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/snaky-conditional | # openai/math challenge `SnakyConditional` (family 187)
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 187 of the release, *Snaky in 21 Maker moves*
(Combinatorics). The family as... | Prove SnakyConditional (openai/math family 187: Snaky in 21 Maker moves) 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/snaky-conditional",
"version": "1.0.0",
"description": "Prove SnakyConditional (openai/math family 187: Snaky in 21 Maker moves) 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/SnakyConditional.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/snaky-conditional |
openai-math/soft-channel204 | # openai/math challenge `SoftChannel204` (family 119)
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 119 of the release, *The Courtade–Kumar and Hellinger conjectures*
(Theoretica... | Prove SoftChannel204 (openai/math family 119: The Courtade–Kumar and Hellinger conjectures) 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/soft-channel204",
"version": "1.0.0",
"description": "Prove SoftChannel204 (openai/math family 119: The Courtade–Kumar and Hellinger conjectures) 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/SoftChannel204.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/soft-channel204 |
openai-math/solenoidal-sheet-programs | # openai/math challenge `SolenoidalSheetPrograms` (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–Stokes fl... | Prove SolenoidalSheetPrograms (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/solenoidal-sheet-programs",
"version": "1.0.0",
"description": "Prove SolenoidalSheetPrograms (openai/math family 376: Universal computation in forced Navier–Stokes flows) 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/SolenoidalSheetPrograms.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/solenoidal-sheet-programs |
openai-math/spherical-field | # openai/math challenge `SphericalField` (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*
(Probab... | Prove SphericalField (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/spherical-field",
"version": "1.0.0",
"description": "Prove SphericalField (openai/math family 222: Perceptron free energies and microscopic jamming) 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/SphericalField.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/spherical-field |
openai-math/split-tangent-integrability | # openai/math challenge `SplitTangentIntegrability` (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... | Prove SplitTangentIntegrability (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/split-tangent-integrability",
"version": "1.0.0",
"description": "Prove SplitTangentIntegrability (openai/math family 052: Tangent-bundle splittings and universal covers) 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/SplitTangentIntegrability.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/split-tangent-integrability |
openai-math/square-difference | # openai/math challenge `SquareDifference` (family 182)
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 182 of the release, *Power savings for polynomial-difference-free sets*
(Com... | Prove SquareDifference (openai/math family 182: Power savings for polynomial-difference-free 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/square-difference",
"version": "1.0.0",
"description": "Prove SquareDifference (openai/math family 182: Power savings for polynomial-difference-free sets) 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/SquareDifference.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/square-difference |
openai-math/square-root-degree | # openai/math challenge `SquareRootDegree` (family 192)
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 192 of the release, *A counterexample to the Gopalan–Servedio conjecture*
(C... | Prove SquareRootDegree (openai/math family 192: A counterexample to the Gopalan–Servedio 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/square-root-degree",
"version": "1.0.0",
"description": "Prove SquareRootDegree (openai/math family 192: A counterexample to the Gopalan–Servedio 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/SquareRootDegree.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/square-root-degree |
openai-math/standard-map-components | # openai/math challenge `StandardMapComponents` (family 146)
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 146 of the release, *Sinai's positive-entropy conjecture for the standa... | Prove StandardMapComponents (openai/math family 146: Sinai's positive-entropy conjecture for the standard map) 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/standard-map-components",
"version": "1.0.0",
"description": "Prove StandardMapComponents (openai/math family 146: Sinai's positive-entropy conjecture for the standard map) 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/StandardMapComponents.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/standard-map-components |
openai-math/standard-map-entropy | # openai/math challenge `StandardMapEntropy` (family 146)
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 146 of the release, *Sinai's positive-entropy conjecture for the standard ... | Prove StandardMapEntropy (openai/math family 146: Sinai's positive-entropy conjecture for the standard map) 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/standard-map-entropy",
"version": "1.0.0",
"description": "Prove StandardMapEntropy (openai/math family 146: Sinai's positive-entropy conjecture for the standard map) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keyw... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/StandardMapEntropy.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/standard-map-entropy |
