Datasets:

amphora
/

researchmath-glm5_23-distill-12k

paper_url string	signal_type string	source_quote string	question string	reasoning string	response string	model string
https://arxiv.org/abs/0704.0095	open_problem	The open question stated at the end of Section 8 ('Coarsely geodesic distances and speed of convergence'), immediately following the discussion of Burago's theorem (abelian case) and Stoll's theorem (2-step nilpotent case): whether the error term O(t^{d-1}) in the volume asymptotics vol_G(B_rho(t)) = c*t^d + O(t^{d-1})...	Let G be a finitely generated nilpotent group and let rho be a word metric on G associated to a finite symmetric generating set. For radius t > 0 let B_rho(t) be the set of group elements at word distance at most t from the identity, and let vol_G(B_rho(t)) denote its cardinality. Let d be the degree of polynomial grow...	The question: is the error term O(t^{d-1}) for all finitely generated nilpotent groups and all word metrics? This is a known open problem in general — Pansu, Gromov, etc. The known result: Breuillard–Le Donne, "On the number of distinct group products..." Actually the relevant result: Breuillard (2012?), and "On volume...	# Answer The question has two logically independent components, and they must be separated, because they have different statuses: * (I) Optimality. Is the exponent $d-1$ the best possible uniform bound, i.e. can one never replace $O(t^{d-1})$ by $O(t^{d-1-\varepsilon})$ or $o(t^{d-1})$? * (II) Validity. Does ...	zai-org/GLM-5.3-Flash
https://arxiv.org/abs/0704.0097	conjecture	Section 5 (Moonshine Conjecture), final open-problems paragraph: 'For a net of factors, we can naturally define a notion of a character for each representation. But even convergence of these characters have not been proved in general, and the modular invariance property, the counterpart of Zhu's result [Z], is unknown,...	Work in the operator-algebraic (algebraic quantum field theory) formulation of chiral conformal field theory. Let {A(I)} be an irreducible local conformal net of factors on the circle: I ranges over the non-empty, non-dense, open connected subsets of S^1; each A(I) is a von Neumann factor acting on a fixed Hilbert spac...	The question asks to prove characters of irreducible representations of a completely rational conformal net converge on the upper half plane, span is SL(2,Z)-invariant, and decide whether the SL(2,Z) representation coincides with the braiding one. This is essentially the content of Kawahigashi–Longo's work? Actually t...	## Answer I will fix the normalization χ_λ(τ) = Tr_{H_λ}(q^{L₀ − c/24}), q = e^{2πiτ}, Im τ > 0, at the outset, as permitted. I will first construct every object the question asks about, explicitly, and verify its properties against the stated hypotheses. I will then state, with the same precision, what those hyp...	zai-org/GLM-5.3-Flash
https://arxiv.org/abs/0704.0097	natural_extension	"Section 5 (Moonshine Conjecture), closing open-problems paragraph: after stating that for a net of (...TRUNCATED)	"Work in the operator-algebraic formulation of chiral conformal field theory. Let {A(I)} be an irred(...TRUNCATED)	"This is asking to prove the S-part of the spin-statistics theorem for completely rational conformal(...TRUNCATED)	"A preliminary statement of intellectual honesty. You have instructed me not to say that a probl(...TRUNCATED)	zai-org/GLM-5.3-Flash
https://arxiv.org/abs/0704.0116	announced_forthcoming	"Section IV (Conclusions), final paragraph: the authors announce two in-progress follow-up direction(...TRUNCATED)	"Setting. Let (M, g_ab) be an n-dimensional spacetime manifold with n >= 3, Levi-Civita connection n(...TRUNCATED)	"The problem asks for a comprehensive development of a congruence theory for a two-parameter family (...TRUNCATED)	"1. The transverse geometry of a string congruence\n\nLet $(M,g_{ab})$ be an $n$-dimensional spa(...TRUNCATED)	nvidia/GLM-5.2-NVFP4
https://arxiv.org/abs/0704.0129	natural_extension	"The explicit future-research direction stated at the close of Section 1 (Introduction): '...It woul(...TRUNCATED)	"Setting: Let M be a compact connected smooth manifold without boundary of dimension d >= 1, equippe(...TRUNCATED)	"This is a research-level open problem in weak KAM theory (Aubry-Mather theory). The question asks f(...TRUNCATED)	"## I have to be straight with you before I build anything\n\nThe question you pose — \"determine (...TRUNCATED)	zai-org/GLM-5.3-Flash
https://arxiv.org/abs/0704.0337	open_problem	"Section 1 (Introduction), the sentence beginning 'A deep open issue of the work by the Gledzer-Obuk(...TRUNCATED)	"Consider the Cauchy problem for the 3D incompressible Euler equations partial_t V + (V.grad)V = -gr(...TRUNCATED)	"The problem asks: does there exist a nonempty class of initial conditions for 3D Euler such that so(...TRUNCATED)	"ANSWER: YES. Below I construct everything explicitly: a Gledzer–Obukhov-type finite-dimension(...TRUNCATED)	zai-org/GLM-5.3-Flash
https://arxiv.org/abs/0704.0380	natural_extension	"Section 1.2 (Application to reaction-diffusion equations): the authors write that they 'expect our (...TRUNCATED)	"Fix constants a > 0, r >= 0, rho >= 0 and a temperature theta > 8r (the high-temperature regime), a(...TRUNCATED)	"The problem asks for substantially broader classes of initial data $f: \\mathbb{R}^2 \\to [0,1]$ fo(...TRUNCATED)	"We construct a substantially broader class of initial data by replacing the rigid $L^2(\\phi)$ inte(...TRUNCATED)	nvidia/GLM-5.2-NVFP4
https://arxiv.org/abs/0704.0390	natural_extension	"The open-ended question posed immediately after the classification theorem (the theorem labeled thm(...TRUNCATED)	"Work in the space of planar n-gons, identifying an n-gon with its vertex vector P = (z_1, ..., z_n)(...TRUNCATED)	"The problem asks: \"Do the n-gons in this classification list possess further special geometric or (...TRUNCATED)	"To answer the question, we construct the explicit dynamical invariant given by the iteration of the(...TRUNCATED)	nvidia/GLM-5.2-NVFP4
https://arxiv.org/abs/0704.0508	announced_forthcoming	"The announced but omitted local-limit-theorem approach in Section 5 to proving an invariance princi(...TRUNCATED)	"Let {xi_k} be i.i.d. real random variables with E\|xi_1\|^(2+delta)<infinity for some delta>0, E xi_1(...TRUNCATED)	"We need to answer: yes, and construct the proof. This is essentially the standard result that the o(...TRUNCATED)	"## Answer: Yes — and here is the construction.\n\nThroughout, $Z^k:=Z_n(k/n)$, $\\Delta^k:=Z^k-Z^(...TRUNCATED)	LibertAIDAI/GLM-5.3-Flash-NVFP4
https://arxiv.org/abs/0704.0517	natural_extension	"In the Discussion (Section 4, item 1 on approximations of household acquisition data), the authors (...TRUNCATED)	"Consider a Kinetic Dietary Exposure Model (KDEM) for chronic dietary exposure to a contaminant, def(...TRUNCATED)	"We need to solve a statistical modeling question: formulate and estimate a Chesher-type correction (...TRUNCATED)	"# A Chesher‑Type Out‑of‑Home Correction for the Household‑to‑Individual Decomposition\n\n(...TRUNCATED)	zai-org/GLM-5.3-Flash

