{"task_id": "task_bude_2021", "title": "Accelerating simulations of electromagnetic waves in hot, magnetized fusion plasmas", "authors": "R H S Budé, D Van Eester, J van Dijk, R J E Jaspers and A B Smolders", "year": 2021, "doi": "10.1088/1361-6587/abd619", "arxiv": null, "paper_files": ["Bude2021.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a plasma physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement electromagnetic wave simulations to reproduce 7 key figures and 1 table.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Accelerating simulations of electromagnetic waves in hot, magnetized fusion plasmas |\n| **Authors** | R H S Budé, D Van Eester, J van Dijk, R J E Jaspers and A B Smolders |\n| **DOI** | 10.1088/1361-6587/abd619 |\n| **Paper File** | `Bude2021.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `Bude2021.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the three electromagnetic wave solver models (Truncated Taylor, Truncated Polynomial Fit, All-Orders)\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - The 1D Helmholtz equation\n   - Hot plasma dielectric tensor (Stix/Swanson notation)\n   - Plasma Dispersion Function\n   - Differential operator replacement for polynomial fit model\n   - RRSE error metric\n   - Power absorption calculation\n3. **Algorithm Details**: Describe the polynomial fitting procedure, finite difference stencil construction, and boundary condition implementation\n4. **Physical Observables**: Explain what each figure/table measures and its physical significance\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduction/`. You need:\n- Core simulation modules (see Section 6 below)\n- Individual scripts for each figure/table\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n### 3.1 Machine Parameters (JET-like)\n| Parameter | Symbol | Value | Unit |\n|-----------|--------|-------|------|\n| Major Radius | $R_0$ | 2.97 | m |\n| Minor Radius | $a$ | 1.05 | m |\n| Spill-over Radius | $a_s$ | 1.35 | m |\n| Magnetic Field Axis | $B_0$ | 3.45 | T |\n| Toroidal Mode | $n_{\\text{tor}}$ | 27 | - |\n| Frequency | $f$ | 51.0 | MHz |\n\n### 3.2 Plasma Profiles\n**Density ($n$) and Temperature ($T$):**\n- **Core ($|x| < a_p$)**: $G_{\\text{core}}(x) = (G_0 - G_p)(1 - (x/a_p)^2)^\\alpha + G_p$\n- **Edge ($|x| \\ge a_p$)**: $G_{\\text{edge}}(x) = G_p e^{-|x-a_p|/\\lambda}$\n- Transition point $a_p = 0.95$ m.\n\n**Specific Coefficients:**\n| Profile | Axis Value ($G_0$) | Edge Value ($G_s$) | $\\alpha$ | $\\lambda$ |\n|---------|--------------------|--------------------|----------|-----------|\n| Density ($n_e, n_i$) | $7 \\times 10^{19}$ m$^{-3}$ | $2 \\times 10^{19}$ m$^{-3}$* | 1.0 | 0.05 |\n| Temperature ($T_e, T_i$) | 5 keV | 100 eV | 1.5 | 0.05 |\n\n*Note: Paper text says $n_s = 2 \\times 10^{19}$, $G_p$ must be calculated to ensure continuity or assumed $G_p \\approx G_s$ given the context.*\n\n**Species:**\n- Deuterium (Major): Fully ionized.\n- Hydrogen (Minor): 5% concentration ($n_H = 0.05 n_e$, $n_D = 0.95 n_e$).\n\n---\n\n## 4. Banned Libraries & Practices\n\nThe following are **NOT allowed**:\n\n| Banned | Reason |\n|--------|--------|\n| `plasma-py` (simulation modules) | Must implement dielectric tensor and wave solvers from scratch. |\n| Closed-source solvers | Code must be pure Python/NumPy/SciPy. |\n| Symbolic Math (SymPy) | Numerical differentiation/fitting should be used as per the paper. |\n\n**Allowed:** `numpy`, `scipy` (specifically `scipy.special` for Bessel/Error functions, `scipy.sparse`, `scipy.linalg`).\n\n---\n\n## 5. Data Files to Reproduce\n\n### 5.1 Figure 2: Plasma Profiles\n**File**: `data/fig2_profiles.csv`\n- **X-axis**: $x$ [m] (-1.5 to 1.5)\n- **Y-axes**: $n_e$ [$10^{19}$ m$^{-3}$], $T_e$ [keV]\n- **Description**: Verify the parabolic core and exponential edge implementation.\n\n### 5.2 Figures 3 & 4: Dielectric Tensor Approximation\n**File**: `data/fig3_4_tensor_fit.csv`\n- **Context**: $x = -0.1$ m (Hydrogen resonance layer).\n- **X-axis**: Normalized wavenumber $k_x \\rho_{LH}$ (-3 to 3).\n- **Y-axes**: $\\text{Re}(\\epsilon_{11})$.\n- **Series**: Calculated exact values, 2nd Order Taylor, 6th Order Polynomial Fit.\n- **Fit Window**: $W = 1.0$ (approx, check paper visual).\n\n### 5.3 Figure 5: Electric Field Comparison\n**File**: `data/fig5_efield.csv`\n- **Domain**: $-0.9 < x < -0.1$ m (IBW region).\n- **Resolution**: $N = 2017$.\n- **Y-axis**: $|E_x|$ [V/m].\n- **Series**: Truncated Taylor, Truncated Polynomial ($N_p=8, W=1.2$).\n- **Note**: The paper compares these against All-Orders. If All-Orders is too expensive, comparing Taylor vs Poly is sufficient.\n\n\n\n### 5.4 Figure 6: Absorbed Power Distribution\n**File**: `data/fig6_power.csv`\n- **Description**: Comparison of power absorption profiles derived from Poynting flux (Eq 50).\n- **X-axis**: $x$ [m] (-1.5 to 1.5).\n- **Y-axis**: $P_{abs}$ [arbitrary units].\n- **Series**:\n    - Per Species: Electron (e), Hydrogen (H), Deuterium (D).\n    - Total Power.\n- **Models**:\n    - Truncated Taylor (illustrating unphysical oscillations/smearing).\n    - Truncated Polynomial Fit ($N_p=8$) (proxy for All-Orders if necessary, as they are visually identical in the paper).\n- **Calculation**: $\\vec{J}_p$ must be calculated by applying the respective differential operator ($\\bar{\\bar{M}}_{op}$) to the solution field $\\vec{E}$.\n\n### 5.5 Figure 7: Convergence (RRSE)\n**File**: `data/fig7_error_scaling.csv`\n- **X-axis**: Number of grid points $N$ (Log scale, 100 to 10,000).\n- **Y-axis**: RRSE (Log scale).\n- **Series**: Truncated Taylor, Truncated Polynomial Fit ($N_p=8$).\n- **Reference**: High resolution Polynomial Fit ($N=12601$) can act as proxy for \"All-Orders\" if full spectral code is not implemented.\n\n### 5.6 Figure 8: Computational Time\n**File**: `data/fig8_timing.csv`\n- **X-axis**: $N$ (Log scale).\n- **Y-axis**: Time [s] (Log scale).\n- **Series**: Matrix Setup Time, Matrix Solve Time (for Poly and Taylor models).\n\n### 5.7 Table 1: Computational Cost Extrapolation\n**File**: `data/table1_extrapolation.csv`\n- **Description**: Extrapolation of runtime scaling to 2D and 3D cases based on 1D benchmarks.\n- **Inputs**: Slope ($\\alpha$) and intercept data derived from Figure 8 (Timing).\n- **Methodology**:\n    1.  **Fit**: Perform linear regression on log-log timing data (from Fig 8) for $N > 2000$ to obtain scaling laws $T \\propto N^\\alpha$ for Setup and Solve phases.\n    2.  **Extrapolate**: Calculate predicted times for:\n        -   $N_{2D} = 200^2 = 40,000$\n        -   $N_{3D} = 200^3 = 8,000,000$\n    3.  **Dimensional Scaling**: Apply the paper's approximation that computational time scales with stencil size $s$ raised to the dimension $D$ ($t \\propto s^D$).\n        -   Truncated Taylor: $s=3$.\n        -   Truncated Polynomial: $s=9$ (for $N_p=8$).\n- **Output Columns**: Model Name, Matrix Setup $\\alpha$, Matrix Invert $\\alpha$, Stencil Size, Time (1D), Time (2D), Time (3D).\n\n### 5.8 Figure 9: Parameter Sweep (RRSE vs Fit Window)\n**File**: `data/fig9_param_sweep.csv`\n-   **Context**: Section 6, analyzing the sensitivity of the Truncated Polynomial Fit model to the window size $W$ and polynomial order $N_p$.\n-   **Fixed Parameter**: Grid resolution $N = 2017$.\n-   **X-axis**: Fit Window $W$ ($0.5$ to $3.0$, step $\\approx 0.1$).\n-   **Y-axis**: RRSE (Log scale).\n-   **Series**:\n    -   Polynomial Orders: $N_p \\in \\{4, 6, 8, 10, 12\\}$.\n    -   Baseline: Truncated Taylor model error (constant line).\n-   **Reference**: Use a high-resolution simulation ($N \\approx 12601$, $N_p=12$) as the ground truth for error calculation.\n\n### 5.9 Figure 10: Component Approximation\n**File**: `data/fig10_function_approx.csv`\n-   **Context**: Section 7 (Discussion), comparing approximation methods for the specific term $f(k) = I_n(\\lambda)e^{-\\lambda}$ (where $\\lambda = \\frac{1}{2} k^2 \\rho^2$).\n-   **Parameters**: Use $n=0$ (Modified Bessel function of the first kind) and normalized units where $\\rho=1$.\n-   **X-axis**: Normalized wavenumber $k \\rho$ (Range: $-2.5$ to $2.5$).\n-   **Y-axis**: Function Value.\n-   **Series**:\n    1.  **Exact**: $I_0(0.5 k^2) e^{-0.5 k^2}$.\n    2.  **Taylor**: 4th Order Taylor expansion around $k=0$.\n    3.  **Polynomial Fit**: 4th Order fit over window $W=2$ (i.e., fit range $[-2, 2]$).\n\n---\n\n## 6. Code Structure\n\n### 6.1 Core Modules\n**Path**: `reproduction/`\n\n1.  `plasma.py`:\n    - Functions for $n(x)$, $T(x)$, $B(x)$.\n    - `get_plasma_parameters(x)` returning $\\omega_{pj}, \\Omega_{cj}, v_{th}, \\rho_L$.\n2.  `dielectric.py`:\n    - `calc_K_tensor(x, k_x, ...)`: Implements Eq (11)-(18).\n    - Uses `scipy.special.wofz` for $Z(\\zeta)$.\n3.  `solvers.py`:\n    - `TaylorSolver`: Constructs sparse matrix using Eq (40)-(43).\n    - `PolyFitSolver`:\n        - Performs polynomial fitting of tensor elements.\n        - Constructs sparse matrix using Eq (46)-(48).\n        - Handles Finite Difference stencils for high order derivatives.\n4.  `run_sim.py`:\n    - Orchestrates the grid generation, solving, and data export.\n\n### 6.2 Figure Scripts\n| Figure/Table | Script Path |\n|--------|-------------|\n| Fig 2 | `reproduction/fig2_profiles.py` |\n| Fig 3,4 | `reproduction/fig3_4_tensor.py` |\n| Fig 5 | `reproduction/fig5_fields.py` |\n| Fig 6 | `reproduction/fig6_power.py` |\n| Fig 7 | `reproduction/fig7_convergence.py` |\n| Fig 8 | `reproduction/fig8_timing.py` |\n| Fig 9 | `reproduction/fig9_params.py` |\n| Fig 10 | `reproduction/fig10_approx.py` |\n| Table 1 | `reproduction/table1_scaling.py` |\n\n### 6.3 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\nMust contain your analysis of the paper's methodology and all formulas needed for reproduction.\n\n### 6.4 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Your methodology and formula analysis\n2. `reproduction/plasma.py` through `reproduction/run_sim.py` — Core simulation modules\n3. `reproduction/fig2_profiles.py` through `reproduction/table1_scaling.py` — Figure/table scripts\n4. `data/fig2_profiles.csv` through `data/table1_extrapolation.csv` — Output data files (9 total)\n\nExport data with 8 decimal places (`%.8e`).\n\n---\n\n## 8. Reproduction Requirements\n\n### 8.1 Computational Constraints\n\n| Requirement | Value | Notes |\n|-------------|-------|-------|\n| **Memory** | 8 GB | High N simulations (10k+) require sparse matrices. |\n| **Precision** | Complex Double | `complex128` in numpy is essential. |\n| **Optimization** | Vectorization | Tensor calculation must be vectorized over $k$ or $x$. |\n| **Total Time Limit** | ~4 hours | For all figures, assuming 1D models only. |\n\n### 8.2 Output Format\n-   **Data Files**: CSV format with headers.\n-   **Precision**: 8 decimal places for floating point values.\n\n---", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the simulations or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/plasma.py", "reproduction/dielectric.py", "reproduction/solvers.py", "reproduction/run_sim.py", "reproduction/fig2_profiles.py", "reproduction/fig3_4_tensor.py", "reproduction/fig5_fields.py", "reproduction/fig6_power.py", "reproduction/fig7_convergence.py", "reproduction/fig8_timing.py", "reproduction/fig9_params.py", "reproduction/fig10_approx.py", "reproduction/table1_scaling.py"], "data": ["data/fig2_profiles.csv", "data/fig3_4_tensor_fit.csv", "data/fig5_efield.csv", "data/fig6_power.csv", "data/fig7_error_scaling.csv", "data/fig8_timing.csv", "data/fig9_param_sweep.csv", "data/fig10_function_approx.csv", "data/table1_extrapolation.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/plasma.py", "reproduction/dielectric.py", "reproduction/solvers.py", "reproduction/run_sim.py", "reproduction/fig2_profiles.py", "reproduction/fig3_4_tensor.py", "reproduction/fig5_fields.py", "reproduction/fig6_power.py", "reproduction/fig7_convergence.py", "reproduction/fig8_timing.py", "reproduction/fig9_params.py", "reproduction/fig10_approx.py", "reproduction/table1_scaling.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "8g", "timeout": 14400, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_davighi_2024", "title": "Topological Portal to the Dark Sector", "authors": "Joe Davighi, Admir Greljo, Nudžeim Selimović", "year": 2024, "doi": null, "arxiv": "2401.09528", "paper_files": ["Davighi2024.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a particle physics phenomenology paper to reproduce. Your goal is to read the paper, understand its methodology, and implement numerical computations to reproduce 2 key figures.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Topological Portal to the Dark Sector |\n| **Authors** | Joe Davighi, Admir Greljo, Nudžeim Selimović |\n| **arXiv** | 2401.09528 |\n| **Paper File** | `paper.md` (in the same task directory) |\n\n---\n\n## 2. Paper Summary\n\nThis letter proposes a novel topological portal between QCD and a dark sector characterized by a global symmetry breaking $K \\to H$. The key insight is that a unique Wess–Zumino–Witten (WZW) term connects three QCD pions to two dark pions on the coset $K/H = SU(2)/SO(2) \\cong S^2$. After gauging QED, this yields dimension-7 interactions coupling $\\gamma \\pi^0 (\\eta)$ to a pair of dark pions $\\chi_1, \\chi_2$.\n\nThe topological portal enables a self-consistent light thermal inelastic dark matter scenario: co-annihilation $\\chi_1 \\chi_2 \\to \\pi^0 \\gamma$ sets the relic abundance via freeze-out below the QCD phase transition, while the inherent antisymmetry of the topological interaction suppresses late-time annihilations and direct detection. The paper computes the relic abundance by solving the Boltzmann equation with a thermally averaged cross section involving a Meijer G-function, and explores the parameter space at Belle II.\n\n---\n\n## 3. Physical Constants and Parameters\n\n| Constant | Symbol | Value |\n|----------|--------|-------|\n| QCD pion decay constant | $f_\\pi$ | 92 MeV |\n| QCD phase transition temperature | $T_{\\mathrm{QCD}}$ | ~160 MeV |\n| Effective relativistic d.o.f. | $g_*$ | ~18 |\n| QED fine structure constant | $\\alpha_Q$ | $e^2/(4\\pi) \\approx 1/137$ |\n| Planck mass | $M_P$ | $1.22 \\times 10^{19}$ GeV |\n| Neutral pion mass | $m_{\\pi^0}$ | 135 MeV |\n| Observed DM relic abundance | $\\Omega_\\chi h^2$ | 0.12 |\n| WZW coefficient | $n$ | 1 (default) |\n\n---\n\n## 4. Tasks\n\n### Task 1: Dark Pion Relic Abundance — Reproduce Fig. 2\n\n**Goal**: Solve the Boltzmann equation for the combined dark pion yield $Y_\\chi(x)$ and reproduce the three qualitatively different freeze-out scenarios shown in Fig. 2 of the paper.\n\n**Physics to implement**:\n- The Boltzmann equation governing the yield evolution is Eq. (6) of the paper, with evolution parameter $x = m_\\chi / T$.\n- The thermally averaged cross section $\\langle \\sigma v \\rangle$ is given by Eq. (8), which involves a Meijer G-function and modified Bessel functions.\n- The equilibrium yield $Y_{\\mathrm{eq}}(x)$ is defined in the text following Eq. (7).\n- The unpolarised cross section $\\sigma$ for $\\chi_1 \\chi_2 \\to \\pi^0 \\gamma$ is given in the text between Eq. (7) and Eq. (8).\n\n**Three scenarios to compute**:\n\n| Scenario | Color in Fig. 2 | $x_{\\mathrm{QCD}}$ | Initial condition |\n|----------|-----------------|---------------------|-------------------|\n| (a) Pre-existing thermal equilibrium | Blue | 12 | $Y_\\chi(x_{\\mathrm{QCD}}) = Y_{\\mathrm{eq}}(x_{\\mathrm{QCD}})$ |\n| (b) Negligible initial yield | Orange | 17 | $Y_\\chi(x_{\\mathrm{QCD}}) \\approx 0$ |\n| (c) Limiting case | Red | 23 | $Y_\\chi(x_{\\mathrm{QCD}}) \\approx 0$ |\n\nFor each scenario, the ratio $x_f = m_\\chi / f_D$ must be chosen such that the asymptotic yield $Y_\\infty$ satisfies the observed relic abundance $\\Omega_\\chi h^2 \\approx 0.12$ via Eq. (9). The paper states that $f_D / m_\\chi \\sim \\mathcal{O}(5.5 - 7) \\times \\sqrt{n}$.\n\n**Output**: `data/fig2.csv`\n\n| Column | Description |\n|--------|-------------|\n| `x` | Evolution parameter $m_\\chi / T$ |\n| `Y_eq` | Equilibrium yield |\n| `Y_blue` | Yield for scenario (a) |\n| `Y_orange` | Yield for scenario (b) |\n| `Y_red` | Yield for scenario (c) |\n\n- $x$ range: from $x = 1$ to $x \\geq 100$, with sufficient resolution to capture freeze-out dynamics.