name stringlengths 16 45 | instruction stringlengths 3.11k 1.41M | description stringlengths 140 209 | keywords listlengths 5 5 | schema_version stringclasses 1
value | config unknown | metadata unknown | files listlengths 15 15 | location stringlengths 10 39 |
|---|---|---|---|---|---|---|---|---|
openai-math/eilenberg-ganea | # openai/math challenge `EilenbergGanea` (family 249)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 249 of the release, *A finitely generated counterexample to Eilenberg–Ganea*
(... | Prove EilenbergGanea (openai/math family 249: A finitely generated counterexample to Eilenberg–Ganea) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"group-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/eilenberg-ganea",
"version": "1.0.0",
"description": "Prove EilenbergGanea (openai/math family 249: A finitely generated counterexample to Eilenberg–Ganea) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EilenbergGanea.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/eilenberg-ganea |
openai-math/elasticity-uniqueness | # openai/math challenge `ElasticityUniqueness` (family 372)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 372 of the release, *Global uniqueness in smooth isotropic elasticity*
(... | Prove ElasticityUniqueness (openai/math family 372: Global uniqueness in smooth isotropic elasticity) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"partial-differential-equations"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/elasticity-uniqueness",
"version": "1.0.0",
"description": "Prove ElasticityUniqueness (openai/math family 372: Global uniqueness in smooth isotropic elasticity) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ElasticityUniqueness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/elasticity-uniqueness |
openai-math/elementary-positivity | # openai/math challenge `ElementaryPositivity` (family 169)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 169 of the release, *The Shareshian–Wachs $e$-positivity conjecture*
(Co... | Prove ElementaryPositivity (openai/math family 169: The Shareshian–Wachs $e$-positivity conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/elementary-positivity",
"version": "1.0.0",
"description": "Prove ElementaryPositivity (openai/math family 169: The Shareshian–Wachs $e$-positivity conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ElementaryPositivity.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/elementary-positivity |
openai-math/entangled-games | # openai/math challenge `EntangledGames` (family 277)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 277 of the release, *Threshold repetition for entangled games*
(Mathematical p... | Prove EntangledGames (openai/math family 277: Threshold repetition for entangled games) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/entangled-games",
"version": "1.0.0",
"description": "Prove EntangledGames (openai/math family 277: Threshold repetition for entangled games) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EntangledGames.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/entangled-games |
openai-math/entropy-photon-number | # openai/math challenge `EntropyPhotonNumber` (family 273)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 273 of the release, *The entropy photon-number inequality*
(Mathematical ... | Prove EntropyPhotonNumber (openai/math family 273: The entropy photon-number inequality) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/entropy-photon-number",
"version": "1.0.0",
"description": "Prove EntropyPhotonNumber (openai/math family 273: The entropy photon-number inequality) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"le... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EntropyPhotonNumber.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/entropy-photon-number |
openai-math/euclidean-five-color | # openai/math challenge `EuclideanFiveColor` (family 158)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 158 of the release, *The Euclidean plane cannot be colored with five color... | Prove EuclideanFiveColor (openai/math family 158: The Euclidean plane cannot be colored with five colors) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/euclidean-five-color",
"version": "1.0.0",
"description": "Prove EuclideanFiveColor (openai/math family 158: The Euclidean plane cannot be colored with five colors) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywor... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EuclideanFiveColor.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/euclidean-five-color |
openai-math/euclidean-ramsey-circle | # openai/math challenge `EuclideanRamseyCircle` (family 172)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 172 of the release, *Classification of finite Euclidean Ramsey configur... | Prove EuclideanRamseyCircle (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/euclidean-ramsey-circle",
"version": "1.0.0",
"description": "Prove EuclideanRamseyCircle (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EuclideanRamseyCircle.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/euclidean-ramsey-circle |
openai-math/euclidean-ramsey-nine | # openai/math challenge `EuclideanRamseyNine` (family 172)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 172 of the release, *Classification of finite Euclidean Ramsey configurat... | Prove EuclideanRamseyNine (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/euclidean-ramsey-nine",
"version": "1.0.0",
"description": "Prove EuclideanRamseyNine (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"ke... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EuclideanRamseyNine.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/euclidean-ramsey-nine |
openai-math/euclidean-ramsey-quadratic | # openai/math challenge `EuclideanRamseyQuadratic` (family 172)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 172 of the release, *Classification of finite Euclidean Ramsey confi... | Prove EuclideanRamseyQuadratic (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/euclidean-ramsey-quadratic",
"version": "1.0.0",
"description": "Prove EuclideanRamseyQuadratic (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EuclideanRamseyQuadratic.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/euclidean-ramsey-quadratic |
openai-math/euclidean-ramsey-spherical | # openai/math challenge `EuclideanRamseySpherical` (family 172)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 172 of the release, *Classification of finite Euclidean Ramsey confi... | Prove EuclideanRamseySpherical (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/euclidean-ramsey-spherical",
"version": "1.0.0",
"description": "Prove EuclideanRamseySpherical (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EuclideanRamseySpherical.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/euclidean-ramsey-spherical |
openai-math/euclidean-ramsey-transitive | # openai/math challenge `EuclideanRamseyTransitive` (family 172)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 172 of the release, *Classification of finite Euclidean Ramsey conf... | Prove EuclideanRamseyTransitive (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/euclidean-ramsey-transitive",
"version": "1.0.0",
"description": "Prove EuclideanRamseyTransitive (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EuclideanRamseyTransitive.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/euclidean-ramsey-transitive |
openai-math/euclidean-ramsey | # openai/math challenge `EuclideanRamsey` (family 172)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 172 of the release, *Classification of finite Euclidean Ramsey configurations... | Prove EuclideanRamsey (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/euclidean-ramsey",
"version": "1.0.0",
"description": "Prove EuclideanRamsey (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EuclideanRamsey.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/euclidean-ramsey |
openai-math/even-barker | # openai/math challenge `EvenBarker` (family 179)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 179 of the release, *The circulant Hadamard conjecture*
(Combinatorics). The famil... | Prove EvenBarker (openai/math family 179: The circulant Hadamard conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/even-barker",
"version": "1.0.0",
"description": "Prove EvenBarker (openai/math family 179: The circulant Hadamard conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"mathlib",... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EvenBarker.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": ... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/even-barker |
openai-math/exact-fourier | # openai/math challenge `ExactFourier` (family 130)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 130 of the release, *Fourier transforms below $n\log n$*