openai-math/standard-map-lyapunov | # openai/math challenge `StandardMapLyapunov` (family 146)
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 146 of the release, *Sinai's positive-entropy conjecture for the standard... | Prove StandardMapLyapunov (openai/math family 146: Sinai's positive-entropy conjecture for the standard map) 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/standard-map-lyapunov",
"version": "1.0.0",
"description": "Prove StandardMapLyapunov (openai/math family 146: Sinai's positive-entropy conjecture for the standard map) 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/StandardMapLyapunov.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/standard-map-lyapunov |
openai-math/steinitz-bergstrom | # openai/math challenge `SteinitzBergstrom` (family 097)
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 097 of the release, *The Euclidean Steinitz–Bergstrom conjecture*
(Convex a... | Prove SteinitzBergstrom (openai/math family 097: The Euclidean Steinitz–Bergstrom 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/steinitz-bergstrom",
"version": "1.0.0",
"description": "Prove SteinitzBergstrom (openai/math family 097: The Euclidean Steinitz–Bergstrom 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/SteinitzBergstrom.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/steinitz-bergstrom |
openai-math/strict-means | # openai/math challenge `StrictMeans` (family 072)
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 072 of the release, *Brennan's conjecture and a counterexample to Kraetzer's pred... | Prove StrictMeans (openai/math family 072: Brennan's conjecture and a counterexample to Kraetzer's prediction) 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/strict-means",
"version": "1.0.0",
"description": "Prove StrictMeans (openai/math family 072: Brennan's conjecture and a counterexample to Kraetzer's prediction) 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/StrictMeans.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/strict-means |
openai-math/strong-kadison-kastler | # openai/math challenge `StrongKadisonKastler` (family 289)
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 289 of the release, *The strong Kadison–Kastler conjecture*
(Operator al... | Prove StrongKadisonKastler (openai/math family 289: The strong Kadison–Kastler 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/strong-kadison-kastler",
"version": "1.0.0",
"description": "Prove StrongKadisonKastler (openai/math family 289: The strong Kadison–Kastler 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/StrongKadisonKastler.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/strong-kadison-kastler |
openai-math/strong-thin-tree | # openai/math challenge `StrongThinTree` (family 174)
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 174 of the release, *Deterministic construction of strong thin spanning trees*... | Prove StrongThinTree (openai/math family 174: Deterministic construction of strong thin spanning trees) 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/strong-thin-tree",
"version": "1.0.0",
"description": "Prove StrongThinTree (openai/math family 174: Deterministic construction of strong thin spanning trees) 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/StrongThinTree.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/strong-thin-tree |
openai-math/strongly-rayleigh-dpp | # openai/math challenge `StronglyRayleighDPP` (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 of IID*... | Prove StronglyRayleighDPP (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/strongly-rayleigh-dpp",
"version": "1.0.0",
"description": "Prove StronglyRayleighDPP (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.",
"keyword... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/StronglyRayleighDPP.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/strongly-rayleigh-dpp |
openai-math/structural-crouzeix | # openai/math challenge `StructuralCrouzeix` (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 analysi... | Prove StructuralCrouzeix (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/structural-crouzeix",
"version": "1.0.0",
"description": "Prove StructuralCrouzeix (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/StructuralCrouzeix.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/structural-crouzeix |
openai-math/subpolynomial-lp | # openai/math challenge `SubpolynomialLp` (family 094)
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 094 of the release, *Subpolynomial dimension reduction in $L_p$*
(Convex and ... | Prove SubpolynomialLp (openai/math family 094: Subpolynomial dimension reduction in $L_p$) 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/subpolynomial-lp",
"version": "1.0.0",
"description": "Prove SubpolynomialLp (openai/math family 094: Subpolynomial dimension reduction in $L_p$) 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/SubpolynomialLp.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/subpolynomial-lp |
openai-math/subsphere-current | # openai/math challenge `SubsphereCurrent` (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 regre... | Prove SubsphereCurrent (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/subsphere-current",
"version": "1.0.0",
"description": "Prove SubsphereCurrent (openai/math family 140: Memory–sample lower bounds for noiseless Gaussian regression) 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/SubsphereCurrent.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/subsphere-current |
