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."
keywords = ["lean4", "mathlib", "theorem-proving", "openai-math", "operator-algebras"]

[metadata]
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"
challenge = "BackwardIntertwiners"
family = "293"
family_title = "A counterexample to the hyperinvariant-subspace problem"
subject = "Operator algebras"
theorems = ["OAI.BackwardIntertwiners.direct_algebra_corollary"]
definition_holes = []
fixed_definitions = []
reference_module = "OAI.Analysis.BackwardIntertwiners.AlgebraCorollary"
reference_modules = 23
reference_lean_bytes = 262844
reference_requires_packages = []
oracle_result = "accepted"
oracle_grade_seconds = 337
difficulty = "research"

[agent]
timeout_sec = 14400
network_mode = "no-network"

[environment]
build_timeout_sec = 5400
cpus = 4
memory_mb = 8192
storage_mb = 10240
workdir = "/workspace"
# Lean sees all host CPUs rather than the sandbox's 4; this bounds `lake build` to 3 parallel jobs.
env = { LEAN_NUM_THREADS = "3" }

[verifier]
timeout_sec = 11936
environment_mode = "separate"
network_mode = "no-network"

[[verifier.collect]]
command = "python3 /opt/openai-math/pack_submission.py"
timeout_sec = 300