name string | instruction string | description string | keywords list | schema_version string | config unknown | metadata unknown | files list | location string |
|---|---|---|---|---|---|---|---|---|
arxivmath-training/arxivmath-1003-1267 | Consider the triangulated category of Artin-Tate motives over a number ring $S$. After constructing a motivic $t$-structure on this category, one obtains the abelian category of mixed Artin-Tate motives as its heart. What is the cohomological dimension of this abelian category of mixed Artin-Tate motives?
Give the exa... | short_form/am_1003_1267 | [
"arxivmath-training",
"short_form",
"am_1003_1267"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1003-1267",
"version": "0.1.0",
"description": "short_form/am_1003_1267",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1003_1267"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1003_1267",
"problem_key": "am_1003_1267",
"tier": "research",
"level": "research",
"source": "arXiv:1003.1267",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1003-1267 |
arxivmath-training/arxivmath-1003-4999-inst | Let $M=(F=0)$ define a germ of an irreducible real analytic Levi-flat hypersurface at $0\in\mathbb{C}^{2}$. Here $F: (\mathbb{C}^2, 0) \rightarrow (\mathbb{R}, 0)$ is a germ of an irreducible real analytic function such that $F(z)=\mathcal{R}e(P(z)) + \text{h.o.t.}$, and $P(z_1,z_2)$ is a homogeneous polynomial of degr... | short_form/am_1003_4999 | [
"arxivmath-training",
"short_form",
"am_1003_4999"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1003-4999-inst",
"version": "0.1.0",
"description": "short_form/am_1003_4999",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1003_4999"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1003_4999",
"problem_key": "am_1003_4999",
"tier": "research",
"level": "research",
"source": "arXiv:1003.4999",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1003-4999-inst |
arxivmath-training/arxivmath-1005-1988 | Consider the two-species totally asymmetric diffusion model on a ring, formulated with a Hamiltonian that possesses $U_q(SU(3))$ symmetry. What is the exact value of the dynamical critical exponent of this model, as determined from the finite-size scaling properties of the eigenvalue with the smallest real part?
Give ... | short_form/am_1005_1988 | [
"arxivmath-training",
"short_form",
"am_1005_1988"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1005-1988",
"version": "0.1.0",
"description": "short_form/am_1005_1988",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1005_1988"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1005_1988",
"problem_key": "am_1005_1988",
"tier": "research",
"level": "research",
"source": "arXiv:1005.1988",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_rat... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1005-1988 |
arxivmath-training/arxivmath-1005-2061 | Consider a mobile communication system utilizing cooperative diversity protocols (such as variable-gain amplify-and-forward, decode-and-forward, or selection decode-and-forward relaying) over slow Rayleigh fading channels. At asymptotically high signal-to-noise ratio (SNR), the average capacity outage duration (AOD) de... | short_form/am_1005_2061 | [
"arxivmath-training",
"short_form",
"am_1005_2061"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1005-2061",
"version": "0.1.0",
"description": "short_form/am_1005_2061",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1005_2061"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1005_2061",
"problem_key": "am_1005_2061",
"tier": "research",
"level": "research",
"source": "arXiv:1005.2061",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_rational"... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1005-2061 |
arxivmath-training/arxivmath-1006-2493 | Let $G$ be a connected planar simple graph with at least two vertices. Let $\operatorname{diam}(G)$ denote the diameter of $G$, and let $r(G) = \sum_{v \in V(G)} \frac{1}{\deg(v)}$ denote the inverse degree of $G$. What is the supremum of the ratio $\frac{\operatorname{diam}(G)}{r(G)}$ over all such connected planar si... | short_form/am_1006_2493 | [
"arxivmath-training",
"short_form",
"am_1006_2493"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1006-2493",
"version": "0.1.0",
"description": "short_form/am_1006_2493",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1006_2493"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1006_2493",
"problem_key": "am_1006_2493",
"tier": "research",
"level": "research",
"source": "arXiv:1006.2493",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_rational"... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1006-2493 |
arxivmath-training/arxivmath-1007-3827-inst | Let $E$ be an elementary abelian $5$-group of rank $r$ and let $k$ be a field of characteristic $5$. Let $F_1$ be the standard functor from finitely generated $kE$-modules of constant Jordan type to vector bundles over the projective space $\mathbb{P}^{r-1}$. If $M$ is any $kE$-module of stable constant Jordan type $[1... | short_form/am_1007_3827 | [
"arxivmath-training",
"short_form",
"am_1007_3827"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1007-3827-inst",
"version": "0.1.0",
"description": "short_form/am_1007_3827",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1007_3827"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1007_3827",
"problem_key": "am_1007_3827",
"tier": "research",
"level": "research",
"source": "arXiv:1007.3827",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1007-3827-inst |
arxivmath-training/arxivmath-1009-2375-inst | Let $X$ be a set with $|X| = 10$. Define the shadow of a pair $(S_1, S_2) \in \binom{X}{3}^2$ (each $S_i$ a 3-element subset of $X$) as the set of all pairs $(S_1', S_2') \in \binom{X}{2}^2$ such that $S_i' \subset S_i$ for $i=1,2$. For a family $\mathcal{F} \subseteq \binom{X}{3}^2$, its shadow $\partial \mathcal{F}$ ... | short_form/am_1009_2375 | [
"arxivmath-training",
"short_form",
"am_1009_2375"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1009-2375-inst",
"version": "0.1.0",
"description": "short_form/am_1009_2375",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1009_2375"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1009_2375",
"problem_key": "am_1009_2375",
"tier": "research",
"level": "research",
"source": "arXiv:1009.2375",
"source_license": "public-domain",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_i... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1009-2375-inst |
arxivmath-training/arxivmath-1010-2014-inst | Consider a one-dimensional random walk on the integers, starting at the origin. At each time step the walker independently moves one unit to the left with probability $l=\tfrac{1}{5}$, moves one unit to the right with probability $r=\tfrac{1}{2}$, or remains at its current position with probability $o=\tfrac{3}{10}$. T... | short_form/am_1010_2014 | [
"arxivmath-training",
"short_form",
"am_1010_2014"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1010-2014-inst",
"version": "0.1.0",
"description": "short_form/am_1010_2014",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1010_2014"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1010_2014",
"problem_key": "am_1010_2014",
"tier": "research",
"level": "research",
"source": "arXiv:1010.2014",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_ratio... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1010-2014-inst |
arxivmath-training/arxivmath-1010-3032 | Consider the quantum maximally superintegrable system on the 3-sphere with a generic 4-parameter potential. The symmetry operators for this system form a closed quadratic algebra. What is the exact number of algebraically independent generators in this algebra?
Give the exact answer as an integer, e.g. "12" or "-1".