openai-math/superstring | # openai/math challenge `Superstring` (family 128)
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 128 of the release, *A factor-two approximation for shortest common superstring*
... | Prove Superstring (openai/math family 128: A factor-two approximation for shortest common superstring) 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/superstring",
"version": "1.0.0",
"description": "Prove Superstring (openai/math family 128: A factor-two approximation for shortest common superstring) 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/Superstring.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/superstring |
openai-math/switch-chain | # openai/math challenge `SwitchChain` (family 131)
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 131 of the release, *Polynomial mixing of graph switches with prescribed degrees*... | Prove SwitchChain (openai/math family 131: Polynomial mixing of graph switches with prescribed degrees) 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/switch-chain",
"version": "1.0.0",
"description": "Prove SwitchChain (openai/math family 131: Polynomial mixing of graph switches with prescribed degrees) 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/SwitchChain.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/switch-chain |
openai-math/symmetric-domains | # openai/math challenge `SymmetricDomains` (family 058)
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 058 of the release, *The Kollar–Pardon universal-cover conjecture*
(Algebrai... | Prove SymmetricDomains (openai/math family 058: The Kollar–Pardon universal-cover conjecture) 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/symmetric-domains",
"version": "1.0.0",
"description": "Prove SymmetricDomains (openai/math family 058: The Kollar–Pardon universal-cover conjecture) 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/SymmetricDomains.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/symmetric-domains |
openai-math/symmetric-mahler-equality | # openai/math challenge `SymmetricMahlerEquality` (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*
(Co... | Prove SymmetricMahlerEquality (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/symmetric-mahler-equality",
"version": "1.0.0",
"description": "Prove SymmetricMahlerEquality (openai/math family 087: The Mahler conjectures and symplectic width) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keyword... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/SymmetricMahlerEquality.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/symmetric-mahler-equality |
openai-math/symmetric-polar | # openai/math challenge `SymmetricPolar` (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 ... | Prove SymmetricPolar (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/symmetric-polar",
"version": "1.0.0",
"description": "Prove SymmetricPolar (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/SymmetricPolar.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/symmetric-polar |
openai-math/tachikawa | # openai/math challenge `Tachikawa` (family 199)
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 199 of the release, *Counterexamples to conjectures of Auslander–Reiten, Tachikawa,... | Prove Tachikawa (openai/math family 199: Counterexamples to conjectures of Auslander–Reiten, Tachikawa, and Nakayama) 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/tachikawa",
"version": "1.0.0",
"description": "Prove Tachikawa (openai/math family 199: Counterexamples to conjectures of Auslander–Reiten, Tachikawa, and Nakayama) 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/Tachikawa.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/tachikawa |
openai-math/talagrand-discrete-convexity | # openai/math challenge `TalagrandDiscreteConvexity` (family 175)
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 175 of the release, *Talagrand's conjectures and graph decompositi... | Prove TalagrandDiscreteConvexity (openai/math family 175: Talagrand's conjectures and graph decompositions at expectation thresholds) 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/talagrand-discrete-convexity",
"version": "1.0.0",
"description": "Prove TalagrandDiscreteConvexity (openai/math family 175: Talagrand's conjectures and graph decompositions at expectation thresholds) in Lean 4 with Mathlib; graded by Comparator ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/TalagrandDiscreteConvexity.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/talagrand-discrete-convexity |
openai-math/talagrand-expectation-threshold | # openai/math challenge `TalagrandExpectationThreshold` (family 175)
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 175 of the release, *Talagrand's conjectures and graph decompos... | Prove TalagrandExpectationThreshold (openai/math family 175: Talagrand's conjectures and graph decompositions at expectation thresholds) 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/talagrand-expectation-threshold",
"version": "1.0.0",
"description": "Prove TalagrandExpectationThreshold (openai/math family 175: Talagrand's conjectures and graph decompositions at expectation thresholds) in Lean 4 with Mathlib; graded by Compa... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/TalagrandExpectationThreshold.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/talagrand-expectation-threshold |
openai-math/thomason-model-structures | # openai/math challenge `ThomasonModelStructures` (family 317)