\n- Include $Y_{\\mathrm{eq}}$ across the full $x$ range for reference.\n- The three $Y_\\chi$ curves each start at their respective $x_{\\mathrm{QCD}}$; fill earlier entries with NaN or leave blank.\n\n---\n\n### Task 2: Relic Abundance Contours in Parameter Space — Reproduce Fig. 4 (Red Lines Only)\n\n**Goal**: Find contours in the $(m_{\\chi_1}, \\, f_D/\\sqrt{n})$ plane that yield the observed relic abundance $\\Omega_\\chi h^2 \\approx 0.12$, corresponding to the red lines in Fig. 4.\n\n**Physics to implement**:\n- For each candidate point $(m_{\\chi_1}, \\, f_D/\\sqrt{n})$, solve the Boltzmann equation (as in Task 1) using the limiting scenario ($x_{\\mathrm{QCD}} = x_{\\mathrm{max}} = 23$) and compute the resulting $\\Omega_\\chi h^2$.\n- The cross section $\\langle \\sigma v \\rangle$ depends on $n^2 / (f_\\pi^2 f_D^4)$, which can be re-expressed in terms of $f_D/\\sqrt{n}$.\n- For non-zero mass splitting $\\Delta m_\\chi = m_{\\chi_2} - m_{\\chi_1}$, include the exponential suppression factor $e^{-x\\Delta}$ in the thermally averaged cross section, where $\\Delta = \\Delta m_\\chi / m_{\\chi_1}$ (see discussion around Eq. (10)).\n\n**Three contours to compute**:\n\n| Contour | Mass splitting $\\Delta m_\\chi$ | Notes |\n|---------|-------------------------------|-------|\n| (i) | 0 | No mass splitting |\n| (ii) | $\\approx 1.7 \\, m_{\\pi^0}$ | Detector-stable $\\chi_2$ regime (see Table I) |\n| (iii) | $\\approx 2.5 \\, m_{\\pi^0}$ | Displaced vertex regime (see Table I) |\n\n**Parameter ranges**:\n- $m_{\\chi_1}$: 0.5 to 3.7 GeV (the upper bound comes from $x_{\\mathrm{max}} = 23$, i.e. $m_{\\chi}^{\\mathrm{max}} = x_{\\mathrm{max}} \\times T_{\\mathrm{QCD}}$)\n- $f_D/\\sqrt{n}$: scan over a range sufficient to find the contour (expect $\\mathcal{O}(1 - 30)$ GeV)\n\n**Output**: `data/fig4_relic.csv`\n\n| Column | Description |\n|--------|-------------|\n| `m_chi1_GeV` | Dark pion mass $m_{\\chi_1}$ in GeV |\n| `fD_over_sqrtn_delta0` | $f_D/\\sqrt{n}$ on the $\\Delta m_\\chi = 0$ contour |\n| `fD_over_sqrtn_delta1` | $f_D/\\sqrt{n}$ on the $\\Delta m_\\chi \\approx 1.7 m_{\\pi^0}$ contour |\n| `fD_over_sqrtn_delta2` | $f_D/\\sqrt{n}$ on the $\\Delta m_\\chi \\approx 2.5 m_{\\pi^0}$ contour |\n\n- Use ~50 points in $m_{\\chi_1}$.\n- Note: The BaBar and Belle II exclusion regions in Fig. 4 require Monte Carlo simulation and are NOT part of this task.\n\n---\n\n## 5. Banned Libraries & Practices\n\n| Category | Banned | Allowed Alternative |\n|----------|--------|---------------------|\n| **Cosmology/DM solvers** | `MicrOMEGAs`, `DarkSUSY`, `MadDM`, `DRAKE` | Implement Boltzmann solver from scratch |\n| **Event generators** | `MadGraph`, `Pythia`, `Herwig`, `Sherpa` | Not needed for these tasks |\n| **Symbolic math** | `SymPy` for primary computation | Use for verification only |\n| **GPU libraries** | `cupy`, `PyTorch`, `JAX`, `TensorFlow` | `NumPy`, `SciPy` |\n\n**Allowed**: `NumPy`, `SciPy` (including `scipy.integrate`, `scipy.special`, `scipy.optimize`), `mpmath`, `matplotlib`.\n\n---\n\n## 6. Output Requirements\n\n- All data files go in `data/`\n- All code goes in `reproduce/`\n- CSV files: comma-separated, header row with column names\n- Numeric precision: at least 6 significant figures (`%.6e` format)\n- No prescribed code structure — organize your implementation as you see fit\n- Include a brief `reproduce/ANALYSIS.md` explaining your methodology, key assumptions, and comparison with paper results\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n\n1. `reproduce/ANALYSIS.md` — Methodology analysis and comparison with paper\n2. Code files in `reproduce/` — Your implementation (structure at your discretion)\n3. `data/fig2.csv` — Dark pion yield for three scenarios (Task 1)\n4. `data/fig4_relic.csv` — Relic abundance contours (Task 2)\n\n---\n\n## 8. Computational Resources\n\n| Requirement | Value | Notes |\n|-------------|-------|-------|\n| **Total time limit** | ~30 min – 1 hour | Boltzmann ODE solving + parameter scan |\n| **Memory limit** | < 1 GB | No large matrix operations needed |\n| **CPU** | 1 core | Parameter scan is embarrassingly parallel but not required |\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduce/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduce/`\n4. **DO NOT** run the scripts or generate data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any data files.\n", "expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/fig2_compute.py", "reproduce/fig4_compute.py"], "data": ["data/fig2.csv", "data/fig4_relic.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/fig2_compute.py", "reproduce/fig4_compute.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 7200, "pip_install": ["numpy", "scipy", "matplotlib", "mpmath"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.15}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.55}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_dimitrov_2000", "title": "Chirality of Nuclear Rotation", "authors": "S. Dimitrov, T. Frauendorf, F. Dönau", "year": 2000, "doi": "10.1103/PhysRevLett.84.5732", "arxiv": null, "paper_files": ["3-Dimitrov2000Phys.Rev.Lett.5732.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a nuclear-structure paper to reproduce. Your goal is to read the paper, understand its TAC methodology, and implement a self-contained Python reproduction for the main `134Pr` benchmark.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n| --- | --- |\n| **Title** | Chirality of Nuclear Rotation |\n| **Authors** | S. Dimitrov, T. Frauendorf, F. Dönau |\n| **DOI** | 10.1103/PhysRevLett.84.5732 |\n| **Paper Files** | `markdown/3-Dimitrov2000Phys.Rev.Lett.5732.md` |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the paper and identify the methodology needed for the `134Pr` benchmark\n\n### Step 2: Implement the Reproduction\nWrite the full runnable code under `reproduce/`.\n\nThe runtime code must be self-contained:\n\n- It must not require reading benchmark targets from `data/`\n- It must not depend on external Fortran executables\n- It must be runnable directly from inside `reproduce/`\n\nThe expected usage is:\n\n```bash\ncd reproduce\npython main.py\n```\n\n### Step 3: Generate Benchmark Comparison Data\nWrite benchmark comparison CSV files under `data/` so another agent can grade the reproduction numerically.\n\n---\n\n## 3. Input Parameters\n\nThese are the mandatory physical inputs that must be provided explicitly, because they are required to start the reproduction and are not fully specified in the paper text alone.\n\n### 3.1 Woods-Saxon Universal Set\nUse the universal Woods-Saxon parameter set from the cited Cwiok reference:\n\n| Parameter | Value |\n| --- | --- |\n| `V0` | `49.6 MeV` |\n| `kappa` | `0.86` |\n| `a` | `0.70 fm` |\n| `r0(P)` | `1.275 fm` |\n| `r0(N)` | `1.347 fm` |\n| `r0_so(P)` | `1.20 fm` |\n| `r0_so(N)` | `1.310 fm` |\n| `lambda_so(P)` | `36.0` |\n| `lambda_so(N)` | `35.0` |\n\n### 3.2 Required Numerical Handling\n\nThe implementation must keep these methodological details:\n\n- spherical Woods-Saxon energies + Nilsson deformation coupling\n- fixed-gap pairing\n- branch-continuous theta / phi search\n- explicit handling of the BC-crossing region so the calculation stays on the `[nu h11/2]` branch\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category | Banned | Allowed Alternative |\n| --- | --- | --- |\n| External TAC solvers | calling the old Fortran executable | pure Python implementation |\n| GPU / autodiff frameworks | `jax`, `torch`, `tensorflow`, `cupy` | `numpy` |\n| Black-box nuclear packages | any package that directly solves TAC for you | implement the numerical chain yourself |\n| Runtime benchmark dependence | reading target benchmark values from `data/` during solving | embed the needed reproduction inputs in the code |\n\n---\n\n## 5. Data Files to Reproduce\n\nWrite CSV files under `data/` for grading.\n\n### Main `134Pr` angle / spin benchmark\n**File**: `data/pr134_final_reproduction_comparison.csv`\n\nColumns:\n\n`omega,theta_calc,phi_calc,theta_paper,phi_paper,J_calc,J_paper,dtheta,dphi,dJ,J1,J2,J3,RJP_theta,RJP_phi,E`\n\n### Main `134Pr` summary metrics\n**File**: `data/pr134_final_reproduction_metrics.csv`\n\nColumns:\n\n`eps2,gamma_deg,delta_p_mev,delta_n_mev,rms_j,rms_theta_deg,rms_phi_deg,max_abs_dj,worst_omega_mev,worst_j_calc,worst_j_paper`\n\n### Paper benchmark tables\nAlso provide the target benchmark tables in CSV form:\n\n- `data/pr134_table1_angles_j.csv`\n- `data/pr134_table1_transitions.csv`\n- `data/paper_table1_134Pr.csv`\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Required Runtime Entry\n**Path**: `reproduce/main.py`\n\nThis must be the single entry point that produces the final accepted reproduction result.\n\n### 6.2 Required Core Modules\nThe final code under `reproduce/` must include the TAC solver and its direct dependencies.\n\nAt minimum:\n\n- `run_pr134_fortran_search.py`\n- `tac3d_python.py`\n- `ws_reference.py`\n- `python_inputs.py`\n- `tac3d_inputs.py`\n- `tac3d_state.py`\n- `support_routines.py`\n- `nilsson_shell.py`\n- `fortran_parsers.py`\n\n### 6.3 Self-Containment Requirement\nThe runtime code in `reproduce/` must be complete enough that:\n\n1. `python main.py` runs from inside `reproduce/`\n2. it does not import benchmark targets from `data/`\n3. it writes its own output files under `reproduce/results/`\n\n---\n\n## 7. Deliverables Summary\n\nYou must provide:\n\n1. A self-contained `reproduce/` directory\n2. A benchmark `data/` directory with CSV files for grading\n3. A technical summary document under `reproduce/`，named ANALYSIS.md\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduce/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduce/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/main.py", "reproduce/tac3d_python.py", "reproduce/ws_reference.py"], "data": ["data/pr134_final_reproduction_comparison.csv", "data/pr134_final_reproduction_metrics.csv", "data/pr134_table1_angles_j.csv", "data/pr134_table1_transitions.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/main.py", "reproduce/tac3d_python.py", "reproduce/ws_reference.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 21600, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.25}, {"name": "data_accuracy", "weight": 0.4}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_dong_2025", "title": "Enhanced nonlinear Hall effect by Cooper pairs near the superconducting phase transition", "authors": "Zi-Hao Dong, Hui Yang, Yi Zhang", "year": 2025, "doi": "10.1103/PhysRevB.111.155120", "arxiv": null, "paper_files": ["PhysRevB.111.155120.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its content, and implement numerical calculations to reproduce Figure 2.\n\n---\n\n## 1. Article Information\n\n| Field          | Value                                                                                   |\n| -------------- | --------------------------------------------------------------------------------------- |\n| **Title**      | Enhanced nonlinear Hall effect by Cooper pairs near the superconducting phase transition |\n| **Authors**    | Zi-Hao Dong, Hui Yang, and Yi Zhang                                                     |\n| **DOI**        | 10.1103/PhysRevB.111.155120                                                             |\n| **Paper File** | `PhysRevB.111.155120.md` (in the same task directory)                                   |\n\n---\n\n## 2. What You Must Do\n\nRead the full paper (including appendices) and reproduce the data shown in Figure 2. The figure shows the nonlinear Hall susceptibility contributions ($\\chi_0$, $\\chi_\\mathrm{DOS}$, $\\chi_\\mathrm{MT}$, $\\chi_\\mathrm{AL}$) as a function of reduced temperature $\\epsilon = (T - T_c)/T_c$ for the tilted massive Dirac fermion model.\n\nGenerate a single CSV file `data/data.csv` containing all computed values. See Section 4 for the exact column format.\n\n---\n\n## 3. Parameters\n\nUse the following parameter values:\n\n| Parameter | Symbol | Value |\n| --------- | ------ | ----- |\n| Tilt | $t$ | 0.1 |\n| Fermi velocity | $v$ | 0.2 |\n| Mass | $m$ | 0.3 |\n| Fermi energy | $E_F$ | 0.3 |\n| Coupling constant | $g$ | 0.23 |\n| Debye frequency | $\\omega_D$ | 0.1 |\n| Critical temperature | $T_c$ | 0.001 |\n| Mean-free time | $\\tau$ | $2/T_c$, $1/T_c$, $0.5/T_c$ |\n| Anisotropy | $r$ | 0 (main panels), 0.1 (insets) |\n| Phase-breaking rate | $\\gamma_\\phi$ | 0.2 |\n| Layer thickness | $l_z$ | 1 |\n| Reduced temperature | $\\epsilon$ | 100 log-spaced points from 0.001 to 0.1 |\n\n---\n\n## 4. Output File\n\n**File**: `data/data.csv`\n\nThe file must have the following columns (all susceptibility values are dimensionless, $\\epsilon$ is the reduced temperature):\n\n| Column | Description |\n| ------ | ----------- |\n| `ε` | Reduced temperature $\\epsilon = (T-T_c)/T_c$ |\n| `BCD` | $\\chi_0$ for $\\tau = 1/T_c$, $r = 0$ |\n| `MT` | $\\chi_\\mathrm{MT}$ for $\\tau = 1/T_c$, $r = 0$ |\n| `DOS` | $\\chi_\\mathrm{DOS}$ for $\\tau = 1/T_c$, $r = 0$ |\n| `AL` | $\\chi_\\mathrm{AL}$ (diagrammatic) for $r = 0$ |\n| `MTtau` | $\\chi_\\mathrm{MT}$ for $\\tau = 2/T_c$, $r = 0$ |\n| `DOStau` | $\\chi_\\mathrm{DOS}$ for $\\tau = 2/T_c$, $r = 0$ |\n| `MTr` | $\\chi_\\mathrm{MT}$ for $\\tau = 1/T_c$, $r = 0.1$ |\n| `DOSr` | $\\chi_\\mathrm{DOS}$ for $\\tau = 1/T_c$, $r = 0.1$ |\n| `ALr` | $\\chi_\\mathrm{AL}$ (diagrammatic) for $r = 0.1$ |\n| `tauMT` | $\\chi_\\mathrm{MT}$ for $\\tau = 0.5/T_c$, $r = 0$ |\n| `tauDOS` | $\\chi_\\mathrm{DOS}$ for $\\tau = 0.5/T_c$, $r = 0$ |\n| `ALL` | $\\chi_\\mathrm{AL}$ (semiclassical) for $r = 0$ |\n| `ALLr` | $\\chi_\\mathrm{AL}$ (semiclassical) for $r = 0.1$ |\n| `BCDtau` | $\\chi_0$ for $\\tau = 2/T_c$, $r = 0$ |\n| `tauBCD` | $\\chi_0$ for $\\tau = 0.5/T_c$, $r = 0$ |\n\n---\n\n## 5. Notes\n\n- You may use any programming language or tools.\n- If you save intermediate numerical data, use the filename `data.npz` for the intermediate file.\n- The final deliverable is `data/data.csv`.\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement your computation under `reproduction/` (any language/format)\n4. **DO NOT** run the scripts or generate any data files\n\nYour deliverables are ONLY the analysis document and implementation code.\nDo NOT produce data.npz or data/data.csv.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/data.npz"], "data": ["data/data.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": []}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 3600, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.15}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.55}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_fu_2001", "title": "Classical collisional trajectories as the source of strong-field double ionization of helium in the knee regime", "authors": "L. B. Fu, J. Liu, J. Chen, S. G. Chen", "year": 2001, "doi": "10.1103/PhysRevA.63.043416", "arxiv": null, "paper_files": ["fu2001.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a classical trajectory Monte Carlo (CTMC) simulation to reproduce the key figure showing the \"knee\" structure in helium double ionization.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Classical collisional trajectories as the source of strong-field double ionization of helium in the knee regime |\n| **Authors** | L. B. Fu, J. Liu, J. Chen, S. G. Chen |\n| **DOI** | 10.1103/PhysRevA.63.043416 |\n| **Year** | 2001 |\n| **Paper File** | `fu2001.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `fu2001.