A... | short_form/am_1010_3032 | [
"arxivmath-training",
"short_form",
"am_1010_3032"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1010-3032",
"version": "0.1.0",
"description": "short_form/am_1010_3032",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1010_3032"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1010_3032",
"problem_key": "am_1010_3032",
"tier": "research",
"level": "research",
"source": "arXiv:1010.3032",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_int... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1010-3032 |
arxivmath-training/arxivmath-1011-0620-inst | The rainbow connection number $rc(G)$ of a connected graph $G$ is the minimum number of colours needed to colour its edges such that every pair of its vertices is connected by at least one path in which no two edges are coloured the same. Let $\mathcal{G}_3$ be the set of all bridgeless connected graphs with radius $3$... | short_form/am_1011_0620 | [
"arxivmath-training",
"short_form",
"am_1011_0620"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1011-0620-inst",
"version": "0.1.0",
"description": "short_form/am_1011_0620",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1011_0620"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1011_0620",
"problem_key": "am_1011_0620",
"tier": "research",
"level": "research",
"source": "arXiv:1011.0620",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1011-0620-inst |
arxivmath-training/arxivmath-1011-6195 | A prudent walk on the square lattice is a self-avoiding walk that never takes a step towards an already occupied site. Prudent polygons are prudent walks that return to a point adjacent to their starting point. In the asymptotic expansion of the number of 3-sided prudent polygons of area $n$ as $n \to \infty$, the ampl... | short_form/am_1011_6195 | [
"arxivmath-training",
"short_form",
"am_1011_6195"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1011-6195",
"version": "0.1.0",
"description": "short_form/am_1011_6195",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1011_6195"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1011_6195",
"problem_key": "am_1011_6195",
"tier": "research",
"level": "research",
"source": "arXiv:1011.6195",
"source_license": "CC-BY-NC-ND-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "canonicalized",
"tags": [
"known_answer",
"answe... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1011-6195 |
arxivmath-training/arxivmath-1101-1410 | Consider a discrete-time interacting urn model with partial memory sharing among $U \ge 2$ urns. At each time step, for each urn, a white or black ball is drawn either from all the urns combined (with probability $p$) or from the urn alone (with probability $1-p$), and a new ball of the drawn color is added to this urn... | short_form/am_1101_1410 | [
"arxivmath-training",
"short_form",
"am_1101_1410"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1101-1410",
"version": "0.1.0",
"description": "short_form/am_1101_1410",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1101_1410"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1101_1410",
"problem_key": "am_1101_1410",
"tier": "research",
"level": "research",
"source": "arXiv:1101.1410",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_rat... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1101-1410 |
arxivmath-training/arxivmath-1103-3545-inst | Let $\mathfrak{g}$ be the complex exceptional simple Lie algebra of type $G_2$, which has dimension $14$. The algebra $\mathfrak{g}$ acts naturally on its exterior algebra $\bigwedge \mathfrak{g}$ via the extension of the adjoint representation. Let $C$ be the standard Casimir operator of $\mathfrak{g}$ associated to t... | short_form/am_1103_3545 | [
"arxivmath-training",
"short_form",
"am_1103_3545"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1103-3545-inst",
"version": "0.1.0",
"description": "short_form/am_1103_3545",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1103_3545"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1103_3545",
"problem_key": "am_1103_3545",
"tier": "research",
"level": "research",
"source": "arXiv:1103.3545",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1103-3545-inst |
arxivmath-training/arxivmath-1103-4242 | Let $k$ be the smallest positive integer such that every finite-dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 can be generated by $k$ elements. What is the value of $k$?
Give the exact answer as an integer, e.g. "12" or "-1".
Answer format: {"answer": "<your answer>"}
Writ... | short_form/am_1103_4242 | [
"arxivmath-training",
"short_form",
"am_1103_4242"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1103-4242",
"version": "0.1.0",
"description": "short_form/am_1103_4242",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1103_4242"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1103_4242",
"problem_key": "am_1103_4242",
"tier": "research",
"level": "research",
"source": "arXiv:1103.4242",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1103-4242 |
arxivmath-training/arxivmath-1103-4431-inst | What is the complex dimension of the moduli space of rank $2$ mathematical instanton bundles on $\mathbb{CP}^3$ with charge $c_2 = 4$?
Give the exact answer as an integer, e.g. "12" or "-1".
Answer format: {"answer": "<your answer>"}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also... | short_form/am_1103_4431 | [
"arxivmath-training",
"short_form",
"am_1103_4431"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1103-4431-inst",
"version": "0.1.0",
"description": "short_form/am_1103_4431",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1103_4431"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1103_4431",
"problem_key": "am_1103_4431",
"tier": "research",
"level": "research",
"source": "arXiv:1103.4431",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1103-4431-inst |
arxivmath-training/arxivmath-1106-2844-inst | Let $\Omega_n$ denote the set of doubly-stochastic $n \times n$ matrices. For $A \in \Omega_n$, define $F(A) = \prod_{1 \leq i,j \leq n} (1- A(i,j))^{1- A(i,j)}$, with the convention $0^0=1$. It is known that $\frac{\text{per}(A)}{F(A)} \geq 1$ for all $A \in \Omega_n$. Take $n=10$ and let $A \in \Omega_{10}$ be the bl... | short_form/am_1106_2844 | [
"arxivmath-training",
"short_form",
"am_1106_2844"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1106-2844-inst",
"version": "0.1.0",
"description": "short_form/am_1106_2844",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1106_2844"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1106_2844",
"problem_key": "am_1106_2844",
"tier": "research",
"level": "research",
"source": "arXiv:1106.2844",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1106-2844-inst |
arxivmath-training/arxivmath-1108-3368 | A generalized Braikenridge-Maclaurin construction produces algebraic plane curves of degree $d$ as follows: consider a line $L$ and $2(d+1)$ additional lines that meet $L$ in $d+1$ triple points. The $2(d+1)$ lines are partitioned into a set of $d+1$ 'red' lines and $d+1$ 'blue' lines such that each of the $d+1$ triple... | short_form/am_1108_3368 | [
"arxivmath-training",
"short_form",
"am_1108_3368"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1108-3368",
"version": "0.1.0",
"description": "short_form/am_1108_3368",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1108_3368"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1108_3368",
"problem_key": "am_1108_3368",
"tier": "research",
"level": "research",
"source": "arXiv:1108.3368",
"source_license": "public-domain",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1108-3368 |
arxivmath-training/arxivmath-1108-6127-inst | Let $M$ be a compact $4$-manifold equipped with a Randers metric $F$ of constant flag curvature. Let $p(M,F)$ denote the projective algebra of $(M,F)$, which consists of all projective vector fields on $M$. It is proven that the dimension of $p(M,F)$ either equals exactly $24$ or is at most a certain value $B$ (the sha... | short_form/am_1108_6127 | [
"arxivmath-training",
"short_form",
"am_1108_6127"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1108-6127-inst",
"version": "0.1.0",
"description": "short_form/am_1108_6127",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1108_6127"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1108_6127",
"problem_key": "am_1108_6127",
"tier": "research",
"level": "research",
"source": "arXiv:1108.6127",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1108-6127-inst |
arxivmath-training/arxivmath-1110-1161-inst | An edge-coloring of a graph $G$ with colors $1, 2, \dots, t$ is called an interval $t$-coloring if all colors are used, and the colors of the edges incident to any vertex of $G$ are distinct and form an interval of integers. Consider all connected cubic simple graphs $G$ on exactly $6$ vertices that admit an interval $... | short_form/am_1110_1161 | [
"arxivmath-training",
"short_form",
"am_1110_1161"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1110-1161-inst",
"version": "0.1.0",
"description": "short_form/am_1110_1161",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1110_1161"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1110_1161",
"problem_key": "am_1110_1161",
"tier": "research",
"level": "research",
"source": "arXiv:1110.1161",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1110-1161-inst |
arxivmath-training/arxivmath-1111-0986-inst | Call a permutation $\pi=\pi_1\pi_2\cdots\pi_n$ of $\{1,2,\ldots,n\}$ alternating (up-down) if $\pi_1 < \pi_2 > \pi_3 < \pi_4 > \cdots$. Count the alternating permutations of $\{1,2,\ldots,10\}$ that contain the classical permutation pattern $123$ exactly once. A $123$ pattern is a subsequence $\pi_i<\pi_j<\pi_k$ with $... | short_form/am_1111_0986 | [
"arxivmath-training",
"short_form",
"am_1111_0986"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1111-0986-inst",
"version": "0.1.0",
"description": "short_form/am_1111_0986",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1111_0986"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1111_0986",