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 317 of the release, *Thomason model structures in every strict higher... | Prove ThomasonModelStructures (openai/math family 317: Thomason model structures in every strict higher dimension) 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/thomason-model-structures",
"version": "1.0.0",
"description": "Prove ThomasonModelStructures (openai/math family 317: Thomason model structures in every strict higher dimension) 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/ThomasonModelStructures.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/thomason-model-structures |
openai-math/thompson-nonamenability | # openai/math challenge `ThompsonNonamenability` (family 248)
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 248 of the release, *Thompson's group $F$ is nonamenable*
(Group theor... | Prove ThompsonNonamenability (openai/math family 248: Thompson's group $F$ is nonamenable) 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/thompson-nonamenability",
"version": "1.0.0",
"description": "Prove ThompsonNonamenability (openai/math family 248: Thompson's group $F$ is nonamenable) 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/ThompsonNonamenability.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/thompson-nonamenability |
openai-math/thorp-first-reciprocal | # openai/math challenge `ThorpFirstReciprocal` (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*
(P... | Prove ThorpFirstReciprocal (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/thorp-first-reciprocal",
"version": "1.0.0",
"description": "Prove ThorpFirstReciprocal (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/ThorpFirstReciprocal.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/thorp-first-reciprocal |
openai-math/thorp-remaining | # openai/math challenge `ThorpRemaining` (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*
(Probabi... | Prove ThorpRemaining (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/thorp-remaining",
"version": "1.0.0",
"description": "Prove ThorpRemaining (openai/math family 238: Optimal logarithmic mixing of the Thorp shuffle) 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/ThorpRemaining.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/thorp-remaining |
openai-math/thorp-routing | # openai/math challenge `ThorpRouting` (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*
(Probabili... | Prove ThorpRouting (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/thorp-routing",
"version": "1.0.0",
"description": "Prove ThorpRouting (openai/math family 238: Optimal logarithmic mixing of the Thorp shuffle) 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/ThorpRouting.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/thorp-routing |
openai-math/thorp-weighted-compatibility | # openai/math challenge `ThorpWeightedCompatibility` (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 shuff... | Prove ThorpWeightedCompatibility (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/thorp-weighted-compatibility",
"version": "1.0.0",
"description": "Prove ThorpWeightedCompatibility (openai/math family 238: Optimal logarithmic mixing of the Thorp shuffle) 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/ThorpWeightedCompatibility.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/thorp-weighted-compatibility |
openai-math/three-machine | # openai/math challenge `ThreeMachine` (family 124)
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 124 of the release, *Polynomial-time scheduling on three identical machines*
(Th... | Prove ThreeMachine (openai/math family 124: Polynomial-time scheduling on three identical machines) 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/three-machine",
"version": "1.0.0",
"description": "Prove ThreeMachine (openai/math family 124: Polynomial-time scheduling on three identical machines) 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/ThreeMachine.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/three-machine |
openai-math/three-state-supercritical | # openai/math challenge `ThreeStateSupercritical` (family 229)
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 229 of the release, *Sharp three- and four-state reconstruction thres... | Prove ThreeStateSupercritical (openai/math family 229: Sharp three- and four-state reconstruction thresholds) 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/three-state-supercritical",
"version": "1.0.0",
"description": "Prove ThreeStateSupercritical (openai/math family 229: Sharp three- and four-state reconstruction thresholds) 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/ThreeStateSupercritical.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/three-state-supercritical |
openai-math/three-state-tree-clauses | # openai/math challenge `ThreeStateTreeClauses` (family 229)
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 229 of the release, *Sharp three- and four-state reconstruction thresho... | Prove ThreeStateTreeClauses (openai/math family 229: Sharp three- and four-state reconstruction thresholds) 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/three-state-tree-clauses",
"version": "1.0.0",
"description": "Prove ThreeStateTreeClauses (openai/math family 229: Sharp three- and four-state reconstruction thresholds) 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/ThreeStateTreeClauses.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/three-state-tree-clauses |
openai-math/three-torus | # openai/math challenge `ThreeTorus` (family 144)
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 144 of the release, *Banach's simple Lebesgue-spectrum problem*