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the quasistatic two-step CTMC model (ADK tunneling + classical propagation)\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - Total potential energy (Coulomb + laser interaction)\n   - Equations of motion for both electrons\n   - Microcanonical distribution for the inner electron\n   - ADK tunneling weight formula\n   - Tunnel exit initial conditions\n   - Laser field envelope function\n   - Ionization classification criteria (SI and DI)\n   - Double ionization yield calculation\n3. **Algorithm Details**: Describe the step-by-step CTMC algorithm including KS regularization\n4. **Physical Observables**: Explain the knee structure and what the He²⁺/He⁺ ratio measures\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduction/`. You need:\n- A main simulation script at `reproduction/fig3_knee_structure.py`\n- The script should implement the full CTMC pipeline: ADK sampling, KS-regularized propagation, final state classification, and yield computation\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n### 3.1 Physical Parameters\n| Parameter | Symbol | Value | Units |\n|-----------|--------|-------|-------|\n| Nuclear charge | $Z$ | 2 | — |\n| First ionization potential | $I_{p1}$ | 0.9 | a.u. |\n| Inner electron energy | $E_2$ | -2.0 | a.u. |\n| Characteristic momentum | $p_c$ | 2.0 | a.u. |\n| Threshold field | $F_{th}$ | 0.338 | a.u. |\n\n### 3.2 Laser Parameters\n| Parameter | Symbol | Value | Units |\n|-----------|--------|-------|-------|\n| Wavelength | $\\lambda$ | 780 | nm |\n| Angular frequency | $\\omega$ | 0.0584 | a.u. |\n| Optical period | $T$ | 107.5 | a.u. |\n| Flat-top cycles | $N_{flat}$ | 10 | — |\n| Ramp-down cycles | $N_{ramp}$ | 3 | — |\n\n### 3.3 Sampling Parameters\n| Parameter | Value |\n|-----------|-------|\n| Number of trajectories | $\\geq 10^5$ per intensity |\n| Tunneling phase range | $[-\\pi/2, +\\pi/2]$ |\n\n### 3.4 Intensity Scan (13 points, W/cm²)\n$4 \\times 10^{14}$, $5 \\times 10^{14}$, $6 \\times 10^{14}$, $7 \\times 10^{14}$, $8 \\times 10^{14}$, $1.0 \\times 10^{15}$, $1.2 \\times 10^{15}$, $1.5 \\times 10^{15}$, $1.8 \\times 10^{15}$, $2.0 \\times 10^{15}$, $2.5 \\times 10^{15}$, $3.0 \\times 10^{15}$, $4.0 \\times 10^{15}$\n\n### 3.5 Integrator Parameters\n| Parameter | Value |\n|-----------|-------|\n| Method | RK4/5 (adaptive) |\n| Relative tolerance | $10^{-8}$ |\n\n---\n\n## 4. Banned Libraries\n\n| Banned | Reason |\n|--------|--------|\n| Pre-built strong-field ionization packages (SFIToolbox, etc.) | Must implement CTMC from scratch |\n| GPU-accelerated libraries (cupy, pytorch) for core physics | Keep in NumPy/SciPy |\n| Pre-computed tunneling rate tables | Compute ADK rates algorithmically |\n\n**Allowed**: `numpy`, `scipy` (integrate, optimize), `matplotlib`\n\n---\n\n## 5. Data Files to Reproduce\n\n### 5.1 Figure 3: Knee Structure\n**File**: `data/fig3_knee_structure.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | He²⁺/He⁺ ratio and DI ion signal vs laser intensity showing the \"knee\" |\n| X-axis | Intensity (W/cm²), log scale, range $4 \\times 10^{14}$ to $4 \\times 10^{15}$ |\n| Y-axis | DI ion signal (arb. units), log scale |\n| Data series | 13 intensity points |\n| Key result | Ratio plateaus at ~0.002 in knee regime ($I > 10^{15}$ W/cm²) |\n\n**Columns**: `intensity_Wcm2, di_ion_signal, he2p_he1p_ratio`\n\n**Benchmark criteria**:\n- He²⁺/He⁺ ratio within factor of 3 of reference values\n- Ratio shows plateau for $I > 10^{15}$ W/cm²\n- DI yield increases monotonically with intensity\n- Ratio in knee regime ~0.002 (within factor 2–3)\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Simulation Script\n**Path**: `reproduction/fig3_knee_structure.py`\n\nMust implement:\n- Laser field with envelope (flat-top 10 cycles + cos² ramp-down 3 cycles)\n- Inner electron microcanonical sampling\n- ADK tunneling weight and tunnel exit conditions\n- Adaptive RK4/5 integrator with Kustaanheimo-Stiefel regularization\n- SI/DI classification from final single-particle energies\n- Weighted yield computation\n\n### 6.2 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\n### 6.3 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Methodology and formula analysis\n2. `reproduction/fig3_knee_structure.py` — Main simulation script\n3. `data/fig3_knee_structure.csv` — Knee structure data (13 intensity points)\n\nExport all data with 8 decimal places.\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the Monte Carlo simulation or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/fig3_knee_structure.py"], "data": ["data/fig3_knee_structure.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/fig3_knee_structure.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 21600, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_fu_2008", "title": "Energetic-Particle-Induced Geodesic Acoustic Mode", "authors": "Guoyong Fu", "year": 2008, "doi": "10.1103/PhysRevLett.101.185002", "arxiv": null, "paper_files": ["fu2008.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a kinetic dispersion relation solver to reproduce 3 key figures (Figure 4, which requires a full global PIC simulation, is explicitly excluded).\n\n---\n\n## 1. Article Information\n\n| Field               | Value                                                        |\n| ------------------- | ------------------------------------------------------------ |\n| **Title**           | Energetic-Particle-Induced Geodesic Acoustic Mode            |\n| **Author**          | Guoyong Fu                                                   |\n| **DOI**             | 10.1103/PhysRevLett.101.185002                               |\n| **Paper File**      | `fu2008.md` (in the same task directory)                     |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `fu2008.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the hybrid fluid-kinetic model used to derive the EGAM dispersion relation.\n2. **Key Formulas**: List and explain the formulas needed for the reproduction, including:\n   - The unperturbed orbit integral and the geometric factor $H_p^\\sigma$.\n   - The zero orbit width limit and the local dispersion relation.\n   - The kinetic integral $Q_h$ and the specific anisotropic slowing-down distribution function.\n3. **Algorithm Details**: Describe how to numerically integrate the 2D phase space $(E, \\Lambda)$ safely across the trapped-passing boundary, and how to evaluate $Q_h$ for complex frequencies.\n4. **Physical Observables**: Explain the physical meaning of the standard GAM branch, the unstable EGAM branch, and the damped EGAM branch shown in Figures 1-3.\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduction/`. You need:\n- Core modules for kinetic integration and dispersion root-finding (see Section 6 below).\n- Individual scripts for Figures 1, 2, and 3.\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications. *(Note: Do not attempt to reproduce Figure 4).*\n\n---\n\n## 3. Input Parameters\n\n| Parameter                           | Symbol                        | Values / Range |\n| ----------------------------------- | ----------------------------- | -------------- |\n| Inverse aspect ratio                | $\\epsilon = r/R$              | 0.16           |\n| Peak pitch angle                    | $\\Lambda_0$                   | 0.5            |\n| Pitch angle width                   | $\\Delta\\Lambda$               | 0.2            |\n| Critical velocity ratio             | $v_{\\text{crit}}^3/v_0^3$     | 0.05           |\n| Transit/GAM frequency ratio         | $Z = \\omega_{b0}/\\omega_{\\text{GAM}}$ | 1.0 (Fig 2), 1.8 (Fig 3) |\n| EP pressure fraction                | $Y$                           | 0.0 to 1.0     |\n| Normalized frequency                | $\\omega/\\omega_{b0}$          | 0.0 to 2.0 (Fig 1) |\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category              | Banned                                                        | Allowed Alternative         |\n| --------------------- | ------------------------------------------------------------- | --------------------------- |\n| **Plasma Codes**      | `NOVA-K`, `GTC`, `ORB5`, `LIGKA`                              | Implement from scratch      |\n| **Black-box Solvers** | Pre-built plasma dispersion relation solvers                  | `scipy.optimize.root`       |\n| **Symbolic Math**     | `SymPy` for the primary numerical integration                 | `scipy.integrate`, NumPy    |\n\n*Note: You must construct the kinetic integral and implement the complex root-finding manually using standard numerical libraries.*\n\n---\n\n## 5. Data Files to Reproduce\n\n### Figure 1: Real and Imaginary parts of $Q_h$\n**File**: `data/fig1_qh.csv`\n\n| Property | Value                                              |\n| -------- | -------------------------------------------------- |\n| X-axis   | $\\omega/\\omega_{b0}$ (0.0 to 2.0)                  |\n| Y-axis   | $\\text{Re}(Q_h)$ and $\\text{Im}(Q_h)$              |\n| System   | Local flux surface ($\\epsilon = 0.16$)             |\n\n**X values**: 100 to 300 evenly spaced points from 0.0 to 2.0.\n**Columns**: `omega_norm, Re_Qh, Im_Qh`\n\n---\n\n### Figure 2: Eigenfrequencies vs EP Pressure Fraction ($Z=1.0$)\n**File**: `data/fig2_roots.csv`\n\n| Property | Value                                              |\n| -------- | -------------------------------------------------- |\n| X-axis   | $Y$ (EP pressure fraction, 0.0 to 1.0)             |\n| Y-axis   | $\\text{Re}(\\omega/\\omega_{\\text{GAM}})$ and $\\text{Im}(\\omega)/\\text{Re}(\\omega)$ |\n| System   | $Z = 1.0$                                          |\n| Series   | Standard GAM, Unstable EGAM, Damped EGAM           |\n\n**X values**: Approximately 30-40 evenly spaced points from 0.01 to 1.0.\n**Columns**: `Y, Re_GAM, Im_GAM, Re_EGAM_unstable, Im_EGAM_unstable, Re_EGAM_damped, Im_EGAM_damped`\n*(Use `NaN` if a branch does not exist at a specific $Y$, e.g., EGAM branches for $Y < 0.15$)*.\n\n---\n\n### Figure 3: Eigenfrequencies vs EP Pressure Fraction ($Z=1.8$)\n**File**: `data/fig3_roots.csv`\n\n| Property | Value                                              |\n| -------- | -------------------------------------------------- |\n| X-axis   | $Y$ (EP pressure fraction, 0.0 to 1.0)             |\n| Y-axis   | $\\text{Re}(\\omega/\\omega_{\\text{GAM}})$ and $\\text{Im}(\\omega)/\\text{Re}(\\omega)$ |\n| System   | $Z = 1.8$                                          |\n| Series   | Standard GAM, Unstable EGAM, Damped EGAM           |\n\n**X values**: Approximately 30-40 evenly spaced points from 0.01 to 1.0.\n**Columns**: `Y, Re_GAM, Im_GAM, Re_EGAM_unstable, Im_EGAM_unstable, Re_EGAM_damped, Im_EGAM_damped`\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Modules\n**Path**: `reproduction/`\n\n| File                     | Description                                                                                   |\n| ------------------------ | --------------------------------------------------------------------------------------------- |\n| `kinetic_integrals.py`   | Handles unperturbed orbit integration, phase-space grid setup, and evaluation of $Q_h$.       |\n| `dispersion_solver.py`   | Implements the complex root-finding logic, including analytic continuation/contour methods.   |\n\n### 6.2 Figure Scripts\n| Figure | Script Path                       |\n| ------ | --------------------------------- |\n| Fig 1  | `reproduction/fig1_compute.py`    |\n| Fig 2  | `reproduction/fig2_compute.py`    |\n| Fig 3  | `reproduction/fig3_compute.py`    |\n\n### 6.3 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\nMust contain your analysis of the paper's methodology and the mathematical formulations for the dispersion relation and kinetic resonance integrals.\n\n### 6.4 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Your methodology and formula analysis.\n2. `reproduction/kinetic_integrals.py` & `dispersion_solver.py` — Core physics solvers.\n3. `reproduction/fig1_compute.py` through `fig3_compute.py` — Figure scripts.\n4. `data/fig1_qh.csv` through `fig3_roots.csv` — Output data files (3 total).\n\nExport data with high precision (e.g., `%.6e` or `%.10e`).\n\n---\n\n## 8. Reproduction Requirements\n\n| Requirement          | Value        | Notes                                                                 |\n| -------------------- | ------------ | --------------------------------------------------------------------- |\n| **Total time limit** | ~10 - 30 mins| Root finding in the complex plane can be fast if the Jacobian/Splines are optimized. |\n| **Memory limit**     | < 4 GB       | 2D Phase space meshes generally require minimal memory.               |\n| **CPU**              | 1 - 4 Cores  | Parallelization is optional but helpful for $Y$ parameter scans.      |", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/` (excluding Figure 4)\n4. **DO NOT** run the kinetic dispersion relation simulations or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/kinetic_integrals.py", "reproduction/dispersion_solver.py", "reproduction/fig1_compute.py", "reproduction/fig2_compute.py", "reproduction/fig3_compute.py"], "data": ["data/fig1_qh.csv", "data/fig2_roots.csv", "data/fig3_roots.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/kinetic_integrals.py", "reproduction/dispersion_solver.py", "reproduction/fig1_compute.py", "reproduction/fig2_compute.py", "reproduction/fig3_compute.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "8g", "timeout": 14400, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_fukushima_2004", "title": "Chiral effective model with the Polyakov loop", "authors": "Kenji Fukushima", "year": 2004, "doi": "10.1016/j.physletb.2004.04.027", "arxiv": null, "paper_files": ["Fukushima.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a PNJL (Polyakov-loop extended Nambu--Jona-Lasinio) model to reproduce 3 key figures.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Chiral effective model with the Polyakov loop |\n| **Author** | Kenji Fukushima |\n| **DOI** | 10.1016/j.physletb.2004.04.027 |\n| **Year** | 2004 |\n| **Paper File** | `Fukushima.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `Fukushima.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the PNJL model combining chiral symmetry breaking (NJL sector) with deconfinement (Polyakov loop)\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - The NJL thermodynamic potential\n   - The PNJL thermodynamic potential with color-traced Polyakov loop\n   - The glue potential (Haar-measure + strong-coupling kinetic term)\n   - The gap equations (minimization conditions)\n   - The curvature matrix and susceptibility definitions\n3. **Algorithm Details**: Describe the minimization strategy (L-BFGS-B) and the temperature sweep procedure\n4. **Physical Observables**: Explain the chiral condensate, Polyakov loop, and their susceptibilities\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduction/`. You need:\n- A core PNJL model library at `reproduction/pnjl_model.py`\n- Individual scripts for each figure (see Section 5 below)\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n### 3.1 Physical Parameters\n| Parameter | Symbol | Value | Description |\n|-----------|--------|-------|-------------|\n| Current quark mass | $m_q$ | 5.5 MeV (Fig. 1, 2); 788 MeV (Fig. 3) | Input quark mass |\n| NJL coupling | $G$ | $2 \\times 5.496\\,\\mathrm{GeV}^{-2}$ | Four-quark coupling |\n| UV cutoff | $\\Lambda$ | 631 MeV | Momentum cutoff |\n| String tension | $\\sigma$ | $(425\\,\\mathrm{MeV})^2$ | Glue potential |\n| Inverse lattice spacing | $a^{-1}$ | 272 MeV | Sets $T_d = 270$ MeV |\n| Flavor number | $N_f$ | 2 | Two light flavors |\n| Color number | $N_c$ | 3 | SU(3) |\n| Spacetime dimension | $d$ | 4 | Used in kinetic term |\n\n### 3.2 Fig. 1 Parameters\n| Parameter | Value |\n|-----------|-------|\n| $m_q$ | 5.5 MeV |\n| $\\mu$ | 0 MeV |\n| $T$ range | 0–300 MeV |\n| $\\chi_0$ | $\\langle\\bar{q}q\\rangle$ at $T = 0$ |\n\n### 3.3 Fig. 2 Parameters\n| Parameter | Value |\n|-----------|-------|\n| $m_q$ | 5.5 MeV |\n| $\\mu_E$ | 321 MeV (at the chiral CEP) |\n| $T$ range | 0–300 MeV |\n\n### 3.4 Fig. 3 Parameters\n| Parameter | Value |\n|-----------|-------|\n| $m_q^D$ | 788 MeV |\n| $\\mu$ | 0 MeV |\n| $T$ range (left panel) | 0–300 MeV |\n| $T$ range (right panel) | ~240–280 MeV (zoomed near $T_D$) |\n| $M_{\\max}$ in solver | $m_q + 700$ MeV |\n\n---\n\n## 4. Banned Libraries\n\nThe following libraries/approaches are **NOT allowed** for the core physics computation:\n\n| Banned | Reason |\n|--------|--------|\n| `sympy` for integrals | Use NumPy vectorized trapz integration |\n| Pre-packaged NJL/PNJL solvers | Implement gap equations from scratch |\n| `scipy.optimize.fsolve` for gap equations | Unstable near Haar singularity at $l=1$; use L-BFGS-B |\n\n**Allowed**: `numpy`, `scipy` (for optimization and fitting only), `matplotlib` (for plotting only)\n\n---\n\n## 5. Data Files to Reproduce\n\n### 5.1 Figure 1: PNJL Order Parameters and Susceptibilities at $\\mu = 0$\n**File**: `data/fig1_pnjl.