"problem_key": "am_1111_0986",
"tier": "research",
"level": "research",
"source": "arXiv:1111.0986",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1111-0986-inst |
arxivmath-training/arxivmath-1202-0023-inst | An edge-coloring of a graph $G$ with colors $1,\dots,t$ is called an interval $t$-coloring if all $t$ colors are used, and the colors of the edges incident to each vertex of $G$ are distinct and form an interval of integers. Let $Q_5$ denote the $5$-dimensional cube graph (vertices are binary strings of length 5, adjac... | short_form/am_1202_0023 | [
"arxivmath-training",
"short_form",
"am_1202_0023"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1202-0023-inst",
"version": "0.1.0",
"description": "short_form/am_1202_0023",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1202_0023"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1202_0023",
"problem_key": "am_1202_0023",
"tier": "research",
"level": "research",
"source": "arXiv:1202.0023",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1202-0023-inst |
arxivmath-training/arxivmath-1202-3513-inst | Let $A$ be a local ring of characteristic $p$ with Krull dimension $7$. Let $M$ be a finitely generated $A$-module of dimension $3$ and finite projective dimension. It has been proven that there exists a system of parameters $\underline{x} = (x_1, x_2, x_3)$ for $M$, which is part of a system of parameters for $A$, wit... | short_form/am_1202_3513 | [
"arxivmath-training",
"short_form",
"am_1202_3513"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1202-3513-inst",
"version": "0.1.0",
"description": "short_form/am_1202_3513",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1202_3513"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1202_3513",
"problem_key": "am_1202_3513",
"tier": "research",
"level": "research",
"source": "arXiv:1202.3513",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1202-3513-inst |
arxivmath-training/arxivmath-1203-4653-inst | A down-up alternating permutation of length $k$ is a permutation $\pi = \pi_1 \pi_2 \dots \pi_k$ of $\{1, 2, \dots, k\}$ such that $\pi_1 > \pi_2 < \pi_3 > \pi_4 < \dots$. A permutation avoids the pattern $4123$ if it contains no four entries $\pi_a, \pi_b, \pi_c, \pi_d$ with $a<b<c<d$ and $\pi_b < \pi_c < \pi_d < \pi_... | short_form/am_1203_4653 | [
"arxivmath-training",
"short_form",
"am_1203_4653"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1203-4653-inst",
"version": "0.1.0",
"description": "short_form/am_1203_4653",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1203_4653"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1203_4653",
"problem_key": "am_1203_4653",
"tier": "research",
"level": "research",
"source": "arXiv:1203.4653",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1203-4653-inst |
arxivmath-training/arxivmath-1207-5306 | Consider the Cauchy problem for the semilinear wave equation $\Box u(t,x) = u(t,x) u_{t}(t,x)^{2} + u(t,x)^{4}$ in two space dimensions ($x\in \mathbb{R}^{2}$), with initial data $u(0,x) = 0$ and $u_t(0,x) = \varepsilon g(x)$, where $g \in C_0^\infty(\mathbb{R}^2)$ is a non-negative, compactly supported radial function... | short_form/am_1207_5306 | [
"arxivmath-training",
"short_form",
"am_1207_5306"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1207-5306",
"version": "0.1.0",
"description": "short_form/am_1207_5306",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1207_5306"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1207_5306",
"problem_key": "am_1207_5306",
"tier": "research",
"level": "research",
"source": "arXiv:1207.5306",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1207-5306 |
arxivmath-training/arxivmath-1207-5329 | It has been proven that any graph that excludes the Kuratowski graphs $K_5$ and $K_{3,3}$ as immersions can be constructed by applying consecutive $i$-edge-sums, for $i \leq 3$, starting from graphs that are either planar sub-cubic or have branch-width at most $c$. What is the exact value of the integer constant $c$ es... | short_form/am_1207_5329 | [
"arxivmath-training",
"short_form",
"am_1207_5329"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1207-5329",
"version": "0.1.0",
"description": "short_form/am_1207_5329",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1207_5329"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1207_5329",
"problem_key": "am_1207_5329",
"tier": "research",
"level": "research",
"source": "arXiv:1207.5329",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_int... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1207-5329 |
arxivmath-training/arxivmath-1208-1915 | A sequence $x=x_1 x_2\dots x_n$ is said to be an ascent sequence of length $n$ if it satisfies $x_1=0$ and $0\leq x_i\leq \operatorname{asc}(x_1x_2\dots x_{i-1})+1$ for all $2\leq i\leq n$, where $\operatorname{asc}(x_1x_2\dots x_{i-1})$ is the number of ascents in the sequence $x_1x_2\dots x_{i-1}$. It has been proven... | short_form/am_1208_1915 | [
"arxivmath-training",
"short_form",
"am_1208_1915"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1208-1915",
"version": "0.1.0",
"description": "short_form/am_1208_1915",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1208_1915"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1208_1915",
"problem_key": "am_1208_1915",
"tier": "research",
"level": "research",
"source": "arXiv:1208.1915",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1208-1915 |
arxivmath-training/arxivmath-1208-2337-inst | Let $Q_n(x)$ denote the $n$-th Yablonskii-Vorob'ev polynomial, defined by the recurrence $Q_{n+1}(x)Q_{n-1}(x) = xQ_n(x)^2 - 4\left(Q_n(x)Q_n''(x) - (Q_n'(x))^2\right)$ with $Q_0(x) = 1$ and $Q_1(x) = x$. How many distinct real roots does $Q_{11}(x)$ have?
Give the exact answer as an integer, e.g. "12" or "-1".
Answer... | short_form/am_1208_2337 | [
"arxivmath-training",
"short_form",
"am_1208_2337"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1208-2337-inst",
"version": "0.1.0",
"description": "short_form/am_1208_2337",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1208_2337"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1208_2337",
"problem_key": "am_1208_2337",
"tier": "research",
"level": "research",
"source": "arXiv:1208.2337",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1208-2337-inst |
arxivmath-training/arxivmath-1210-5318 | Let $V_n$ denote the ${\rm SL}_2(\mathbb{C})$-module of complex binary forms of degree $n$. Consider the direct sum representation $V = V_1 \oplus V_3 \oplus V_4$. What is the minimum number of generators of the invariant algebra $R = \mathbb{C}[V]^{{\rm SL}_2(\mathbb{C})}$ (the algebra of polynomial functions on $V$ i... | short_form/am_1210_5318 | [
"arxivmath-training",
"short_form",
"am_1210_5318"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1210-5318",
"version": "0.1.0",
"description": "short_form/am_1210_5318",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1210_5318"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1210_5318",
"problem_key": "am_1210_5318",
"tier": "research",
"level": "research",
"source": "arXiv:1210.5318",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_int... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1210-5318 |
arxivmath-training/arxivmath-1210-7363-inst | Consider the power-of-mean curvature flow for surfaces in $\mathbb{R}^3$, where a surface evolves in its normal direction with speed equal to $H^\alpha$, with $H$ the mean curvature and $\alpha = 2$. Let $z = u(x)$ for $x \in \mathbb{R}^2$ be an entire convex translating solution that translates in the positive $z$-dir... | short_form/am_1210_7363 | [
"arxivmath-training",
"short_form",
"am_1210_7363"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1210-7363-inst",
"version": "0.1.0",
"description": "short_form/am_1210_7363",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1210_7363"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1210_7363",
"problem_key": "am_1210_7363",
"tier": "research",
"level": "research",
"source": "arXiv:1210.7363",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_expre... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1210-7363-inst |
arxivmath-training/arxivmath-1211-2188 | For what integer $n$ is there a sporadic point on the modular curve $X_1(n)$ of degree $3$ (the lowest possible degree of a sporadic point on any modular curve $X_1(m)$) that arises from a rational elliptic curve over a cubic field having torsion subgroup isomorphic to $\mathbb{Z}/n\mathbb{Z}$?
Give the exact answer a... | short_form/am_1211_2188 | [
"arxivmath-training",
"short_form",
"am_1211_2188"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1211-2188",
"version": "0.1.0",
"description": "short_form/am_1211_2188",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1211_2188"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1211_2188",
"problem_key": "am_1211_2188",
"tier": "research",
"level": "research",
"source": "arXiv:1211.2188",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1211-2188 |
arxivmath-training/arxivmath-1212-6347-inst | Let $B$ be a bi-fractional Brownian motion with indices $H=\tfrac{2}{3}$ and $K=\tfrac{3}{4}$, so that $2HK=1$. Let $\mathscr{L}(x,t)$ be its local time process. For functions $f$ in a suitable Banach space of measurable functions, the quadratic covariation $[f(B),B]_t$ exists and satisfies a Bouleau-Yor type identity ... | short_form/am_1212_6347 | [
"arxivmath-training",
"short_form",
"am_1212_6347"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1212-6347-inst",
"version": "0.1.0",
"description": "short_form/am_1212_6347",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1212_6347"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1212_6347",
"problem_key": "am_1212_6347",
"tier": "research",
"level": "research",
"source": "arXiv:1212.6347",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1212-6347-inst |
arxivmath-training/arxivmath-1301-6349 | Up to isomorphism, how many nilpotent Jordan algebras of dimension 4 exist over an algebraically closed field of characteristic not 2?
Give the exact answer as an integer, e.g. "12" or "-1".
