Datasets:

ProCreations
/

Beam-Reasoning-Traces

id stringlengths 21 25	domain stringclasses 2 values	source stringclasses 2 values	difficulty float64 5 10 ⌀	teacher stringclasses 3 values	reasoning_effort stringclasses 2 values	messages listlengths 2 2	gold stringlengths 1 76	n_samples int64 1 5	n_correct int64 1 5
deepmath-e93a13375b31	math	deepmath	5.5	selfhost-fp8	medium	[ { "role": "user", "content": "Given positive rational numbers \$a, b, c\$ such that \$a + b + c = abc\$, find the value of the expression:\n\\[\n\\frac{a}{b} + \\frac{a}{c} + \\frac{b}{a} + \\frac{b}{c} + \\frac{c}{a} + \\frac{c}{b} - ab - bc - ca.\n\\]\n\nPut your final answer within \\boxed{}.", "...	-3	4	4
deepmath-5e8b1f08af32	math	deepmath	8	api	high	[ { "role": "user", "content": "For a sphere in \$\\mathbb{R}^n\$, determine the maximum possible ratio between the arc length and the chord length of a minor arc of a great circle, given that the chord length is fixed.\n\nPut your final answer within \\boxed{}.", "reasoning_content": null }, { ...	\dfrac{\pi}{2}	4	4
deepmath-b0ef47bae66f	math	deepmath	6.5	api	high	[ { "role": "user", "content": "Determine the number of automorphisms of the symmetric group $S_6$. Provide your answer as a single integer.\n\nPut your final answer within \\boxed{}.", "reasoning_content": null }, { "role": "assistant", "content": "The inner automorphism group of \$S_6\$ ha...	1440	4	4
openscience2-7c8b681715ee	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDuring VATS right upper lobectomy for a 3.5 cm metastatic sarcoma in the posterior segment, unexpected dense calcification of the superior pulmonary vein and adherent interlobar lymp...	D	4	4
openscience2-bba74721f4b0	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA study investigates the effect of a new educational program on the number of absences per semester in high schools. The researchers use Poisson regression with an offset for the log...	B	4	4
deepmath-c53f94386446	math	deepmath	9	api	medium	[ { "role": "user", "content": "What is the probability that a subset $X$ of $\\mathbb{R}$, formed by independently including each real number with a coin toss, is a Lebesgue measurable subset of $\\mathbb{R}$?\n\nPut your final answer within \\boxed{}.", "reasoning_content": null }, { "role": "as...	0	4	3
openscience2-2caa970dc1dd	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDuring crystallographic studies of the Thermus thermophilus 70S ribosome complexed with EF-Tu•GTP and kirromycin-stalled aa-tRNA, the catalytic His84 residue in EF-Tu's GTPase doma...	C	4	3
openscience2-cfb754df57e3	science	openscience2	null	selfhost-nvfp4	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nAugustus's constitutional arrangements under the Principate relied on a delicate interplay between traditional republican offices and extraordinary powers. Considering the functional...	C	4	4
openscience2-e69501225c0f	science	openscience2	null	api	high	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn the Z-scheme of oxygenic photosynthesis, plastoquinone (PQ) accepts electrons directly from which complex and donates electrons directly to which complex?\nA: Photosystem I; Ferre...	C	4	4
openscience2-cf3da63511bf	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhen evaluating cost-effectiveness of nuclear medicine procedures, consider a hypothetical scenario comparing PET/CT versus standard CT alone for early dementia diagnosis. Clinical d...	A	4	4