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Left: $\\chi/\\chi_0$ and $l$ vs $T$; Right: $\\chi_q$ and $\\chi_l$ vs $T$ |\n| X-axis | Temperature [MeV], 0–300 |\n| Y-axis (left panel) | Order parameters, 0–1 |\n| Y-axis (right panel, left) | Chiral susceptibility $\\chi_q$, 0–30 |\n| Y-axis (right panel, right) | Polyakov loop susceptibility $\\chi_l$, 0–4 |\n| Parameters | $m_q = 5.5\\,\\mathrm{MeV}$, $\\mu = 0$ |\n| Data series | PNJL: $\\chi/\\chi_0$, $l$; Decoupled: $\\chi/\\chi_0$ from $\\Omega_{\\mathrm{NJL}}$, $l$ from $V_{\\mathrm{glue}}$ |\n\n**Columns**: `T, chi_chi0_pnjl, l_pnjl, chi_chi0_njl, l_glue, chi_q, chi_l`\n\n---\n\n### 5.2 Figure 2: Order Parameters and Susceptibilities near Chiral CEP\n**File**: `data/fig2_pnjl.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Left: $\\chi/\\chi_0$ and $l$ vs $T$ at $\\mu_E = 321\\,\\mathrm{MeV}$; Right: susceptibilities |\n| X-axis | Temperature [MeV], 0–300 |\n| Y-axis (left panel) | Order parameters, 0–1 |\n| Y-axis (right panel, left) | Chiral susceptibility $\\chi_q$, 0–30 |\n| Y-axis (right panel, right) | Polyakov loop susceptibility $\\chi_l$, 0–6 |\n| Parameters | $m_q = 5.5\\,\\mathrm{MeV}$, $\\mu = 321\\,\\mathrm{MeV}$ |\n\n**Columns**: `T, chi_chi0, l, chi_q, chi_l`\n\n---\n\n### 5.3 Figure 3: Order Parameters and Susceptibilities near Deconfinement CEP\n**File**: `data/fig3_pnjl.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Left: $\\chi/\\chi_0$ and $l$ vs $T$ at $m_q^D = 788\\,\\mathrm{MeV}$; Right: zoomed susceptibilities |\n| X-axis (left) | Temperature [MeV], 0–300 |\n| X-axis (right) | Temperature [MeV], 240–280 (zoomed) |\n| Y-axis (left panel) | Order parameters, 0–1 |\n| Y-axis (right panel, left) | Chiral susceptibility $\\chi_q$, 1–3 |\n| Y-axis (right panel, right) | Polyakov loop susceptibility $\\chi_l$, 0–40 |\n| Parameters | $m_q = 788\\,\\mathrm{MeV}$, $\\mu = 0$ |\n| Note | $\\chi_l$ diverges at $T_D \\approx 257\\,\\mathrm{MeV}$ (second-order deconfinement) |\n\n**Columns**: `T, chi_chi0, l, chi_q, chi_l`\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Module\n**Path**: `reproduction/pnjl_model.py`\n\nMust contain:\n- Vacuum NJL zero-point energy (integrated up to cutoff)\n- Standard NJL thermal part\n- PNJL thermal part with color-traced Polyakov loop\n- Glue potential\n- Full PNJL thermodynamic potential\n- L-BFGS-B minimizer returning optimal $(M^*, l^*)$\n- Curvature matrix and susceptibility computation\n- Vectorized temperature sweep\n\n### 6.2 Figure Scripts\n| Figure | Script Path |\n|--------|-------------|\n| Fig 1 | `reproduction/fig1_pnjl.py` |\n| Fig 2 | `reproduction/fig2_pnjl.py` |\n| Fig 3 | `reproduction/fig3_pnjl.py` |\n\n### 6.3 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\n### 6.4 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Your methodology and formula analysis\n2. `reproduction/pnjl_model.py` — Core PNJL model library\n3. `reproduction/fig1_pnjl.py` through `reproduction/fig3_pnjl.py` — Figure scripts\n4. `data/fig1_pnjl.csv` through `data/fig3_pnjl.csv` — Output data files\n\nExport all data with 8 decimal places.\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the simulation scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/pnjl_model.py", "reproduction/fig1_pnjl.py", "reproduction/fig2_pnjl.py", "reproduction/fig3_pnjl.py"], "data": ["data/fig1_pnjl.csv", "data/fig2_pnjl.csv", "data/fig3_pnjl.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/pnjl_model.py", "reproduction/fig1_pnjl.py", "reproduction/fig2_pnjl.py", "reproduction/fig3_pnjl.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 7200, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_gralla_2018", "title": "Observational Signature of High Spin at the Event Horizon Telescope", "authors": "Samuel E. Gralla, Alexandru Lupsasca, Andrew Strominger", "year": 2018, "doi": "10.1093/mnras/sty039", "arxiv": null, "paper_files": ["1710.11112v2.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a general relativity paper to reproduce. Your goal is to read the paper, understand its methodology, and implement the near-extremal Kerr photon ray-tracing computation to reproduce the brightest-image data in Figure 3.\n\n---\n\n## 1. Article Information\n\n| Field               | Value                                                                    |\n| ------------------- | ------------------------------------------------------------------------ |\n| **Title**           | Observational Signature of High Spin at the Event Horizon Telescope      |\n| **Authors**         | Samuel E. Gralla, Alexandru Lupsasca, Andrew Strominger                  |\n| **DOI**             | 10.1093/mnras/sty039                                              |\n| **arXiv**           | 1710.11112v2                                                             |\n| **Paper File**      | `1710.11112v2.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the matched asymptotic expansion framework for photon geodesics in near-extremal Kerr\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - Angular potential and turning points (Eq. 2.9b)\n   - Angular integrals $G_\\theta, \\hat{G}_\\theta, G_\\phi, \\hat{G}_\\phi, G_t, \\hat{G}_t$ (Eqs. 2.22a–c)\n   - Near-extremal parametrization: $\\bar{m}$, $\\Upsilon$, $\\lambda(q)$, $D_s$, $D_o$ (Eqs. 3.20–3.36)\n   - Radial integrals $I_r, \\tilde{I}_r, J_r, \\tilde{J}_r$ (Eqs. 3.18–3.40)\n   - Observation time equation $\\hat{t}_o = N + \\mathcal{G}(q)$ (Eq. 3.38)\n   - Flux formula $F_o/F_N$ with Jacobian determinant (Eqs. 3.47–3.51)\n   - Redshift factor $g$ (Eq. 3.11)\n   - Position on screen $\\beta/\\beta_{\\max}$ (Eq. 3.9)\n3. **Algorithm Details**: Describe the track segment finding procedure (Sec. 4) and the stitching of segments into continuous image tracks\n4. **Physical Observables**: Explain what Figure 3 measures and its physical significance (NHEKline, caustics, primary vs secondary images)\n\n### Step 2: Implement the Computation\nWrite your implementation under `reproduction/`. You may use any language or tool (Python scripts, a single notebook, Mathematica `.nb`, etc.). See Section 6 for what the code must compute.\n\n### Step 3: Generate Data Files\nRun your computation to produce the 9 CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n| Parameter             | Symbol         | Values                           |\n| --------------------- | -------------- | -------------------------------- |\n| Near-extremal param   | $\\epsilon$     | 0.15, 0.01, 0.001               |\n| Source radius          | $\\bar{R}$      | $2^{1/3}$ (ISCO)                |\n| Observer radius        | $R_o$          | 100                              |\n| Observer inclination   | $\\theta_o$     | $\\pi/2 - 0.1$                   |\n| Equatorial crossings   | $m$            | 0–20                            |\n| Radial bounce          | $b$            | 0 (direct), 1 (reflected)       |\n| $\\theta$-direction sign| $s$            | $+1, -1$                        |\n| Winding number         | $N$            | Integers (determined by $\\mathcal{G}$) |\n| NHEKline parameter     | $q$            | $[0.05,\\; q_{\\max})$            |\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category              | Banned                                                          | Allowed Alternative           |\n| --------------------- | --------------------------------------------------------------- | ----------------------------- |\n| **GR Libraries**      | `kerr`, `einsteinpy`, `geodesics`, `pykerr`, `gyoto`            | Implement from scratch        |\n| **Ray-tracing Pkgs**  | `RAPTOR`, `GYOTO`, `Odyssey`, `YNOGK`, `GRay`                  | Build geodesic solver manually|\n| **GPU Libraries**     | `cupy`, `PyTorch`, `JAX`, `TensorFlow`                          | `NumPy`, `SciPy`              |\n| **Symbolic Math**     | `SymPy` for numerical computation                               | Use for verification only     |\n| **Auto-diff**         | `autograd`, `JAX`                                               | Manual / finite differences   |\n\n---\n\n## 5. Data Files to Reproduce\n\nYou must generate the following 9 CSV files, one per (observable, $\\epsilon$) combination. All correspond to Figure 3 of the paper: brightest image tracks for three spin values.\n\n> **Note**: A reference image `data/fig3.png` is provided for visual orientation only. It is **not** part of the grading criteria.\n\n### Figure 3: Position $\\beta/\\beta_{\\max}$ vs $\\hat{t}_o$\n\n| File                  | Columns                          |\n| --------------------- | -------------------------------- |\n| `data/beta_0.15.csv`  | `curve, x, beta_normalized`     |\n| `data/beta_0.01.csv`  | `curve, x, beta_normalized`     |\n| `data/beta_0.001.csv` | `curve, x, beta_normalized`     |\n\n- `curve`: integer curve/track index (1-based)\n- `x`: observation time phase $\\hat{t}_o \\in [0, 1]$\n- `beta_normalized`: screen position $\\beta/\\beta_{\\max} \\in [-1, 1]$\n\nEach file contains all bright image tracks for that $\\epsilon$, with one row per sampled point. Scan all $(m, b, s)$ combinations, stitch into continuous tracks, and output every track that contributes to the brightest images.\n\n---\n\n### Figure 3: Rescaled Flux vs $\\hat{t}_o$\n\n| File              | Columns                          |\n| ----------------- | -------------------------------- |\n| `data/f_0.15.csv` | `curve, x, flux_normalized`     |\n| `data/f_0.01.csv` | `curve, x, flux_normalized`     |\n| `data/f_0.001.csv`| `curve, x, flux_normalized`     |\n\n- `curve`: integer curve/track index (1-based, matching corresponding `beta_*.csv`)\n- `x`: observation time phase $\\hat{t}_o \\in [0, 1]$\n- `flux_normalized`: rescaled flux $F_o/F_N \\cdot |\\log\\epsilon|/\\epsilon$\n\n---\n\n### Figure 3: Redshift $g$ vs $\\hat{t}_o$\n\n| File              | Columns                   |\n| ----------------- | ------------------------- |\n| `data/g_0.15.csv` | `curve, x, g_value`      |\n| `data/g_0.01.csv` | `curve, x, g_value`      |\n| `data/g_0.001.csv`| `curve, x, g_value`      |\n\n- `curve`: integer curve/track index (1-based, matching corresponding `beta_*.csv`)\n- `x`: observation time phase $\\hat{t}_o \\in [0, 1]$\n- `g_value`: photon redshift factor $g = \\sqrt{3}\\,\\bar{R}/(3\\bar{R} + 4\\lambda)$\n\n---\n\n## 6. Code Requirements\n\nYour implementation under `reproduction/` must correctly compute:\n\n1. **Angular integrals**: $G_\\theta$, $\\hat{G}_\\theta$, $G_\\phi$, $\\hat{G}_\\phi$, $G_t$, $\\hat{G}_t$ and their derivatives with respect to $q$ (Eqs. 2.22a–c)\n2. **Near-extremal quantities**: $\\bar{m}$, $\\Upsilon$, $\\lambda(q)$, $D_s$, $D_o$ (Eqs. 3.20–3.36)\n3. **Radial integrals**: $I_r$, $\\tilde{I}_r$, $J_r$, $\\tilde{J}_r$ (Eqs. 3.18–3.40)\n4. **Observables**: $\\hat{t}_o = N + \\mathcal{G}(q)$, flux $F_o/F_N$, redshift $g$, position $\\beta/\\beta_{\\max}$\n5. **Track finding and stitching**: scan $(m, b, s, N)$ combinations, invert $\\mathcal{G}(q)$ to find segments, stitch continuous image tracks\n6. **Output**: generate the 9 CSV files described in Section 5\n\n**Recommended format**: A Mathematica notebook (`reproduction/NumericalCode.nb`) is the recommended implementation format, as it naturally expresses the symbolic–numerical workflow of this paper and makes code review straightforward. However, other formats (Python scripts/modules, Julia, etc.) are also accepted — use whatever you are most comfortable with. There are no prescribed file names. The file `reproduction/ANALYSIS.md` is required regardless of implementation language.\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n\n1. `reproduction/ANALYSIS.md` — methodology and formula analysis\n2. At least one implementation file under `reproduction/` (any format/language)\n3. **9 CSV data files** (primary grading criterion):\n   - `data/beta_0.15.csv`, `data/beta_0.01.csv`, `data/beta_0.001.csv`\n   - `data/f_0.15.csv`, `data/f_0.01.csv`, `data/f_0.001.csv`\n   - `data/g_0.15.csv`, `data/g_0.01.csv`, `data/g_0.001.csv`\n\n---\n\n## 8. Reproduction Requirements\n\n### 8.1 Computational Resources\n\n| Requirement          | Value         | Notes                                          |\n| -------------------- | ------------- | ---------------------------------------------- |\n| **Total time limit** | ~30–60 min    | Dominated by G integral cache and track stitching |\n| **Memory limit**     | 2–4 GB        | Segment storage for all $(m,b,s)$ combinations |\n| **CPU**              | 1–4 Cores     | No parallelization required                    |\n\n### 8.2 Key Numerical Considerations\n\n| Issue                          | Recommendation                                                          |\n| ------------------------------ | ----------------------------------------------------------------------- |\n| Angular integral singularities | Use $\\mu = \\cos\\theta$ substitution to regularize turning points        |\n| $q$ grid resolution            | $\\geq 400$ points in $[0.05, q_{\\max})$ for smooth $\\mathcal{G}(q)$    |\n| G integral derivatives         | Central finite differences with $\\Delta q = 10^{-5}$                   |\n| Flux near $D_s = 0$            | Expect divergence at $m = m_0$; this is physical (caustic)             |\n| Segment stitching              | Match endpoints with tolerances $\\Delta t < 0.02$, $\\Delta q < 0.08$   |\n| $b = 1$ tilde integrals        | Only valid for $\\lambda < 0$; check this condition before evaluating    |\n| $m = 0$ special case           | Only one sign of $s$ contributes; $G^{0,s} = \\hat{G}$ (not $0 \\cdot G - s\\hat{G}$) |\n\n---\n\n## 9. Validation Checks\n\n| Check                                    | Expected Value                            |\n| ---------------------------------------- | ----------------------------------------- |\n| $q_{\\max}$ at $\\theta_o = \\pi/2 - 0.1$  | $\\approx 1.7233$                          |\n| $\\mathcal{G}(q)$ range ($m=2, b=0, s=+1, \\epsilon=0.01$) | $\\approx [6.2, 9.2]$ |\n| $m_0(q=3/2, \\epsilon=0.01, s=+1)$       | $\\approx 2.73$                            |\n| $m_0(q=3/2, \\epsilon=0.01, s=-1)$       | $\\approx 2.58$                            |\n| Redshift at primary peak (Fig 3)         | $g \\approx \\sqrt{3} \\approx 1.73$        |\n| Redshift of secondary images (Fig 3)     | $g \\approx 1/\\sqrt{3} \\approx 0.577$     |\n| Primary composed of segments (Fig 3)     | 3, 4, 5 segments for $\\epsilon = 0.15, 0.01, 0.001$ |\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement your computation under `reproduction/` (any language/format)\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and implementation files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": [], "data": ["data/beta_0.15.csv", "data/beta_0.01.csv", "data/beta_0.001.csv", "data/f_0.15.csv", "data/f_0.01.csv", "data/f_0.001.csv", "data/g_0.15.csv", "data/g_0.01.csv", "data/g_0.001.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": []}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.2}, {"name": "data_accuracy", "weight": 0.45}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_harris_1989", "title": "Lasers without Inversion: Interference of Lifetime-Broadened Resonances", "authors": "S. E. Harris", "year": 1989, "doi": "10.1103/PhysRevLett.62.1033", "arxiv": null, "paper_files": ["10_1989_Lasers_Without_Inversion.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and  to reproduce 3 key figures.\n\n## 1. Article Information\n\n\n\n| Field          | Value                                                                   |\n| :------------- | :---------------------------------------------------------------------- |\n| **Title**      | Lasers without Inversion: Interference of Lifetime-Broadened Resonances |\n| **Author**     | S. E. Harris                                                            |\n| **DOI**        | 10.1103/PhysRevLett.62.1033                                             |\n| **Paper File** | `10_1989_Lasers_Without_Inversion.md` (in the same task directory)      |\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\n\nRead the full paper at `10_1989_Lasers_Without_Inversion.