Answer format: {"answer": "<your answer>"}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also... | short_form/am_1301_6349 | [
"arxivmath-training",
"short_form",
"am_1301_6349"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1301-6349",
"version": "0.1.0",
"description": "short_form/am_1301_6349",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1301_6349"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1301_6349",
"problem_key": "am_1301_6349",
"tier": "research",
"level": "research",
"source": "arXiv:1301.6349",
"source_license": "public-domain",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1301-6349 |
arxivmath-training/arxivmath-1302-1236 | In compressed sensing, consider the recovery of a $k$-sparse signal $eta \in \mathbb{R}^p$ (where $2 \le k \le p/2$) from exact linear measurements $y = A\beta$ via constrained $\ell_1$ minimization. Let $\delta_k^A$ denote the restricted isometry constant of the measurement matrix $A$ of order $k$. What is the exact ... | short_form/am_1302_1236 | [
"arxivmath-training",
"short_form",
"am_1302_1236"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1302-1236",
"version": "0.1.0",
"description": "short_form/am_1302_1236",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1302_1236"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1302_1236",
"problem_key": "am_1302_1236",
"tier": "research",
"level": "research",
"source": "arXiv:1302.1236",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_rat... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1302-1236 |
arxivmath-training/arxivmath-1302-4618-inst | Consider phase retrieval over the complex vector space $\mathbb{C}^3$ (so $M=3$). We want to recover every signal $x\in\mathbb{C}^3$ uniquely, up to a global phase factor, from magnitude-only measurements $|\langle x, \varphi_n\rangle|$, $n=1,\dots,N$. The map $x \mapsto (|\langle x,\varphi_n\rangle|)_{n=1}^N$ is requi... | short_form/am_1302_4618 | [
"arxivmath-training",
"short_form",
"am_1302_4618"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1302-4618-inst",
"version": "0.1.0",
"description": "short_form/am_1302_4618",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1302_4618"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1302_4618",
"problem_key": "am_1302_4618",
"tier": "research",
"level": "research",
"source": "arXiv:1302.4618",
"source_license": "public-domain",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_i... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1302-4618-inst |
arxivmath-training/arxivmath-1302-7084 | Consider the well-posedness and ill-posedness of the 3D incompressible Navier-Stokes equations in the critical Triebel-Lizorkin spaces $\dot{F}^{-1,q}_{\infty}(\mathbb{R}^3)$. There exists a critical threshold $q_c$ such that the equations are well-posed for $q = q_c$ but ill-posed for all $q > q_c$ (in the sense that ... | short_form/am_1302_7084 | [
"arxivmath-training",
"short_form",
"am_1302_7084"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1302-7084",
"version": "0.1.0",
"description": "short_form/am_1302_7084",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1302_7084"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1302_7084",
"problem_key": "am_1302_7084",
"tier": "research",
"level": "research",
"source": "arXiv:1302.7084",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_int... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1302-7084 |
arxivmath-training/arxivmath-1303-1039 | An edge-coloring of a graph $G$ with colors $1,\ldots,t$ is called an interval $t$-coloring if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of integers. For an interval colorable graph $G$, the least value of $t$ for which $G$ has an interval $t$-coloring ... | short_form/am_1303_1039 | [
"arxivmath-training",
"short_form",
"am_1303_1039"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1303-1039",
"version": "0.1.0",
"description": "short_form/am_1303_1039",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1303_1039"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1303_1039",
"problem_key": "am_1303_1039",
"tier": "research",
"level": "research",
"source": "arXiv:1303.1039",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1303-1039 |
arxivmath-training/arxivmath-1303-5965 | A matchstick graph is a graph that can be drawn in the Euclidean plane with non-crossing straight-line edges of unit length. Up to abstract graph isomorphism, how many connected matchstick graphs are there with exactly 9 edges?
Give the exact answer as an integer, e.g. "12" or "-1".
Answer format: {"answer": "<your an... | short_form/am_1303_5965 | [
"arxivmath-training",
"short_form",
"am_1303_5965"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1303-5965",
"version": "0.1.0",
"description": "short_form/am_1303_5965",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1303_5965"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1303_5965",
"problem_key": "am_1303_5965",
"tier": "research",
"level": "research",
"source": "arXiv:1303.5965",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1303-5965 |
arxivmath-training/arxivmath-1304-2506-inst | Let $A_0, A_1, A_2$ be generic $3 \times 3$ matrices over $\mathbb{Q}$, that is, their entries are independent indeterminates. Let $K=\mathbb{Q}(E)$, where $E$ is the set of all entries of $A_0, A_1, A_2$, and let $\overline{K}$ be the algebraic closure of $K$. What is the number of solutions $X\in\mathcal{M}_3(\overli... | short_form/am_1304_2506 | [
"arxivmath-training",
"short_form",
"am_1304_2506"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1304-2506-inst",
"version": "0.1.0",
"description": "short_form/am_1304_2506",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1304_2506"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1304_2506",
"problem_key": "am_1304_2506",
"tier": "research",
"level": "research",
"source": "arXiv:1304.2506",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1304-2506-inst |
arxivmath-training/arxivmath-1306-1154-inst | In compressed sensing, exact recovery of all $k$-sparse signals in the noiseless case can be achieved via constrained $\ell_1$ minimization under certain conditions on the restricted isometry constant (RIC) of the measurement matrix. Let $\delta_{3k}$ denote the RIC of order $3k$. It is known that there is a constant $... | short_form/am_1306_1154 | [
"arxivmath-training",
"short_form",
"am_1306_1154"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1306-1154-inst",
"version": "0.1.0",
"description": "short_form/am_1306_1154",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1306_1154"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1306_1154",
"problem_key": "am_1306_1154",
"tier": "research",
"level": "research",
"source": "arXiv:1306.1154",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_expre... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1306-1154-inst |
arxivmath-training/arxivmath-1307-7176-inst | In phase retrieval, consider complex signals $x \in \mathbb{C}^M$ with $M = 3$, measured through intensity measurements $|\langle x, \varphi_n \rangle|^2$, $n = 1, \dots, N$. A measurement ensemble is called injective if these intensities determine $x$ up to a global phase factor. An explicit ensemble has been construc... | short_form/am_1307_7176 | [
"arxivmath-training",
"short_form",
"am_1307_7176"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1307-7176-inst",
"version": "0.1.0",
"description": "short_form/am_1307_7176",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1307_7176"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1307_7176",
"problem_key": "am_1307_7176",
"tier": "research",
"level": "research",
"source": "arXiv:1307.7176",
"source_license": "public-domain",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_i... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1307-7176-inst |
arxivmath-training/arxivmath-1308-0741-inst | Let $A$ be a finite set of integers with $|A| = 10$ such that $|A+A| = 27$ (that is, $|A+A| = 3|A|-3$). A detailed structure theorem for sets with $|A+A| = 3|A|-3$ states that $A$ must fall into one of several structural categories. Either $A$ is a bi-arithmetic progression, or $A$ is Freiman isomorphic to certain high... | short_form/am_1308_0741 | [
"arxivmath-training",
"short_form",
"am_1308_0741"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1308-0741-inst",
"version": "0.1.0",
"description": "short_form/am_1308_0741",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1308_0741"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1308_0741",
"problem_key": "am_1308_0741",
"tier": "research",
"level": "research",
"source": "arXiv:1308.0741",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1308-0741-inst |
arxivmath-training/arxivmath-1308-3665 | Assuming $\text{NP} \not\subseteq \text{coNP/poly}$, no polynomial-time algorithm can reduce an arbitrary $n$-vertex instance of the Treewidth problem to an equivalent instance of any problem with bit size $\mathcal{O}(n^{c-\epsilon})$ for any $\epsilon > 0$. What is the largest integer $c$ for which this impossibility... | short_form/am_1308_3665 | [
"arxivmath-training",
"short_form",
"am_1308_3665"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1308-3665",
"version": "0.1.0",
"description": "short_form/am_1308_3665",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1308_3665"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1308_3665",
"problem_key": "am_1308_3665",
"tier": "research",
"level": "research",
"source": "arXiv:1308.3665",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1308-3665 |
arxivmath-training/arxivmath-1308-3754-inst | Given a polynomial $f \in \mathbb{Z}[x]$ and a positive integer $n$, the discriminator $D_f(n)$ is defined as the smallest positive integer $m$ such that the values $f(1), f(2), \ldots, f(n)$ are pairwise distinct modulo $m$. Consider the polynomial $f(x) = x(2^2 x - 1) = 4x^2 - x$. What is the exact value of $D_f(20)$... | short_form/am_1308_3754 | [
"arxivmath-training",
"short_form",
"am_1308_3754"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1308-3754-inst",
"version": "0.1.0",
"description": "short_form/am_1308_3754",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1308_3754"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1308_3754",
"problem_key": "am_1308_3754",
"tier": "research",
"level": "research",
"source": "arXiv:1308.3754",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1308-3754-inst |
arxivmath-training/arxivmath-1308-3771-inst | Consider a strongly asymptotically flat initial data set for the Einstein-Maxwell equations. Assume it satisfies the charged dominant energy condition and has no charged matter outside the outermost apparent horizon. Suppose the total ADM mass is $m = 5$ and the total charge is $q = 3$ (in geometrized units). Let $A = ... | short_form/am_1308_3771 | [
"arxivmath-training",
"short_form",
"am_1308_3771"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1308-3771-inst",
"version": "0.1.0",
