name stringlengths 16 45 | instruction stringlengths 3.11k 1.41M | description stringlengths 140 209 | keywords listlengths 5 5 | schema_version stringclasses 1
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|---|---|---|---|---|---|---|---|---|
openai-math/abhyankar-sathaye | # openai/math challenge `AbhyankarSathaye` (family 049)
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 049 of the release, *A stable-coordinate counterexample in four variables*
(... | Prove AbhyankarSathaye (openai/math family 049: A stable-coordinate counterexample in four variables) 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/abhyankar-sathaye",
"version": "1.0.0",
"description": "Prove AbhyankarSathaye (openai/math family 049: A stable-coordinate counterexample in four variables) 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/AbhyankarSathaye.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/abhyankar-sathaye |
openai-math/affine-bernstein | # openai/math challenge `AffineBernstein` (family 353)
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 353 of the release, *The sharp dimension threshold for affine Bernstein rigid... | Prove AffineBernstein (openai/math family 353: The sharp dimension threshold for affine Bernstein rigidity) 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/affine-bernstein",
"version": "1.0.0",
"description": "Prove AffineBernstein (openai/math family 353: The sharp dimension threshold for affine Bernstein rigidity) 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/AffineBernstein.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/affine-bernstein |
openai-math/algorithmic-thin-trees | # openai/math challenge `AlgorithmicThinTrees` (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 ... | Prove AlgorithmicThinTrees (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/algorithmic-thin-trees",
"version": "1.0.0",
"description": "Prove AlgorithmicThinTrees (openai/math family 174: Deterministic construction of strong thin spanning trees) 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/AlgorithmicThinTrees.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/algorithmic-thin-trees |
openai-math/amplitude-damping | # openai/math challenge `AmplitudeDamping` (family 276)
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 276 of the release, *The classical capacity of generalized amplitude damping... | Prove AmplitudeDamping (openai/math family 276: The classical capacity of generalized amplitude damping) 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/amplitude-damping",
"version": "1.0.0",
"description": "Prove AmplitudeDamping (openai/math family 276: The classical capacity of generalized amplitude damping) 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/AmplitudeDamping.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/amplitude-damping |
openai-math/artin-cat0 | # openai/math challenge `ArtinCAT0` (family 254)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 254 of the release, *Classifying spaces and geometric obstructions for Artin groups... | Prove ArtinCAT0 (openai/math family 254: Classifying spaces and geometric obstructions for Artin groups) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"group-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/artin-cat0",
"version": "1.0.0",
"description": "Prove ArtinCAT0 (openai/math family 254: Classifying spaces and geometric obstructions for Artin groups) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ArtinCAT0.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/artin-cat0 |
openai-math/artin-parabolic-intersections | # openai/math challenge `ArtinParabolicIntersections` (family 254)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 254 of the release, *Classifying spaces and geometric obstruction... | Prove ArtinParabolicIntersections (openai/math family 254: Classifying spaces and geometric obstructions for Artin groups) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"group-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/artin-parabolic-intersections",
"version": "1.0.0",
"description": "Prove ArtinParabolicIntersections (openai/math family 254: Classifying spaces and geometric obstructions for Artin groups) in Lean 4 with Mathlib; graded by Comparator in a separ... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ArtinParabolicIntersections.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/artin-parabolic-intersections |
openai-math/asymptotically-minimal-littlewood | # openai/math challenge `AsymptoticallyMinimalLittlewood` (family 076)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 076 of the release, *Ultraflat real Littlewood polynomials*
(... | Prove AsymptoticallyMinimalLittlewood (openai/math family 076: Ultraflat real Littlewood polynomials) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"real-and-complex-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/asymptotically-minimal-littlewood",
"version": "1.0.0",
"description": "Prove AsymptoticallyMinimalLittlewood (openai/math family 076: Ultraflat real Littlewood polynomials) 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/AsymptoticallyMinimalLittlewood.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset r... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/asymptotically-minimal-littlewood |
openai-math/auslander-reiten | # openai/math challenge `AuslanderReiten` (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, Tach... | Prove AuslanderReiten (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/auslander-reiten",
"version": "1.0.0",
"description": "Prove AuslanderReiten (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.... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/AuslanderReiten.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/auslander-reiten |
openai-math/backward-intertwiners | # openai/math challenge `BackwardIntertwiners` (family 293)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 293 of the release, *A counterexample to the hyperinvariant-subspace pro... | Prove BackwardIntertwiners (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/backward-intertwiners",
"version": "1.0.0",
"description": "Prove BackwardIntertwiners (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) 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/BackwardIntertwiners.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/backward-intertwiners |
openai-math/balanced-box-routing | # openai/math challenge `BalancedBoxRouting` (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 flows*
... | Prove BalancedBoxRouting (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/balanced-box-routing",
"version": "1.0.0",
"description": "Prove BalancedBoxRouting (openai/math family 376: Universal computation in forced Navier–Stokes flows) 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/BalancedBoxRouting.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/balanced-box-routing |
openai-math/balanced-ryser | # openai/math challenge `BalancedRyser` (family 162)
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 162 of the release, *Counterexamples to Ryser's covering and Gyarfas's tree-cov... | Prove BalancedRyser (openai/math family 162: Counterexamples to Ryser's covering and Gyarfas's tree-cover conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/balanced-ryser",
"version": "1.0.0",
"description": "Prove BalancedRyser (openai/math family 162: Counterexamples to Ryser's covering and Gyarfas's tree-cover conjectures) 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/BalancedRyser.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/balanced-ryser |
openai-math/balanced-three-stack | # openai/math challenge `BalancedThreeStack` (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 flows*
... | Prove BalancedThreeStack (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/balanced-three-stack",
"version": "1.0.0",
"description": "Prove BalancedThreeStack (openai/math family 376: Universal computation in forced Navier–Stokes flows) 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/BalancedThreeStack.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/balanced-three-stack |
openai-math/ball-packing-necessity | # openai/math challenge `BallPackingNecessity` (family 343)