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n\n   * Coupled amplitude equations\n\n   * Hamitonian of the system\n\n   * The absorption transition rate\n\n   * Fano parameters\n\n   * Absorption cross section\n\n   * Emission cross section\n\n2. **Algorithm Details**: Describe the way you solve the coupled amplitude equations\n\n3. **Physical Observables**: Explain what each figure measures and its physical significance\n\n### Step 2: Implement the Simulation\n\nWrite all code under `reproduction/`. You need individual scripts for each figure\n\n### Step 3: Generate Data Files\n\nRun your scripts to produce CSV data files under `data/`. See Section 4 for exact specifications.\n\n\n\n## 3. Banned Libraries & Practices\n\n| Category          | Banned                                 | Allowed Alternative       |\n| :---------------- | :------------------------------------- | :------------------------ |\n| **GPU Libraries** | `cupy`, `PyTorch`, `JAX`, `TensorFlow` | `NumPy`, `SciPy`          |\n| **Symbolic Math** | `SymPy` for numerical computation      | Use for verification only |\n| **Auto-diff**     | `autograd`, `JAX`                      | Manual derivatives**      |\n\n## 4. Data Files to Reproduce\n\n### Figure 2: Gain and loss Profiles of Interfering Levels (3 subfigures)\n\n**File**: `data/fig2.csv`\n\n| Property | Value                                                                                                    |\n| :------- | :------------------------------------------------------------------------------------------------------- |\n| X-axis   | relative detuning $\\eta_2$, ranged from -8 to 8                                                          |\n| Y-axis   | cross section $\\sigma/\\sigma_c$&#x20;                                                                    |\n| System   | $q_3^2=1000$, $\\Gamma_2=1, \\Gamma_3=250$, levels $\\vert2\\rangle$ and $\\vert 3\\rangle$ are separated by 2000 linewidths of level $\\vert 2\\rangle$. For loss profiles, $a_1=1,a_2=a_3=0$ at $t=0$. For Gain profiles, $a_2=1, a_1=a_3 =0$.|\n| Series   | gain profile and loss profile at $q_2^2=1000$ (figure 2a), $q_2^2=10$ (figure 2b), $q_2^2=0$ (figure 2c) |\n\n**X values**: -8, -7.99, -7.98, ..., 7.98, 7.99, 8\n\n**Columns**: `eta2,\"Gain, q_2^2=1000\",\"Loss, q_2^2=1000\",\"Gain, q_2^2=10\",\"Loss, q_2^2=10\",\"Gain, q_2^2=0\",\"Loss, q_2^2=0\"`\n## 5. Code Structure Requirements\n\n### 5.1 Figure Scripts\n\n| Figure | Script Path                    |\n| ------ | ------------------------------ |\n| Fig 2  | `reproduction/fig2_compute.py` |\n\n\n### 5.2 Analysis Document\n\n**Path**: `reproduction/ANALYSIS.md`\n\nMust contain your analysis of the paper's methodology and all formulas needed for reproduction.\n\n### 5.3 Output Directories\n\n* Data files: `data/`\n\n* Code files: `reproduction/`\n\n## 6. Deliverables Summary\n\nUpon completion, the following files must exist:\n\n1. `reproduction/ANALYSIS.md` — Your methodology and formula analysis\n\n2.  `reproduction/fig2_compute.py`  — Figure scripts\n\n3. `data/fig2.csv` — Output data files (7 total)\n\nExport data with 10 decimal places (`%.10e`).\n\n## 7. Reproduction Requirements\n\n### 7.1 Computational Resources\n\n| Requirement          | Value        | Notes                              |\n| -------------------- | ------------ | ---------------------------------- |\n| **Total time limit** | <30 minutes | - |\n| **Memory limit**     | 4 - 8 GB     | -|\n| **CPU**              | 1 - 4 Cores  | No parallelization required        |\n\n\n\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/fig2_compute.py"], "data": ["data/fig2.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/fig2_compute.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.2}, {"name": "data_accuracy", "weight": 0.45}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_harris_1999", "title": "Nonlinear Optics at Low Light Levels", "authors": "S. E. Harris and Lene Vestergaard Hau", "year": 1999, "doi": "10.1103/PhysRevLett.82.4611", "arxiv": null, "paper_files": ["harris1999.md"], "input_files": [], "instruction": "\n# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and reproduce 2 key figures.\n\n---\n\n\n## 1. Article Information\n\n| Field               | Value                                                        |\n| ------------------- | ------------------------------------------------------------ |\n| **Title**           | Nonlinear Optics at Low Light Levels |\n| **Author**          | S. E. Harris and Lene Vestergaard Hau                                              |\n| **Paper File**      | `harris1999.pdf` (in the same task directory)                  |\n\n---\n\n## 2. What You Must Do\n\n### Step 0: File Convert\n\nCheck first: `ls input/` (PDFs) and `ls markdown/` (Converted).\nIf PDF exists but Markdown does not:\n1.  Run: `python convert.py input/<paper>.pdf`\n2.  Wait for conversion.\n3.  **Read** the resulting file in `markdown/` before proceeding.\n4.  If the resulting file is almost the same as the original `pdf/` file, output it as an `input/<paper>.md` file. If not, check the convert process untile the resulting file can be output.\n\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `harris1999.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Key Formulas**: List and explain every formula needed for the reproduction.\n2. **Physical Observables**: Explain what each figure measures and its physical significance\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduction/`. You need:\n- Individual scripts for each figure\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category              | Banned                                                        | Allowed Alternative         |\n| --------------------- | ------------------------------------------------------------- | --------------------------- |\n| **DMRG/TN Libraries** | `TeNPy`, `ITensor`, `ALPS`, `TenPy`, `quimb`, `tensornetwork` | Implement from scratch      |\n| **ED Packages**       | `QuSpin`, `EDKit`, `exact_diag`                               | Build Hamiltonians manually |\n| **GPU Libraries**     | `cupy`, `PyTorch`, `JAX`, `TensorFlow`                        | `NumPy`, `SciPy`            |\n| **Symbolic Math**     | `SymPy` for numerical computation                             | Use for verification only   |\n| **Auto-diff**         | `autograd`, `JAX`                                             | Manual derivatives          |\n\n---\n\n## 5. Data Files to Reproduce\n\n* **Schematic figures:** If a figure is a conceptual/illustrative diagram (示意图) rather than a numerical result (e.g., vector diagrams, geometric illustrations, flow charts), **skip it entirely**,including Figure 2.Only reproduce figures that contain quantitative data or computed curves.                                                                             \n* **Figure 1:** Use the **Normalized Detunning** as the x-axis of Figure 1, with the same units and normalization as the original paper, which is ranging from -0.4 to 0.4. The left Y-axis of Figure 1 is transmission ranging from 0 to 1, while the right Y-axis of Figure 1 is phase ranging from -30 deg to 30 deg. The phase curve is continuously changing.\n* **Figure 3:** use the **Normalized Length** as the x-axis of Figure 3 (ranging from 0 to 4) and function of $\\Phi(\\eta, r)$ ranging from 0 to 0.08 as the Y-axis. There are three curves, corresponding to quantity $r$ of 0.5, 1.0 and 2.0.\n* **Figure 4:**use the **Normalized Length** as the x-axis of Figure 4(ranging from 0 to 1.5). Use the function of $\\Psi(\\eta)$ ranging from 0 to 1 as the Y-axis. There is only one curve without any other lines.\n\n**Requirement:**The shape of reproduced lines and figures are the same as original ones, especially the phase curve in Figure 1. All the settings about coefficients and constant should follow the original files.\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Figure Scripts\n| Figure | Script Path                    |\n| ------ | ------------------------------ |\n| Fig 1  | `reproduction/fig1.py` |\n| Fig 3  | `reproduction/fig3.py` |\n| Fig 4  | `reproduction/fig4.py` |\n\n### 6.2 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\nMust contain your analysis of the paper's methodology and all formulas needed for reproduction.\n\n### 6.3 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Your methodology and formula analysis\n2. `reproduction/fig1.py`, `reproduction/fig3.py` and `reproduction/fig4.py` — Figure scripts\n3. `data/fig1_data.csv`, `data/fig3_data.csv` and `data/fig4_data.csv` — Output data files (3 total)\n\nExport data with 10 decimal places (`%.10e`).\n\n---\n\n## 8. Reproduction Requirements\n\n### 8.1 Computational Resources\n\n| Requirement          | Value        | Notes                              |\n| -------------------- | ------------ | ---------------------------------- |\n| **Total time limit** | ~2 - 4 hours | PBC with $m=200$ and finite sweeps |\n| **Memory limit**     | 4 - 8 GB     | Superblock for $m=200$, $S=1$      |\n| **CPU**              | 1 - 4 Cores  | No parallelization required        |\n\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/fig1.py", "reproduction/fig3.py", "reproduction/fig4.py"], "data": ["data/fig1_data.csv", "data/fig3_data.csv", "data/fig4_data.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/fig1.py", "reproduction/fig3.py", "reproduction/fig4.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_ishikawa_1982", "title": "The glueball mass spectrum in QCD: first results of a lattice Monte Carlo calculation", "authors": "K. Ishikawa, M. Teper, G. Schierholz", "year": 1982, "doi": "", "arxiv": null, "paper_files": ["ishikawa1982.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a lattice gauge theory glueball mass calculation to reproduce the key mass results.\n\n---\n\n## 1. Article Information\n\n| Field               | Value                                                        |\n| ------------------- | ------------------------------------------------------------ |\n| **Title**           | The glueball mass spectrum in QCD: first results of a lattice Monte Carlo calculation |\n| **Authors**         | K. Ishikawa, M. Teper, G. Schierholz                        |\n| **Year**            | 1982                                                         |\n| **Paper File**      | `ishikawa1982.md` (in the same task directory)               |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `ishikawa1982.md`. Write a detailed analysis document at `reproduce/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the variational method with the transfer matrix for glueball mass extraction\n2. **Key Formulas**: List and explain every formula needed, including:\n   - Wilson plaquette action for SU(2)\n   - Transfer matrix expectation values Γ_a/Γ_0, Γ_{2a}/Γ_a\n   - Generalized eigenvalue problem (GEVP) from variational method\n   - Jackknife error estimation\n   - Two-loop lattice spacing formula for SU(2)\n3. **Algorithm Details**: Describe the heat bath algorithm, operator construction for each J^{PC} channel, and correlator measurement\n4. **Physical Observables**: Explain each glueball channel (0++, 2++, 0--) and its significance\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduce/`. You need:\n- Core SU(2) gauge simulation module\n- Glueball operator construction and correlator measurement\n- GEVP solver with jackknife errors\n- Mass extraction scripts\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n| Parameter     | Symbol    | Values                |\n| ------------- | --------- | --------------------- |\n| Gauge group   | —         | SU(2)                 |\n| Lattice (0++/2++) | —     | 4³ × 8               |\n| Lattice (0--)| —         | 6⁴                    |\n| Coupling (0++/2++)| $\\beta$ | 2.3                 |\n| Coupling (0--)| $\\beta$  | 2.5                   |\n| Configurations| —        | 6000 (0++/2++), 12000+ (0--) |\n| Decorrelation | —         | 10 sweeps             |\n| 0++ operators | —         | 4 (plaquette, rectangular, square, 3D 8-link) |\n| 2++ operators | —         | 3 (standard, rectangular, square anisotropic) |\n| 0-- operator  | —         | Clover topological charge density |\n| Lattice spacing| $a(2.3)$ | 0.340 Λ_mom⁻¹        |\n| Lattice spacing| $a(2.5)$ | 0.206 Λ_mom⁻¹        |\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category              | Banned                                           | Allowed Alternative         |\n| --------------------- | ------------------------------------------------ | --------------------------- |\n| **Lattice Libs**      | Chroma, QUDA, Grid, pyQCD                        | Implement from scratch      |\n| **GPU Libraries**     | `cupy`, `PyTorch`, `JAX`, `TensorFlow`            | `NumPy`, `SciPy`            |\n\n---\n\n## 5. Data Files to Reproduce\n\n### Figure 1: 0++ and 2++ Mass Convergence\n**File**: `data/fig1.csv`\n\n| Property | Value                                    |\n| -------- | ---------------------------------------- |\n| X-axis   | $N_\\mathrm{cfg}$ (number of configurations) |\n| Y-axis   | Glueball mass in units of $\\Lambda_\\mathrm{mom}$ |\n| System   | 4³ × 8, β = 2.3                          |\n| Series   | 0++ mass, 0++ error, 0++ upper bound, 2++ mass, 2++ error, 2++ upper bound |\n\n**X values**: 1000, 2000, 3000, 4000, 5000, 6000\n\n**Columns**: `N_cfg,mass_0pp,err_0pp,upper_0pp,mass_2pp,err_2pp,upper_2pp`\n\nNote: 2++ entries may be empty (failed) at low statistics.\n\n---\n\n### Figure 2: 0-- Mass Convergence\n**File**: `data/fig2.csv`\n\n| Property | Value                                    |\n| -------- | ---------------------------------------- |\n| X-axis   | $N_\\mathrm{cfg}$ (number of configurations) |\n| Y-axis   | Correlator values and mass/upper bound in $\\Lambda_\\mathrm{mom}$ |\n| System   | 6⁴, β = 2.5                              |\n| Series   | C(0), C(1), C(3), mass or upper bound     |\n\n**X values**: 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000\n\n**Columns**: `N_cfg,C0,C1,C3,mass_or_upper_bound`\n\n---\n\n### Figure 3: Final Glueball Mass Spectrum\n**File**: `data/fig3.csv`\n\n| Property | Value                                    |\n| -------- | ---------------------------------------- |\n| Content  | Final mass results for all channels       |\n| Units    | $\\Lambda_\\mathrm{mom}$                   |\n| Comparison| Paper reference values                   |\n\n**Columns**: `channel,lattice,beta,N_cfg,mass,err,upper_bound,paper_mass,paper_err`\n\n**Rows**: 0++, 2++, 0--\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Module\n**Path**: `reproduce/`\n\n| File                     | Description                                           |\n| ------------------------ | ----------------------------------------------------- |\n| `glueball_simulation.py` | Full SU(2) gauge simulation with glueball operators   |\n\n### 6.2 Figure Scripts\n| Figure | Script Path                      |\n| ------ | -------------------------------- |\n| Fig 1  | `reproduce/fig1_compute.py`      |\n| Fig 2  | `reproduce/fig2_compute.py`      |\n| Fig 3  | `reproduce/fig3_compute.py`      |\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduce/glueball_simulation.py` — Core simulation module\n2. `reproduce/fig1_compute.py` through `reproduce/fig3_compute.py` — Figure scripts\n3. `data/fig1.csv` through `data/fig3.csv` — Output data files (3 total)\n\nExport data with 10 decimal places (`%.10e`).