(Theoretical computer s... | Prove ExactFourier (openai/math family 130: Fourier transforms below $n\log n$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/exact-fourier",
"version": "1.0.0",
"description": "Prove ExactFourier (openai/math family 130: Fourier transforms below $n\\log n$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"mat... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ExactFourier.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/exact-fourier |
openai-math/exact-infiniteness | # openai/math challenge `ExactInfiniteness` (family 303)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 303 of the release, *From ordinary to strong pure infiniteness*
(Operator a... | Prove ExactInfiniteness (openai/math family 303: From ordinary to strong pure infiniteness) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/exact-infiniteness",
"version": "1.0.0",
"description": "Prove ExactInfiniteness (openai/math family 303: From ordinary to strong pure infiniteness) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"le... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ExactInfiniteness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/exact-infiniteness |
openai-math/exact-quantum-factoring | # openai/math challenge `ExactQuantumFactoring` (family 279)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 279 of the release, *Exact quantum factoring over a fixed finite gate s... | Prove ExactQuantumFactoring (openai/math family 279: Exact quantum factoring over a fixed finite gate set) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/exact-quantum-factoring",
"version": "1.0.0",
"description": "Prove ExactQuantumFactoring (openai/math family 279: Exact quantum factoring over a fixed finite gate set) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"ke... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ExactQuantumFactoring.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/exact-quantum-factoring |
openai-math/factor-generation | # openai/math challenge `FactorGeneration` (family 296)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 296 of the release, *The generator problem for finite factors*
(Operator alg... | Prove FactorGeneration (openai/math family 296: The generator problem for finite factors) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/factor-generation",
"version": "1.0.0",
"description": "Prove FactorGeneration (openai/math family 296: The generator problem for finite factors) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FactorGeneration.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/factor-generation |
openai-math/falconer-all-dimensions | # openai/math challenge `FalconerAllDimensions` (family 073)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 073 of the release, *The Falconer distance conjecture*
(Real and comple... | Prove FalconerAllDimensions (openai/math family 073: The Falconer distance conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"real-and-complex-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/falconer-all-dimensions",
"version": "1.0.0",
"description": "Prove FalconerAllDimensions (openai/math family 073: The Falconer distance conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"le... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FalconerAllDimensions.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/falconer-all-dimensions |
openai-math/filling-coefficient | # openai/math challenge `FillingCoefficient` (family 337)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 337 of the release, *Cartan–Hadamard isoperimetry and CAT$(0)$ fillings*
(... | Prove FillingCoefficient (openai/math family 337: Cartan–Hadamard isoperimetry and CAT$(0)$ fillings) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"differential-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/filling-coefficient",
"version": "1.0.0",
"description": "Prove FillingCoefficient (openai/math family 337: Cartan–Hadamard isoperimetry and CAT$(0)$ fillings) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FillingCoefficient.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/filling-coefficient |
openai-math/finite-circle | # openai/math challenge `FiniteCircle` (family 099)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 099 of the release, *The sharp distortion of edit distance into $\ell_1$*
(Conve... | Prove FiniteCircle (openai/math family 099: The sharp distortion of edit distance into $\ell_1$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/finite-circle",
"version": "1.0.0",
"description": "Prove FiniteCircle (openai/math family 099: The sharp distortion of edit distance into $\\ell_1$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FiniteCircle.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/finite-circle |
openai-math/finite-congruence-graph | # openai/math challenge `FiniteCongruenceGraph` (family 206)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 206 of the release, *Finite lattice representation: counterexamples and... | Prove FiniteCongruenceGraph (openai/math family 206: Finite lattice representation: counterexamples and undecidability) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebra"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/finite-congruence-graph",
"version": "1.0.0",
"description": "Prove FiniteCongruenceGraph (openai/math family 206: Finite lattice representation: counterexamples and undecidability) in Lean 4 with Mathlib; graded by Comparator in a separate sandb... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FiniteCongruenceGraph.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/finite-congruence-graph |
openai-math/finite-entropy-separation | # openai/math challenge `FiniteEntropySeparation` (family 298)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 298 of the release, *A counterexample to Voiculescu’s free-entropy eq... | Prove FiniteEntropySeparation (openai/math family 298: A counterexample to Voiculescu’s free-entropy equality conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/finite-entropy-separation",
"version": "1.0.0",
"description": "Prove FiniteEntropySeparation (openai/math family 298: A counterexample to Voiculescu’s free-entropy equality conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate s... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FiniteEntropySeparation.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/finite-entropy-separation |
openai-math/finite-factor | # openai/math challenge `FiniteFactor` (family 293)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 293 of the release, *A counterexample to the hyperinvariant-subspace problem*
(O... | Prove FiniteFactor (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/finite-factor",
"version": "1.0.0",
"description": "Prove FiniteFactor (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FiniteFactor.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/finite-factor |
openai-math/finitistic-asymmetry | # openai/math challenge `FinitisticAsymmetry` (family 198)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 198 of the release, *A counterexample to the little finitistic-dimension ... | Prove FinitisticAsymmetry (openai/math family 198: A counterexample to the little finitistic-dimension conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebra"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/finitistic-asymmetry",
"version": "1.0.0",
"description": "Prove FinitisticAsymmetry (openai/math family 198: A counterexample to the little finitistic-dimension conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FinitisticAsymmetry.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/finitistic-asymmetry |
openai-math/fixed-clause-threshold | # openai/math challenge `FixedClauseThreshold` (family 235)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 235 of the release, *Random-SAT thresholds, sharp variance and computabi... | Prove FixedClauseThreshold (openai/math family 235: Random-SAT thresholds, sharp variance and computability) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/fixed-clause-threshold",
"version": "1.0.0",
"description": "Prove FixedClauseThreshold (openai/math family 235: Random-SAT thresholds, sharp variance and computability) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"k... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FixedClauseThreshold.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/fixed-clause-threshold |
openai-math/fkcrt | # openai/math challenge `FKCRT` (family 211)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 211 of the release, *Geometry, diffusion, and spectra of random planar maps*
(Probabili... | Prove FKCRT (openai/math family 211: Geometry, diffusion, and spectra of random planar maps) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/fkcrt",