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 343 of the release, *Sharp symplectic ball-packing criteria in higher di... | Prove BallPackingNecessity (openai/math family 343: Sharp symplectic ball-packing criteria in higher dimensions) 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/ball-packing-necessity",
"version": "1.0.0",
"description": "Prove BallPackingNecessity (openai/math family 343: Sharp symplectic ball-packing criteria in higher dimensions) 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/BallPackingNecessity.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/ball-packing-necessity |
openai-math/ball-packing | # openai/math challenge `BallPacking` (family 343)
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 343 of the release, *Sharp symplectic ball-packing criteria in higher dimensions*... | Prove BallPacking (openai/math family 343: Sharp symplectic ball-packing criteria in higher dimensions) 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/ball-packing",
"version": "1.0.0",
"description": "Prove BallPacking (openai/math family 343: Sharp symplectic ball-packing criteria in higher dimensions) 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/BallPacking.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/ball-packing |
openai-math/barnette-hamiltonian | # openai/math challenge `BarnetteHamiltonian` (family 180)
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 180 of the release, *Barnette's Hamiltonian-cycle conjecture*
(Combinator... | Prove BarnetteHamiltonian (openai/math family 180: Barnette's Hamiltonian-cycle 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/barnette-hamiltonian",
"version": "1.0.0",
"description": "Prove BarnetteHamiltonian (openai/math family 180: Barnette's Hamiltonian-cycle 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/BarnetteHamiltonian.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/barnette-hamiltonian |
openai-math/bass-torsion-free | # openai/math challenge `BassTorsionFree` (family 207)
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 207 of the release, *The $\ell^1$-Bass and complex Bass trace conjectures*
(A... | Prove BassTorsionFree (openai/math family 207: The $\ell^1$-Bass and complex Bass trace conjectures) 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/bass-torsion-free",
"version": "1.0.0",
"description": "Prove BassTorsionFree (openai/math family 207: The $\\ell^1$-Bass and complex Bass trace conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/BassTorsionFree.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/bass-torsion-free |
openai-math/bass-trace | # openai/math challenge `BassTrace` (family 207)
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 207 of the release, *The $\ell^1$-Bass and complex Bass trace conjectures*
(Algebra... | Prove BassTrace (openai/math family 207: The $\ell^1$-Bass and complex Bass trace conjectures) 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/bass-trace",
"version": "1.0.0",
"description": "Prove BassTrace (openai/math family 207: The $\\ell^1$-Bass and complex Bass trace 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/BassTrace.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/bass-trace |
openai-math/benjamini-schramm | # openai/math challenge `BenjaminiSchramm` (family 214)
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 214 of the release, *The Benjamini–Schramm nonuniqueness conjecture*
(Probab... | Prove BenjaminiSchramm (openai/math family 214: The Benjamini–Schramm nonuniqueness conjecture) 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/benjamini-schramm",
"version": "1.0.0",
"description": "Prove BenjaminiSchramm (openai/math family 214: The Benjamini–Schramm nonuniqueness 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/BenjaminiSchramm.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/benjamini-schramm |
openai-math/bernoulli-nonflat-in-seven | # openai/math challenge `BernoulliNonflatInSeven` (family 367)
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 367 of the release, *The critical dimension for the one-phase Bernoul... | Prove BernoulliNonflatInSeven (openai/math family 367: The critical dimension for the one-phase Bernoulli problem) 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/bernoulli-nonflat-in-seven",
"version": "1.0.0",
"description": "Prove BernoulliNonflatInSeven (openai/math family 367: The critical dimension for the one-phase Bernoulli problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/BernoulliNonflatInSeven.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/bernoulli-nonflat-in-seven |
openai-math/biholder-transport | # openai/math challenge `BiholderTransport` (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 tra... | Prove BiholderTransport (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/biholder-transport",
"version": "1.0.0",
"description": "Prove BiholderTransport (openai/math family 360: Villani’s convexity conjecture and regular optimal transport) 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/BiholderTransport.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/biholder-transport |
openai-math/bin-packing-gap | # openai/math challenge `BinPackingGap` (family 118)
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 118 of the release, *Unbounded bin-packing gaps and the modified integer round-... | Prove BinPackingGap (openai/math family 118: Unbounded bin-packing gaps and the modified integer round-up 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/bin-packing-gap",
"version": "1.0.0",
"description": "Prove BinPackingGap (openai/math family 118: Unbounded bin-packing gaps and the modified integer round-up 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/BinPackingGap.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/bin-packing-gap |
openai-math/binary-edit-lower | # openai/math challenge `BinaryEditLower` (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 $\ell_1$*
(Co... | Prove BinaryEditLower (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/binary-edit-lower",
"version": "1.0.0",
"description": "Prove BinaryEditLower (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": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/BinaryEditLower.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/binary-edit-lower |
openai-math/binary-matching | # openai/math challenge `BinaryMatching` (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 con... | Prove BinaryMatching (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/binary-matching",
"version": "1.0.0",
"description": "Prove BinaryMatching (openai/math family 113: Approximate counting and the perfect-matching entropy conjecture) 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/BinaryMatching.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/binary-matching |
openai-math/binary-sweep | # openai/math challenge `BinarySweep` (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*
(Probabilit... | Prove BinarySweep (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/binary-sweep",
"version": "1.0.0",
"description": "Prove BinarySweep (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/BinarySweep.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/binary-sweep |
openai-math/bipartite-crossing | # openai/math challenge `BipartiteCrossing` (family 165)
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 165 of the release, *Exact crossing numbers of complete and complete bipart... | Prove BipartiteCrossing (openai/math family 165: Exact crossing numbers of complete and complete bipartite graphs) 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/bipartite-crossing",
"version": "1.0.0",
"description": "Prove BipartiteCrossing (openai/math family 165: Exact crossing numbers of complete and complete bipartite graphs) 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/BipartiteCrossing.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/bipartite-crossing |
openai-math/bogomolov-pop-injectivity | # openai/math challenge `BogomolovPopInjectivity` (family 009)
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 009 of the release, *Bogomolov–Pop and Milnor $K$-theoretic reconstru... | Prove BogomolovPopInjectivity (openai/math family 009: Bogomolov–Pop and Milnor $K$-theoretic reconstruction) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"number-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/bogomolov-pop-injectivity",
