	math	math	nvidia/OpenMathReasoning	default	cot	8	has_answer_extracted	[ { "role": "user", "content": "Given a positive integer \$ k \$, find the condition on the positive integer \$ m \$ such that there exists exactly one positive integer \$ n \$ satisfying \$ n^m \\mid 5^{n^k} + 1 \$." } ]	140
fa559bccbb30d8037c4265c1b08f058dc073a1562e8cde7091d50fc85a134fcb	$\frac{\sqrt{3}}{3}$	math	math	nvidia/OpenMathReasoning	default	cot	26	has_answer_extracted	[ { "role": "user", "content": "Given a triangle with angles $\\alpha$, $\\beta$, and $\\gamma$, if $\\tan (\\alpha) = \\frac{1}{\\tan (\\beta)}$, what is $\\tan \\left(\\frac{\\gamma}{3}\\right)$?" } ]	142
24a94f44e64fcda56c6c9fa0565702ed8ad8b177672be6e46cda520f6e93ac6f	50225	math	math	nvidia/OpenMathReasoning	default	cot	6	has_answer_extracted	[ { "role": "user", "content": "Find the minimum positive integer \$ N = \\overline{a_1a_2 \\ldots a_k} \$ such that \$ 2009 \\times \\overline{a_4a_5 \\ldots a_k} = \\overline{a_1a_2 \\ldots a_k} \$." } ]	145
4e3e6c59424960c45e02ae3cee77b9b9ee958f5cd22ff14d1eb0c7ade504ada9	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nConsidering N. Katherine Hayles's arguments in How We Became Posthuman regarding the impact of information technologies on conceptions of identity, which of the following statement...	147
3276ff9f52a5d9ce13790daea72be674209e163c82b2e2c8d0c8fdde86dc5381	$\frac{4}{3}$	math	math	nvidia/OpenMathReasoning	default	cot	108	has_answer_extracted	[ { "role": "user", "content": "If $pq = -1$, find the minimum value of the area $S$ enclosed by the segments $OP$, $OQ$, and the parabola $C: y=1-x^2$, where $P(p, 1-p^2)$ and $Q(q, 1-q^2)$ are points on $C$ with $p < q$." } ]	153
48d5a8df5c7440478ad25f7cdca1bd0e5817f703fa7a239d1f157e01211681ad	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhich nanoscale bioseparation technique utilizes magnetic nanoparticles to isolate target biomolecules from complex mixtures?\n\nA: Size exclusion chromatography \nB: Ultracentrifug...	157
4dc8f5d0644c3659f23d6ba477f3e9ac4b7a1a793cbc4c1d634b60462bb3daea	J	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA patient is mechanically ventilated following traumatic lung injury. The ICU team implements a comprehensive VAP prevention bundle. According to current evidence-based guidelines, w...	158
a84c23ae993f722bcb3897467c101ddef3788bc6a749fe5ffbb374a7cd5766d3	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn a synchronous CDMA system with spreading factor N=32, operating with negligible background noise and equal received power for all users, the signal-to-interference ratio (SIR) at ...	161
cbc1eadb7b4b24727f99b29e157ea159d95a2871ff478aaeabfcd2b7479f490c	E	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nAn aircraft flies at Mach 2.0 at an altitude where the static pressure is 10 kPa. Using a pitot tube to measure total pressure, what is the approximate ratio of the measured total pr...	166
57220d2327b16802e20f1c485332c59708168112d0d6acfca65d53af8ab3f788	$\frac{2^{2014}-3022}{3}$	math	math	nvidia/OpenMathReasoning	default	cot	108	has_answer_extracted	[ { "role": "user", "content": "Find the sum of \\[\\left[\\frac{1}{3}\\right]+\\left[\\frac{2}{3}\\right]+\\left[\\frac{2^2}{3}\\right]+\\cdots+\\left[\\frac{2^{2013}}{3}\\right],\\] where $[x]$ denotes the greatest integer less than or equal to $x$." } ]	167
f329dd259f00c8cab8389b489e6303bd80ebc912461687030b77341a44639a62	$\ln 2$	math	math	nvidia/OpenMathReasoning	default	cot	6	has_answer_extracted	[ { "role": "user", "content": "Calculate the limit\n$$\\lim_{x\\rightarrow 0}\\int\\limits_{0}^{x}\\frac{\\cos t^3}{t+x}dt$$" } ]	168
95172775f5ef563f7c5a31d10e62fb8f0d5318cc5ebc9f15385402ba8950a9d9	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA family therapist observes a recurring pattern: Adolescent children explicitly avoid discussing their online activities with parents. Paradoxically, when parents discover these acti...	171
542d304aaa600c4a6092ce5a28758933a15c2f1c69492323de8fa78808bc9933	B	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn Rudolf Otto's analysis of the numinous, the mysterium tremendum et fascinans is characterized by an irreducible paradox. The \"tremendum\" aspect induces dread, awe, and the sense...	175