End of preview.

ResearchMath GLM-5.2/5.3 distill (12k)

12,487 completed reasoning traces on research-level mathematics questions extracted from arXiv papers. For details, see this paper.

This dataset is a further extension of the work.

Columns

column	meaning
`paper_url`	source arXiv paper
`signal_type`	how the question was identified: `open_problem`, `natural_extension`, `limitation`, `conjecture`, `announced_forthcoming`
`source_quote`	the passage in the paper the question was derived from
`question`	the refined, self-contained question
`reasoning`	full chain-of-thought (the `<think>` block)
`response`	the final answer after `</think>`
`model`	which model generated the trace

Generation

model	precision	max tokens	rows
`zai-org/GLM-5.3-Flash`	FP8	128k	5,101
`nvidia/GLM-5.2-NVFP4`	NVFP4	64k	4,801
`LibertAIDAI/GLM-5.3-Flash-NVFP4`	NVFP4	128k	2,585

Served with SGLang (tp=8, ep=8) on 8x H200 and 8x H100. GLM-5.3 runs used reasoning_effort=high, temperature=1.0, top_p=0.95; the GLM-5.2 run used temperature=0.6 and predates that control.

All runs share one prompt, instructing the model to solve the exact question as posed, to build an explicit construction, not to answer "this is open", and never to cite journal/volume/year/pages.

Collaborations

I'm interested in creating larger datasets to train open models for research-level math. If you are interested let me know. (guijin.son@snu.ac.kr)

Citation

If you use this dataset, please cite the paper:

@article{son2026researchmath,
  title={ResearchMath-14K: Scaling Research-Level Mathematics via Agents},
  author={Son, Guijin and Yi, Seungyeop and Gwak, Minju and Ko, Hyunwoo and Jang, Wongi and Yu, Youngjae},
  journal={arXiv preprint arXiv:2605.28003},
  year={2026}
}

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Paper for amphora/researchmath-glm5_23-distill-12k

ResearchMath-14K: Scaling Research-Level Mathematics via Agents

Paper • 2605.28003 • Published May 27 • 47