(Dynamical systems... | Prove ThreeTorus (openai/math family 144: Banach's simple Lebesgue-spectrum problem) 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/three-torus",
"version": "1.0.0",
"description": "Prove ThreeTorus (openai/math family 144: Banach's simple Lebesgue-spectrum problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"m... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ThreeTorus.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/three-torus |
openai-math/tingley-sphere-isometry | # openai/math challenge `TingleySphereIsometry` (family 322)
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 322 of the release, *Tingley's sphere-isometry problem*
(Functional ana... | Prove TingleySphereIsometry (openai/math family 322: Tingley's sphere-isometry problem) 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/tingley-sphere-isometry",
"version": "1.0.0",
"description": "Prove TingleySphereIsometry (openai/math family 322: Tingley's sphere-isometry problem) 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/TingleySphereIsometry.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/tingley-sphere-isometry |
openai-math/torsion-free-hyperbolic | # openai/math challenge `TorsionFreeHyperbolic` (family 252)
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 252 of the release, *A non-residually-finite torsion-free hyperbolic gr... | Prove TorsionFreeHyperbolic (openai/math family 252: A non-residually-finite torsion-free hyperbolic group) 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/torsion-free-hyperbolic",
"version": "1.0.0",
"description": "Prove TorsionFreeHyperbolic (openai/math family 252: A non-residually-finite torsion-free hyperbolic group) 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/TorsionFreeHyperbolic.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/torsion-free-hyperbolic |
openai-math/torsion-free-zero-divisors | # openai/math challenge `TorsionFreeZeroDivisors` (family 196)
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 196 of the release, *A counterexample to Kaplansky's zero-divisor con... | Prove TorsionFreeZeroDivisors (openai/math family 196: A counterexample to Kaplansky's zero-divisor 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/torsion-free-zero-divisors",
"version": "1.0.0",
"description": "Prove TorsionFreeZeroDivisors (openai/math family 196: A counterexample to Kaplansky's zero-divisor 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/TorsionFreeZeroDivisors.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/torsion-free-zero-divisors |
openai-math/trace-reconstruction | # openai/math challenge `TraceReconstruction` (family 122)
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 122 of the release, *Superpolynomial lower bounds and quasipolynomial rec... | Prove TraceReconstruction (openai/math family 122: Superpolynomial lower bounds and quasipolynomial reconstruction from deletion traces) 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/trace-reconstruction",
"version": "1.0.0",
"description": "Prove TraceReconstruction (openai/math family 122: Superpolynomial lower bounds and quasipolynomial reconstruction from deletion traces) 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/TraceReconstruction.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/trace-reconstruction |
openai-math/tree-edit | # openai/math challenge `TreeEdit` (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 $\ell_1$*
(Convex an... | Prove TreeEdit (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/tree-edit",
"version": "1.0.0",
"description": "Prove TreeEdit (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": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/TreeEdit.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "T... | [
"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/tree-edit |
openai-math/triangle-face | # openai/math challenge `TriangleFace` (family 113)
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 113 of the release, *Approximate counting and the perfect-matching entropy conje... | Prove TriangleFace (openai/math family 113: Approximate counting and the perfect-matching entropy 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/triangle-face",
"version": "1.0.0",
"description": "Prove TriangleFace (openai/math family 113: Approximate counting and the perfect-matching entropy 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/TriangleFace.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/triangle-face |
openai-math/triangle-removal | # openai/math challenge `TriangleRemoval` (family 188)
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 188 of the release, *The sharp constant in random triangle removal*
(Combinat... | Prove TriangleRemoval (openai/math family 188: The sharp constant in random triangle removal) 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/triangle-removal",
"version": "1.0.0",
"description": "Prove TriangleRemoval (openai/math family 188: The sharp constant in random triangle removal) 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/TriangleRemoval.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/triangle-removal |
openai-math/triangular-covering | # openai/math challenge `TriangularCovering` (family 100)
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 100 of the release, *A counterexample to Bang's cylinder-covering bound*
(... | Prove TriangularCovering (openai/math family 100: A counterexample to Bang's cylinder-covering bound) 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/triangular-covering",
"version": "1.0.0",