"version": "1.0.0",
"description": "Prove BogomolovPopInjectivity (openai/math family 009: Bogomolov–Pop and Milnor $K$-theoretic reconstruction) 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/BogomolovPopInjectivity.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/bogomolov-pop-injectivity |
openai-math/boltzmann-nonuniqueness | # openai/math challenge `BoltzmannNonuniqueness` (family 363)
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 363 of the release, *Boltzmann nonuniqueness with exact local conserva... | Prove BoltzmannNonuniqueness (openai/math family 363: Boltzmann nonuniqueness with exact local conservation) 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/boltzmann-nonuniqueness",
"version": "1.0.0",
"description": "Prove BoltzmannNonuniqueness (openai/math family 363: Boltzmann nonuniqueness with exact local conservation) 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/BoltzmannNonuniqueness.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/boltzmann-nonuniqueness |
openai-math/boone-higman | # openai/math challenge `BooneHigman` (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*
(Group th... | Prove BooneHigman (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/boone-higman",
"version": "1.0.0",
"description": "Prove BooneHigman (openai/math family 250: The Boone–Higman conjecture and higher finiteness) 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/BooneHigman.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/boone-higman |
openai-math/borsuk-nine | # openai/math challenge `BorsukNine` (family 156)
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 156 of the release, *Borsuk's conjecture fails in dimension nine*
(Combinatorics).... | Prove BorsukNine (openai/math family 156: Borsuk's conjecture fails in dimension nine) 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/borsuk-nine",
"version": "1.0.0",
"description": "Prove BorsukNine (openai/math family 156: Borsuk's conjecture fails in dimension nine) 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/BorsukNine.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/borsuk-nine |
openai-math/bounded-recovery | # openai/math challenge `BoundedRecovery` (family 290)
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 290 of the release, *Connes' bicentralizer conjecture and relative bicentrali... | Prove BoundedRecovery (openai/math family 290: Connes' bicentralizer conjecture and relative bicentralizers) 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/bounded-recovery",
"version": "1.0.0",
"description": "Prove BoundedRecovery (openai/math family 290: Connes' bicentralizer conjecture and relative bicentralizers) 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/BoundedRecovery.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/bounded-recovery |
openai-math/bounded-tree-potentials | # openai/math challenge `BoundedTreePotentials` (family 331)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 331 of the release, *Asymptotic midpoint uniform convexity without asym... | Prove BoundedTreePotentials (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/bounded-tree-potentials",
"version": "1.0.0",
"description": "Prove BoundedTreePotentials (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparat... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/BoundedTreePotentials.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/bounded-tree-potentials |
openai-math/bounded-treewidth-l1 | # openai/math challenge `BoundedTreewidthL1` (family 089)
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 089 of the release, *Bounded-distortion $L_1$ embeddings of planar and bou... | Prove BoundedTreewidthL1 (openai/math family 089: Bounded-distortion $L_1$ embeddings of planar and bounded-treewidth graphs) 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/bounded-treewidth-l1",
"version": "1.0.0",
"description": "Prove BoundedTreewidthL1 (openai/math family 089: Bounded-distortion $L_1$ embeddings of planar and bounded-treewidth graphs) in Lean 4 with Mathlib; graded by Comparator in a separate sa... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/BoundedTreewidthL1.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/bounded-treewidth-l1 |
openai-math/brenier | # openai/math challenge `Brenier` (family 374)
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 374 of the release, *Sharp one-third stability of optimal transport maps*
(Partial di... | Prove Brenier (openai/math family 374: Sharp one-third stability of optimal transport maps) 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/brenier",
"version": "1.0.0",
"description": "Prove Brenier (openai/math family 374: Sharp one-third stability of optimal transport maps) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/Brenier.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "Br... | [
"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/brenier |
openai-math/brennan-sharp | # openai/math challenge `BrennanSharp` (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 pre... | Prove BrennanSharp (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/brennan-sharp",
"version": "1.0.0",
"description": "Prove BrennanSharp (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.",
"keyword... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/BrennanSharp.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/brennan-sharp |
openai-math/brennan | # openai/math challenge `Brennan` (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 predicti... | Prove Brennan (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/brennan",
"version": "1.0.0",
"description": "Prove Brennan (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/Brennan.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "Br... | [
"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/brennan |
openai-math/buffered-ising | # openai/math challenge `BufferedIsing` (family 218)
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 218 of the release, *Conformal universality for weakly interacting and disorder... | Prove BufferedIsing (openai/math family 218: Conformal universality for weakly interacting and disordered Ising models) 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/buffered-ising",
"version": "1.0.0",
"description": "Prove BufferedIsing (openai/math family 218: Conformal universality for weakly interacting and disordered Ising models) 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/BufferedIsing.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/buffered-ising |
openai-math/c0-absorption | # openai/math challenge `C0Absorption` (family 324)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 324 of the release, *Lipschitz equivalence without linear isomorphism*
(Function... | Prove C0Absorption (openai/math family 324: Lipschitz equivalence without linear isomorphism) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/c0-absorption",
"version": "1.0.0",
"description": "Prove C0Absorption (openai/math family 324: Lipschitz equivalence without linear isomorphism) 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/C0Absorption.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/c0-absorption |
openai-math/c1-entropy-counterexample | # openai/math challenge `C1EntropyCounterexample` (family 151)
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 151 of the release, *A $C^1$ counterexample to Shub’s entropy conject... | Prove C1EntropyCounterexample (openai/math family 151: A $C^1$ counterexample to Shub’s entropy conjecture) 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/c1-entropy-counterexample",
"version": "1.0.0",
"description": "Prove C1EntropyCounterexample (openai/math family 151: A $C^1$ counterexample to Shub’s entropy 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/C1EntropyCounterexample.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/c1-entropy-counterexample |
openai-math/cannon-geometric-action | # openai/math challenge `CannonGeometricAction` (family 246)
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 246 of the release, *Cannon's conjecture*