"version": "1.0.0",
"description": "Prove FKCRT (openai/math family 211: Geometry, diffusion, and spectra of random planar maps) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FKCRT.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "FKCR... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/fkcrt |
openai-math/forced-navier-stokes-computation | # openai/math challenge `ForcedNavierStokesComputation` (family 376)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 376 of the release, *Universal computation in forced Navier–Sto... | Prove ForcedNavierStokesComputation (openai/math family 376: Universal computation in forced Navier–Stokes flows) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"partial-differential-equations"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/forced-navier-stokes-computation",
"version": "1.0.0",
"description": "Prove ForcedNavierStokesComputation (openai/math family 376: Universal computation in forced Navier–Stokes flows) in Lean 4 with Mathlib; graded by Comparator in a separate sa... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ForcedNavierStokesComputation.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset roo... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/forced-navier-stokes-computation |
openai-math/forest-space | # openai/math challenge `ForestSpace` (family 331)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 331 of the release, *Asymptotic midpoint uniform convexity without asymptotically... | Prove ForestSpace (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/forest-space",
"version": "1.0.0",
"description": "Prove ForestSpace (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a separate sand... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ForestSpace.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge":... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/forest-space |
openai-math/formula-hitting | # openai/math challenge `FormulaHitting` (family 116)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 116 of the release, *Uniform identity testing for noncommutative formulas*
(Th... | Prove FormulaHitting (openai/math family 116: Uniform identity testing for noncommutative formulas) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/formula-hitting",
"version": "1.0.0",
"description": "Prove FormulaHitting (openai/math family 116: Uniform identity testing for noncommutative formulas) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FormulaHitting.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/formula-hitting |
openai-math/foulkes-howe | # openai/math challenge `FoulkesHowe` (family 210)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 210 of the release, *Foulkes’ conjecture for sixth powers and quadratic stabiliza... | Prove FoulkesHowe (openai/math family 210: Foulkes’ conjecture for sixth powers and quadratic stabilization) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebra"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/foulkes-howe",
"version": "1.0.0",
"description": "Prove FoulkesHowe (openai/math family 210: Foulkes’ conjecture for sixth powers and quadratic stabilization) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FoulkesHowe.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge":... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/foulkes-howe |
openai-math/four-row-permanent | # openai/math challenge `FourRowPermanent` (family 238)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 238 of the release, *Optimal logarithmic mixing of the Thorp shuffle*
(Proba... | Prove FourRowPermanent (openai/math family 238: Optimal logarithmic mixing of the Thorp shuffle) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/four-row-permanent",
"version": "1.0.0",
"description": "Prove FourRowPermanent (openai/math family 238: Optimal logarithmic mixing of the Thorp shuffle) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FourRowPermanent.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/four-row-permanent |
openai-math/free-ising | # openai/math challenge `FreeIsing` (family 236)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 236 of the release, *The factor-of-IID threshold for free Ising states on trees*
(P... | Prove FreeIsing (openai/math family 236: The factor-of-IID threshold for free Ising states on trees) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/free-ising",
"version": "1.0.0",
"description": "Prove FreeIsing (openai/math family 236: The factor-of-IID threshold for free Ising states on trees) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FreeIsing.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/free-ising |
openai-math/free-uniform-spanning-forest | # openai/math challenge `FreeUniformSpanningForest` (family 231)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 231 of the release, *The free uniform spanning forest is a factor o... | Prove FreeUniformSpanningForest (openai/math family 231: The free uniform spanning forest is a factor of IID) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/free-uniform-spanning-forest",
"version": "1.0.0",
"description": "Prove FreeUniformSpanningForest (openai/math family 231: The free uniform spanning forest is a factor of IID) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/FreeUniformSpanningForest.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/free-uniform-spanning-forest |
openai-math/gamma-passage | # openai/math challenge `GammaPassage` (family 212)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 212 of the release, *No bigeodesics and smooth limit shapes in planar first-pass... | Prove GammaPassage (openai/math family 212: No bigeodesics and smooth limit shapes in planar first-passage percolation) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/gamma-passage",
"version": "1.0.0",
"description": "Prove GammaPassage (openai/math family 212: No bigeodesics and smooth limit shapes in planar first-passage percolation) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GammaPassage.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/gamma-passage |
openai-math/gaussian-finite-entropy | # openai/math challenge `GaussianFiniteEntropy` (family 140)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 140 of the release, *Memory–sample lower bounds for noiseless Gaussian ... | Prove GaussianFiniteEntropy (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/gaussian-finite-entropy",
"version": "1.0.0",
"description": "Prove GaussianFiniteEntropy (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GaussianFiniteEntropy.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/gaussian-finite-entropy |
openai-math/gaussian-information | # openai/math challenge `GaussianInformation` (family 140)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 140 of the release, *Memory–sample lower bounds for noiseless Gaussian re... | Prove GaussianInformation (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/gaussian-information",
"version": "1.0.0",
"description": "Prove GaussianInformation (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GaussianInformation.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/gaussian-information |
openai-math/gaussian-moat | # openai/math challenge `GaussianMoat` (family 028)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 028 of the release, *The Gaussian moat conjecture*
(Number theory). The family a... | Prove GaussianMoat (openai/math family 028: The Gaussian moat conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"number-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/gaussian-moat",
"version": "1.0.0",
"description": "Prove GaussianMoat (openai/math family 028: The Gaussian moat conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"mathlib",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GaussianMoat.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/gaussian-moat |
openai-math/gaussian-propeller | # openai/math challenge `GaussianPropeller` (family 096)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 096 of the release, *The Gaussian propeller conjecture*
(Convex and metric ... | Prove GaussianPropeller (openai/math family 096: The Gaussian propeller conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/gaussian-propeller",
"version": "1.0.0",
"description": "Prove GaussianPropeller (openai/math family 096: The Gaussian propeller conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GaussianPropeller.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/gaussian-propeller |
openai-math/gaussian-replacement | # openai/math challenge `GaussianReplacement` (family 140)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 140 of the release, *Memory–sample lower bounds for noiseless Gaussian re... | Prove GaussianReplacement (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/gaussian-replacement",