"description": "Prove TriangularCovering (openai/math family 100: A counterexample to Bang's cylinder-covering 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/TriangularCovering.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/triangular-covering |
openai-math/triangular-energy | # openai/math challenge `TriangularEnergy` (family 090)
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 090 of the release, *Universal optimality of the triangular lattice*
(Convex... | Prove TriangularEnergy (openai/math family 090: Universal optimality of the triangular lattice) 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/triangular-energy",
"version": "1.0.0",
"description": "Prove TriangularEnergy (openai/math family 090: Universal optimality of the triangular lattice) 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/TriangularEnergy.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/triangular-energy |
openai-math/triangular-gaussian | # openai/math challenge `TriangularGaussian` (family 090)
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 090 of the release, *Universal optimality of the triangular lattice*
(Conv... | Prove TriangularGaussian (openai/math family 090: Universal optimality of the triangular lattice) 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/triangular-gaussian",
"version": "1.0.0",
"description": "Prove TriangularGaussian (openai/math family 090: Universal optimality of the triangular lattice) 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/TriangularGaussian.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/triangular-gaussian |
openai-math/triangular-hilbert | # openai/math challenge `TriangularHilbert` (family 082)
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 082 of the release, *Maximal and variational bounds for the triangular Hilb... | Prove TriangularHilbert (openai/math family 082: Maximal and variational bounds for the triangular Hilbert transform) 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/triangular-hilbert",
"version": "1.0.0",
"description": "Prove TriangularHilbert (openai/math family 082: Maximal and variational bounds for the triangular Hilbert transform) 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/TriangularHilbert.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/triangular-hilbert |
openai-math/truffet-counterexample | # openai/math challenge `TruffetCounterexample` (family 104)
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 104 of the release, *Quasipolynomial algorithms for mean-payoff, stocha... | Prove TruffetCounterexample (openai/math family 104: Quasipolynomial algorithms for mean-payoff, stochastic and parity games) 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/truffet-counterexample",
"version": "1.0.0",
"description": "Prove TruffetCounterexample (openai/math family 104: Quasipolynomial algorithms for mean-payoff, stochastic and parity games) 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/TruffetCounterexample.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/truffet-counterexample |
openai-math/two-way-complementation | # openai/math challenge `TwoWayComplementation` (family 129)
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 129 of the release, *Exponential state costs for two-way automata*
(The... | Prove TwoWayComplementation (openai/math family 129: Exponential state costs for two-way automata) 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/two-way-complementation",
"version": "1.0.0",
"description": "Prove TwoWayComplementation (openai/math family 129: Exponential state costs for two-way automata) 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/TwoWayComplementation.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/two-way-complementation |
openai-math/two-way-determinization | # openai/math challenge `TwoWayDeterminization` (family 129)
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 129 of the release, *Exponential state costs for two-way automata*
(The... | Prove TwoWayDeterminization (openai/math family 129: Exponential state costs for two-way automata) 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/two-way-determinization",
"version": "1.0.0",
"description": "Prove TwoWayDeterminization (openai/math family 129: Exponential state costs for two-way automata) 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/TwoWayDeterminization.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/two-way-determinization |
openai-math/type-system-normalization | # openai/math challenge `TypeSystemNormalization` (family 245)
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 245 of the release, *The $\beta$-Barendregt–Geuvers–Klop conjecture*
... | Prove TypeSystemNormalization (openai/math family 245: The $\beta$-Barendregt–Geuvers–Klop conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-logic"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/type-system-normalization",
"version": "1.0.0",
"description": "Prove TypeSystemNormalization (openai/math family 245: The $\\beta$-Barendregt–Geuvers–Klop 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/TypeSystemNormalization.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/type-system-normalization |
openai-math/uniform-commutator | # openai/math challenge `UniformCommutator` (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 UniformCommutator (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/uniform-commutator",
"version": "1.0.0",
"description": "Prove UniformCommutator (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/UniformCommutator.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/uniform-commutator |