(Group theory). The family as... | Prove CannonGeometricAction (openai/math family 246: Cannon's conjecture) 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/cannon-geometric-action",
"version": "1.0.0",
"description": "Prove CannonGeometricAction (openai/math family 246: Cannon's 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/CannonGeometricAction.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/cannon-geometric-action |
openai-math/cayley-percolation | # openai/math challenge `CayleyPercolation` (family 214)
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 214 of the release, *The Benjamini–Schramm nonuniqueness conjecture*
(Proba... | Prove CayleyPercolation (openai/math family 214: The Benjamini–Schramm nonuniqueness conjecture) 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/cayley-percolation",
"version": "1.0.0",
"description": "Prove CayleyPercolation (openai/math family 214: The Benjamini–Schramm nonuniqueness 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/CayleyPercolation.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/cayley-percolation |
openai-math/ch-obstruction | # openai/math challenge `CHObstruction` (family 240)
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 240 of the release, *Shelah's eventual categoricity conjecture*
(Mathematical l... | Prove CHObstruction (openai/math family 240: Shelah's eventual categoricity 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/ch-obstruction",
"version": "1.0.0",
"description": "Prove CHObstruction (openai/math family 240: Shelah's eventual categoricity 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/CHObstruction.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/ch-obstruction |
openai-math/character-criterion | # openai/math challenge `CharacterCriterion` (family 299)
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 299 of the release, *The Kirchberg–R\o rdam character criterion*
(Operator... | Prove CharacterCriterion (openai/math family 299: The Kirchberg–R\o rdam character criterion) 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/character-criterion",
"version": "1.0.0",
"description": "Prove CharacterCriterion (openai/math family 299: The Kirchberg–R\\o rdam character criterion) 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/CharacterCriterion.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/character-criterion |
openai-math/choiceless-polynomial-time | # openai/math challenge `ChoicelessPolynomialTime` (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... | Prove ChoicelessPolynomialTime (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/choiceless-polynomial-time",
"version": "1.0.0",
"description": "Prove ChoicelessPolynomialTime (openai/math family 243: Choiceless counting does not capture polynomial time) 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/ChoicelessPolynomialTime.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/choiceless-polynomial-time |
openai-math/circulant-hadamard | # openai/math challenge `CirculantHadamard` (family 179)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 179 of the release, *The circulant Hadamard conjecture*
(Combinatorics). Th... | Prove CirculantHadamard (openai/math family 179: The circulant Hadamard conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"combinatorics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/circulant-hadamard",
"version": "1.0.0",
"description": "Prove CirculantHadamard (openai/math family 179: The circulant Hadamard 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/CirculantHadamard.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/circulant-hadamard |
openai-math/cks-bondi-penrose | # openai/math challenge `CKSBondiPenrose` (family 260)
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 260 of the release, *Spacetime Penrose inequalities and rigidity*
(Mathematic... | Prove CKSBondiPenrose (openai/math family 260: Spacetime Penrose inequalities and rigidity) 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/cks-bondi-penrose",
"version": "1.0.0",
"description": "Prove CKSBondiPenrose (openai/math family 260: Spacetime Penrose inequalities and rigidity) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lea... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/CKSBondiPenrose.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/cks-bondi-penrose |
openai-math/classical-on | # openai/math challenge `ClassicalON` (family 215)
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 215 of the release, *Massive continuum limits and exact mass asymptotics for plan... | Prove ClassicalON (openai/math family 215: Massive continuum limits and exact mass asymptotics for planar $O(n)$ models) 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/classical-on",
"version": "1.0.0",
"description": "Prove ClassicalON (openai/math family 215: Massive continuum limits and exact mass asymptotics for planar $O(n)$ models) 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/ClassicalON.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/classical-on |
openai-math/clique-free-log | # openai/math challenge `CliqueFreeLog` (family 184)
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 184 of the release, *Coloring and independence in graphs with forbidden subgrap... | Prove CliqueFreeLog (openai/math family 184: Coloring and independence in graphs with forbidden subgraphs) 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/clique-free-log",
"version": "1.0.0",
"description": "Prove CliqueFreeLog (openai/math family 184: Coloring and independence in graphs with forbidden subgraphs) 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/CliqueFreeLog.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/clique-free-log |
openai-math/coboundary-expanders | # openai/math challenge `CoboundaryExpanders` (family 177)
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 177 of the release, *Bounded-degree coboundary expanders in every dimensi... | Prove CoboundaryExpanders (openai/math family 177: Bounded-degree coboundary expanders in every dimension) 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/coboundary-expanders",
"version": "1.0.0",
"description": "Prove CoboundaryExpanders (openai/math family 177: Bounded-degree coboundary expanders in every dimension) 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/CoboundaryExpanders.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/coboundary-expanders |
openai-math/common-bases-fpras | # openai/math challenge `CommonBasesFPRAS` (family 114)
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 114 of the release, *Approximate counting of common integer polymatroid base... | Prove CommonBasesFPRAS (openai/math family 114: Approximate counting of common integer polymatroid bases) 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/common-bases-fpras",
"version": "1.0.0",
"description": "Prove CommonBasesFPRAS (openai/math family 114: Approximate counting of common integer polymatroid bases) 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/CommonBasesFPRAS.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/common-bases-fpras |
openai-math/commuting-derivations | # openai/math challenge `CommutingDerivations` (family 049)
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 049 of the release, *A stable-coordinate counterexample in four variable... | Prove CommutingDerivations (openai/math family 049: A stable-coordinate counterexample in four variables) 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/commuting-derivations",
"version": "1.0.0",
"description": "Prove CommutingDerivations (openai/math family 049: A stable-coordinate counterexample in four variables) 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/CommutingDerivations.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/commuting-derivations |
openai-math/compact-banach | # openai/math challenge `CompactBanach` (family 098)
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 098 of the release, *A negative answer to the Lang–Plaut problem*
(Convex and m... | Prove CompactBanach (openai/math family 098: A negative answer to the Lang–Plaut problem) 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/compact-banach",
"version": "1.0.0",