0708827b97d8e307bc7df1515e7edc6b6219258c7065012f060ae8b24d6a669a	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhich of the following is a key implication of the first Hohenberg-Kohn theorem in Density Functional Theory?\n\nA: The ground state electron density minimizes the total energy funct...	176
48fe52681dc8e7080bdbf76ba7983fa62c8beab0c23f18758ab65164115f20a5	B	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn the sociology of animals, which concept explains how cultural contexts shape human perceptions of animals, such as viewing cows as sacred in one society but as food in another?\nA...	178
33162a9e110f51bfa45025e7250d3f30f35481d1bc52904fb19daf9e8e7082e0	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn an equivalence trial comparing a novel biologic (Drug X) to an approved biologic (Drug Y) for treating rheumatoid arthritis, the equivalence margin is defined as ±1.2 units on the...	181
cf0b6ecd6e2d51360584742190d9dda1d3c7dce0959d8be488b83527cb18c8a8	$(\pm \sqrt{1.5}, \pm \sqrt{5}), (\pm \sqrt{2}, \pm 2)$	math	math	nvidia/OpenMathReasoning	default	cot	57	has_answer_extracted	[ { "role": "user", "content": "Find all real solutions to the system of equations:\n\\[ 2^{2x^2-1} + 2^{y^2-2} = 12 \\]\n\\[ 3^{2x^2-1} + 3^{y^2-2} = 36 \\]" } ]	182
17471521fb680e16c5d0a28e54c2b04263938bc151b2b8d13467d81f5c9b9e04	$60^\circ$	math	math	nvidia/OpenMathReasoning	default	cot	6	has_answer_extracted	[ { "role": "user", "content": "In triangle \$ABC\$ with \$AB > AC\$, the angle bisectors of \$\\angle B\$ and \$\\angle C\$ intersect sides \$AC\$ and \$AB\$ at points \$P\$ and \$Q\$, respectively. Let \$I\$ be the incenter of \$\\Delta ABC\$. Given that \$IP = IQ\$, find the value of ...	183
a8cb655596967225ab436b63fa32101e3535d791eeed7946fdd90ff3c0c57e35	$ f(m) = m + d $ for any integer $ d $.	math	math	nvidia/OpenMathReasoning	default	cot	8	has_answer_extracted	[ { "role": "user", "content": "Find all functions \$ f: \\mathbb{Z} \\rightarrow \\mathbb{Z} \$ that satisfy the following conditions:\n\\[ f(m+19) \\geq f(m) + 19 \\quad \\forall m \\in \\mathbb{Z} \\]\n\\[ f(m+99) \\leq f(m) + 99 \\quad \\forall m \\in \\mathbb{Z} \\]" } ]	187
ac5dbea778ad6110ac5ba627bbb4488a7d1ec3e2ee74e093629b6155a8a7633e	$\frac{11}{46}$	math	math	nvidia/OpenMathReasoning	default	cot	28	has_answer_extracted	[ { "role": "user", "content": "Find the probability that at least two out of three randomly chosen knights from a round table of 25 knights are sitting next to each other." } ]	189
3f82b5883fce71152384e1220b1837a15304e354df08a0d0402ed58d1804324d	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA portfolio consists of two assets: 40% invested in Asset A and 60% in Asset B. Asset A has a beta of 1.3 and a Jensen's Alpha of 2.5%. The risk-free rate is 4%, and the market retur...	190
300ebd26c6624aff4eb10bf9590dd8195a805a0f7745bb968f0099295dad7429	16	math	math	nvidia/OpenMathReasoning	default	cot	57	has_answer_extracted	[ { "role": "user", "content": "Let $ABC$ be an acute triangle in which the altitude $BH$ relative to the side $AC$ has length $4$. If $\\angle A = 2\\angle C$ and $AC = 11$, find the value of the area of the right triangle $BHC$." } ]	192
79e65d67ad97d04b1afd44959a79553288aba9ba39f064981dcf07d0c34852e1	96	math	math	nvidia/OpenMathReasoning	default	cot	6	has_answer_extracted	[ { "role": "user", "content": "Find the number of $7$-tuples of positive integers $(a,b,c,d,e,f,g)$ that satisfy the following systems of equations:\n\\[\nabc = 70, \\quad cde = 71, \\quad efg = 72.\n\\]" } ]	195
34c77ff43363abb5565eaab1e59e6b00f40f1639d6f98bd70b58573f1b6d56e2	88	math	math	nvidia/OpenMathReasoning	default	cot	139	has_answer_extracted	[ { "role": "user", "content": "A positive two-digit number is even and is a multiple of 11. The product of its digits is a perfect cube. What is this two-digit number?" } ]	200
c2edc65ce76e190bf3ac0fabb1cdd8b3881b17fb08cf624b9ce9c64da42b3148	$4e^2 - 4$	math	math	nvidia/OpenMathReasoning	default	cot	7	has_answer_extracted	[ { "role": "user", "content": "Evaluate the integral $\\int_0^4 (x^2 - x - 2)e^{\|x-2\|} \\, dx$." } ]	202