"description": "short_form/am_1308_3771",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1308_3771"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1308_3771",
"problem_key": "am_1308_3771",
"tier": "research",
"level": "research",
"source": "arXiv:1308.3771",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1308-3771-inst |
arxivmath-training/arxivmath-1309-2003-inst | Let a network be modeled as a graph where each edge is assigned a distinct real-valued label representing the time of interaction. A temporal path in such a network is a path in which sequential edge labels are strictly increasing. Two such edge-labeled networks with the same underlying graph structure are temporally i... | short_form/am_1309_2003 | [
"arxivmath-training",
"short_form",
"am_1309_2003"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1309-2003-inst",
"version": "0.1.0",
"description": "short_form/am_1309_2003",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1309_2003"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1309_2003",
"problem_key": "am_1309_2003",
"tier": "research",
"level": "research",
"source": "arXiv:1309.2003",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1309-2003-inst |
arxivmath-training/arxivmath-1309-5083-inst | Let $G$ be a connected graph and $S$ be a set of vertices. The $h$-extra connectivity of $G$ is defined as the minimum cardinality of a set $S$ such that $G-S$ is disconnected and each connected component of $G-S$ has at least $h+1$ vertices. What is the $3$-extra connectivity of the $3$-ary $4$-cube network $Q_4^3$ (t... | short_form/am_1309_5083 | [
"arxivmath-training",
"short_form",
"am_1309_5083"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1309-5083-inst",
"version": "0.1.0",
"description": "short_form/am_1309_5083",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1309_5083"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1309_5083",
"problem_key": "am_1309_5083",
"tier": "research",
"level": "research",
"source": "arXiv:1309.5083",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1309-5083-inst |
arxivmath-training/arxivmath-1312-7253 | Consider the Maximum Rainbow Matching problem, which asks for the size of the largest matching whose edges have distinct colors in a given edge-colored graph. The problem exhibits a complexity dichotomy on edge-colored trees based on forbidden path subgraphs: there exists an integer $k$ such that the problem is solvabl... | short_form/am_1312_7253 | [
"arxivmath-training",
"short_form",
"am_1312_7253"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1312-7253",
"version": "0.1.0",
"description": "short_form/am_1312_7253",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1312_7253"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1312_7253",
"problem_key": "am_1312_7253",
"tier": "research",
"level": "research",
"source": "arXiv:1312.7253",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1312-7253 |
arxivmath-training/arxivmath-1403-1530-inst | Let $(-\Delta)^{1/2}$ denote the fractional Laplacian of order $\alpha = 1/2$ in $\mathbb{R}^3$. For $k>0$ and $p \in (0, \tfrac{3}{2})$, let $u_k$ be a nonnegative weak solution to the equation $(-\Delta)^{1/2} u + u^p = k\delta_0$ in $\mathbb{R}^3$ with $\lim_{|x| \to \infty} u_k(x) = 0$, where $\delta_0$ denotes the... | short_form/am_1403_1530 | [
"arxivmath-training",
"short_form",
"am_1403_1530"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1403-1530-inst",
"version": "0.1.0",
"description": "short_form/am_1403_1530",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1403_1530"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1403_1530",
"problem_key": "am_1403_1530",
"tier": "research",
"level": "research",
"source": "arXiv:1403.1530",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_ratio... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1403-1530-inst |
arxivmath-training/arxivmath-1404-1567-inst | Let $m=6$ and $n=5$. Consider the set of all nonnegative primitive tensors of order $m=6$ and dimension $n=5$. What is the maximum possible (primitive) exponent of a tensor in this set?
Give the exact answer as an integer, e.g. "12" or "-1".
Answer format: {"answer": "<your answer>"}
Write your final answer as JSON t... | short_form/am_1404_1567 | [
"arxivmath-training",
"short_form",
"am_1404_1567"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1404-1567-inst",
"version": "0.1.0",
"description": "short_form/am_1404_1567",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1404_1567"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1404_1567",
"problem_key": "am_1404_1567",
"tier": "research",
"level": "research",
"source": "arXiv:1404.1567",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1404-1567-inst |
arxivmath-training/arxivmath-1404-3955 | How many simple objects are there in the Drinfeld center of the fusion category associated with the extended Haagerup subfactor?
Give the exact answer as an integer, e.g. "12" or "-1".
Answer format: {"answer": "<your answer>"}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/... | short_form/am_1404_3955 | [
"arxivmath-training",
"short_form",
"am_1404_3955"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1404-3955",
"version": "0.1.0",
"description": "short_form/am_1404_3955",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1404_3955"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1404_3955",
"problem_key": "am_1404_3955",
"tier": "research",
"level": "research",
"source": "arXiv:1404.3955",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1404-3955 |
arxivmath-training/arxivmath-1406-7017-inst | Let $k=3$ and $t=8$. For any set $W$ of $t=8$ words of length $n$ over a $3$-letter alphabet, let $L(W)$ denote the maximum length of a longest common subsequence between any two distinct words in $W$. Let $f(n,3,8)$ be the minimum of $L(W)$ over all sets $W$ of $8$ words of length $n$ over a $3$-letter alphabet. As $n... | short_form/am_1406_7017 | [
"arxivmath-training",
"short_form",
"am_1406_7017"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1406-7017-inst",
"version": "0.1.0",
"description": "short_form/am_1406_7017",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1406_7017"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1406_7017",
"problem_key": "am_1406_7017",
"tier": "research",
"level": "research",
"source": "arXiv:1406.7017",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1406-7017-inst |
arxivmath-training/arxivmath-1407-3578 | Let $b \ge 2$ be an integer. The Cantor sequence $(c_n)_{n \ge 0}$ is defined such that $c_n = 1$ if the ternary expansion of $n$ contains no digit $1$, and $c_n = 0$ otherwise. Consider the transcendental number $C_b$ defined by its $b$-ary expansion as $C_b = \sum_{n=0}^{\infty} c_n b^{-n}$. What is the exact value o... | short_form/am_1407_3578 | [
"arxivmath-training",
"short_form",
"am_1407_3578"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1407-3578",
"version": "0.1.0",
"description": "short_form/am_1407_3578",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1407_3578"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1407_3578",
"problem_key": "am_1407_3578",
"tier": "research",
"level": "research",
"source": "arXiv:1407.3578",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1407-3578 |
arxivmath-training/arxivmath-1407-4633-inst | Consider the one-dimensional non-Hermitian Hamiltonian $H = p^2 - gx^4 + a/x^2$ and the Hermitian Hamiltonian $h = p^2 + 4gx^4 + bx$. Here $p$ is the momentum operator, $x$ is the position operator, and $a, b, g$ are real parameters. Work in units where the reduced Planck constant is $\hbar = 1$, and take $g = 2$ and $... | short_form/am_1407_4633 | [
"arxivmath-training",
"short_form",
"am_1407_4633"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1407-4633-inst",
"version": "0.1.0",
"description": "short_form/am_1407_4633",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1407_4633"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1407_4633",
"problem_key": "am_1407_4633",
"tier": "research",
"level": "research",
"source": "arXiv:1407.4633",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1407-4633-inst |
arxivmath-training/arxivmath-1407-4778-inst | Tautological relations in the tautological ring of $\overline M_{g,n}$ can be obtained from semisimple cohomological field theories. One can compare the relations coming from the equivariant Gromov-Witten theory of the projective space $\mathbb P^3$ with those coming from $r$-spin structures. It has been shown that the... | short_form/am_1407_4778 | [
"arxivmath-training",
"short_form",
"am_1407_4778"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1407-4778-inst",
"version": "0.1.0",
"description": "short_form/am_1407_4778",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1407_4778"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1407_4778",
"problem_key": "am_1407_4778",
"tier": "research",
"level": "research",
"source": "arXiv:1407.4778",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1407-4778-inst |
arxivmath-training/arxivmath-1407-5751 | Consider the defocusing integrable discrete nonlinear Schrödinger equation. As $t \to \infty$, the solution exhibits different asymptotic regimes depending on the relationship between the spatial lattice variable $n$ and the time $t$. In the transition region near $|n|=2t$, the solution exhibits a decaying oscillation ... | short_form/am_1407_5751 | [
"arxivmath-training",
"short_form",
"am_1407_5751"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1407-5751",
"version": "0.1.0",
"description": "short_form/am_1407_5751",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1407_5751"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1407_5751",
"problem_key": "am_1407_5751",
"tier": "research",
"level": "research",
"source": "arXiv:1407.5751",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_rat... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1407-5751 |
arxivmath-training/arxivmath-1408-2317-inst | A total coloring of a graph $G$ is an assignment of colors to its vertices and edges such that no two adjacent vertices, no two adjacent edges, and no incident vertex and edge share the same color. An interval total $t$-coloring of $G$ is a total coloring of $G$ using colors $1, 2, \dots, t$ such that all $t$ colors ar... | short_form/am_1408_2317 | [
"arxivmath-training",
"short_form",
"am_1408_2317"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1408-2317-inst",
"version": "0.1.0",
"description": "short_form/am_1408_2317",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1408_2317"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1408_2317",
"problem_key": "am_1408_2317",
"tier": "research",
"level": "research",
"source": "arXiv:1408.2317",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1408-2317-inst |
arxivmath-training/arxivmath-1408-3457-inst | Let $E_{4,5}$ denote the set of all possible primitive degrees (also known as exponents) of nonnegative primitive tensors of order $m = 4$ and dimension $n = 5$. What is the cardinality of the set $E_{4,5}$?