"version": "1.0.0",
"description": "Prove GaussianReplacement (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GaussianReplacement.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/gaussian-replacement |
openai-math/general-mahler | # openai/math challenge `GeneralMahler` (family 087)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 087 of the release, *The Mahler conjectures and symplectic width*
(Convex and m... | Prove GeneralMahler (openai/math family 087: The Mahler conjectures and symplectic width) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/general-mahler",
"version": "1.0.0",
"description": "Prove GeneralMahler (openai/math family 087: The Mahler conjectures and symplectic width) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GeneralMahler.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/general-mahler |
openai-math/generalized-star-height | # openai/math challenge `GeneralizedStarHeight` (family 134)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 134 of the release, *Generalized star height at most three*
(Theoretica... | Prove GeneralizedStarHeight (openai/math family 134: Generalized star height at most three) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/generalized-star-height",
"version": "1.0.0",
"description": "Prove GeneralizedStarHeight (openai/math family 134: Generalized star height at most three) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GeneralizedStarHeight.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/generalized-star-height |
openai-math/gotsman-linial | # openai/math challenge `GotsmanLinial` (family 127)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 127 of the release, *The asymptotic Gotsman–Linial conjecture*
(Theoretical com... | Prove GotsmanLinial (openai/math family 127: The asymptotic Gotsman–Linial conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/gotsman-linial",
"version": "1.0.0",
"description": "Prove GotsmanLinial (openai/math family 127: The asymptotic Gotsman–Linial conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GotsmanLinial.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/gotsman-linial |
openai-math/graham-spherical | # openai/math challenge `GrahamSpherical` (family 172)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 172 of the release, *Classification of finite Euclidean Ramsey configurations... | Prove GrahamSpherical (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/graham-spherical",
"version": "1.0.0",
"description": "Prove GrahamSpherical (openai/math family 172: Classification of finite Euclidean Ramsey configurations) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GrahamSpherical.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/graham-spherical |
openai-math/grothendieck-elementary-expansion | # openai/math challenge `GrothendieckElementaryExpansion` (family 312)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 312 of the release, *The Grothendieck homotopy hypothesis*
(T... | Prove GrothendieckElementaryExpansion (openai/math family 312: The Grothendieck homotopy hypothesis) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"topology"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/grothendieck-elementary-expansion",
"version": "1.0.0",
"description": "Prove GrothendieckElementaryExpansion (openai/math family 312: The Grothendieck homotopy hypothesis) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GrothendieckElementaryExpansion.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset r... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/grothendieck-elementary-expansion |
openai-math/group-ring-determinant | # openai/math challenge `GroupRingDeterminant` (family 197)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 197 of the release, *Nonsofic groups and group-ring counterexamples*
(Al... | Prove GroupRingDeterminant (openai/math family 197: Nonsofic groups and group-ring counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebra"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/group-ring-determinant",
"version": "1.0.0",
"description": "Prove GroupRingDeterminant (openai/math family 197: Nonsofic groups and group-ring counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords":... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/GroupRingDeterminant.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/group-ring-determinant |
openai-math/hadamard-cube-fiber | # openai/math challenge `HadamardCubeFiber` (family 266)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 266 of the release, *Exactly three mutually unbiased bases in dimension six... | Prove HadamardCubeFiber (openai/math family 266: Exactly three mutually unbiased bases in dimension six) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/hadamard-cube-fiber",
"version": "1.0.0",
"description": "Prove HadamardCubeFiber (openai/math family 266: Exactly three mutually unbiased bases in dimension six) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HadamardCubeFiber.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/hadamard-cube-fiber |
openai-math/halving-lines | # openai/math challenge `HalvingLines` (family 183)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 183 of the release, *Power savings for planar halving lines and $k$-sets*
(Combi... | Prove HalvingLines (openai/math family 183: Power savings for planar halving lines and $k$-sets) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/halving-lines",
"version": "1.0.0",
"description": "Prove HalvingLines (openai/math family 183: Power savings for planar halving lines and $k$-sets) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"le... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HalvingLines.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/halving-lines |
openai-math/hard-sphere | # openai/math challenge `HardSphere` (family 267)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 267 of the release, *Positive-temperature Bose–Einstein condensation and quantum d... | Prove HardSphere (openai/math family 267: Positive-temperature Bose–Einstein condensation and quantum depletion) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/hard-sphere",
"version": "1.0.0",
"description": "Prove HardSphere (openai/math family 267: Positive-temperature Bose–Einstein condensation and quantum depletion) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HardSphere.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": ... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/hard-sphere |
openai-math/harmonic-artin | # openai/math challenge `HarmonicArtin` (family 254)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 254 of the release, *Classifying spaces and geometric obstructions for Artin gr... | Prove HarmonicArtin (openai/math family 254: Classifying spaces and geometric obstructions for Artin groups) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"group-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/harmonic-artin",
"version": "1.0.0",
"description": "Prove HarmonicArtin (openai/math family 254: Classifying spaces and geometric obstructions for Artin groups) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HarmonicArtin.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/harmonic-artin |
openai-math/harmonic-growth | # openai/math challenge `HarmonicGrowth` (family 361)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 361 of the release, *Counterexamples to Yau's harmonic dimension bound*
(Diffe... | Prove HarmonicGrowth (openai/math family 361: Counterexamples to Yau's harmonic dimension bound) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"differential-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/harmonic-growth",
"version": "1.0.0",
"description": "Prove HarmonicGrowth (openai/math family 361: Counterexamples to Yau's harmonic dimension bound) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HarmonicGrowth.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/harmonic-growth |
openai-math/heilbronn-triangle | # openai/math challenge `HeilbronnTriangle` (family 191)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 191 of the release, *A power improvement in the Heilbronn triangle problem*... | Prove HeilbronnTriangle (openai/math family 191: A power improvement in the Heilbronn triangle problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/heilbronn-triangle",
"version": "1.0.0",
"description": "Prove HeilbronnTriangle (openai/math family 191: A power improvement in the Heilbronn triangle problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords":... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HeilbronnTriangle.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/heilbronn-triangle |
openai-math/heisenberg | # openai/math challenge `Heisenberg` (family 271)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 271 of the release, *Bloch's law and spontaneous ferromagnetic order*