4b1750ceb18c717e3992ca039619670127327ba1ac46056d52657569e4ca3f4c	A	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn an environment with depleting resource patches, a forager's cumulative gain from a patch is given by \$ R(t) = k t^p \$ (with \$ k > 0 \$, \$ 0 < p < 1 \$). The travel time ...	204
046d4a324a787d0c05fb96df4ac469ca45848a66d84215ecfb713ced5e9ef231	E	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA patient with Stage 4 CKD (eGFR 25 mL/min/1.73m²) presents with fatigue and pallor. Laboratory studies reveal: hemoglobin 9.0 g/dL, serum ferritin 250 ng/mL, transferrin saturation ...	205
8fd80003c61800abe858f59976b4aac22e70b9bb0408c5859dab3191353df357	B	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nTechnetium-99m dimercaptosuccinic acid (Tc-99m DMSA) is a radiopharmaceutical used primarily for renal cortical imaging. Under certain pathological conditions or patient factors, its...	207
4243a20aa7bcd9e1741f7bcb5de3ef87617a07edcc04bc066eaee3a339ab65cd	A	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn the Saffman-Taylor instability, when a less viscous fluid displaces a more viscous fluid in a Hele-Shaw cell, finger-like patterns form. The dominant wavelength (λ) of these finge...	208
84fc2c16db761baa7a817de119b803964cb4ef1db15dea0d35e395dbc9b69be6	96	math	math	nvidia/OpenMathReasoning	default	cot	22	has_answer_extracted	[ { "role": "user", "content": "From 8 distinct colors, a cube is painted so that no two faces sharing a common vertex are painted with the same color. If the number of such different colorings is \$ N \$, find the largest 2-digit factor of \$ N \$." } ]	209
66dbe4fa33e46ed87f7794b3c05aecc356b10c65ed744120ba6953ced9c1f8e6	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhat was a primary motivation for Charlemagne's promotion of the Carolingian minuscule script reform in the 9th century?\nA: To simplify the alphabet by reducing the number of letter...	211
e581ae123a6b61c5c1de100f5f7cd23170717d1dcdfb7363deac75a1fcf87890	$ \frac{\pi\sqrt{3}}{9} $	math	math	nvidia/OpenMathReasoning	default	cot	35	has_answer_extracted	[ { "role": "user", "content": "Evaluate the integral \$ \\int_{0}^{\\infty} \\frac{x}{x^{6}+1} \\, dx \$." } ]	215
e9af5e91c7c19f82c8679f1c21047d4fd2fc22af7970cfe185cd94117b6696ee	-1 or 8	math	math	nvidia/OpenMathReasoning	default	cot	70	has_answer_extracted	[ { "role": "user", "content": "Let \$ x, y, z \\in \\mathbb{R} \$ such that \$ xyz \\neq 0 \$ and \$ \\frac{x+y}{z} = \\frac{y+z}{x} = \\frac{z+x}{y} = a \$. Find all values of \$ a^3 \$." } ]	217
b8d41a8a0321eef0a394fc6fe51b1c19d70bd6e81d7503a44ac4d3aa77ce6555	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA patient undergoes renal artery embolization using 500-700μm Gelfoam particles for traumatic hemorrhage. Imaging at 48 hours shows persistent occlusion, but follow-up at 2 weeks dem...	218
2fe0f84f3cbe9730b0d09d7c9a0c0b9d0a110ce0694eaff33484a885b31934a6	$ y = (1 + x)^p $	math	math	nvidia/OpenMathReasoning	default	cot	108	has_answer_extracted	[ { "role": "user", "content": "Consider the differential equation \$(1 + x)y' = py\$ where \$p\$ is a constant. Assume that the equation has a power series solution \$y = \\sum_{n=0}^{\\infty} a_n x^n\$. Given that \$y(0) = 1\$, find a closed form solution to the equation." } ]	219
f3b73f0cb4816e864a05bc9fd5168f795eb8d8071316f4c2789f8b9eb5f51386	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhat is the primary clinical indication for performing corneal cross-linking (CXL) in ophthalmology?\n\nA: Treatment of bacterial keratitis\nB: Management of glaucoma\nC: Halting the...	220
52d3a07f789cbf74143a40d3ad797055e3bbd552a11bfd94cb8af8dfb92a90e9	$\frac{197}{8}$	math	math	nvidia/OpenMathReasoning	default	cot	108	has_answer_extracted	[ { "role": "user", "content": "Find the minimum possible value of the expression \$ x^2 + (x + 3)^4 + (x + 4)^4 + (x + 7)^2 \$, where \$ x \$ is a real number." } ]	221