"description": "Prove CompactBanach (openai/math family 098: A negative answer to the Lang–Plaut problem) 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/CompactBanach.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/compact-banach |
openai-math/complete-crossing | # openai/math challenge `CompleteCrossing` (family 165)
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 165 of the release, *Exact crossing numbers of complete and complete biparti... | Prove CompleteCrossing (openai/math family 165: Exact crossing numbers of complete and complete bipartite graphs) 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/complete-crossing",
"version": "1.0.0",
"description": "Prove CompleteCrossing (openai/math family 165: Exact crossing numbers of complete and complete bipartite graphs) 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/CompleteCrossing.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/complete-crossing |
openai-math/complete-crouzeix | # openai/math challenge `CompleteCrouzeix` (family 325)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 325 of the release, *The complete Crouzeix conjecture*
(Functional analysis)... | Prove CompleteCrouzeix (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/complete-crouzeix",
"version": "1.0.0",
"description": "Prove CompleteCrouzeix (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/CompleteCrouzeix.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/complete-crouzeix |
openai-math/complex-cancellation | # openai/math challenge `ComplexCancellation` (family 047)
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 047 of the release, *Complex counterexamples to cancellation and affine f... | Prove ComplexCancellation (openai/math family 047: Complex counterexamples to cancellation and affine fibrations) 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/complex-cancellation",
"version": "1.0.0",
"description": "Prove ComplexCancellation (openai/math family 047: Complex counterexamples to cancellation and affine fibrations) 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/ComplexCancellation.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/complex-cancellation |
openai-math/conductivity | # openai/math challenge `Conductivity` (family 365)
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 365 of the release, *Joint metric and connection recovery from one boundary patc... | Prove Conductivity (openai/math family 365: Joint metric and connection recovery from one boundary patch) 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/conductivity",
"version": "1.0.0",
"description": "Prove Conductivity (openai/math family 365: Joint metric and connection recovery from one boundary patch) 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/Conductivity.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/conductivity |
openai-math/conjugate-points | # openai/math challenge `ConjugatePoints` (family 358)
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 358 of the release, *A three-manifold with no conjugate points and no nonposi... | Prove ConjugatePoints (openai/math family 358: A three-manifold with no conjugate points and no nonpositively curved metric) 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/conjugate-points",
"version": "1.0.0",
"description": "Prove ConjugatePoints (openai/math family 358: A three-manifold with no conjugate points and no nonpositively curved metric) 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/ConjugatePoints.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/conjugate-points |
openai-math/contingency-tables | # openai/math challenge `ContingencyTables` (family 115)
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 115 of the release, *Sampling and counting contingency tables with arbitrar... | Prove ContingencyTables (openai/math family 115: Sampling and counting contingency tables with arbitrary margins) 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/contingency-tables",
"version": "1.0.0",
"description": "Prove ContingencyTables (openai/math family 115: Sampling and counting contingency tables with arbitrary margins) 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/ContingencyTables.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/contingency-tables |
openai-math/continuous-circle-weight | # openai/math challenge `ContinuousCircleWeight` (family 293)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 293 of the release, *A counterexample to the hyperinvariant-subspace p... | Prove ContinuousCircleWeight (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"operator-algebras"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/continuous-circle-weight",
"version": "1.0.0",
"description": "Prove ContinuousCircleWeight (openai/math family 293: A counterexample to the hyperinvariant-subspace problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/ContinuousCircleWeight.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/continuous-circle-weight |
openai-math/continuum-transition | # openai/math challenge `ContinuumTransition` (family 228)
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 228 of the release, *Continuum phase transitions for radial pair potentia... | Prove ContinuumTransition (openai/math family 228: Continuum phase transitions for radial pair potentials) 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/continuum-transition",
"version": "1.0.0",
"description": "Prove ContinuumTransition (openai/math family 228: Continuum phase transitions for radial pair potentials) 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/ContinuumTransition.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/continuum-transition |
openai-math/coordinate-sweeps | # openai/math challenge `CoordinateSweeps` (family 238)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 238 of the release, *Optimal logarithmic mixing of the Thorp shuffle*
(Proba... | Prove CoordinateSweeps (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/coordinate-sweeps",
"version": "1.0.0",
"description": "Prove CoordinateSweeps (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/CoordinateSweeps.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/coordinate-sweeps |
openai-math/coordinate-trace | # openai/math challenge `CoordinateTrace` (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*
(Probab... | Prove CoordinateTrace (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/coordinate-trace",
"version": "1.0.0",
"description": "Prove CoordinateTrace (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/CoordinateTrace.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/coordinate-trace |
openai-math/cotype | # openai/math challenge `Cotype` (family 326)
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 326 of the release, *The cotype–cotype conjecture under the approximation property*
(F... | Prove Cotype (openai/math family 326: The cotype–cotype conjecture under the approximation property) 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/cotype",
"version": "1.0.0",
"description": "Prove Cotype (openai/math family 326: The cotype–cotype conjecture under the approximation property) 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/Cotype.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "Cot... | [
"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/cotype |
openai-math/coulomb-counterexample | # openai/math challenge `CoulombCounterexample` (family 373)
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 373 of the release, *Nonattainment in three-marginal Coulomb transport*... | Prove CoulombCounterexample (openai/math family 373: Nonattainment in three-marginal Coulomb transport) 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/coulomb-counterexample",
"version": "1.0.0",
"description": "Prove CoulombCounterexample (openai/math family 373: Nonattainment in three-marginal Coulomb transport) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywor... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/CoulombCounterexample.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/coulomb-counterexample |
openai-math/coulomb-ionization | # openai/math challenge `CoulombIonization` (family 263)
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 263 of the release, *The ionization and generalized ionization conjectures*... | Prove CoulombIonization (openai/math family 263: The ionization and generalized ionization conjectures) 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/coulomb-ionization",