deepmath-129e4084d4fb	math	deepmath	6	api	high	[ { "role": "user", "content": "Consider the system of differential equations:\n\n$$\\frac{dx}{dt}=\\frac{y}{y+x}+\\ln(x+y)$$\n$$\\frac{dy}{dt}=-\\frac{y}{y+x}$$\n\nFind the expression for $x(t)$ given that $y(t) = e^{-t}$. Provide your answer in terms of $t$.\n\nPut your final answer within \\boxed{}.", ...	1 - e^{-t}	4	4
openscience2-58495274c32c	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn studying CDK2 activation, a researcher introduces a mutated version of CAK (CDK-activating kinase) that specifically phosphorylates only the T-loop residue (Thr160 in CDK2) but is...	B	4	4
deepmath-80554acf985f	math	deepmath	5.5	api	medium	[ { "role": "user", "content": "Determine the number of ways to distribute 32 indistinguishable objects into five distinct bins labeled B1, B2, B3, B4, and B5 such that each of B1, B2, B3, and B4 contains an odd number of objects, and B5 contains an even number of objects, specifically x objects, where x is c...	1005	4	4
openscience2-35c0b816816a	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA CEO is drafting a formal letter to the board of directors explaining a significant strategic shift. The intended register is highly formal and deferential. The CEO writes the sente...	C	4	4
openscience2-a9d8381b41e9	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nArchaeologist Dr. Chen re-evaluates a 19th-century excavation report describing a highly polished jade disk (\"Disk A\") found in a ritual context, initially interpreted as a symbol ...	C	4	4
deepmath-29febe748f89	math	deepmath	5	selfhost-nvfp4	medium	[ { "role": "user", "content": "Determine the number of elements in the conjugacy class of the permutation \$ \\tau = (56789)(3456)(234)(12) \$ in the symmetric group \$ S_9 \$.\n\nPut your final answer within \\boxed{}.", "reasoning_content": null }, { "role": "assistant", "content": "The...	15120	4	4
deepmath-b18c73f17b60	math	deepmath	7	api	medium	[ { "role": "user", "content": "In an acute triangle $\\triangle ABC$, let $O$ be the circumcenter, $H$ be the orthocenter, and $I$ be the incenter. Given that $IO = IH$ and $\\angle BAC = 2 \\cdot \\angle CAO$, determine the measure of $\\angle BHC$. \$ \\text{(Express your answer in degrees.)} \$\n\nPut y...	120	4	4
deepmath-d3adaa902730	math	deepmath	9	selfhost-fp8	medium	[ { "role": "user", "content": "Let $R$ be a Noetherian ring and $I$ be a proper ideal of $R$. Suppose $b \\notin I$ is such that $I + Rb$ and $(I:b) = \\{x \\in R : xb \\in I\\}$ are projective as $R$-modules. Is the ideal $I$ projective as an $R$-module?\n\nPut your final answer within \\boxed{}.", "rea...	Yes	4	4
openscience2-2520a8056ba4	science	openscience2	null	api	medium	[ { "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 decompensated cirrhosis (Child-Pugh C), type 2 diabetes mellitus, and coronary artery disease undergoes diagnostic coronary angiography for unstable angina. Hi...	B	4	1
deepmath-f2923b598a72	math	deepmath	8	api	medium	[ { "role": "user", "content": "Determine whether there are any solutions in positive integers to the equation \$ a^n + b^{n-i} = c^{n-2i} \$ where \$ n-2i > 1 \$.\n\nPut your final answer within \\boxed{}.", "reasoning_content": null }, { "role": "assistant", "content": "Yes. For example,...	Yes	4	3
deepmath-a33d77cd2c04	math	deepmath	7	api	medium	[ { "role": "user", "content": "Given a finite prefix-closed set $A$ with an operation $\\cdot$, where $A$ is a semigroup, and the property that if $x \\cdot y \\in A$, then $x \\in A$, consider the set $B\|_a = \\{b \\mid a \\cdot b \\in A\\}$. Does this definition imply that for all $a' = a \\cdot b \\in A$,...	Yes	4	4