openai-math/uniform-gamma | # openai/math challenge `UniformGamma` (family 291)
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 291 of the release, *Toms–Winter and equivariant Jiang–Su stability*
(Operator a... | Prove UniformGamma (openai/math family 291: Toms–Winter and equivariant Jiang–Su stability) 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/uniform-gamma",
"version": "1.0.0",
"description": "Prove UniformGamma (openai/math family 291: Toms–Winter and equivariant Jiang–Su stability) 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/UniformGamma.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/uniform-gamma |
openai-math/uniform-k-server | # openai/math challenge `UniformKServer` (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*... | Prove UniformKServer (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/uniform-k-server",
"version": "1.0.0",
"description": "Prove UniformKServer (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": [... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/UniformKServer.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/uniform-k-server |
openai-math/uniform-sparsest-cut | # openai/math challenge `UniformSparsestCut` (family 117)
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 117 of the release, *Uniform sparsest cut: hardness and semidefinite gaps*... | Prove UniformSparsestCut (openai/math family 117: Uniform sparsest cut: hardness and semidefinite gaps) 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/uniform-sparsest-cut",
"version": "1.0.0",
"description": "Prove UniformSparsestCut (openai/math family 117: Uniform sparsest cut: hardness and semidefinite gaps) 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/UniformSparsestCut.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/uniform-sparsest-cut |
openai-math/unique-games-theorem | # openai/math challenge `UniqueGamesTheorem` (family 102)
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 102 of the release, *The Unique Games Conjecture and optimal approximation... | Prove UniqueGamesTheorem (openai/math family 102: The Unique Games Conjecture and optimal approximation thresholds) 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/unique-games-theorem",
"version": "1.0.0",
"description": "Prove UniqueGamesTheorem (openai/math family 102: The Unique Games Conjecture and optimal approximation thresholds) 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/UniqueGamesTheorem.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/unique-games-theorem |
openai-math/universal-f-infinity | # openai/math challenge `UniversalFInfinity` (family 250)
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 250 of the release, *The Boone–Higman conjecture and higher finiteness*
(G... | Prove UniversalFInfinity (openai/math family 250: The Boone–Higman conjecture and higher finiteness) 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/universal-f-infinity",
"version": "1.0.0",
"description": "Prove UniversalFInfinity (openai/math family 250: The Boone–Higman conjecture and higher finiteness) 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/UniversalFInfinity.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/universal-f-infinity |
openai-math/variable-wl | # openai/math challenge `VariableWL` (family 133)
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 133 of the release, *The complexity of Weisfeiler–Leman refinement*
(Theoretical c... | Prove VariableWL (openai/math family 133: The complexity of Weisfeiler–Leman refinement) 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/variable-wl",
"version": "1.0.0",
"description": "Prove VariableWL (openai/math family 133: The complexity of Weisfeiler–Leman refinement) 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/VariableWL.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/variable-wl |
openai-math/velocity-hemisphere | # openai/math challenge `VelocityHemisphere` (family 220)
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 220 of the release, *Directional zero–one laws and ballisticity in random ... | Prove VelocityHemisphere (openai/math family 220: Directional zero–one laws and ballisticity in random environments) 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/velocity-hemisphere",
"version": "1.0.0",
"description": "Prove VelocityHemisphere (openai/math family 220: Directional zero–one laws and ballisticity in random environments) 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/VelocityHemisphere.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/velocity-hemisphere |
openai-math/vertex-algebra-net | # openai/math challenge `VertexAlgebraNet` (family 280)
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 280 of the release, *Strong locality for strongly rational unitary vertex op... | Prove VertexAlgebraNet (openai/math family 280: Strong locality for strongly rational unitary vertex operator algebras) 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/vertex-algebra-net",
"version": "1.0.0",
"description": "Prove VertexAlgebraNet (openai/math family 280: Strong locality for strongly rational unitary vertex operator algebras) 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/VertexAlgebraNet.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/vertex-algebra-net |
openai-math/vertex-cover | # openai/math challenge `VertexCover` (family 102)
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 102 of the release, *The Unique Games Conjecture and optimal approximation thresh... | Prove VertexCover (openai/math family 102: The Unique Games Conjecture and optimal approximation thresholds) 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/vertex-cover",