\n\n---\n\n## 8. Reproduction Requirements\n\n### 8.1 Computational Resources\n\n| Requirement          | Value           | Notes                              |\n| -------------------- | --------------- | ---------------------------------- |\n| **Total time limit** | ~2-6 hours      | 6000 configs for 0++/2++          |\n| **Memory limit**     | 2-4 GB          | Small lattice volumes              |\n| **CPU**              | 1-4 Cores       | Heat bath is sequential            |\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduce/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduce/`\n4. **DO NOT** run the simulation scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/glueball_simulation.py", "reproduce/fig1_compute.py", "reproduce/fig2_compute.py", "reproduce/fig3_compute.py"], "data": ["data/fig1.csv", "data/fig2.csv", "data/fig3.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/glueball_simulation.py", "reproduce/fig1_compute.py", "reproduce/fig2_compute.py", "reproduce/fig3_compute.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 21600, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_kolb_2003", "title": "Hydrodynamic description of ultrarelativistic heavy-ion collisions", "authors": "Peter F. Kolb and Ulrich Heinz", "year": 2003, "doi": "nucl-th/0305084v2", "arxiv": null, "paper_files": ["P.Kolb2003IdealHydro.md"], "input_files": ["eosq.dat"], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement the simulation to reproduce figures.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Hydrodynamic description of ultrarelativistic heavy-ion collisions |\n| **Author** | Peter F. Kolb and Ulrich Heinz |\n| **DOI** | ---\n| **arXiv** | nucl-th/0305084v2 |\n| **Source Markdown** | `P.Kolb2003IdealHydro.md` |\n\n## 2. What You Must Do\n\n### Step 1: Read the paper and Analyze the Paper\nRead the full paper at `P.Kolb2003IdealHydro.md` and the Section 3 below.\n**Notation:** \n- If there is any conflict between Section 3 and `P.Kolb2003IdealHydro.md` in parameter settings, **follow the Section 3**.\n\n**Your goal is to reproduce the following figures in the paper:**\n- Figure 2\n- Figure 4\n- Figure 9\n\nPlease capture the **input parameters and equations** that are used to reproduce each figure. \n\n### Step 2: Coding    \nWrite all code under `reproduction/`. You need:\n- Core modules for solving the system evolution\n- Individual scripts for each figure. \n\n### Step 3: Generate Data Files\n\nRun your scripts to produce data files under `data/`. See Section 5 for exact specifications. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Key Formulas**: List and explain every formula needed for the reproduction.\n2. **Algorithm Details**: Describe the algorithm you implement to reproduce figures.\n3. **Physical Observables**: Explain what each figure measures and its physical significance.\n\n---\n\n## 3. Input Parameters & Supplementary Material\nThis Section provides parameters and knowledge that are not explicitly mentioned in the paper but crucial for the simulation.\n### 3.1 Equation of State \nThis knowledge is not explicitly mentioned in the paper but crucial for the simulation. \n**Ideal equation of state:**\nThe relation between energy density $e$, pressure $p$ and temperature $T$ is given by\n$$\ne=\\frac{\\pi^2}{30} \\left(16+\\frac{21}{2}N_f\\right) T^4,\\; p=e/3,\n$$\nwhere the effective flaver number $N_f=2.5$.\n**Eos Q:** Load this equation of state table from `eosq.dat`.\n\n### 3.2 Smooth Glauber Model Parameters\n\n| Parameter | Symbol | Typical Values | Description |\n|-----------|--------|----------------|-------------|\n| Mass number | $A$ | 197 (Au+Au), 208 (Pb+Pb) | Number of nucleons per nucleus |\n| Nuclear radius | $R_A$ | $(1.12\\, A^{1/3} - 0.86\\, A^{-1/3})\\,\\text{fm}$ | Half-density radius of the Woods-Saxon profile |\n| Surface diffuseness | $a$ | 0.535 fm (Au), 0.546 fm (Pb) | Skin depth of the Woods-Saxon distribution |\n| Central nuclear density | $\\rho_0$ | --- | Nuclear saturation density; fixes $T_A$ normalization to $A$ |\n| Inelastic NN cross section | $\\sigma_{\\rm NN}$ | 40 mb ($\\sqrt{s}=130\\;\\text{GeV}$), 42 mb ($\\sqrt{s}=200\\;\\text{GeV}$) | Total inelastic nucleon-nucleon cross section |\n| Impact parameter | $b$ | 0 – $2R_A$ | Transverse separation between the two nuclear centers |\n| Participant/binary mixing | $\\alpha$ | 0 (pure $N_{\\rm part}$) – 1 (pure $N_{\\rm bc}$) | Weight of binary collision term relative to wounded-nucleon term: $s~\\text{or}~e\\propto (1-\\alpha)\\,n_{\\rm wn} + \\alpha\\,n_{\\rm bc}$ |\n| Center entropy density | $s_{\\mathrm{cent}}(\\mathrm{fm}^{-3})$ | --- | Initial entropy density at the fireball center |\n| Thermalization time | $\\tau_0$ |   $\\lesssim 1~\\mathrm{fm}/c$ | Proper time at which hydrodynamic evolution begins |\n\n### 3.3 Equation of State Parameters\n\n| Parameter | Symbol | Typical Values | Description |\n|-----------|--------|----------------|-------------|\n| Critical temperature | $T_c$ | 165 – 170 MeV | QCD deconfinement/crossover temperature |\n| Latent heat | $\\Delta e$ | $\\sim 1.15\\;\\text{GeV/fm}^3$ (first-order) | Energy density discontinuity at $T_c$ (set to 0 for crossover) |\n| Bag constant | $B^{1/4}$ | $\\sim 230\\;\\text{MeV}$ | QGP bag pressure (Bag-model EOS only) |\n| Hadronic resonance gas cutoff | $T_{\\rm had}$ | $\\lesssim T_c$ | Temperature below which hadron resonance gas is used |\n| Speed of sound (QGP) | $c_s^2$ | $1/3$ | Conformal limit for massless QGP |\n\n### 3.4 Numerical Grid Parameters\n\n| Parameter | Symbol | Typical Values | Description |\n|-----------|--------|----------------|-------------|\n| Spatial domain half-width | $L$ | $\\geq R_A + (\\tau_{\\rm max}-\\tau_0)\\cdot c$ | Grid covers $[-L,L]\\times[-L,L]$; chosen so the fireball (expanding at most at $c=1$) cannot reach the boundary during $[\\tau_0,\\tau_{\\rm max}]$ |\n| Grid spacing | $\\Delta x = \\Delta y$ | 0.1 – 0.2 fm | Uniform Cartesian grid spacing |\n| Time step | $\\Delta\\tau$ | --- | Small enough to guarantee CFL condition |\n| Maximum evolution time | $\\tau_{\\rm max}$ | 10 – 20 fm/$c$ | Proper time at which the run is terminated (or when all cells have frozen out) |\n| Output interval | $\\Delta\\tau_{\\rm out}$ | 0.1 – 0.5 fm/$c$ | Proper-time interval between saved snapshots |\n\n### 3.5 Parameter Settings of figures\n| Figure | Parameters |\n|--------|--------|\n| **Fig 2** | $\\sigma_0 = 40\\,\\mathrm{mb}$ |\n| **Fig 4** | Initialized by $s\\propto (1-\\alpha)\\,n_{\\rm wn} + \\alpha\\,n_{\\rm bc}$. $\\sqrt{s} = 200\\,\\mathrm{GeV}$, Impact parameter $b=0$, $s_{\\mathrm{cent}}=110 \\,\\mathrm{fm}^{-3}$ |\n| **Fig 9** | Initialized by $e\\propto (1-\\alpha)\\,n_{\\rm wn} + \\alpha\\,n_{\\rm bc}$. Impact parameter $b=7\\,\\text{fm}$, $\\sqrt{s} = 130\\,\\mathrm{GeV}$,  EOSI: $\\tau_0=0.1~\\mathrm{fm}/c$, initial temperature at the fireball center $T=2~\\mathrm{GeV}$; EOSQ: $\\tau_0=0.6~\\mathrm{fm}/c$, initial temperature at the fireball center $T=0.34~\\mathrm{GeV}$ |\n\n---\n\n## 4. Banned Libraries\n| Banned | Reason |\n|--------|--------|\n| `Clawpack`, `PyClaw`, `Dedalus`, `FiPy`, `FEniCS` | Must implement finite volume/difference schemes (e.g., MUSCL, WENO) from scratch |\n| `SciPy` PDE solvers (`scipy.integrate.solve_ivp` for method-of-lines) | Must manually construct spatial discretization and time-stepping loops |\n| GPU-accelerated libraries (`cupy`, `pytorch`, `jax` for simulation) | Keep implementation in pure NumPy for clarity and educational value |\n| Pre-built Riemann solvers or flux limiters | Implement algorithms (e.g., HLLC, Roe, Minmod, Van Leer) directly |\n| External ODE integrators for source terms | Implement time-integration schemes (e.g., RK4, IMEX) explicitly |\n\n---\n\n## 5. Data Files to Reproduce\n\n### Figure 2: Impact parameter ($b$) dependence of total numbers and central densities for wounded nucleons and binary collisions\n**File:** `data/fig2_data.csv`\n**Data Format(Header lines):** The header lines of the data file, which provide the description of the columns, are given as follows,\n```\n# Figure 2: Glauber model for Au+Au, sigma_NN=40 mb\n# Columns: b(fm)  N_WN  N_BC  n_WN(0,0)(fm^-2)  n_BC(0,0)(fm^-2)\n```\n| Property | Value |\n|----------|-------|\n| Description | Impact parameter ($b$) dependence of total numbers and central densities for wounded nucleons and binary collisions |\n| Structure | Multi-panel (Left: Total counts; Right: Central densities at $x,y=0$) |\n| X-axis (Both) | Impact parameter $b$ (fm), linear, 0–12 |\n| Y-axis (Left Panel) | Total counts $N_{\\mathrm{WN}}$, $N_{\\mathrm{BC}}$, linear, 0–1200 |\n| Y-axis (Right Panel) | Central densities $n_{\\mathrm{WN}}(0,0)$, $n_{\\mathrm{BC}}(0,0)$ (fm$^{-2}$), linear, 0–20 |\n| Data Series | Red solid: Wounded Nucleons ($N_{\\mathrm{WN}}$, $n_{\\mathrm{WN}}$); Blue dashed: Binary Collisions ($N_{\\mathrm{BC}}$, $n_{\\mathrm{BC}}$) |\n\n\n\n### Figure 4: Time Evolution of Entropy Density and Temperature (Au+Au, 200 AGeV, b=0)\n**Files:** `data/fig4_R0fm.csv`, `data/fig4_R3fm.csv`, `data/fig4_R5fm.csv`\n**Data Format(Header lines):** all of these 3 files have the same format:\n```\n# Figure 4: Au+Au 200 AGeV, b=0, EOS Q, R=0 fm\n# Columns: tau(fm/c)  s(fm^-3)  T(MeV)\n```\n| Property | Value |\n|----------|-------|\n| Description | Time evolution of entropy density ($s$) and temperature ($T$) at different radial positions ($R$) |\n| Structure | Multi-panel (a: Entropy Density; b: Temperature) |\n| X-axis (Both) | Proper time $\\tau$ (fm/c), log scale, 0.1–10 |\n| Y-axis (Panel a) | Entropy density $s$ (fm⁻³), log scale, 1–100 |\n| Y-axis (Panel b) | Temperature $T$ (MeV), log scale, 100–400 |\n| Data Series | Solid lines: $R=0$ (Red), $R=3$ (Blue), $R=5$ (Green); Dashed/Dotted: Scaling laws ($\\tau^{-1}, \\tau^{-3}, \\tau^{-1/3}$) |\n\n### Figure 9: Time Evolution of Spatial Eccentricity and Momentum Anisotropy (Au+Au, RHIC, b=7 fm)\n**Files:** `data/fig9_eosi.csv`, `data/fig9_eosq.csv`\n**Data Format(Header lines):** These 2 files have the similar format:\n```\n# Figure 9: Au+Au 200 AGeV, b=7 fm, EOS I/Q, s0/T0=...\n# Columns: tau(fm/c)  epsilon_x  epsilon_p\n```\n| Property | Value |\n|----------|-------|\n| Description | Time evolution of spatial eccentricity ($\\epsilon_x$) and momentum anisotropy ($\\epsilon_p$) comparing realistic EOS (RHIC) vs. ideal gas EOS (EOS I) |\n| Structure | Single plot with dual Y-axes |\n| X-axis | Proper time $\\tau$ (fm/c), linear, 0–15 |\n| Left Y-axis | Spatial eccentricity $\\epsilon_x$, linear, -0.15–0.3 |\n| Right Y-axis | Momentum anisotropy $\\epsilon_p$, linear, -0.05–0.18 |\n| Data Series | Blue lines: $\\epsilon_x$; Red lines: $\\epsilon_p$; Solid: RHIC (Realistic EOS); Dashed: EOS I (Ideal Gas) |\n\n## 6. Code Structure\n```\n.\n├── data                            # Reproduced data for varification\n│   ├── fig2_glauber.csv\n│   ├── fig4_R0fm.csv\n│   ├── fig4_R3fm.csv\n│   ├── fig4_R5fm.csv\n│   ├── fig9_eosi.csv\n│   └── fig9_eosq.csv\n├── eosq.dat                     # Equatio of State table\n├── instruction.md\n├── P.Kolb2003IdealHydro.md          # Source markdown file for the paper\n├── plots                            # Reproduced figure\n│   ├── fig2_glauber.png\n│   ├── fig4_entropy_temp.png\n│   └── fig9_eccentricity.png\n├── reproduction                     # Reproduction program                    \n│   ├── eos.py\n│   ├── fig2_glauber.py\n│   ├── fig4_entropy_temp.py\n│   ├── fig9_eccentricity.py\n│   ├── glauber.py\n│   ├── hydro_core.py\n│   └── __pycache__   \n```\n### Code Path: `reproduction/`\n|**Module**|**Description**|\n|----------|--------------------------------------------------|\n| `reproduction/hydro_core.py`| Core hydrodynamics solver module |\n| `reproduction/eos.py`| Realistic and ideal EoS |\n| `reproduction/glauber.py`| Use glauber model to initialize the hydrodynamics |\n| `reproduction/fig2_glauber.py`| Reproduce Figure 2 |\n| `reproduction/fig4_entropy_temp.py`| Reproduce Figure 4 |\n| `reproduction/fig9_eccentricity.py`| Reproduce Figure 9 |\n### Output Directories: \n**Data**:`data/`\n**Figures**:`plots/`\n\n\n\n\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the simulation scripts or generate data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/hydro_core.py", "reproduction/eos.py", "reproduction/glauber.py", "reproduction/fig2_glauber.py", "reproduction/fig4_entropy_temp.py", "reproduction/fig9_eccentricity.py"], "data": ["data/fig2_glauber.csv", "data/fig4_R0fm.csv", "data/fig4_R3fm.csv", "data/fig4_R5fm.csv", "data/fig9_eosi.csv", "data/fig9_eosq.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/hydro_core.py", "reproduction/eos.py", "reproduction/glauber.py", "reproduction/fig2_glauber.py", "reproduction/fig4_entropy_temp.py", "reproduction/fig9_eccentricity.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_li_2014", "title": "Classical-Quantum Correspondence for Above-Threshold Ionization", "authors": "Min Li, Ji-Wei Geng, Hong Liu, Yongkai Deng, Chengyin Wu, Liang-You Peng, Qihuang Gong, Yunquan Liu", "year": 2014, "doi": "10.1103/PhysRevLett.112.113002", "arxiv": null, "paper_files": ["qtmc.md"], "input_files": [], "instruction": "# Paper Reproduction Task: Quantum-Trajectory Monte Carlo Simulation\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand the Quantum-Trajectory Monte Carlo (QTMC) methodology, and implement a simulation to reproduce the photoelectron momentum distribution (PMD) for xenon atoms in strong laser fields.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Classical-Quantum Correspondence for Above-Threshold Ionization |\n| **Authors** | Min Li et al. |\n| **DOI** | 10.1103/PhysRevLett.112.113002 |\n| **Paper File** | `qtmc.md` |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `qtmc.md`. Focus on understanding the QTMC methodology and the physical system described.\n\n### Step 2: Implement the QTMC Simulation\nWrite a QTMC simulation code that reproduces the photoelectron momentum distribution for xenon atoms. Write a detailed analysis document at `reproduction/ANALYSIS.md` covering your understanding and methodology.\n\n### Step 3: Generate Data Files\nRun your simulation to produce a CSV data file with the photoelectron momentum distribution.\n\n---\n\n## 3. Input Parameters\n\n### Laser Parameters\n| Parameter | Symbol | Value | Unit |\n|-----------|--------|-------|------|\n| Fundamental electric field | E₁ | 0.0534 | a.u. |\n| Fundamental frequency | ω₁ | 0.0570 | a.u. |\n| Laser wavelength | λ | 795 | nm |\n| Laser intensity | I | 0.75×10¹⁴ | W/cm² |\n| Pulse shape | - | Trapezoidal | - |\n| Pulse parameters | pls | [2T₁, 4T₁, 2T₁, 8T₁] | a.u. |\n\n### Atomic Parameters (Xenon)\n| Parameter | Symbol | Value | Unit |\n|-----------|--------|-------|------|\n| Ionization potential | IP | 0.4456 | a.u. |\n| Atomic charge | Z | 1 | - |\n\n### Simulation Parameters\n| Parameter | Symbol | Value | Description |\n|-----------|--------|-------|-------------|\n| Number of trajectories | n | 8×10⁶ | Quantum trajectories to sample |\n| Momentum grid size | mx | 1001 | Grid points in each dimension |\n| Momentum step | dk | 0.005 | a.u. |\n| Momentum range | p | [-2.5, 2.5] | a.u. in both px and py |\n| Numerical tolerance | atol, rtol | 1×10⁻⁸ | Absolute/relative tolerance for ODE solver |\n\n### Laser Pulse Definition\n- **Pulse shape**: Trapezoidal (laser_mode = 3)\n- **Parameters**:\n  - pls(1): Ramp-on time = 2T₁\n  - pls(2): Plateau time = 4T₁\n  - pls(3): Ramp-off time = 2T₁\n  - pls(4): Total simulation time = 8T₁\n- **Fundamental period**: T₁ = 2π/ω₁\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category | Banned | Allowed Alternative |\n|----------|--------|---------------------|\n| **QTMC Libraries** | Pre-built QTMC packages | Implement from scratch |\n| **Quantum Solvers** | TDSE solvers, quantum propagation libraries | Classical trajectory integration |\n| **GPU Acceleration** | `cupy`, `PyTorch`, `JAX`, `TensorFlow` | `NumPy`, `SciPy` for CPU |\n\n---\n\n## 5. Data File to Reproduce\n\n### Output File: `data/fig1d.csv`\n\n**Format**: CSV with three columns and a header row:\n- Column 1 (`px`): px momentum (a.u.)\n- Column 2 (`py`): py momentum (a.u.)\n- Column 3 (`intensity`): Intensity/probability density (arbitrary units, will be normalized)\n\n**Grid Specifications**:\n- px range: [-2.500, 2.500] a.u.\n- py range: [-2.500, 2.500] a.u.\n- Grid points: 1001 × 1001 = 1,002,001 total data rows\n- Order: Row-major order (py changes fastest)\n\n**File Structure Example**:\n```\npx,py,intensity\n-2.5000000000000000,-2.5000000000000000,0.0000000000000000\n-2.5000000000000000,-2.4950000000000001,0.0000000000000000\n...