Give the exact answer as an integer, e.g. "12" or "-1".
Answer format: {"answer": "<your answer>"}
Write your ... | short_form/am_1408_3457 | [
"arxivmath-training",
"short_form",
"am_1408_3457"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1408-3457-inst",
"version": "0.1.0",
"description": "short_form/am_1408_3457",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1408_3457"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1408_3457",
"problem_key": "am_1408_3457",
"tier": "research",
"level": "research",
"source": "arXiv:1408.3457",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1408-3457-inst |
arxivmath-training/arxivmath-1408-3892 | A known theorem regarding the Morrison-Kawamata cone conjecture for hyperkähler manifolds establishes that if $M$ is a simple holomorphically symplectic manifold (i.e., a simply connected holomorphically symplectic manifold of Kähler type with $h^{2,0}=1$), then the group of holomorphic automorphisms of $M$ acts on the... | short_form/am_1408_3892 | [
"arxivmath-training",
"short_form",
"am_1408_3892"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1408-3892",
"version": "0.1.0",
"description": "short_form/am_1408_3892",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1408_3892"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1408_3892",
"problem_key": "am_1408_3892",
"tier": "research",
"level": "research",
"source": "arXiv:1408.3892",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1408-3892 |
arxivmath-training/arxivmath-1409-2117 | A finite, simple graph of order $n$ is $p$-factor-critical (where $p$ is an integer of the same parity as $n$) if the removal of any set of $p$ vertices results in a graph with a perfect matching. What is the minimum integer $d$ such that every finite, simple, connected, vertex-transitive, non-bipartite graph of even o... | short_form/am_1409_2117 | [
"arxivmath-training",
"short_form",
"am_1409_2117"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1409-2117",
"version": "0.1.0",
"description": "short_form/am_1409_2117",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1409_2117"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1409_2117",
"problem_key": "am_1409_2117",
"tier": "research",
"level": "research",
"source": "arXiv:1409.2117",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_integer",... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1409-2117 |
arxivmath-training/arxivmath-1410-5134 | What is the minimum possible value for the ZL-amenability constant of a finite non-abelian group?
Give the exact answer as an exact rational number, e.g. "3/2".
Answer format: {"answer": "<your answer>"}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. ... | short_form/am_1410_5134 | [
"arxivmath-training",
"short_form",
"am_1410_5134"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1410-5134",
"version": "0.1.0",
"description": "short_form/am_1410_5134",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1410_5134"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1410_5134",
"problem_key": "am_1410_5134",
"tier": "research",
"level": "research",
"source": "arXiv:1410.5134",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_rational"... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1410-5134 |
arxivmath-training/arxivmath-1412-3685-inst | Let $K_{n_1,4}$ be the complete bipartite graph with parts of sizes $n_1$ and $4$. Let $B_k^{(m)}$ denote the poly-Bernoulli numbers, defined by $\sum_{k\ge 0} B_k^{(m)} \frac{x^k}{k!} = \frac{\mathrm{Li}_m(1-e^{-x})}{1-e^{-x}}$, where $\mathrm{Li}_m(z)=\sum_{j\ge1} z^j/j^m$ and $m$ is any integer. It is known that the... | short_form/am_1412_3685 | [
"arxivmath-training",
"short_form",
"am_1412_3685"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1412-3685-inst",
"version": "0.1.0",
"description": "short_form/am_1412_3685",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1412_3685"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1412_3685",
"problem_key": "am_1412_3685",
"tier": "research",
"level": "research",
"source": "arXiv:1412.3685",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integ... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1412-3685-inst |
arxivmath-training/arxivmath-1412-4413 | Let $\alpha \in (0, 1]$ be the supremum of all constants $c$ such that there exists a polynomial-time algorithm approximating the non-commutative Grothendieck problem to within a factor of $c$. Assuming $\textsf{P} \neq \textsf{NP}$, what is the exact value of $\alpha$?
Give the exact answer as an exact rational numbe... | short_form/am_1412_4413 | [
"arxivmath-training",
"short_form",
"am_1412_4413"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1412-4413",
"version": "0.1.0",
"description": "short_form/am_1412_4413",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1412_4413"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1412_4413",
"problem_key": "am_1412_4413",
"tier": "research",
"level": "research",
"source": "arXiv:1412.4413",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_rational"... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1412-4413 |
arxivmath-training/arxivmath-1412-5842-inst | For a directed graph $G$, a directed resolving set is a subset $S \subseteq V(G)$ with the property that every vertex of $G$ is uniquely distinguished by its tuple of directed shortest-path distances to the vertices in $S$. Let $\vec{\mathcal{B}}(3,3)$ denote the directed de Bruijn graph whose vertex set consists of al... | short_form/am_1412_5842 | [
"arxivmath-training",
"short_form",
"am_1412_5842"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1412-5842-inst",
"version": "0.1.0",
"description": "short_form/am_1412_5842",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1412_5842"
]
},
"metadata": ... | {
"subset": "short_form",
"family": "am_1412_5842",
"problem_key": "am_1412_5842",
"tier": "research",
"level": "research",
"source": "arXiv:1412.5842",
"source_license": "CC0-1.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_integer... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1412-5842-inst |
arxivmath-training/arxivmath-1501-03380 | Consider a slotted Aloha network operating under the signal-to-interference-plus-noise ratio (SINR) capture model in saturated conditions, where the received SNRs of all nodes' packets are independent and exponentially distributed with an identical mean received SNR. As the mean received SNR grows large, the maximum su... | short_form/am_1501_03380 | [
"arxivmath-training",
"short_form",
"am_1501_03380"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1501-03380",
"version": "0.1.0",
"description": "short_form/am_1501_03380",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1501_03380"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1501_03380",
"problem_key": "am_1501_03380",
"tier": "research",
"level": "research",
"source": "arXiv:1501.03380",
"source_license": "CC-BY-NC-SA-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1501-03380 |
arxivmath-training/arxivmath-1501-04179 | Let $n$ be an odd positive integer that can be expressed as the sum of two fourth powers in two different ways, i.e., $n=u^4+v^4=r^4+s^4$, where $u, v, r, s$ are positive integers such that $\gcd(u,v)=\gcd(r,s)=1$. Let $p$ be a prime. Under the assumption of the parity conjecture, it is proven that the elliptic curve $... | short_form/am_1501_04179 | [
"arxivmath-training",
"short_form",
"am_1501_04179"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1501-04179",
"version": "0.1.0",
"description": "short_form/am_1501_04179",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1501_04179"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1501_04179",
"problem_key": "am_1501_04179",
"tier": "research",
"level": "research",
"source": "arXiv:1501.04179",
"source_license": "CC-BY-NC-SA-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1501-04179 |
arxivmath-training/arxivmath-1501-06242-inst | Let $N = 3$ and $\alpha = \tfrac{3}{4}$. Consider the fractional elliptic boundary value problem
\[
\begin{cases}
(-\Delta)^{3/4} u + u^p = 0 & \text{in } B_1(e_3), \\
u = \delta_0 & \text{in } \mathbb{R}^3 \setminus B_1(e_3),
\end{cases}
\]
where:
- $p>0$;
- $(-\Delta)^{3/4}$ denotes the fractional Laplacian of order ... | short_form/am_1501_06242 | [
"arxivmath-training",
"short_form",
"am_1501_06242"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1501-06242-inst",
"version": "0.1.0",
"description": "short_form/am_1501_06242",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1501_06242"
]
},
"metadata... | {
"subset": "short_form",
"family": "am_1501_06242",
"problem_key": "am_1501_06242",
"tier": "research",
"level": "research",
"source": "arXiv:1501.06242",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_ra... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1501-06242-inst |