(Mathematica... | Prove Heisenberg (openai/math family 271: Bloch's law and spontaneous ferromagnetic order) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/heisenberg",
"version": "1.0.0",
"description": "Prove Heisenberg (openai/math family 271: Bloch's law and spontaneous ferromagnetic order) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/Heisenberg.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": ... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/heisenberg |
openai-math/henon-emden | # openai/math challenge `HenonEmden` (family 370)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 370 of the release, *The subcritical Lane–Emden and Henon–Lane–Emden conjectures*
... | Prove HenonEmden (openai/math family 370: The subcritical Lane–Emden and Henon–Lane–Emden conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"partial-differential-equations"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/henon-emden",
"version": "1.0.0",
"description": "Prove HenonEmden (openai/math family 370: The subcritical Lane–Emden and Henon–Lane–Emden conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HenonEmden.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": ... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/henon-emden |
openai-math/hilbert-crouzeix | # openai/math challenge `HilbertCrouzeix` (family 325)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 325 of the release, *The complete Crouzeix conjecture*
(Functional analysis).... | Prove HilbertCrouzeix (openai/math family 325: The complete Crouzeix conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/hilbert-crouzeix",
"version": "1.0.0",
"description": "Prove HilbertCrouzeix (openai/math family 325: The complete Crouzeix conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HilbertCrouzeix.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/hilbert-crouzeix |
openai-math/honeycomb-bridge-finiteness | # openai/math challenge `HoneycombBridgeFiniteness` (family 237)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 237 of the release, *The three-quarter diameter exponent for honeyc... | Prove HoneycombBridgeFiniteness (openai/math family 237: The three-quarter diameter exponent for honeycomb walks) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/honeycomb-bridge-finiteness",
"version": "1.0.0",
"description": "Prove HoneycombBridgeFiniteness (openai/math family 237: The three-quarter diameter exponent for honeycomb walks) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HoneycombBridgeFiniteness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/honeycomb-bridge-finiteness |
openai-math/honeycomb-free-energy | # openai/math challenge `HoneycombFreeEnergy` (family 237)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 237 of the release, *The three-quarter diameter exponent for honeycomb wa... | Prove HoneycombFreeEnergy (openai/math family 237: The three-quarter diameter exponent for honeycomb walks) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/honeycomb-free-energy",
"version": "1.0.0",
"description": "Prove HoneycombFreeEnergy (openai/math family 237: The three-quarter diameter exponent for honeycomb walks) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"key... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HoneycombFreeEnergy.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/honeycomb-free-energy |
openai-math/hot-spots | # openai/math challenge `HotSpots` (family 369)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 369 of the release, *The hot spots conjecture for simply connected planar domains*
(... | Prove HotSpots (openai/math family 369: The hot spots conjecture for simply connected planar domains) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"partial-differential-equations"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/hot-spots",
"version": "1.0.0",
"description": "Prove HotSpots (openai/math family 369: The hot spots conjecture for simply connected planar domains) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HotSpots.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "H... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/hot-spots |
openai-math/hyperbolic-cones | # openai/math challenge `HyperbolicCones` (family 095)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 095 of the release, *Hyperbolicity cones without semidefinite lifts*
(Convex ... | Prove HyperbolicCones (openai/math family 095: Hyperbolicity cones without semidefinite lifts) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/hyperbolic-cones",
"version": "1.0.0",
"description": "Prove HyperbolicCones (openai/math family 095: Hyperbolicity cones without semidefinite lifts) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HyperbolicCones.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/hyperbolic-cones |
openai-math/hyperbolic-obstruction | # openai/math challenge `HyperbolicObstruction` (family 257)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 257 of the release, *A hyperbolic group with no geometric CAT(0) action... | Prove HyperbolicObstruction (openai/math family 257: A hyperbolic group with no geometric CAT(0) action) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"group-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/hyperbolic-obstruction",
"version": "1.0.0",
"description": "Prove HyperbolicObstruction (openai/math family 257: A hyperbolic group with no geometric CAT(0) action) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywo... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HyperbolicObstruction.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"c... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/hyperbolic-obstruction |
openai-math/hyperinvariant-subspaces | # openai/math challenge `HyperinvariantSubspaces` (family 293)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 293 of the release, *A counterexample to the hyperinvariant-subspace ... | Prove HyperinvariantSubspaces (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/hyperinvariant-subspaces",
"version": "1.0.0",
"description": "Prove HyperinvariantSubspaces (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/HyperinvariantSubspaces.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/hyperinvariant-subspaces |
openai-math/independent-products | # openai/math challenge `IndependentProducts` (family 331)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 331 of the release, *Asymptotic midpoint uniform convexity without asympt... | Prove IndependentProducts (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/independent-products",
"version": "1.0.0",
"description": "Prove IndependentProducts (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/IndependentProducts.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/independent-products |
openai-math/independent-sets | # openai/math challenge `IndependentSets` (family 106)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 106 of the release, *Hardness of coloring three-colorable graphs*
(Theoretica... | Prove IndependentSets (openai/math family 106: Hardness of coloring three-colorable graphs) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/independent-sets",
"version": "1.0.0",
"description": "Prove IndependentSets (openai/math family 106: Hardness of coloring three-colorable graphs) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/IndependentSets.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/independent-sets |
openai-math/individual-strong-infiniteness | # openai/math challenge `IndividualStrongInfiniteness` (family 303)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 303 of the release, *From ordinary to strong pure infiniteness*
... | Prove IndividualStrongInfiniteness (openai/math family 303: From ordinary to strong pure infiniteness) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/individual-strong-infiniteness",
"version": "1.0.0",
"description": "Prove IndividualStrongInfiniteness (openai/math family 303: From ordinary to strong pure infiniteness) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/IndividualStrongInfiniteness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/individual-strong-infiniteness |
openai-math/infinite-matroid-corollaries | # openai/math challenge `InfiniteMatroidCorollaries` (family 185)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 185 of the release, *Counterexamples to infinite matroid intersect... | Prove InfiniteMatroidCorollaries (openai/math family 185: Counterexamples to infinite matroid intersection and packing/covering) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/infinite-matroid-corollaries",
"version": "1.0.0",