deepmath-4a2d951398fd	math	deepmath	8.5	api	high	[ { "role": "user", "content": "Let $M$ and $N$ be smooth manifolds, let $p \\in M$, and let $L:T_p M \\rightarrow T_{f(p)} N$ be a linear map. Determine whether there always exists a smooth map $F:M \\rightarrow N$ on a neighborhood of $p$ such that $L$ is the differential map of $F$ at $p$. Provide a justif...	Yes	4	4
deepmath-23840f7c4bcf	math	deepmath	6	selfhost-fp8	medium	[ { "role": "user", "content": "Determine the value of the parameter \$ \\alpha \$ such that the sequence \$ a_{n} = \\frac{3^n+(-2)^n}{3^{n+1}+(-2)^{n+1}}+\\left(\\frac{n+1}{n-1}\\right)^n+(1+\\alpha)\\sin\\frac{n\\pi}{2} \$ is convergent.\n\nPut your final answer within \\boxed{}.", "reasoning_conte...	-1	4	4
deepmath-e505d6a3f067	math	deepmath	7	api	high	[ { "role": "user", "content": "Calculate the n-th Lebesgue measure of the set \$\\{ (x_1, x_2, \\dots, x_n) \\in \\mathbb{R}^n : x_i \\geq 0, i = 1, 2, \\dots, n, \\sum_{i=1}^n x_i \\leq 1 \\}\$ using Fubini's theorem.\n\nPut your final answer within \\boxed{}.", "reasoning_content": null }, { ...	\dfrac{1}{n!}	4	4
deepmath-4fd8e4ac7f55	math	deepmath	6.5	api	medium	[ { "role": "user", "content": "Evaluate the limit \$ \\lim_{n\\to \\infty} nI_n \$, where \$ I_n=\\int_0^1 \\frac{x^n}{x^2+2019}\\,\\mathrm{d}x \$.\n\nPut your final answer within \\boxed{}.", "reasoning_content": null }, { "role": "assistant", "content": "We use the standard fact that fo...	\dfrac{1}{2020}	4	4
deepmath-1b010706ac7d	math	deepmath	9	api	medium	[ { "role": "user", "content": "Let $P\\subset\\mathbb{R}^n$ be a convex lattice polytope. Does there always exist a lattice simplex $\\Delta\\subset P$ and an affine hyperplane $H\\subset\\mathbb{R}^n$ that separates $\\Delta$ from the convex hull of the integer points of $P\\setminus \\Delta$? Equivalently,...	No	4	1
deepmath-9c520d70738a	math	deepmath	8.5	api	medium	[ { "role": "user", "content": "Is it true that for every IA automorphism \$\\alpha \\in \\text{Aut}(F(X_n))\$, the map \$x_i \\mapsto \\varphi(\\alpha(x_i))\$ for \$1 \\le i \\le n-1\$ defines an element in \$\\text{Aut}(F(X_{n-1}))\$?\n\nPut your final answer within \\boxed{}.", "reasoning_conte...	Yes	4	2
deepmath-811cb7f3d5a5	math	deepmath	5	api	medium	[ { "role": "user", "content": "Let $a_1,$ $a_2,$ $\\dots,$ $a_{4001}$ be an arithmetic sequence such that $a_1 + a_{4001} = 50$ and\n\\[\\frac{1}{a_1 a_2} + \\frac{1}{a_2 a_3} + \\dots + \\frac{1}{a_{4000} a_{4001}} = 10.\\]Find $\|a_1 - a_{4001}\|.$\n\nPut your final answer within \\boxed{}.", "reasoning_...	30	1	1
openscience2-651705cb4e0f	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn computational models of evolutionary modularity (e.g., NK landscapes or gene regulatory networks), modular structures frequently emerge under regimes of high environmental variabi...	B	2	2
openscience2-69cc5cdcf874	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA manufacturing company aims to enhance eco-efficiency in its operations by implementing green manufacturing technologies. Its strategy involves locating a new facility adjacent to a...	A	1	1
deepmath-8cbe52995914	math	deepmath	9	api	medium	[ { "role": "user", "content": "Evaluate the infinite tetration expression: $$ 2^{2^{2^{2^{2^{.^{.^.}}}}}} $$\n\nPut your final answer within \\boxed{}.", "reasoning_content": null }, { "role": "assistant", "content": "The infinite power tower \$2^{2^{2^{\\cdots}}}\$ converges only if the ba...	\infty	2	2
openscience2-958d62c3145e	science	openscience2	null	selfhost-fp8	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA manufacturing company has the following resource intensities per unit output in the base year: Material = 10 kg/unit, Energy = 50 MJ/unit, Water = 300 L/unit. The company implement...	B	2	2