"version": "1.0.0",
"description": "Prove CoulombIonization (openai/math family 263: The ionization and generalized ionization conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords":... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/CoulombIonization.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/coulomb-ionization |
openai-math/coulomb-radii | # openai/math challenge `CoulombRadii` (family 263)
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 263 of the release, *The ionization and generalized ionization conjectures*
(Mat... | Prove CoulombRadii (openai/math family 263: The ionization and generalized ionization conjectures) 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/coulomb-radii",
"version": "1.0.0",
"description": "Prove CoulombRadii (openai/math family 263: The ionization and generalized ionization conjectures) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/CoulombRadii.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/coulomb-radii |
openai-math/courtade-kumar | # openai/math challenge `CourtadeKumar` (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*
(Theoretical... | Prove CourtadeKumar (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/courtade-kumar",
"version": "1.0.0",
"description": "Prove CourtadeKumar (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/CourtadeKumar.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/courtade-kumar |
openai-math/covering-density | # openai/math challenge `CoveringDensity` (family 092)
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 092 of the release, *The optimal order of convex-body covering density*
(Conv... | Prove CoveringDensity (openai/math family 092: The optimal order of convex-body covering density) 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/covering-density",
"version": "1.0.0",
"description": "Prove CoveringDensity (openai/math family 092: The optimal order of convex-body covering density) 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/CoveringDensity.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/covering-density |
openai-math/critical-percolation | # openai/math challenge `CriticalPercolation` (family 213)
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 213 of the release, *No infinite critical clusters on quasi-transitive gr... | Prove CriticalPercolation (openai/math family 213: No infinite critical clusters on quasi-transitive graphs) 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/critical-percolation",
"version": "1.0.0",
"description": "Prove CriticalPercolation (openai/math family 213: No infinite critical clusters on quasi-transitive graphs) 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/CriticalPercolation.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/critical-percolation |
openai-math/critical-sk-mixing | # openai/math challenge `CriticalSKMixing` (family 227)
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 227 of the release, *The dynamical phase transition in the Sherrington–Kirkp... | Prove CriticalSKMixing (openai/math family 227: The dynamical phase transition in the Sherrington–Kirkpatrick model) 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/critical-sk-mixing",
"version": "1.0.0",
"description": "Prove CriticalSKMixing (openai/math family 227: The dynamical phase transition in the Sherrington–Kirkpatrick model) 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/CriticalSKMixing.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/critical-sk-mixing |
openai-math/critical-sk | # openai/math challenge `CriticalSK` (family 227)
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 227 of the release, *The dynamical phase transition in the Sherrington–Kirkpatrick... | Prove CriticalSK (openai/math family 227: The dynamical phase transition in the Sherrington–Kirkpatrick model) 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/critical-sk",
"version": "1.0.0",
"description": "Prove CriticalSK (openai/math family 227: The dynamical phase transition in the Sherrington–Kirkpatrick model) 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/CriticalSK.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/critical-sk |
openai-math/critical-strip-mass | # openai/math challenge `CriticalStripMass` (family 237)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 237 of the release, *The three-quarter diameter exponent for honeycomb walk... | Prove CriticalStripMass (openai/math family 237: The three-quarter diameter exponent for honeycomb walks) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/critical-strip-mass",
"version": "1.0.0",
"description": "Prove CriticalStripMass (openai/math family 237: The three-quarter diameter exponent for honeycomb walks) 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/CriticalStripMass.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/critical-strip-mass |
openai-math/critical-z3 | # openai/math challenge `CriticalZ3` (family 213)
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 213 of the release, *No infinite critical clusters on quasi-transitive graphs*
(Pr... | Prove CriticalZ3 (openai/math family 213: No infinite critical clusters on quasi-transitive graphs) 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/critical-z3",
"version": "1.0.0",
"description": "Prove CriticalZ3 (openai/math family 213: No infinite critical clusters on quasi-transitive graphs) 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/CriticalZ3.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/critical-z3 |
openai-math/crouzeix-hilbert | # openai/math challenge `CrouzeixHilbert` (family 325)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 325 of the release, *The complete Crouzeix conjecture*
(Functional analysis).... | Prove CrouzeixHilbert (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/crouzeix-hilbert",
"version": "1.0.0",
"description": "Prove CrouzeixHilbert (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/CrouzeixHilbert.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/crouzeix-hilbert |
openai-math/cubic-torus | # openai/math challenge `CubicTorus` (family 354)
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 354 of the release, *Isoperimetric regions in the cubic three-torus*
(Differential... | Prove CubicTorus (openai/math family 354: Isoperimetric regions in the cubic three-torus) 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/cubic-torus",
"version": "1.0.0",
"description": "Prove CubicTorus (openai/math family 354: Isoperimetric regions in the cubic three-torus) 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/CubicTorus.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/cubic-torus |
openai-math/cycle-decomposition | # openai/math challenge `CycleDecomposition` (family 181)
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 181 of the release, *The Erd\H{o}s–Gallai cycle-decomposition conjecture*
... | Prove CycleDecomposition (openai/math family 181: The Erd\H{o}s–Gallai cycle-decomposition 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/cycle-decomposition",
"version": "1.0.0",
"description": "Prove CycleDecomposition (openai/math family 181: The Erd\\H{o}s–Gallai cycle-decomposition 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/CycleDecomposition.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/cycle-decomposition |
openai-math/cylinder-covering | # openai/math challenge `CylinderCovering` (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*
(Co... | Prove CylinderCovering (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/cylinder-covering",
"version": "1.0.0",
"description": "Prove CylinderCovering (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/CylinderCovering.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/cylinder-covering |
openai-math/daugavet-moduli | # openai/math challenge `DaugavetModuli` (family 331)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 331 of the release, *Asymptotic midpoint uniform convexity without asymptotica... | Prove DaugavetModuli (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/daugavet-moduli",
"version": "1.0.0",