"description": "Prove InfiniteMatroidCorollaries (openai/math family 185: Counterexamples to infinite matroid intersection and packing/covering) in Lean 4 with Mathlib; graded by Comparator in a ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/InfiniteMatroidCorollaries.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/infinite-matroid-corollaries |
openai-math/infinite-matroid | # openai/math challenge `InfiniteMatroid` (family 185)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 185 of the release, *Counterexamples to infinite matroid intersection and pac... | Prove InfiniteMatroid (openai/math family 185: Counterexamples to infinite matroid intersection and packing/covering) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/infinite-matroid",
"version": "1.0.0",
"description": "Prove InfiniteMatroid (openai/math family 185: Counterexamples to infinite matroid intersection and packing/covering) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/InfiniteMatroid.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/infinite-matroid |
openai-math/interpolated-factors | # openai/math challenge `InterpolatedFactors` (family 287)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 287 of the release, *All nonabelian free group factors are isomorphic*
(O... | Prove InterpolatedFactors (openai/math family 287: All nonabelian free group factors are isomorphic) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/interpolated-factors",
"version": "1.0.0",
"description": "Prove InterpolatedFactors (openai/math family 287: All nonabelian free group factors are isomorphic) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/InterpolatedFactors.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/interpolated-factors |
openai-math/invariant-ising | # openai/math challenge `InvariantIsing` (family 234)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 234 of the release, *All-temperature pressure for orthogonally invariant Ising... | Prove InvariantIsing (openai/math family 234: All-temperature pressure for orthogonally invariant Ising spin glasses) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/invariant-ising",
"version": "1.0.0",
"description": "Prove InvariantIsing (openai/math family 234: All-temperature pressure for orthogonally invariant Ising spin glasses) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/InvariantIsing.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/invariant-ising |
openai-math/irrational-rotation | # openai/math challenge `IrrationalRotation` (family 293)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 293 of the release, *A counterexample to the hyperinvariant-subspace probl... | Prove IrrationalRotation (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/irrational-rotation",
"version": "1.0.0",
"description": "Prove IrrationalRotation (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywor... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/IrrationalRotation.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/irrational-rotation |
openai-math/irrational-triangle-billiard | # openai/math challenge `IrrationalTriangleBilliard` (family 150)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 150 of the release, *Weak mixing of irrational triangular billiard... | Prove IrrationalTriangleBilliard (openai/math family 150: Weak mixing of irrational triangular billiards) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"dynamical-systems-and-ergodic-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/irrational-triangle-billiard",
"version": "1.0.0",
"description": "Prove IrrationalTriangleBilliard (openai/math family 150: Weak mixing of irrational triangular billiards) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/IrrationalTriangleBilliard.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/irrational-triangle-billiard |
openai-math/ising-finiteness | # openai/math challenge `IsingFiniteness` (family 222)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 222 of the release, *Perceptron free energies and microscopic jamming*
(Proba... | Prove IsingFiniteness (openai/math family 222: Perceptron free energies and microscopic jamming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/ising-finiteness",
"version": "1.0.0",
"description": "Prove IsingFiniteness (openai/math family 222: Perceptron free energies and microscopic jamming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/IsingFiniteness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/ising-finiteness |
openai-math/isometric-immersion | # openai/math challenge `IsometricImmersion` (family 334)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 334 of the release, *A smooth surface metric with no local immersion in $\... | Prove IsometricImmersion (openai/math family 334: A smooth surface metric with no local immersion in $\mathbb R^3$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"differential-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/isometric-immersion",
"version": "1.0.0",
"description": "Prove IsometricImmersion (openai/math family 334: A smooth surface metric with no local immersion in $\\mathbb R^3$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/IsometricImmersion.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chal... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/isometric-immersion |
openai-math/k-median-recovery | # openai/math challenge `KMedianRecovery` (family 125)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 125 of the release, *The approximation threshold for metric $k$-median*
(Theo... | Prove KMedianRecovery (openai/math family 125: The approximation threshold for metric $k$-median) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/k-median-recovery",
"version": "1.0.0",
"description": "Prove KMedianRecovery (openai/math family 125: The approximation threshold for metric $k$-median) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KMedianRecovery.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/k-median-recovery |
openai-math/k-median-refined-recovery | # openai/math challenge `KMedianRefinedRecovery` (family 125)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 125 of the release, *The approximation threshold for metric $k$-median... | Prove KMedianRefinedRecovery (openai/math family 125: The approximation threshold for metric $k$-median) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/k-median-refined-recovery",
"version": "1.0.0",
"description": "Prove KMedianRefinedRecovery (openai/math family 125: The approximation threshold for metric $k$-median) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"ke... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KMedianRefinedRecovery.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/k-median-refined-recovery |
openai-math/k-median-threshold | # openai/math challenge `KMedianThreshold` (family 125)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 125 of the release, *The approximation threshold for metric $k$-median*
(The... | Prove KMedianThreshold (openai/math family 125: The approximation threshold for metric $k$-median) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/k-median-threshold",
"version": "1.0.0",
"description": "Prove KMedianThreshold (openai/math family 125: The approximation threshold for metric $k$-median) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KMedianThreshold.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/k-median-threshold |
openai-math/k-server | # openai/math challenge `KServer` (family 110)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 110 of the release, *Optimal-order randomized $k$-server on arbitrary metrics*
(Theor... | Prove KServer (openai/math family 110: Optimal-order randomized $k$-server on arbitrary metrics) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/k-server",
"version": "1.0.0",
"description": "Prove KServer (openai/math family 110: Optimal-order randomized $k$-server on arbitrary metrics) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KServer.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "KS... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/k-server |
openai-math/kadison-ringrose | # openai/math challenge `KadisonRingrose` (family 295)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 295 of the release, *The Kadison–Ringrose cohomology conjecture*
(Operator al... | Prove KadisonRingrose (openai/math family 295: The Kadison–Ringrose cohomology conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/kadison-ringrose",
"version": "1.0.0",
"description": "Prove KadisonRingrose (openai/math family 295: The Kadison–Ringrose cohomology conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KadisonRingrose.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/kadison-ringrose |
openai-math/kadison-similarity | # openai/math challenge `KadisonSimilarity` (family 288)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 288 of the release, *Kadison's similarity conjecture*