deepmath-0cbb4a1f1149	math	deepmath	8	api	medium	[ { "role": "user", "content": "Let $X_i \\sim \\text{Bernoulli}\\left(\\frac{\\theta}{n}\\right)$ and $Y_i \\sim \\text{Poisson}\\left(\\frac{\\theta}{n}\\right)$ be independent and identically distributed random variables, where $n \\ge \\theta \\ge 0$. Define $T_n = \\sum_{i=1}^{n^2} X_i$ and $S_n = \\sum_...	1	2	1
openscience2-bc922b6584d6	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA Shakespearean sonnet opens with three distinct quatrains, but the volta occurs midway through the third quatrain (line 10), preceding the couplet. The couplet features enjambment l...	D	1	1
deepmath-afcae734887e	math	deepmath	7.5	api	medium	[ { "role": "user", "content": "Find the value of the constant \$ \\lambda > 0 \$ such that the equation \$ 2\\lfloor{\\lambda n}\\rfloor = 1 - n + \\lfloor\\lambda \\lfloor\\lambda n \\rfloor\\rfloor \$ holds true for all positive integers \$ n \$.\n\nPut your final answer within \\boxed{}.", "reas...	1 + \sqrt{2}	2	2
deepmath-4ca60237a8da	math	deepmath	9	api	medium	[ { "role": "user", "content": "Determine whether there exists an embedding \$ j: \\mathbb{Q}^c \\hookrightarrow \\mathbb{Q}_p^c \$, where \$ \\mathbb{Q}^c \$ is the algebraic closure of \$ \\mathbb{Q} \$ in \$ \\mathbb{C} \$ and \$ \\mathbb{Q}_p^c \$ is the algebraic closure of \\( \\mathbb{Q}_p \\...	Yes	1	1
deepmath-05139e38c669	math	deepmath	6.5	api	medium	[ { "role": "user", "content": "Evaluate the summation: \\[ \\sum_{k=0}^{m}\\frac{k^m}{k!(m-k)!}(-1)^{m-k} = 1 \\]\n\nPut your final answer within \\boxed{}.", "reasoning_content": null }, { "role": "assistant", "content": "We rewrite the summand using binomial coefficients:\n\n\\[\n\\frac{1}{...	1	1	1
deepmath-4b4842c186c6	math	deepmath	7	api	medium	[ { "role": "user", "content": "Let $P$ be a nonempty polyhedron in $\\mathbb{R}^n$, and let $l_i, u_i \\in \\mathbb{R}$ for all $i \\in I$, where $I \\subseteq \\{1,\\dots,n\\}$. Consider the feasible region $$ F := P \\cap \\{x \\in \\mathbb{R}^n \\mid l_i \\leq x_i \\leq u_i,\\; x_i \\in \\mathbb{Z} \\quad...	Yes	1	1
deepmath-9a295ea6c88f	math	deepmath	8	api	medium	[ { "role": "user", "content": "Determine whether there exists a strictly increasing sequence $\\{a_k\\}_{k\\in\\mathbb N}\\subset\\mathbb N$ such that \$ \\sum_{k=1}^{\\infty}\\frac{1}{(\\log a_k)^{1+\\delta}} < \\infty \$, where $\\delta>0$ is given, and \\( \\lim_{k\\to \\infty }\\frac{a_{k+1}}{a_k}=1.\\...	Yes	1	1
deepmath-89b66252c37f	math	deepmath	7	api	medium	[ { "role": "user", "content": "Evaluate the principal value of the improper integral \$ P.V. \\int_{-\\infty}^{\\infty} \\frac{dx}{x(x^2+1)} \$ using the residue theorem. Verify if the principal value is \$ 0 \$.\n\nPut your final answer within \\boxed{}.", "reasoning_content": null }, { "rol...	0	1	1
openscience2-7cdf94a2acc5	science	openscience2	null	api	medium	[ { "role": "user", "content": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA healthcare worker in a region co-endemic for onchocerciasis and lymphatic filariasis is planning mass drug administration (MDA). Ivermectin will be used, potentially with albendazo...	E	2	2
deepmath-221b8ca5e920	math	deepmath	5.5	api	medium	[ { "role": "user", "content": "Given that $z_1$ and $z_2$ are complex numbers satisfying $z + \\bar{z} = 2\|z - 1\|$ and $\\arg(z_1 - z_2) = \\frac{\\pi}{4}$, find the value of $\\Im(z_1 + z_2)$. \$z_1\$ and \$z_2\$ both satisfy the equation \$z + \\bar{z} = 2\|z - 1\|\$.\n\nPut your final answer within \\...	2	2	2