arxivmath-training/arxivmath-1503-06070-inst | Let $G$ be a finite abelian group. The Erdős-Ginzburg-Ziv constant $\mathsf{s}(G)$ is the smallest integer $l$ such that every sequence over $G$ of length at least $l$ contains a zero-sum subsequence of length exactly $\exp(G)$, where $\exp(G)$ is the exponent of the group $G$. Let $C_m$ denote the cyclic group of orde... | short_form/am_1503_06070 | [
"arxivmath-training",
"short_form",
"am_1503_06070"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1503-06070-inst",
"version": "0.1.0",
"description": "short_form/am_1503_06070",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1503_06070"
]
},
"metadata... | {
"subset": "short_form",
"family": "am_1503_06070",
"problem_key": "am_1503_06070",
"tier": "research",
"level": "research",
"source": "arXiv:1503.06070",
"source_license": "CC-BY-3.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_in... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1503-06070-inst |
arxivmath-training/arxivmath-1507-08181 | Consider an algebraic variety $X$ in $\mathbb{C}^4$ of degree $d$, such that the polynomials defining $X$ are not all of the form $F(x,y,s,t) = G(x,y)H(x,y,s,t) + K(s,t)L(x,y,s,t)$ where $G$ and $K$ are non-constant polynomials. Let $P$ and $Q$ be finite subsets of $\mathbb{C}^2$, each of size $n$. It has been establis... | short_form/am_1507_08181 | [
"arxivmath-training",
"short_form",
"am_1507_08181"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1507-08181",
"version": "0.1.0",
"description": "short_form/am_1507_08181",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1507_08181"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1507_08181",
"problem_key": "am_1507_08181",
"tier": "research",
"level": "research",
"source": "arXiv:1507.08181",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_ration... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1507-08181 |
arxivmath-training/arxivmath-1509-05836-inst | Let $\Omega \subset \mathbb{R}^3$ be a bounded $C^2$ domain containing the origin and let $\alpha = \tfrac14$. Consider nonnegative classical solutions $u$ to the fractional semi-linear elliptic equation $(-\Delta)^{1/4} u = u^p$ in $\Omega \setminus \{0\}$ (where the fractional Laplacian is defined in the principal va... | short_form/am_1509_05836 | [
"arxivmath-training",
"short_form",
"am_1509_05836"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1509-05836-inst",
"version": "0.1.0",
"description": "short_form/am_1509_05836",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1509_05836"
]
},
"metadata... | {
"subset": "short_form",
"family": "am_1509_05836",
"problem_key": "am_1509_05836",
"tier": "research",
"level": "research",
"source": "arXiv:1509.05836",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_ra... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1509-05836-inst |
arxivmath-training/arxivmath-1509-07406 | Let $p$ be a large prime and $c$ an integer coprime to $p$. The minimum $L_\infty$ distance between two distinct points on the modular hyperbola $xy \equiv c \pmod p$ with coordinates in $\{0, 1, \dots, p-1\}$ is known to be bounded by $p^{1/4 + \epsilon}$ for any $\epsilon > 0$. A further result establishes a dichotom... | short_form/am_1509_07406 | [
"arxivmath-training",
"short_form",
"am_1509_07406"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1509-07406",
"version": "0.1.0",
"description": "short_form/am_1509_07406",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1509_07406"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1509_07406",
"problem_key": "am_1509_07406",
"tier": "research",
"level": "research",
"source": "arXiv:1509.07406",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "canonicalized",
"tags": [
"known_answer",
"answer_e... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1509-07406 |
arxivmath-training/arxivmath-1511-02403 | Let $M$ be a simple hyperkähler manifold. What is the smallest integer $k$ such that any such $M$ with Picard number at least $k$ is guaranteed to admit a nef isotropic line bundle on some hyperkähler birational model of $M$?
Give the exact answer as an integer, e.g. "12" or "-1".
Answer format: {"answer": "<your answ... | short_form/am_1511_02403 | [
"arxivmath-training",
"short_form",
"am_1511_02403"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1511-02403",
"version": "0.1.0",
"description": "short_form/am_1511_02403",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1511_02403"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1511_02403",
"problem_key": "am_1511_02403",
"tier": "research",
"level": "research",
"source": "arXiv:1511.02403",
"source_license": "CC-BY-SA-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_int... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1511-02403 |
arxivmath-training/arxivmath-1601-02381 | Let $S$ be the set of all integers $g \ge 2$ such that the affine cone over a general primitively polarised K3 surface of genus $g$ is smoothable. What is the maximum element of $S$?
Give the exact answer as an integer, e.g. "12" or "-1".
Answer format: {"answer": "<your answer>"}
Write your final answer as JSON to `... | short_form/am_1601_02381 | [
"arxivmath-training",
"short_form",
"am_1601_02381"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1601-02381",
"version": "0.1.0",
"description": "short_form/am_1601_02381",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1601_02381"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1601_02381",
"problem_key": "am_1601_02381",
"tier": "research",
"level": "research",
"source": "arXiv:1601.02381",
"source_license": "CC-BY-SA-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_int... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1601-02381 |
arxivmath-training/arxivmath-1602-03328-inst | Consider an $8$-user ($K=8$) SISO interference channel with blind channel state information at the transmitters (CSIT). Every receiver is equipped with one reconfigurable antenna, and channel values are known only to the receivers. What is the exact sum degrees-of-freedom (DoF) achieved by linear blind interference ali... | short_form/am_1602_03328 | [
"arxivmath-training",
"short_form",
"am_1602_03328"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1602-03328-inst",
"version": "0.1.0",
"description": "short_form/am_1602_03328",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1602_03328"
]
},
"metadata... | {
"subset": "short_form",
"family": "am_1602_03328",
"problem_key": "am_1602_03328",
"tier": "research",
"level": "research",
"source": "arXiv:1602.03328",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_ra... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1602-03328-inst |
arxivmath-training/arxivmath-1603-07175-inst | Consider the singularly perturbed problem $\epsilon^2 \Delta u - V(y)u + u^3 = 0$ with $u>0$ in a bounded two-dimensional domain $\Omega$ with smooth boundary. The problem is subject to the homogeneous Neumann boundary condition $\frac{\partial u}{\partial \nu} = 0$ on $\partial \Omega$. Here $\epsilon>0$ is a small pa... | short_form/am_1603_07175 | [
"arxivmath-training",
"short_form",
"am_1603_07175"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1603-07175-inst",
"version": "0.1.0",
"description": "short_form/am_1603_07175",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1603_07175"
]
},
"metadata... | {
"subset": "short_form",
"family": "am_1603_07175",
"problem_key": "am_1603_07175",
"tier": "research",
"level": "research",
"source": "arXiv:1603.07175",
"source_license": "CC0-1.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_rati... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1603-07175-inst |
arxivmath-training/arxivmath-1605-09777 | Consider a forest structure on the set of all permutations of $\{1, \dots, n\}$ defined as follows: the parent of a permutation (unless its first entry is 1, in which case it is a root) is obtained by taking the first entry of the permutation in one-line notation and inserting it into the position of its own value, shi... | short_form/am_1605_09777 | [
"arxivmath-training",
"short_form",
"am_1605_09777"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1605-09777",
"version": "0.1.0",
"description": "short_form/am_1605_09777",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1605_09777"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1605_09777",
"problem_key": "am_1605_09777",
"tier": "research",
"level": "research",
"source": "arXiv:1605.09777",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_expres... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1605-09777 |
arxivmath-training/arxivmath-1606-02868 | In combinatorics on words, an anti-power of order $k$ is defined as a concatenation of $k$ consecutive pairwise distinct blocks of the same length. What is the smallest integer $k \ge 1$ for which there exists an aperiodic infinite word avoiding anti-powers of order $k$?