(Operator algebras). ... | Prove KadisonSimilarity (openai/math family 288: Kadison's similarity conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/kadison-similarity",
"version": "1.0.0",
"description": "Prove KadisonSimilarity (openai/math family 288: Kadison's similarity conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KadisonSimilarity.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/kadison-similarity |
openai-math/kahler-splitting | # openai/math challenge `KahlerSplitting` (family 052)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 052 of the release, *Tangent-bundle splittings and universal covers*
(Algebra... | Prove KahlerSplitting (openai/math family 052: Tangent-bundle splittings and universal covers) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebraic-and-complex-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/kahler-splitting",
"version": "1.0.0",
"description": "Prove KahlerSplitting (openai/math family 052: Tangent-bundle splittings and universal covers) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KahlerSplitting.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/kahler-splitting |
openai-math/kaplansky-direct-finiteness | # openai/math challenge `KaplanskyDirectFiniteness` (family 197)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 197 of the release, *Nonsofic groups and group-ring counterexamples... | Prove KaplanskyDirectFiniteness (openai/math family 197: Nonsofic groups and group-ring counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebra"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/kaplansky-direct-finiteness",
"version": "1.0.0",
"description": "Prove KaplanskyDirectFiniteness (openai/math family 197: Nonsofic groups and group-ring counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KaplanskyDirectFiniteness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/kaplansky-direct-finiteness |
openai-math/kaplansky-finitely-presented | # openai/math challenge `KaplanskyFinitelyPresented` (family 197)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 197 of the release, *Nonsofic groups and group-ring counterexample... | Prove KaplanskyFinitelyPresented (openai/math family 197: Nonsofic groups and group-ring counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebra"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/kaplansky-finitely-presented",
"version": "1.0.0",
"description": "Prove KaplanskyFinitelyPresented (openai/math family 197: Nonsofic groups and group-ring counterexamples) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KaplanskyFinitelyPresented.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/kaplansky-finitely-presented |
openai-math/kaplansky-quasitrace | # openai/math challenge `KaplanskyQuasitrace` (family 294)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 294 of the release, *A counterexample to Kaplansky's quasitrace conjectur... | Prove KaplanskyQuasitrace (openai/math family 294: A counterexample to Kaplansky's quasitrace conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/kaplansky-quasitrace",
"version": "1.0.0",
"description": "Prove KaplanskyQuasitrace (openai/math family 294: A counterexample to Kaplansky's quasitrace conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywor... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KaplanskyQuasitrace.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"cha... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/kaplansky-quasitrace |
openai-math/kaplansky-stable-finiteness | # openai/math challenge `KaplanskyStableFiniteness` (family 294)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 294 of the release, *A counterexample to Kaplansky's quasitrace con... | Prove KaplanskyStableFiniteness (openai/math family 294: A counterexample to Kaplansky's quasitrace conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/kaplansky-stable-finiteness",
"version": "1.0.0",
"description": "Prove KaplanskyStableFiniteness (openai/math family 294: A counterexample to Kaplansky's quasitrace conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox."... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KaplanskyStableFiniteness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/kaplansky-stable-finiteness |
openai-math/kervaire | # openai/math challenge `Kervaire` (family 256)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 256 of the release, *Howie's conjecture on equations over groups*
(Group theory). Th... | Prove Kervaire (openai/math family 256: Howie's conjecture on equations over groups) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"group-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/kervaire",
"version": "1.0.0",
"description": "Prove Kervaire (openai/math family 256: Howie's conjecture on equations over groups) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"math... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/Kervaire.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "K... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/kervaire |
openai-math/kl-invariance | # openai/math challenge `KLInvariance` (family 168)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 168 of the release, *Combinatorial invariance of Kazhdan–Lusztig polynomials*
(C... | Prove KLInvariance (openai/math family 168: Combinatorial invariance of Kazhdan–Lusztig polynomials) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/kl-invariance",
"version": "1.0.0",
"description": "Prove KLInvariance (openai/math family 168: Combinatorial invariance of Kazhdan–Lusztig polynomials) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/KLInvariance.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/kl-invariance |
openai-math/laughlin-fock | # openai/math challenge `LaughlinFock` (family 269)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 269 of the release, *The Laughlin gap and stability under scalar disorder*
(Math... | Prove LaughlinFock (openai/math family 269: The Laughlin gap and stability under scalar disorder) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/laughlin-fock",
"version": "1.0.0",
"description": "Prove LaughlinFock (openai/math family 269: The Laughlin gap and stability under scalar disorder) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LaughlinFock.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/laughlin-fock |
openai-math/laughlin-gap | # openai/math challenge `LaughlinGap` (family 269)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 269 of the release, *The Laughlin gap and stability under scalar disorder*
(Mathe... | Prove LaughlinGap (openai/math family 269: The Laughlin gap and stability under scalar disorder) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/laughlin-gap",
"version": "1.0.0",
"description": "Prove LaughlinGap (openai/math family 269: The Laughlin gap and stability under scalar disorder) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lea... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LaughlinGap.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge":... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/laughlin-gap |
openai-math/laughlin-planar | # openai/math challenge `LaughlinPlanar` (family 269)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 269 of the release, *The Laughlin gap and stability under scalar disorder*
(Ma... | Prove LaughlinPlanar (openai/math family 269: The Laughlin gap and stability under scalar disorder) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/laughlin-planar",
"version": "1.0.0",
"description": "Prove LaughlinPlanar (openai/math family 269: The Laughlin gap and stability under scalar disorder) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LaughlinPlanar.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/laughlin-planar |
openai-math/laughlin | # openai/math challenge `Laughlin` (family 269)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 269 of the release, *The Laughlin gap and stability under scalar disorder*
(Mathemat... | Prove Laughlin (openai/math family 269: The Laughlin gap and stability under scalar disorder) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/laughlin",
"version": "1.0.0",
"description": "Prove Laughlin (openai/math family 269: The Laughlin gap and stability under scalar disorder) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/Laughlin.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "L... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/laughlin |
openai-math/lieb-thirring | # openai/math challenge `LiebThirring` (family 262)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 262 of the release, *Sharp one-dimensional Lieb–Thirring inequalities*
(Mathemat... | Prove LiebThirring (openai/math family 262: Sharp one-dimensional Lieb–Thirring inequalities) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-physics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/lieb-thirring",