\n```\n\n---\n\n## 6. Deliverables Summary\n\nUpon completion, the following files must exist:\n\n1. **Analysis document**: `reproduction/ANALYSIS.md` with your understanding and methodology\n2. **Simulation code**: Complete QTMC implementation under `reproduction/`\n3. **Output data**: `data/fig1d.csv` with photoelectron momentum distribution\n\n**Data precision**: Output with 16 decimal places.\n\n---\n\n## 7. Reproduction Requirements\n\n### 7.1 Computational Resources\n| Requirement | Value | Notes |\n|-------------|-------|-------|\n| **Total time limit** | ~1-2 hours | For 8×10⁶ trajectories |\n| **Memory limit** | 4 GB | For 1001×1001 grid |\n| **CPU** | 1-4 Cores | |\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis and all formulas\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the simulation or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/qtmc_simulation.py"], "data": ["data/fig1d.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/qtmc_simulation.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 7200, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_lin_2020", "title": "Bootstraps to Strings: Solving Random Matrix Models with Positivity", "authors": "Henry W. Lin", "year": 2020, "doi": "arXiv:2002.08387", "arxiv": null, "paper_files": ["Lin_2020.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a bootstrap computation to reproduce 4 key figures.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Bootstraps to Strings: Solving Random Matrix Models with Positivity |\n| **Author** | Henry W. Lin |\n| **arXiv** | arXiv:2002.08387 [hep-th] |\n| **Paper File** | `Lin_2020.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `Lin_2020.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the bootstrap approach used (loop equations, positivity constraints, inner product matrices)\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - The matrix model potentials (quartic and cubic)\n   - The loop equations (Schwinger-Dyson equations) for each model\n   - The Gram matrix construction\n   - The positivity constraint and how it is checked\n   - The two-matrix model potential and its loop equations\n3. **Algorithm Details**: Describe the step-by-step bootstrap algorithm\n4. **Physical Observables**: Explain what each figure measures and its physical significance\n\n### Step 2: Implement the Computation\nWrite all code under `reproduction/`. You need:\n- A core bootstrap library at `reproduction/matrix_bootstrap.py`\n- A two-matrix bootstrap module at `reproduction/two_matrix_bootstrap.py`\n- Individual scripts for each figure (see Section 5 below)\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n### 3.1 Physical Parameters for Figure 1 (Quartic Model, g > 0)\n| Parameter | Symbol | Values | Description |\n|-----------|--------|--------|-------------|\n| Coupling constant | $g$ | $(0, 5]$, 100 equally spaced points excluding 0 | Coefficient of $M^4/4$ term |\n| Search parameter | $t_2$ | 0.0 to 1.0 | $\\langle \\mathrm{tr}\\, M^2 \\rangle$ |\n| Matrix dimension | $d$ | 4, 5, 6 | Size of inner product matrix |\n\n### 3.2 Physical Parameters for Figure 4 (Quartic Model, g < 0)\n| Parameter | Symbol | Values | Description |\n|-----------|--------|--------|-------------|\n| Coupling constant | $g$ | $(-1/9, 0)$, 100 equally spaced points excluding endpoints | Coefficient of $M^4/4$ term |\n| Search parameter | $t_2$ | 1.0 to 3.0 | $\\langle \\mathrm{tr}\\, M^2 \\rangle$ |\n| Matrix dimension | $d$ | 4, 5, 6 | Size of inner product matrix |\n\n### 3.3 Physical Parameters for Figure 5 (Cubic Model)\n| Parameter | Symbol | Values | Description |\n|-----------|--------|--------|-------------|\n| Coupling constant | $g_3$ | $(0, 0.25]$, 100 equally spaced points excluding 0 | Coefficient of $M^3/3$ term |\n| Search parameter | $t_1$ | -1.0 to 0.0 | $\\langle \\mathrm{tr}\\, M \\rangle$ |\n| Matrix dimension | $d$ | 3, 4, 6 | Size of inner product matrix |\n\n### 3.4 Physical Parameters for Figure 8 (Two-Matrix Model)\n| Parameter | Symbol | Values | Description |\n|-----------|--------|--------|-------------|\n| Coupling | $h$ | 1.0 | Coefficient of $AB^2 + B^2A$ |\n| Search parameter 1 | $\\mathrm{tr}\\, A$ | -3.0 to 0.0 | First moment of $A$ |\n| Search parameter 2 | $\\mathrm{tr}\\, A^2$ | 0.0 to 9.0 | Second moment of $A$ |\n| Matrix dimension | $k$ | 15 | Size of inner product matrix |\n| Max operator length | - | 6 | Maximum degree of correlators |\n\n### 3.5 Grid Resolution\n| Figure | X-axis points | Y-axis points | Notes |\n|--------|---------------|---------------|-------|\n| Figure 1 | 100 | - | $g \\in (0, 5]$, excluding 0 |\n| Figure 4 | 100 | - | $g \\in (-1/9, 0)$, excluding endpoints |\n| Figure 5 | 100 | - | $g_3 \\in (0, 0.25]$, excluding 0 |\n| Figure 8 | - | - | Output boundary points of allowed region |\n\n---\n\n## 4. Banned Libraries\n\nThe following libraries/approaches are **NOT allowed** for the core physics simulation:\n\n| Banned | Reason |\n|--------|--------|\n| Pre-built random matrix libraries | Must implement loop equations from scratch |\n| Symbolic algebra packages for solving loop equations | Numerical implementation required |\n| Pre-computed exact solutions | Bootstrap bounds should be computed independently |\n| GPU-accelerated SDP solvers | Keep implementation in NumPy/SciPy for clarity |\n\n**Allowed libraries**:\n- NumPy (numerical arrays and linear algebra)\n- SciPy (eigenvalue computation, optimization)\n- Matplotlib (plotting)\n\n---\n\n## 5. Data Files to Reproduce\n\n### 5.1 Figure 1: Bootstrap Constraints for Quartic Model (g > 0)\n**Files**:\n- `data/fig1-d=4.csv` (for $d = 4$)\n- `data/fig1-d=5.csv` (for $d = 5$)\n- `data/fig1-d=6.csv` (for $d = 6$)\n\n| Property | Value |\n|----------|-------|\n| Description | Allowed region for $t_2$ vs coupling $g$ with positivity constraints |\n| X-axis | $g$, linear scale, range: $(0, 5]$ |\n| Y-axis | $\\mathrm{tr}\\, M^2$ ($t_2$), linear scale, range: 0.0 to 1.0 |\n| Parameters | $d = 4, 5, 6$ (one file per $d$ value) |\n| Data content | Upper and lower bounds on $t_2$ for each $g$ value |\n| Number of $g$ points | 100 equally spaced points in $(0, 5]$, excluding 0 |\n\n**Columns**: `g, lower, upper`\n- `g`: coupling constant value in **rational number form** (e.g., `1/20`, `1/10`, `3/20`, ...)\n- `lower`: lower bound of $t_2$ (floating point)\n- `upper`: upper bound of $t_2$ (floating point)\n\n**Grid**: $g_i = i/20$ for $i = 1, 2, \\ldots, 100$ (i.e., $1/20, 2/20=1/10, 3/20, \\ldots, 100/20=5$)\n\n---\n\n### 5.2 Figure 4: Peninsula Region (g < 0)\n**Files**:\n- `data/fig4-d=4.csv` (for $d = 4$)\n- `data/fig4-d=5.csv` (for $d = 5$)\n- `data/fig4-d=6.csv` (for $d = 6$)\n\n| Property | Value |\n|----------|-------|\n| Description | \"Peninsula\" shaped allowed region approaching critical point |\n| X-axis | $g$, linear scale, range: $(-1/9, 0)$ |\n| Y-axis | $\\mathrm{tr}\\, M^2$ ($t_2$), linear scale, range: 1.0 to 3.0 |\n| Parameters | $d = 4, 5, 6$ (one file per $d$ value) |\n| Data content | Upper and lower bounds on $t_2$ for each $g$ value, only rows with valid solutions |\n| Number of $g$ points | 100 equally spaced points in $(-1/9, 0)$, excluding both endpoints |\n\n**Columns**: `g, lower, upper`\n- `g`: coupling constant value in **rational number form** (e.g., `-1/10`, `-1/11`, ...)\n- `lower`: lower bound of $t_2$ (floating point)\n- `upper`: upper bound of $t_2$ (floating point)\n\n**Grid**: $g_i = -1/9 + i \\cdot (1/9) / 101$ for $i = 1, 2, \\ldots, 100$\n\n**Only output rows where a valid solution exists** (i.e., non-empty allowed region for this $d$).\n\n---\n\n### 5.3 Figure 5: Cubic Model Constraints\n**Files**:\n- `data/fig5-d=3.csv` (for $d = 3$)\n- `data/fig5-d=4.csv` (for $d = 4$)\n- `data/fig5-d=6.csv` (for $d = 6$)\n\n| Property | Value |\n|----------|-------|\n| Description | Allowed region for $t_1$ vs coupling $g_3$ in cubic model |\n| X-axis | $g_3$, linear scale, range: $(0, 0.25]$ |\n| Y-axis | $\\mathrm{tr}\\, M$ ($t_1$), linear scale, range: -1.0 to 0.0 |\n| Parameters | $d = 3, 4, 6$ (one file per $d$ value) |\n| Data content | Upper and lower bounds on $t_1$ for each $g_3$ value, only rows with valid solutions |\n| Number of $g_3$ points | 100 equally spaced points in $(0, 0.25]$, excluding 0 |\n\n**Columns**: `g, lower, upper`\n- `g`: coupling constant $g_3$ value in **rational number form** (e.g., `1/400`, `1/200`, `3/400`, ...)\n- `lower`: lower bound of $t_1$ (floating point)\n- `upper`: upper bound of $t_1$ (floating point)\n\n**Grid**: $g_{3,i} = i/400$ for $i = 1, 2, \\ldots, 100$ (i.e., $1/400, 2/400=1/200, \\ldots, 100/400=1/4$)\n\n**Only output rows where a valid solution exists**.\n\n---\n\n### 5.4 Figure 8: Two-Matrix Model Constraints\n**File**: `data/fig8_two_matrix.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Boundary points of the allowed region for quartic two-matrix model with $k=15$ inner product matrix |\n| X-axis | $\\mathrm{tr}\\, A$, linear scale, range: -3.0 to 0.0 |\n| Y-axis | $\\mathrm{tr}\\, A^2$, linear scale, range: 0 to 8 |\n| Constraint | $t_2 \\geq t_1^2$ (a priori) |\n\n**Columns**: `trA, trA2`\n\n**Data content**: Coordinates of boundary points of the allowed region (not a grid of all points, but specifically the boundary curve).\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Module\n**Path**: `reproduction/matrix_bootstrap.py`\n\nMust contain:\n- Functions to compute correlators via loop equations for both quartic and cubic models\n- Function to build inner product matrix (Gram matrix) from correlators\n- Function to check positive semi-definiteness\n\n### 6.2 Two-Matrix Module\n**Path**: `reproduction/two_matrix_bootstrap.py`\n\nMust contain:\n- Functions to generate independent monomials and solve multi-matrix loop equations\n- Function to build multi-matrix Gram matrix\n\n### 6.3 Figure Scripts\n| Figure | Script Path |\n|--------|-------------|\n| Fig 1 | `reproduction/fig1_quartic_bootstrap.py` |\n| Fig 4 | `reproduction/fig4_peninsula.py` |\n| Fig 5 | `reproduction/fig5_cubic_bootstrap.py` |\n| Fig 8 | `reproduction/fig8_two_matrix.py` |\n\n### 6.4 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\nMust contain your analysis of the paper's methodology and all formulas needed for reproduction.\n\n### 6.5 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Your methodology and formula analysis\n2. `reproduction/matrix_bootstrap.py` — Core bootstrap library\n3. `reproduction/two_matrix_bootstrap.py` — Two-matrix model module\n4. `reproduction/fig1_quartic_bootstrap.py` through `reproduction/fig8_two_matrix.py` — Figure scripts\n5. `data/fig1-d=4.csv` through `data/fig8_two_matrix.csv` — Output data files (10 total)\n\nExport all data with 8 decimal places.\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/matrix_bootstrap.py", "reproduction/two_matrix_bootstrap.py", "reproduction/fig1_quartic_bootstrap.py", "reproduction/fig4_peninsula.py", "reproduction/fig5_cubic_bootstrap.py", "reproduction/fig8_two_matrix.py"], "data": ["data/fig1-d=4.csv", "data/fig1-d=5.csv", "data/fig1-d=6.csv", "data/fig4-d=4.csv", "data/fig4-d=5.csv", "data/fig4-d=6.csv", "data/fig5-d=3.csv", "data/fig5-d=4.csv", "data/fig5-d=6.csv", "data/fig8_two_matrix.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/matrix_bootstrap.py", "reproduction/two_matrix_bootstrap.py", "reproduction/fig1_quartic_bootstrap.py", "reproduction/fig4_peninsula.py", "reproduction/fig5_cubic_bootstrap.py", "reproduction/fig8_two_matrix.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 7200, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_liu_2025", "title": "Scattering Entanglement Entropy and Its Implications for Electroweak Phase Transitions", "authors": "Jia Liu, Masanori Tanaka, Xiao-Ping Wang, Jing-Jun Zhang, Zifan Zheng", "year": 2025, "doi": "arXiv:2505.06001v2", "arxiv": null, "paper_files": ["liu2025.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a numerical computation to reproduce 8 data files corresponding to Figures 3, 4, and 5.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Scattering Entanglement Entropy and Its Implications for Electroweak Phase Transitions |\n| **Authors** | Jia Liu, Masanori Tanaka, Xiao-Ping Wang, Jing-Jun Zhang, Zifan Zheng |\n| **arXiv** | 2505.06001v2 |\n| **Paper File** | `liu2025.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `liu2025.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the O(N) singlet model, the Hilbert space decomposition for scattering, and how the entanglement power is defined and computed.\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - The scalar potential and mass relations\n   - The linear entropy definition and the density matrix construction\n   - The closed-form expressions for $E_2(s)$ and $E_4(s)$ in the O(N) singlet model\n   - The definition of maximal entanglement power $E_{\\max}$\n3. **Algorithm Details**: Describe the step-by-step numerical procedure (grid scan over $s$, parameter grids, etc.)\n4. **Physical Observables**: Explain what each figure measures and its physical significance\n\n### Step 2: Implement the Computation\nWrite all code under `reproduction/`. You need:\n- `reproduction/entanglement_power.py` — implementation of $E_2(s)$ and $E_4(s)$ and the $E_{\\max}$ scan\n- `reproduction/fig3_lambda_hS_lambda_S.py` — generates data for Fig. 3\n- `reproduction/fig4_mS_lambda_hS.py` — generates data for Fig. 4\n- `reproduction/fig5_vh_lambda_hS.py` — generates data for Fig. 5\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 4 for exact specifications.\n\n---\n\n## 3. Shared Setup\n\nUse:\n- $m_h = 125$ GeV (fixed),\n- $v_h = 246$ GeV (fixed),\n- $\\lambda_h = m_h^2 / (2 v_h^2)$ (from the electroweak vacuum condition),\n- A 1D grid of 200 $s$ values in $[4m_S^2,\\ 8m_S^2 + 1]$ to evaluate $E_N(s)$ when computing $E_{\\max}$.\n\nFor each parameter point, only **tree-level** quantities are needed to evaluate $E_N(s)$.\n\nIf $E_{\\max}$ is negative or very small due to numerical issues, clamp to a minimum positive floor before taking $\\log_{10}$, or treat the point as empty ($Z = -\\infty$).\n\n---\n\n## 4. Data Files to Reproduce\n\n### 4.1 Figure 3: $E_{\\max}$ in $(\\lambda_{hS}, \\lambda_S)$ Plane\n\nProduce **three** parameter slices:\n\n| Slice | $N$ | $m_S$ (GeV) |\n|-------|-----|-------------|\n| 1 | 2 | 500 |\n| 2 | 4 | 400 |\n| 3 | 4 | 500 |\n\nFor each slice, scan:\n- $\\lambda_{hS} \\in [0.1, 8.0]$ with step 0.1,\n- $\\lambda_S \\in [0.1, 8.0]$ with step 0.1.\n\n**Files**:\n- `data/fig3_N2_mS500_lambda_hS_lambda_S.csv`\n- `data/fig3_N4_mS400_lambda_hS_lambda_S.csv`\n- `data/fig3_N4_mS500_lambda_hS_lambda_S.csv`\n\n**Columns**: `lambda_hS, lambda_S, log10_Emax`\n\n---\n\n### 4.2 Figure 4: $E_{\\max}$ in $(m_S, \\lambda_{hS})$ Plane\n\nProduce **three** parameter slices:\n\n| Slice | $N$ | $\\lambda_S$ |\n|-------|-----|-------------|\n| 1 | 2 | 1 |\n| 2 | 4 | 1 |\n| 3 | 4 | 3 |\n\nFor each slice, scan:\n- $\\lambda_{hS} \\in [0.1, 8.0]$ with step 0.1,\n- $m_S \\in [400, 1000]$ GeV with step 6 GeV.\n\n**Files**:\n- `data/fig4_N2_lambdaS1_mS_lambda_hS.csv`\n- `data/fig4_N4_lambdaS1_mS_lambda_hS.csv`\n- `data/fig4_N4_lambdaS3_mS_lambda_hS.csv`\n\n**Columns**: `lambda_hS, mS_GeV, log10_Emax`\n\n---\n\n### 4.3 Figure 5: $E_{\\max}$ in $(v_h, \\lambda_{hS})$ Plane\n\nUse $N = 4$, $m_S = 500$ GeV, and two choices of $\\lambda_S$:\n\n| Slice | $\\lambda_S$ |\n|-------|-------------|\n| 1 | 1 |\n| 2 | 3 |\n\nFor each slice, scan:\n- $\\lambda_{hS} \\in [0.1, 8.0]$ with step 0.1,\n- $v_h \\in [0, 250]$ GeV with step 2.5 GeV.\n\nFor each $v_h$, define an effective Higgs mass consistent with the paper's treatment of varying $v_h$. Keep $\\lambda_h$ fixed at its SM value and scale $m_h$ accordingly.