429d0cb0463626628bd64b1837eca746f85ee749a9b3f52fdbb2bff95960f6bb	2013	math	math	nvidia/OpenMathReasoning	default	cot	62	has_answer_extracted	[ { "role": "user", "content": "Let \$ a = \\sqrt{1 + 2013 \\times 2012 \\times 2011 \\times 2010} \$, \$ b = \\sqrt{1 + 2012 \\times 2011 \\times 2010 \\times 2009} \$, \$ c = \\sqrt{1 + 2011 \\times 2010 \\times 2009 \\times 2008} \$, and \\( d = \\sqrt{1 + 2010 \\times 2009 \\times 2008 \\times 2007}...	224
214621f7cf19f7a5c0d18b42c0a4304cebd1034e314cb3d1ffa11a757c7b7a76	B	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nThe Pessimistic Meta-Induction (PMI) argument contends that since historically successful scientific theories (e.g., phlogiston chemistry or Newtonian mechanics) were ultimately deem...	225
a8654c4a8191bbffadd540168597f539e6ff3f1e12a84fa77ec954e794d98415	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn the context of a spinning top under the influence of gravity, which description best characterizes nutation?\n\nA: The steady circular motion of the top's axis around the vertical...	229
e50797ac7071e3a87a526ee6182ef491ec56fa4eeee0c34f57033d5abbda4f32	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn an n-type semiconductor silicon doped with phosphorus at a concentration of \$10^{17}\$ cm\$^{-3}\$ at room temperature (300 K), where the intrinsic carrier concentration \\(n...	231
34835b75b6eb2a57fc31f48900ea7479b8c0866e6dda122da372fe80768f0621	I	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nConsider the following dynamic programming problem: \nA robot is located at the top-left corner of a grid with \$ m \$ rows and \$ n \$ columns. The grid has obstacles and treasu...	233
8c8b7970795da8bfa88dc5ebf3c87a9adc73a33204259fde065f47c3780283f2	$7^n$	math	math	nvidia/OpenMathReasoning	default	cot	7	has_answer_extracted	[ { "role": "user", "content": "Let \$ S = \\{1, 2, \\ldots, n\\} \$ and let \$ T \$ be the set of all ordered triples of subsets \$(A_1, A_2, A_3)\$ such that \$ A_1 \\cup A_2 \\cup A_3 = S \$. Find the cardinality of \$ T \$." } ]	244
32048070a254233ed28d68048b902b681b22ff5494553047796195246156b4e2	C	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn Lojban, the `y`-rafsi for a gismu is formed by taking the first letter (a consonant), followed by 'y', and then the final vowel of the gismu. What is the `y`-rafsi for the gismu \...	245
7398580d1445e636025dc1ae7b07a11eb277314c1e8ae4e8fe4096d70a74eb80	G	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhich of the following is the primary method to prevent or reduce aliasing (wrap-around artifact) in MRI?\n\nA: Decreasing the field of view (FOV)\nB: Increasing the receiver bandwid...	246
cc8329949258e27eed15c1160e1ac67be46297eb2f624a80823ea6a75a7c5233	$\frac{7}{16}$	math	math	nvidia/OpenMathReasoning	default	cot	6	has_answer_extracted	[ { "role": "user", "content": "In a contest with multiple choice questions having 3 alternatives each, a candidate knows 30% of the answers and has a 1/3 chance of guessing correctly. If the candidate gave the correct answer to a question, what is the probability that the candidate guessed it?" } ]	250
40b41616a7e608c5b5dc0e5cbc97f8b7fb44e6ea28941d28b6192ac1e1e6b328	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	2		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nThe Tokugawa Shogunate implemented the sankin-kotai (alternate attendance) system primarily to achieve what key objective?\nA: To stimulate the economy of Edo through increased spend...	251
3e1eb909ba55e8d9442e5672d05d30ef0ec8e2a9a6ced6a96b1aad173d3e1a04	D	choice	science	nvidia/OpenScienceReasoning-2	default	train	1		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn lung transplant recipients diagnosed with Bronchiolitis Obliterans Syndrome (BOS), which of the following factors is most strongly associated with an increased risk of BOS develop...	253
374acbb290cbe8ccca0843982cd28c972d516f476a343f5ee462cebc1a3b3238	B	choice	science	nvidia/OpenScienceReasoning-2	default	train	0		[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nAccording to Fried's frailty phenotype, which component of frailty is primarily linked to increased caregiver burden due to safety concerns during physical assistance?\n\nA: Unintent...	254