Give the exact answer as an integer, e.g. "12" ... | short_form/am_1606_02868 | [
"arxivmath-training",
"short_form",
"am_1606_02868"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1606-02868",
"version": "0.1.0",
"description": "short_form/am_1606_02868",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1606_02868"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1606_02868",
"problem_key": "am_1606_02868",
"tier": "research",
"level": "research",
"source": "arXiv:1606.02868",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_intege... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1606-02868 |
arxivmath-training/arxivmath-1607-04074-inst | Let $D$ be a strongly connected balanced bipartite directed graph of order $2a \geq 8$ that is not a directed cycle. A pair of distinct vertices $\{x,y\}$ in $D$ is called a dominating pair if there exists a vertex $z$ such that there are directed edges $x \to z$ and $y \to z$. Let $d(v)$ denote the total degree (sum o... | short_form/am_1607_04074 | [
"arxivmath-training",
"short_form",
"am_1607_04074"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1607-04074-inst",
"version": "0.1.0",
"description": "short_form/am_1607_04074",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1607_04074"
]
},
"metadata... | {
"subset": "short_form",
"family": "am_1607_04074",
"problem_key": "am_1607_04074",
"tier": "research",
"level": "research",
"source": "arXiv:1607.04074",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_in... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1607-04074-inst |
arxivmath-training/arxivmath-1607-05675-inst | Let $S = \mathbb{Z}_2^8$ and consider the action of the group $G = \mathbb{Z}_2^8$ on $S$ by translation. The $k$-deck of a subset $T \subseteq S$ is the multiset of all subsets of $T$ of size at most $k$, each given up to translation by $G$. The reconstruction number of $T$ is the minimum integer $k$ such that the $k$... | short_form/am_1607_05675 | [
"arxivmath-training",
"short_form",
"am_1607_05675"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1607-05675-inst",
"version": "0.1.0",
"description": "short_form/am_1607_05675",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1607_05675"
]
},
"metadata... | {
"subset": "short_form",
"family": "am_1607_05675",
"problem_key": "am_1607_05675",
"tier": "research",
"level": "research",
"source": "arXiv:1607.05675",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_in... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1607-05675-inst |
arxivmath-training/arxivmath-1607-07636 | Consider a two-player game where the players start with $m$ and $n$ units, respectively. In each round, a winner is decided with probability proportional to each player's current fortune, and the loser's fortune is reduced by one unit. The game ends when one player's fortune reaches zero. Let the initial fortunes be $m... | short_form/am_1607_07636 | [
"arxivmath-training",
"short_form",
"am_1607_07636"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1607-07636",
"version": "0.1.0",
"description": "short_form/am_1607_07636",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1607_07636"
]
},
"metadata": {
... | {
"subset": "short_form",
"family": "am_1607_07636",
"problem_key": "am_1607_07636",
"tier": "research",
"level": "research",
"source": "arXiv:1607.07636",
"source_license": "CC-BY-NC-SA-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "original",
"tags": [
"known_answer",
"answer_... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1607-07636 |
arxivmath-training/arxivmath-1608-00904-inst | A proper $t$-edge-coloring of a graph $G$ is a mapping $\alpha: E(G)\rightarrow \{1,\ldots,t\}$ such that all colors are used, and $\alpha(e)\neq \alpha(e')$ for every pair of adjacent edges $e,e'\in E(G)$. For a proper edge-coloring $\alpha$ and a vertex $v\in V(G)$, the spectrum $S(v,\alpha)$ is the set of colors on ... | short_form/am_1608_00904 | [
"arxivmath-training",
"short_form",
"am_1608_00904"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1608-00904-inst",
"version": "0.1.0",
"description": "short_form/am_1608_00904",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1608_00904"
]
},
"metadata... | {
"subset": "short_form",
"family": "am_1608_00904",
"problem_key": "am_1608_00904",
"tier": "research",
"level": "research",
"source": "arXiv:1608.00904",
"source_license": "CC-BY-4.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_in... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1608-00904-inst |
arxivmath-training/arxivmath-1608-05249-inst | In the study of the Dirac equation in non-extreme Kerr-Newman-AdS spacetime, consider the result that there are no nontrivial Dirac particles in $L^p$ outside and away from the event horizon for every $p$ in a range $\frac{4}{3} < p \leq P$. This holds provided the eigenvalue $\lambda$ satisfies $|\lambda| > q\kappa$, ... | short_form/am_1608_05249 | [
"arxivmath-training",
"short_form",
"am_1608_05249"
] | 1.4 | {
"schema_version": "1.4",
"artifacts": [],
"task": {
"name": "arxivmath-training/arxivmath-1608-05249-inst",
"version": "0.1.0",
"description": "short_form/am_1608_05249",
"authors": [],
"keywords": [
"arxivmath-training",
"short_form",
"am_1608_05249"
]
},
"metadata... | {
"subset": "short_form",
"family": "am_1608_05249",
"problem_key": "am_1608_05249",
"tier": "research",
"level": "research",
"source": "arXiv:1608.05249",
"source_license": "CC0-1.0",
"origin": "MathArena/arxivmath-training",
"rewrite": "instantiated",
"tags": [
"known_answer",
"answer_inte... | [
"environment/Dockerfile",
"environment/instance.json",
"instruction.md",
"solution/solve.sh",
"task.toml",
"tests/check.py",
"tests/instance.json",
"tests/run.py",
"tests/test.sh"
] | tasks/arxivmath-1608-05249-inst |
End of preview. Expand in Data Studio
ArXivMath-Training short-form (Harbor)
Harbor-format short-form RL tasks built from MathArena/arxivmath-training (2,605 research-level questions from arXiv papers), made compatible with the deterministic short-form grader of amphora/arxiv-answer-verifiers-Envs-harbor (exact closed-form numbers only; same tests/check.py, run.py, test.sh, Dockerfile).
All 2,018 checker-compatible tasks. train_1.5k.txt lists the 1,500 used for the JUPITER run rlmath_q35_9b_arxivmath1500_jupiter_v1 (also published as amphora/arxivmath-training-shortform-harbor-1.5k).
| tasks | |
|---|---|
| original (gold already a closed-form number) | 1095 |
| canonicalized (LaTeX closed form re-written as a sympy string; question unchanged) | 66 |
| instantiated (parameter-formula gold; question specialized to concrete parameter values) | 857 |
| total | 2018 |
Answer types: integer 1250, rational 578, closed-form expression 190.
How instantiated tasks were made
For gold answers that are formulas in parameters (e.g. q^{n-1}), anthropic/claude-opus-5.5 chose parameter values satisfying every hypothesis of the question and rewrote the question with those values fixed. The new gold answer was computed by sympy substitution into the parsed original gold formula (never written by an LLM). An independent verifier (openai/gpt-6.1-sol) checked that each rewrite is a faithful, non-degenerate specialization at which the formula holds; rejected and answer-leaking rewrites were dropped. These questions are LLM-generated specializations of the papers' results, not questions from the papers -- filter on rewrite if needed.
Exclusions
Not included: asymptotic answers, answers naming objects (graphs etc.), tuples/sets/intervals, unparseable answers, failed rewrites, and the 2 papers that also appear in our researchmath2 held-out validation set.
Files
tasks/<name>/:instruction.md,task.toml(metadata:sourcearXiv id,source_license,rewrite, and for instantiated tasksoriginal_answer+assignments),environment/,tests/(instance.jsonholds the gold answer),solution/solve.sh(oracle).manifest.parquet: one row per task (question, answer, answer_type, original question/answer, license).
Each row keeps the license of its source paper (source_license).
- Downloads last month
- 225