"version": "1.0.0",
"description": "Prove VertexCover (openai/math family 102: The Unique Games Conjecture and optimal approximation thresholds) 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/VertexCover.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/vertex-cover |
openai-math/vlasov-maxwell | # openai/math challenge `VlasovMaxwell` (family 362)
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 362 of the release, *Global smoothness for relativistic Vlasov–Maxwell*
(Partia... | Prove VlasovMaxwell (openai/math family 362: Global smoothness for relativistic Vlasov–Maxwell) 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/vlasov-maxwell",
"version": "1.0.0",
"description": "Prove VlasovMaxwell (openai/math family 362: Global smoothness for relativistic Vlasov–Maxwell) 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/VlasovMaxwell.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/vlasov-maxwell |
openai-math/weak-hessian | # openai/math challenge `WeakHessian` (family 356)
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 356 of the release, *Gigli's characterization of Alexandrov curvature*
(Different... | Prove WeakHessian (openai/math family 356: Gigli's characterization of Alexandrov curvature) 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/weak-hessian",
"version": "1.0.0",
"description": "Prove WeakHessian (openai/math family 356: Gigli's characterization of Alexandrov curvature) 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/WeakHessian.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/weak-hessian |
openai-math/weak-mtw-global-support | # openai/math challenge `WeakMTWGlobalSupport` (family 360)
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 360 of the release, *Villani’s convexity conjecture and regular optimal ... | Prove WeakMTWGlobalSupport (openai/math family 360: Villani’s convexity conjecture and regular optimal transport) 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/weak-mtw-global-support",
"version": "1.0.0",
"description": "Prove WeakMTWGlobalSupport (openai/math family 360: Villani’s convexity conjecture and regular optimal transport) 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/WeakMTWGlobalSupport.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/weak-mtw-global-support |
openai-math/weighted-sweep-moments | # openai/math challenge `WeightedSweepMoments` (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*
(P... | Prove WeightedSweepMoments (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/weighted-sweep-moments",
"version": "1.0.0",
"description": "Prove WeightedSweepMoments (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/WeightedSweepMoments.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/weighted-sweep-moments |
openai-math/weisfeiler-leman | # openai/math challenge `WeisfeilerLeman` (family 133)
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 133 of the release, *The complexity of Weisfeiler–Leman refinement*
(Theoreti... | Prove WeisfeilerLeman (openai/math family 133: The complexity of Weisfeiler–Leman refinement) 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/weisfeiler-leman",
"version": "1.0.0",
"description": "Prove WeisfeilerLeman (openai/math family 133: The complexity of Weisfeiler–Leman refinement) 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/WeisfeilerLeman.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/weisfeiler-leman |
openai-math/witnessed-choice | # openai/math challenge `WitnessedChoice` (family 243)
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 243 of the release, *Choiceless counting does not capture polynomial time*
(M... | Prove WitnessedChoice (openai/math family 243: Choiceless counting does not capture polynomial time) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"mathematical-logic"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/witnessed-choice",
"version": "1.0.0",
"description": "Prove WitnessedChoice (openai/math family 243: Choiceless counting does not capture polynomial time) 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/WitnessedChoice.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/witnessed-choice |
openai-math/wl-identification | # openai/math challenge `WLIdentification` (family 133)
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 133 of the release, *The complexity of Weisfeiler–Leman refinement*
(Theoret... | Prove WLIdentification (openai/math family 133: The complexity of Weisfeiler–Leman refinement) 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/wl-identification",
"version": "1.0.0",
"description": "Prove WLIdentification (openai/math family 133: The complexity of Weisfeiler–Leman refinement) 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/WLIdentification.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/wl-identification |
openai-math/yau-counterexample | # openai/math challenge `YauCounterexample` (family 350)
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 350 of the release, *Yau's nodal conjecture: surfaces and counterexamples*
... | Prove YauCounterexample (openai/math family 350: Yau's nodal conjecture: surfaces and counterexamples) 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/yau-counterexample",
"version": "1.0.0",
"description": "Prove YauCounterexample (openai/math family 350: Yau's nodal conjecture: surfaces and 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/YauCounterexample.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/yau-counterexample |
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