"description": "Prove DaugavetModuli (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a separat... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/DaugavetModuli.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/daugavet-moduli |
openai-math/degree-rigidity | # openai/math challenge `DegreeRigidity` (family 241)
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 241 of the release, *Rigidity of the Turing degrees*
(Mathematical logic). The... | Prove DegreeRigidity (openai/math family 241: Rigidity of the Turing degrees) 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/degree-rigidity",
"version": "1.0.0",
"description": "Prove DegreeRigidity (openai/math family 241: Rigidity of the Turing degrees) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"math... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/DegreeRigidity.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/degree-rigidity |
openai-math/deligne-drinfeld | # openai/math challenge `DeligneDrinfeld` (family 008)
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 008 of the release, *The Deligne–Drinfeld conjecture*
(Number theory). The fa... | Prove DeligneDrinfeld (openai/math family 008: The Deligne–Drinfeld conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"number-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/deligne-drinfeld",
"version": "1.0.0",
"description": "Prove DeligneDrinfeld (openai/math family 008: The Deligne–Drinfeld conjecture) 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/DeligneDrinfeld.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/deligne-drinfeld |
openai-math/depth-five | # openai/math challenge `DepthFive` (family 135)
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 135 of the release, *Sharp homogeneous depth-five complexity of matrix products*
(T... | Prove DepthFive (openai/math family 135: Sharp homogeneous depth-five complexity of matrix products) 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/depth-five",
"version": "1.0.0",
"description": "Prove DepthFive (openai/math family 135: Sharp homogeneous depth-five complexity of matrix products) 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/DepthFive.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/depth-five |
openai-math/depth-three | # openai/math challenge `DepthThree` (family 112)
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 112 of the release, *Beyond the square-root exponent for depth-three circuits*
(Th... | Prove DepthThree (openai/math family 112: Beyond the square-root exponent for depth-three circuits) 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/depth-three",
"version": "1.0.0",
"description": "Prove DepthThree (openai/math family 112: Beyond the square-root exponent for depth-three circuits) 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/DepthThree.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/depth-three |
openai-math/diamond-distortion | # openai/math challenge `DiamondDistortion` (family 331)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 331 of the release, *Asymptotic midpoint uniform convexity without asymptot... | Prove DiamondDistortion (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"functional-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/diamond-distortion",
"version": "1.0.0",
"description": "Prove DiamondDistortion (openai/math family 331: Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming) in Lean 4 with Mathlib; graded by Comparator in a s... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/DiamondDistortion.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/diamond-distortion |
openai-math/diluted-spin | # openai/math challenge `DilutedSpin` (family 221)
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 221 of the release, *The Mezard–Parisi formula for diluted spin glasses*
(Probabi... | Prove DilutedSpin (openai/math family 221: The Mezard–Parisi formula for diluted spin glasses) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"probability-and-statistical-mechanics"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/diluted-spin",
"version": "1.0.0",
"description": "Prove DilutedSpin (openai/math family 221: The Mezard–Parisi formula for diluted spin glasses) 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/DilutedSpin.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/diluted-spin |
openai-math/dimension-ten-channel | # openai/math challenge `DimensionTenChannel` (family 272)
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 272 of the release, *Entanglement without secret key and the PPT-square c... | Prove DimensionTenChannel (openai/math family 272: Entanglement without secret key and the PPT-square conjecture) 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/dimension-ten-channel",
"version": "1.0.0",
"description": "Prove DimensionTenChannel (openai/math family 272: Entanglement without secret key and the PPT-square 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/DimensionTenChannel.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/dimension-ten-channel |
openai-math/dimension-ten-pair | # openai/math challenge `DimensionTenPair` (family 272)
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 272 of the release, *Entanglement without secret key and the PPT-square conj... | Prove DimensionTenPair (openai/math family 272: Entanglement without secret key and the PPT-square conjecture) 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/dimension-ten-pair",
"version": "1.0.0",
"description": "Prove DimensionTenPair (openai/math family 272: Entanglement without secret key and the PPT-square 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/DimensionTenPair.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/dimension-ten-pair |
openai-math/direct-crouzeix | # openai/math challenge `DirectCrouzeix` (family 325)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 325 of the release, *The complete Crouzeix conjecture*
(Functional analysis). ... | Prove DirectCrouzeix (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/direct-crouzeix",
"version": "1.0.0",
"description": "Prove DirectCrouzeix (openai/math family 325: The complete Crouzeix conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"ma... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/DirectCrouzeix.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/direct-crouzeix |
openai-math/directed-feedback | # openai/math challenge `DirectedFeedback` (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 t... | Prove DirectedFeedback (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/directed-feedback",
"version": "1.0.0",
"description": "Prove DirectedFeedback (openai/math family 102: The Unique Games Conjecture and optimal approximation thresholds) 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/DirectedFeedback.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/directed-feedback |
openai-math/directional-ballisticity | # openai/math challenge `DirectionalBallisticity` (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 ra... | Prove DirectionalBallisticity (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/directional-ballisticity",
"version": "1.0.0",
"description": "Prove DirectionalBallisticity (openai/math family 220: Directional zero–one laws and ballisticity in random environments) in Lean 4 with Mathlib; graded by Comparator in a separate sa... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/DirectionalBallisticity.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/directional-ballisticity |
openai-math/directional-walk | # openai/math challenge `DirectionalWalk` (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 env... | Prove DirectionalWalk (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/directional-walk",
"version": "1.0.0",
"description": "Prove DirectionalWalk (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.",
"ke... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/DirectionalWalk.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/directional-walk |
openai-math/discrete-lipschitz-free | # openai/math challenge `DiscreteLipschitzFree` (family 330)
