{"taskset": {"n_runnable": 0, "name": null, "url_data": null, "catalog_id": null, "owner_type": null, "cited_by": null, "taskset": "replicationbench", "domain": "web-research", "task_kind": null, "environment": null, "grading": null, "path": "datasets/replicationbench", "n_single_container": 90, "n_tasks": 90, "domain_raw": null, "sample_instruction": "# ewald_force_accuracy\n\n## Description\n\nCalculate the median fractional force error compared to a high-precision Ewald summation for a random particle distribution.\n\n## Instructions\n\n1. Simulate a random distribution of 65536 particles in a periodic box (assume unit volume, L=1, particle mass $m=1/N$, G=1).\n2. Implement the Abacus force calculation with Cells Per Dimension (CPD) $K=11$ and multipole order $p=8$, as detailed in the Abacus paper (primarily sections 'Force Solver' and 'Far-field Computation'). This involves:\n   a. An exact decomposition of forces into near-field and far-field components. The simulation volume is partitioned into a $K \\times K \\times K$ (here $11 \\times 11 \\times 11$) cubic lattice of cells.\n   b. Near-field forces: Calculated by direct $1/r^2$ summation for particles in the central cell and its $5^3-1 = 124$ nearest neighboring cells (for a near-field radius of R=2 cell widths). Use the spline softening force law: $F(r) = [10 - 15(r/\\epsilon_s) + 6(r/\\epsilon_s)^2]r/\\epsilon_s^3$ for $r < \\epsilon_s$, and $F(r) = r/r^3$ for $r \\ge \\epsilon_s$. The spline softening length $\\epsilon_s$ is typically $2.16 \\epsilon_p$, where $\\epsilon_p$ is a Plummer-equivalent softening length.\n   c. Far-field forces (static multipole mesh method):\n      i. For each of the $K^3$ cells, compute Cartesian multipole moments $M^{a,b,c} = \\sum_q m_q x_q^a y_q^b z_q^c$ up to order $p=8$. Convert these to a reduced basis of $(p+1)^2$ values.\n      ii. Utilize a precompute", "owner_org": null, "url_repo": null, "url_paper": null, "license": null, "languages": [], "difficulties": {"easy": 37, "hard": 12, "medium": 41}, "categories": ["research"]}, "tasks": [{"agent_timeout": 3600, "category": "research", "compose": false, "difficulty": "hard", "language": "", "oracle": null, "runnable": false, "tags": ["research", "reproduction", "scientific-computing", "astrophysics"], "task": "abacus__ewald_force_accuracy", "taskset": "replicationbench"}, {"agent_timeout": 3600, "category": "research", "compose": false, "difficulty": "hard", "language": "", "oracle": null, "runnable": false, "tags": ["research", "reproduction", "scientific-computing", "astrophysics"], "task": "abacus__ewald_force_comparison", "taskset": "replicationbench"}, {"agent_timeout": 3600, "category": "research", "compose": false, "difficulty": "hard", "language": "", "oracle": null, "runnable": false, "tags": ["research", "reproduction", "scientific-computing", 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"difficulty": "medium", "language": "", "oracle": null, "runnable": false, "tags": ["research", "reproduction", "scientific-computing", "astrophysics"], "task": "astm3__spectra_classification_accuracy_limited_data_10_percent", "taskset": "replicationbench"}, {"agent_timeout": 3600, "category": "research", "compose": false, "difficulty": "easy", "language": "", "oracle": null, "runnable": false, "tags": ["research", "reproduction", "scientific-computing", "astrophysics"], "task": "astm3__spectral_similarity_search", "taskset": "replicationbench"}, {"agent_timeout": 3600, "category": "research", "compose": false, "difficulty": "medium", "language": "", "oracle": null, "runnable": false, "tags": ["research", "reproduction", "scientific-computing", "astrophysics"], "task": "bayes_cal__cold_hot_tandem", "taskset": "replicationbench"}, {"agent_timeout": 3600, "category": "research", "compose": false, "difficulty": "easy", "language": "", "oracle": null, "runnable": false, "tags": 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