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M9 Verifier 38K Aligned

This dataset contains 38,564 prompts with verifier-compatible gold answers for an M9 RLVR-GRPO experiment in a unified post-training study with Qwen3-1.7B. It is an independent research artifact, not an official release from the model or paper authors.

The bank was reconstructed from the frozen YangyiH/openreasoning_mixed_100k prompt mixture. Every recovered row was matched to the frozen base row by domain, source shard, and prompt SHA-256 before verifier filtering.

This is a prompt-and-answer bank, not a model-rollout dataset. Thinking mode, sampling parameters, and group size are selected by the downstream trainer and are not properties of these rows.

Composition

Domain	Rows	Answer type	Upstream dataset
Math	19,282	symbolic/numeric math	`nvidia/OpenMathReasoning`
Science	19,282	categorical choice	`nvidia/OpenScienceReasoning-2`
Total	38,564

There are 36,741 unique prompt hashes and 1,823 repeated prompt rows. Repeated rows with equivalent gold answers are retained. Prompts having incompatible gold answers were removed conservatively.

Fields

prompt: one-message chat record containing the user question
solution: gold answer consumed by the verifier
answer_type: math or choice
domain: math or science
problem_type: upstream problem classification when available
source_dataset, source_config, source_split, source_shard: upstream provenance
prompt_sha256: SHA-256 of the prompt text
base_row_index: position in the frozen 100K mixture

Construction and filtering

Base mixture size: 100,000 rows
Seed: 42
Initially recovered Math/Science rows: 66,667
Math rows require problem_type=has_answer_extracted and a gold answer parseable by math_verify.
Single-letter Science answers use categorical exact matching; other Science answers must pass the same math-answer parseability check.
Code rows are excluded because the source records do not provide executable tests; reference-code string equality is not treated as a correctness verifier.
Seven rows from three prompt hashes with verifier-inconsistent duplicate golds were excluded.
Science was deterministically downsampled to 19,282 rows to balance the two retained domains. Frozen base-row order was then restored.

The repository includes a complete construction_manifest.json with exclusion counts, upstream revisions, duplicate-gold audit, and domain-balance audit.

Integrity

Prompt-order SHA-256: db1c2f96dd5b6822c9765c7ceedeac25c0a9035c847baeb6278547e582c8362c
Base-row-index SHA-256: 42abbad0b3c0edd37dfd708df9933ae182c7a0e161e48c431c8c0c9ea8e07962

Usage

from datasets import load_dataset

dataset = load_dataset("YangyiH/m9-verifier-38k-aligned", split="train")

The exact matching and mathematical-equivalence reward functions used by the experiments live in the accompanying TRL research code. Users should validate reward behavior against their own generation format before training.

Source data and licensing

Prompt and answer content is derived from NVIDIA OpenMathReasoning and OpenScienceReasoning-2. This repository does not assert a new blanket license over upstream content. Users should review and comply with the source dataset cards, licenses, terms, and attribution requirements.

Limitations

Gold-answer parseability is a conservative engineering filter, not a general measure of question quality or difficulty.
The dataset has not been exhaustively audited for benchmark contamination, sensitive content, or all possible symbolic-answer equivalences.
Equivalent-answer checking can still have false positives or false negatives.
Code is absent, so training on this bank changes the domain mixture relative to the original Math/Science/Code 100K pool.
Duplicate prompts inherited from the upstream sources are intentionally retained when their gold answers are verifier-consistent.

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