"version": "1.0.0",
"description": "Prove LiebThirring (openai/math family 262: Sharp one-dimensional Lieb–Thirring inequalities) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LiebThirring.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/lieb-thirring |
openai-math/lipschitz-equivalence | # openai/math challenge `LipschitzEquivalence` (family 324)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 324 of the release, *Lipschitz equivalence without linear isomorphism*
(... | Prove LipschitzEquivalence (openai/math family 324: Lipschitz equivalence without linear isomorphism) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/lipschitz-equivalence",
"version": "1.0.0",
"description": "Prove LipschitzEquivalence (openai/math family 324: Lipschitz equivalence without linear isomorphism) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LipschitzEquivalence.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"ch... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/lipschitz-equivalence |
openai-math/lipschitz-hilbert | # openai/math challenge `LipschitzHilbert` (family 083)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 083 of the release, *Stein's conjecture for Hilbert transforms along Lipschi... | Prove LipschitzHilbert (openai/math family 083: Stein's conjecture for Hilbert transforms along Lipschitz directions) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"real-and-complex-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/lipschitz-hilbert",
"version": "1.0.0",
"description": "Prove LipschitzHilbert (openai/math family 083: Stein's conjecture for Hilbert transforms along Lipschitz directions) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LipschitzHilbert.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/lipschitz-hilbert |
openai-math/list-hadwiger | # openai/math challenge `ListHadwiger` (family 157)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 157 of the release, *Counterexamples to the Hadwiger and Colin de Verdiere conje... | Prove ListHadwiger (openai/math family 157: Counterexamples to the Hadwiger and Colin de Verdiere conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/list-hadwiger",
"version": "1.0.0",
"description": "Prove ListHadwiger (openai/math family 157: Counterexamples to the Hadwiger and Colin de Verdiere conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ListHadwiger.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge"... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/list-hadwiger |
openai-math/little-finitistic | # openai/math challenge `LittleFinitistic` (family 198)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 198 of the release, *A counterexample to the little finitistic-dimension con... | Prove LittleFinitistic (openai/math family 198: A counterexample to the little finitistic-dimension conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebra"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/little-finitistic",
"version": "1.0.0",
"description": "Prove LittleFinitistic (openai/math family 198: A counterexample to the little finitistic-dimension conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"key... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LittleFinitistic.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/little-finitistic |
openai-math/littlewood-finite-flatness | # openai/math challenge `LittlewoodFiniteFlatness` (family 076)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 076 of the release, *Ultraflat real Littlewood polynomials*
(Real an... | Prove LittlewoodFiniteFlatness (openai/math family 076: Ultraflat real Littlewood polynomials) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"real-and-complex-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/littlewood-finite-flatness",
"version": "1.0.0",
"description": "Prove LittlewoodFiniteFlatness (openai/math family 076: Ultraflat real Littlewood polynomials) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LittlewoodFiniteFlatness.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/littlewood-finite-flatness |
openai-math/log-brunn-minkowski | # openai/math challenge `LogBrunnMinkowski` (family 091)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 091 of the release, *The logarithmic Brunn–Minkowski conjecture*
(Convex an... | Prove LogBrunnMinkowski (openai/math family 091: The logarithmic Brunn–Minkowski conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/log-brunn-minkowski",
"version": "1.0.0",
"description": "Prove LogBrunnMinkowski (openai/math family 091: The logarithmic Brunn–Minkowski conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LogBrunnMinkowski.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"chall... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/log-brunn-minkowski |
openai-math/log-concave-query | # openai/math challenge `LogConcaveQuery` (family 139)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 139 of the release, *Subpolynomial queries for log-concave sampling*
(Theoret... | Prove LogConcaveQuery (openai/math family 139: Subpolynomial queries for log-concave sampling) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"theoretical-computer-science"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/log-concave-query",
"version": "1.0.0",
"description": "Prove LogConcaveQuery (openai/math family 139: Subpolynomial queries for log-concave sampling) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LogConcaveQuery.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challen... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/log-concave-query |
openai-math/log-kodaira-fiber-negative | # openai/math challenge `LogKodairaFiberNegative` (family 033)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 033 of the release, *Campana's orbifold Iitaka conjecture and logarit... | Prove LogKodairaFiberNegative (openai/math family 033: Campana's orbifold Iitaka conjecture and logarithmic subadditivity) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"algebraic-and-complex-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/log-kodaira-fiber-negative",
"version": "1.0.0",
"description": "Prove LogKodairaFiberNegative (openai/math family 033: Campana's orbifold Iitaka conjecture and logarithmic subadditivity) in Lean 4 with Mathlib; graded by Comparator in a separate... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/LogKodairaFiberNegative.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/log-kodaira-fiber-negative |
openai-math/mahler-conjecture | # openai/math challenge `MahlerConjecture` (family 087)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 087 of the release, *The Mahler conjectures and symplectic width*
(Convex an... | Prove MahlerConjecture (openai/math family 087: The Mahler conjectures and symplectic width) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"convex-and-metric-geometry"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/mahler-conjecture",
"version": "1.0.0",
"description": "Prove MahlerConjecture (openai/math family 087: The Mahler conjectures and symplectic width) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"le... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MahlerConjecture.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challe... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/mahler-conjecture |
openai-math/markov-type | # openai/math challenge `MarkovType` (family 327)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 327 of the release, *Markov type characterizes superreflexivity*
(Functional analy... | Prove MarkovType (openai/math family 327: Markov type characterizes superreflexivity) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/markov-type",
"version": "1.0.0",
"description": "Prove MarkovType (openai/math family 327: Markov type characterizes superreflexivity) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MarkovType.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": ... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/markov-type |
openai-math/mass-action | # openai/math challenge `MassAction` (family 149)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 149 of the release, *Permanence for weakly reversible reaction networks*
(Dynamica... | Prove MassAction (openai/math family 149: Permanence for weakly reversible reaction networks) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"dynamical-systems-and-ergodic-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/mass-action",
"version": "1.0.0",
"description": "Prove MassAction (openai/math family 149: Permanence for weakly reversible reaction networks) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/MassAction.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": ... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/mass-action |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.