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 330 of the release, *A negative answer to Kalton's Lipschitz-free appro... | Prove DiscreteLipschitzFree (openai/math family 330: A negative answer to Kalton's Lipschitz-free approximation question) 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/discrete-lipschitz-free",
"version": "1.0.0",
"description": "Prove DiscreteLipschitzFree (openai/math family 330: A negative answer to Kalton's Lipschitz-free approximation question) in Lean 4 with Mathlib; graded by Comparator in a separate san... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/DiscreteLipschitzFree.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/discrete-lipschitz-free |
openai-math/disk-maximal | # openai/math challenge `DiskMaximal` (family 085)
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 085 of the release, *Endpoint regularity of the planar centered maximal function*... | Prove DiskMaximal (openai/math family 085: Endpoint regularity of the planar centered maximal function) 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/disk-maximal",
"version": "1.0.0",
"description": "Prove DiskMaximal (openai/math family 085: Endpoint regularity of the planar centered maximal function) 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/DiskMaximal.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/disk-maximal |
openai-math/dixmier-all-discrete | # openai/math challenge `DixmierAllDiscrete` (family 251)
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 251 of the release, *Amenability, unitarizability, and Ulam stability*
(Gr... | Prove DixmierAllDiscrete (openai/math family 251: Amenability, unitarizability, and Ulam stability) 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/dixmier-all-discrete",
"version": "1.0.0",
"description": "Prove DixmierAllDiscrete (openai/math family 251: Amenability, unitarizability, and Ulam stability) 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/DixmierAllDiscrete.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/dixmier-all-discrete |
openai-math/dixmier | # openai/math challenge `Dixmier` (family 251)
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 251 of the release, *Amenability, unitarizability, and Ulam stability*
(Group theory)... | Prove Dixmier (openai/math family 251: Amenability, unitarizability, and Ulam stability) 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/dixmier",
"version": "1.0.0",
"description": "Prove Dixmier (openai/math family 251: Amenability, unitarizability, and Ulam stability) 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/Dixmier.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challenge": "Di... | [
"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/dixmier |
openai-math/doubling-hilbert | # openai/math challenge `DoublingHilbert` (family 098)
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 098 of the release, *A negative answer to the Lang–Plaut problem*
(Convex and... | Prove DoublingHilbert (openai/math family 098: A negative answer to the Lang–Plaut problem) 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/doubling-hilbert",
"version": "1.0.0",
"description": "Prove DoublingHilbert (openai/math family 098: A negative answer to the Lang–Plaut problem) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/DoublingHilbert.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/doubling-hilbert |
openai-math/dutta-domain | # openai/math challenge `DuttaDomain` (family 194)
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 194 of the release, *Lech's multiplicity conjecture*
(Algebra). The family as a w... | Prove DuttaDomain (openai/math family 194: Lech's multiplicity 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/dutta-domain",
"version": "1.0.0",
"description": "Prove DuttaDomain (openai/math family 194: Lech's multiplicity conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"lean4",
"mathlib",
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/DuttaDomain.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/dutta-domain |
openai-math/dyadic-avoidance | # openai/math challenge `DyadicAvoidance` (family 084)
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 084 of the release, *The geometric case of the Erd\H{o}s similarity conjectur... | Prove DyadicAvoidance (openai/math family 084: The geometric case of the Erd\H{o}s similarity conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"real-and-complex-analysis"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/dyadic-avoidance",
"version": "1.0.0",
"description": "Prove DyadicAvoidance (openai/math family 084: The geometric case of the Erd\\H{o}s similarity 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/DyadicAvoidance.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/dyadic-avoidance |
openai-math/edit-approximation | # openai/math challenge `EditApproximation` (family 121)
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 121 of the release, *Almost-linear expected-time approximation of edit dist... | Prove EditApproximation (openai/math family 121: Almost-linear expected-time approximation of edit distance) 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/edit-approximation",
"version": "1.0.0",
"description": "Prove EditApproximation (openai/math family 121: Almost-linear expected-time approximation of edit distance) 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/EditApproximation.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/edit-approximation |
openai-math/edit-distance | # openai/math challenge `EditDistance` (family 099)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 099 of the release, *The sharp distortion of edit distance into $\ell_1$*
(Conve... | Prove EditDistance (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/edit-distance",
"version": "1.0.0",
"description": "Prove EditDistance (openai/math family 099: The sharp distortion of edit distance into $\\ell_1$) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
"l... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EditDistance.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/edit-distance |
openai-math/egyptian-fractions | # openai/math challenge `EgyptianFractions` (family 025)
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 025 of the release, *Erd\H{o}s’s short Egyptian-fraction conjecture*
(Numbe... | Prove EgyptianFractions (openai/math family 025: Erd\H{o}s’s short Egyptian-fraction conjecture) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"number-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/egyptian-fractions",
"version": "1.0.0",
"description": "Prove EgyptianFractions (openai/math family 025: Erd\\H{o}s’s short Egyptian-fraction 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/EgyptianFractions.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/egyptian-fractions |
openai-math/eilenberg-ganea | # openai/math challenge `EilenbergGanea` (family 249)
Prove the following result from OpenAI's [openai/math](https://github.com/openai/math) release in
Lean 4, with a proof the Lean kernel accepts.
Context: this statement belongs to family 249 of the release, *A finitely generated counterexample to Eilenberg–Ganea*
(... | Prove EilenbergGanea (openai/math family 249: A finitely generated counterexample to Eilenberg–Ganea) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox. | [
"lean4",
"mathlib",
"theorem-proving",
"openai-math",
"group-theory"
] | 1.4 | {
"schema_version": "1.4",
"task": {
"name": "openai-math/eilenberg-ganea",
"version": "1.0.0",
"description": "Prove EilenbergGanea (openai/math family 249: A finitely generated counterexample to Eilenberg–Ganea) in Lean 4 with Mathlib; graded by Comparator in a separate sandbox.",
"keywords": [
... | {
"source": "https://github.com/openai/math",
"source_commit": "adc7f1241b42e322a6451854ab7e4b4c146bf78a",
"source_license": "Apache-2.0",
"source_notice": "tests/Challenge.lean is lean/ComparatorChallenges/EilenbergGanea.lean from openai/math, (c) OpenAI, unchanged; see NOTICE at the dataset root",
"challeng... | [
"environment/Dockerfile",
"environment/fetch_mathlib.sh",
"environment/lake-manifest.json",
"environment/lakefile.lean",
"environment/lean_setup.sh",
"environment/pack_submission.py",
"instruction.md",
"solution/closure.txt",
"solution/reference.py",
"solution/solve.sh",
"task.toml",
"tests/Ch... | tasks/eilenberg-ganea |
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