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Beam Reasoning Traces

Verified math and science reasoning traces from Reflection's Beam-1.0-501B-A23B at reasoning_effort=medium. They were built to distill Beam into a small model, and were used to train ProCreations/Dory-Beam-4B, a looped NVIDIA Dory-4B that reasons about half as long as the base model at the same accuracy. Made for the Build with Beam challenge.

Config	Rows	What it is
`sft` (default)	53,306	One verified-correct trace per prompt (the shortest correct one), in chat `messages` form
`all`	124,945	Every generation over 62,417 prompts, correct or not, with the grader's verdict

Evaluation outputs

The eval configs hold every graded answer behind the Dory-Beam-4B results, so the tables can be audited without re-running anything:

Config	Rows	What it is
`eval`	29,376	16 model × loop-count configurations, 1,836 answers each (GPQA-Diamond ×2 samples, MATH-500 ×1, AIME 2024/2025 ×8, AMC 2023 ×4, 300 held-out ×1)
`eval_ifeval`	2,164	IFEval at 2 loops for base Dory and Dory-Beam-4B (541 prompts × 2 samples), with strict and loose per-instruction results
`eval_problems`	900	Prompt and reference answer for every non-GPQA problem

Models: dory1.0-4b (base, also its efficient mode), dory-beam-4b (the released 50/50 blend), run-a-sft (the fine-tune before blending) with its step400/step800 checkpoints, run-a2-random-trace (the ablation trained on random correct traces), and blend-70-30. Each row has model, loops, reasoning_mode, bench, problem_id, sample, correct, extracted_answer, reference_answer, output_tokens, finish_reason, thinking_closed and the full text (reasoning, then </think> and the answer). GPQA rows omit the question and text, because GPQA's authors ask that its questions not appear online in plain text. Grades, extracted letters and token counts are kept.

audit_eval.py recomputes every table and the paired bootstrap confidence intervals straight from these files: python audit_eval.py dory-beam-4b:2 dory1.0-4b:2.

How it was made

Prompts. These are decontaminated, auto-verifiable problems from two sources:

zwhe99/DeepMath-103K (MIT): difficulty 5–9, closed-form answers
nvidia/OpenScienceReasoning-2 (CC-BY-4.0): multiple choice, single-letter answers

Any prompt sharing a 13-gram with MATH-500, AIME 2024/2025, AMC 2023 or GPQA was dropped. A separate check against the 198 GPQA-Diamond questions found zero 13-gram overlap. 300 further pool prompts were held out for evaluation and are not in this dataset.

Generation. Every trace comes from Beam-1.0-501B-A23B with reasoning_effort=medium, apart from 30 pilot rows at high. Most were generated by self-hosting the open weights with SGLang (lmsysorg/sglang:beam) at temperature 0.7 and top-p 0.99, usually with 2 samples per prompt. The rest came from the Reflection API with its default sampling:

`teacher`	Checkpoint	`sft` rows	Math accuracy	Science accuracy	Median tokens
`selfhost-nvfp4`	Beam NVFP4 on 2× B300	48,826	85.8%	76.5%	1,248
`selfhost-fp8`	Beam FP8 on 4× B300	2,640	86.3%	78.1%	1,152
`api`	Reflection API	1,840	83.5%	78.7%	987

Self-hosted Beam matched the API's accuracy but wrote about 30–37% longer reasoning on token-identical prompts. This held for both NVFP4 and FP8, so quantization is unlikely to be the cause; sampling or serving differences on Reflection's side are more likely. Keeping the shortest correct of two samples narrows the gap.

Verification. Math answers are taken from the last \boxed{} and compared with math-verify. Science answers must match the gold letter. Truncated generations always count as incorrect.

Fields

sft: id, domain (math/science), source, difficulty (DeepMath only), teacher, reasoning_effort, messages (user prompt, then an assistant turn with reasoning_content and content), gold, n_samples and n_correct (Beam's generations and correct ones for this prompt).

all: id, domain, source, topic, difficulty, teacher, reasoning_effort, prompt, reasoning, content, gold, answer_type, pred (the extracted answer), correct, finish_reason, completion_tokens. Self-hosted SGLang requests reported only total usage across samples, so their per-sample token counts are approximate.

run_a_ids.txt lists the 52,660 prompts in the snapshot that Dory-Beam-4B was trained on. Later rows come from nightly API top-ups.

Use

from datasets import load_dataset
ds = load_dataset("ProCreations/Beam-Reasoning-Traces", "sft", split="train")

The messages format works with any chat template that renders reasoning_content, including Dory's and Qwen3's. To train on another model, the code in the model repo rebuilds everything: build_pool.py, generate.py, verify.py and build_dataset.py.

License

CC-BY-4.0. Prompts come from DeepMath-103K (MIT) and OpenScienceReasoning-2 (CC-BY-4.0, please credit NVIDIA). Responses were generated by Beam-1.0-501B-A23B, which is released under Apache-2.0.