\n\n**Files**:\n- `data/fig5_N4_mS500_lambdaS1_vh_lambda_hS.csv`\n- `data/fig5_N4_mS500_lambdaS3_vh_lambda_hS.csv`\n\n**Columns**: `lambda_hS, vh_GeV, log10_Emax`\n\n---\n\n## 5. Deliverables Summary\n\nUpon completion, the following files must exist:\n\n1. `reproduction/ANALYSIS.md` — Your methodology and formula analysis\n2. `reproduction/entanglement_power.py` — Core entanglement power library\n3. `reproduction/fig3_lambda_hS_lambda_S.py` — Fig. 3 data generation\n4. `reproduction/fig4_mS_lambda_hS.py` — Fig. 4 data generation\n5. `reproduction/fig5_vh_lambda_hS.py` — Fig. 5 data generation\n6. `data/fig3_N2_mS500_lambda_hS_lambda_S.csv`\n7. `data/fig3_N4_mS400_lambda_hS_lambda_S.csv`\n8. `data/fig3_N4_mS500_lambda_hS_lambda_S.csv`\n9. `data/fig4_N2_lambdaS1_mS_lambda_hS.csv`\n10. `data/fig4_N4_lambdaS1_mS_lambda_hS.csv`\n11. `data/fig4_N4_lambdaS3_mS_lambda_hS.csv`\n12. `data/fig5_N4_mS500_lambdaS1_vh_lambda_hS.csv`\n13. `data/fig5_N4_mS500_lambdaS3_vh_lambda_hS.csv`\n\nExport all CSV data with 8 decimal places.\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis and all formulas\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/entanglement_power.py", "reproduction/fig3_lambda_hS_lambda_S.py", "reproduction/fig4_mS_lambda_hS.py", "reproduction/fig5_vh_lambda_hS.py"], "data": ["data/fig3_N2_mS500_lambda_hS_lambda_S.csv", "data/fig3_N4_mS400_lambda_hS_lambda_S.csv", "data/fig3_N4_mS500_lambda_hS_lambda_S.csv", "data/fig4_N2_lambdaS1_mS_lambda_hS.csv", "data/fig4_N4_lambdaS1_mS_lambda_hS.csv", "data/fig4_N4_lambdaS3_mS_lambda_hS.csv", "data/fig5_N4_mS500_lambdaS1_vh_lambda_hS.csv", "data/fig5_N4_mS500_lambdaS3_vh_lambda_hS.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/entanglement_power.py", "reproduction/fig3_lambda_hS_lambda_S.py", "reproduction/fig4_mS_lambda_hS.py", "reproduction/fig5_vh_lambda_hS.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 3600, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_luscher_1991", "title": "Signatures of unstable particles in finite volume", "authors": "Martin Luscher", "year": 1991, "doi": "10.1016/0550-3213(91)90584-K", "arxiv": null, "paper_files": ["luscher1991.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement the Lüscher finite-volume quantization condition to reproduce 2 key figures.\n\n---\n\n## 1. Article Information\n\n| Field               | Value                                                        |\n| ------------------- | ------------------------------------------------------------ |\n| **Title**           | Signatures of unstable particles in finite volume            |\n| **Author**          | Martin Lüscher                                               |\n| **DOI**             | Nuclear Physics B 364 (1991) 237-251                         |\n| **Paper File**      | `luscher1991.md` (in the same task directory)                |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `luscher1991.md`. Write a detailed analysis document at `reproduce/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the Lüscher quantization condition for extracting resonance properties from finite-volume energy spectra\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n3. **Algorithm Details**: Describe the root-finding procedure for energy levels\n4. **Physical Observables**: Explain what each figure measures and its physical significance\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduce/`. You need:\n- Core modules for zeta functions and quantization conditions\n- Individual scripts for each figure\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n| Parameter             | Symbol        | Values                          |\n| --------------------- | ------------- | ------------------------------- |\n| Pion mass             | $m_\\pi$       | 140 MeV (Fig 1), variable      |\n| Rho mass              | $m_\\rho$      | 770 MeV (Fig 1), variable      |\n| Rho width             | $\\Gamma_\\rho$ | 150 MeV (Fig 1), variable      |\n| Mass ratio            | $m_\\rho/m_\\pi$| 5.5 (Fig 1), 3.0 (2a), 2.2 (2b)|\n| Width ratio           | $\\Gamma_\\rho/m_\\pi$ | varies                    |\n| Box size              | $L$           | scan range                      |\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category              | Banned                                           | Allowed Alternative         |\n| --------------------- | ------------------------------------------------ | --------------------------- |\n| **Scattering Libs**   | Pre-built Lüscher quantization condition solvers  | Implement from scratch      |\n| **GPU Libraries**     | `cupy`, `PyTorch`, `JAX`, `TensorFlow`            | `NumPy`, `SciPy`            |\n\n---\n\n## 5. Data Files to Reproduce\n\n### Figure 1: Physical ρ-meson Energy Spectrum\n**File**: `data/fig1.csv`\n\n| Property | Value                              |\n| -------- | ---------------------------------- |\n| X-axis   | $L \\cdot m_\\pi$ (dimensionless box size) |\n| Y-axis   | $W / m_\\pi$ (energy levels)        |\n| System   | Physical ρ: m_π=140 MeV, m_ρ=770 MeV, Γ_ρ=150 MeV |\n| Series   | Multiple energy levels in elastic region 2m_π < W < 4m_π |\n\n**X values**: 80 evenly spaced points in $L \\cdot m_\\pi \\in [3, 10]$\n\n**Columns**: `Lmpi,level_1,level_2,level_3,level_4,level_5,level_6,level_7`\n\nEach `level_n` column contains $W/m_\\pi$ for the n-th energy level at that $L \\cdot m_\\pi$. Empty entries where a level does not exist at a given L.\n\n---\n\n### Figure 2: Two Cases with ρ in Elastic Region\n**File**: `data/fig2.csv`\n\n| Property | Value                                    |\n| -------- | ---------------------------------------- |\n| X-axis   | $L \\cdot m_\\pi$                          |\n| Y-axis   | $W / m_\\pi$                              |\n| Panel a  | $m_\\rho/m_\\pi = 3.0$, $\\Gamma_\\rho/m_\\pi = 0.30$ |\n| Panel b  | $m_\\rho/m_\\pi = 2.2$, $\\Gamma_\\rho/m_\\pi = 0.038$ |\n\n**X values**: 120 evenly spaced points in $L \\cdot m_\\pi \\in [2.2, 8]$\n\n**Columns**: `Lmpi,panel_a_level_1,...,panel_a_level_6,panel_b_level_1,...,panel_b_level_6`\n\nEach column contains $W/m_\\pi$ for the n-th energy level in the corresponding panel. Empty entries where a level does not exist.\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Modules\n**Path**: `reproduce/`\n\n| File                        | Description                                           |\n| --------------------------- | ----------------------------------------------------- |\n| `zeta_functions.py`         | Generalized zeta functions Z₀₀(s; q²) and φ(q)       |\n| `luscher_quantization.py`   | Quantization condition solver                         |\n| `reproduce_figures_final.py`| Level tracking and plotting utilities                 |\n\n### 6.2 Figure Scripts\n| Figure | Script Path                      |\n| ------ | -------------------------------- |\n| Fig 1  | `reproduce/fig1_compute.py`      |\n| Fig 2  | `reproduce/fig2_compute.py`      |\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduce/zeta_functions.py` — Zeta function implementation\n2. `reproduce/luscher_quantization.py` — Quantization condition solver\n3. `reproduce/reproduce_figures_final.py` — Level tracking and plotting utilities\n4. `reproduce/fig1_compute.py` — Figure 1 generation script\n5. `reproduce/fig2_compute.py` — Figure 2 generation script\n6. `data/fig1.csv` — Output data (Figure 1)\n7. `data/fig2.csv` — Output data (Figure 2)\n\nExport data with 10 decimal places (`%.10e`).\n\n---\n\n## 8. Reproduction Requirements\n\n### 8.1 Computational Resources\n\n| Requirement          | Value        | Notes                              |\n| -------------------- | ------------ | ---------------------------------- |\n| **Total time limit** | < 1 minute   | Pure numerical computation         |\n| **Memory limit**     | < 1 GB       | Lightweight calculation            |\n| **Dependencies**     | numpy, scipy, matplotlib | Standard scientific Python |\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduce/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduce/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/zeta_functions.py", "reproduce/luscher_quantization.py", "reproduce/reproduce_figures_final.py", "reproduce/fig1_compute.py", "reproduce/fig2_compute.py"], "data": ["data/fig1.csv", "data/fig2.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/zeta_functions.py", "reproduce/luscher_quantization.py", "reproduce/reproduce_figures_final.py", "reproduce/fig1_compute.py", "reproduce/fig2_compute.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "2g", "timeout": 3600, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_monmayrant_2010", "title": "A newcomer's guide to ultrashort pulse shaping and characterization", "authors": "Antoine Monmayrant, Sébastien Weber, Béatrice Chatel", "year": 2010, "doi": "10.1088/0953-4075/43/10/103001", "arxiv": null, "paper_files": ["Monmayrant_2010.md"], "input_files": [], "instruction": "# Reproduction Instructions for AI Agent\n\nReproduce **Figure 3: Pulse Shaping Gallery** from the paper:\n- **Title**: A newcomer's guide to ultrashort pulse shaping and characterization\n- **Authors**: Antoine Monmayrant, Sébastien Weber, Béatrice Chatel\n- **DOI**: 10.1088/0953-4075/43/10/103001\n- **Journal**: J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 103001\n\n---\n\n## Task Description\n\nReproduce Figure 3 from the paper, which displays five different types of ultrashort laser pulses, each shown with four different representations:\n\n1. Spectral intensity and phase\n2. Temporal intensity\n3. Wigner function\n4. Spectrogram\n\nThe five pulse types are:\n- (a) Fourier transform-limited pulse\n- (b) Chirped pulse (quadratic phase)\n- (c) Cubic phase pulse\n- (d) Spectral π-jump pulse\n- (e) Two-pulse sequence\n\n---\n\n## Input Parameters\n\n### Physical Parameters\n\n| Parameter | Value | Description |\n|-----------|-------|-------------|\n| Central wavelength (λ₀) | 800 nm | Carrier wavelength |\n| Frequency display range | 275 - 475 THz | For Wigner/Spectrogram plots |\n| Time display range | -100 to +100 fs | For temporal plots |\n| Spectrogram gate FWHM | 10 fs | Fourier-limited Gaussian gate |\n\n### Pulse Specifications\n\n- **Pulse (a)**: Fourier transform-limited Gaussian pulse\n- **Pulse (b)**: Chirped pulse with quadratic spectral phase\n- **Pulse (c)**: Cubic spectral phase\n- **Pulse (d)**: Spectral π-jump (phase discontinuity)\n- **Pulse (e)**: Two-pulse sequence with temporal delay\n\n**Note**: The exact numerical values for phase coefficients and pulse delays are not specified. You should determine appropriate values that produce qualitatively similar results to Figure 3 in the paper.\n\n---\n\n## Output Requirements\n\n### Code Files\n\nAll code must be placed in the **`reproduction/`** directory:\n\n| File | Description |\n|------|-------------|\n| `reproduction/fig3.py` | Main script to generate Figure 3 and export data |\n| `reproduction/ANALYSIS.md` | (Optional) Technical notes, formula derivations, or methodology description |\n\n### Data Files\n\nExport data to the **`data/`** directory:\n\n| File | Description | Required Columns |\n|------|-------------|------------------|\n| `data/spectral_data.csv` | Spectral intensity and phase for all pulses | `freq_THz, intensity_a, phase_a, intensity_b, phase_b, intensity_c, phase_c, intensity_d, phase_d, intensity_e, phase_e` |\n| `data/temporal_data.csv` | Temporal intensity for all pulses | `time_fs, intensity_a, intensity_b, intensity_c, intensity_d, intensity_e` |\n| `data/pulse_features.csv` | Key pulse parameters | `pulse_type, peak_time_fs, fwhm_fs, max_intensity, phase_coeff_2, phase_coeff_3, delay_fs` |\n\n**Data format specifications:**\n- Spectral data: frequency range 275-475 THz, normalized intensity [0, 1], phase in radians\n- Temporal data: time range -100 to +100 fs, normalized intensity [0, 1]\n- Pulse features: summary statistics for each pulse (a, b, c, d, e)\n- Use scientific notation with 8 decimal places (e.g., `1.23456789e-02`)\n\n---\n\n## Figure Requirements\n\nCreate a multi-panel figure with:\n- **5 rows** (one per pulse type: a, b, c, d, e)\n- **4 columns** (spectral, temporal, Wigner, spectrogram)\n- Proper axis labels and titles\n- Save as `reproduction/figure3_pulse_gallery_final.png` or similar\n\n---\n\n## Success Criteria\n\nThe reproduction is successful if:\n1. All five pulse types are generated\n2. The four representations (spectral, temporal, Wigner, spectrogram) are computed and visualized\n3. The figure layout matches the paper's Figure 3 structure (5×4 grid)\n4. All required CSV files are exported with correct structure\n5. The qualitative features of each pulse type match the paper\n\n---\n\n## Important Notes\n\n- Read the paper carefully to understand the definitions of Wigner function and spectrogram\n- The paper provides the necessary equations and methodology\n- You must determine implementation details and appropriate parameter values yourself\n- Focus on reproducing the qualitative physical features shown in Figure 3\n", "code_only_instruction_suffix": "## Code-Only Mode\nWrite the code to reproduce Figure 3 and export the data files.\nDO NOT run the simulation or generate the actual CSV files.\n", "expected_outputs": {"code": ["reproduction/fig3.py"], "data": ["data/spectral_data.csv", "data/temporal_data.csv", "data/pulse_features.csv"]}, "code_only_expected_outputs": {"code": ["reproduction/fig3.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "2g", "timeout": 1800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.2}, {"name": "data_accuracy", "weight": 0.4}, {"name": "completeness", "weight": 0.2}]}
{"task_id": "task_parke_1986", "title": "Amplitude for n-Gluon Scattering", "authors": "Stephen J. Parke and T. R. Taylor", "year": 1986, "doi": "10.1103/PhysRevLett.56.2459", "arxiv": null, "paper_files": ["parke_1986.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a computation to reproduce the 5-gluon scattering amplitude results.\n\n---\n\n## 1. Article Information\n\n| Field               | Value                                                        |\n| ------------------- | ------------------------------------------------------------ |\n| **Title**           | Amplitude for n-Gluon Scattering                             |\n| **Author**          | Stephen J. Parke and T. R. Taylor                            |\n| **DOI**             | 10.1103/PhysRevLett.56.2459                                  |\n| **Paper File**      | `parke1986_with_appendix.md` (in the same task directory)    |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `parke1986_with_appendix.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the Feynman diagram approach for computing gluon scattering amplitudes\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - Gluon propagator (Eq. A.1, A.4)\n   - Three-gluon vertex (Eq. A.2, A.5)\n   - Four-gluon vertex (Eq. A.3, A.6)\n   - Color decomposition and trace basis\n   - Spinor helicity formalism (Appendix B)\n   - Polarization vectors (Eq. B.6)\n3. **Color Algebra**: Explain the color structure and how to extract color-ordered amplitudes from full-color amplitudes\n4. **Physical Observables**: Explain the squared amplitude formula (Eq. 3) and its physical significance\n\n### Step 2: Implement the Computation\nWrite all code under `reproduction/`. You need:\n- Core amplitude computation modules (see Section 6 below)\n- Individual scripts for each computation task\n\n### Step 3: Generate Data Files\nRun your scripts to produce output files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Computation Tasks\n\n### Task 1: Full-Color Tree Amplitude for 5-Gluon Scattering\nCompute the full-color tree-level scattering amplitude for 5 gluons using Feynman diagrams with the Feynman rules given in Appendix A.1.\n\n**Note**: You may use the provided QGRAF（which need \"fortran\"） tool to generate Feynman diagrams, but this is optional. You can also enumerate the diagrams manually.\n\n### Task 2: Extract Color-Ordered Amplitude\nFrom the full-color amplitude computed in Task 1, extract the color-ordered (partial) amplitude corresponding to the color trace $\\mathrm{tr}(T^{a_1}T^{a_2}T^{a_3}T^{a_4}T^{a_5})$, i.e., the tr(1,2,3,4,5) order.\n\n### Task 3: Numerical Evaluation of Color-Ordered Amplitude\nEvaluate the color-ordered amplitude from Task 2 with the following kinematic values:\n\n**Polarization vector dot products** $\\varepsilon_i \\cdot \\varepsilon_j$:\n\n| Variable | Value |\n| -------- | ----- |\n| $\\varepsilon_1 \\cdot \\varepsilon_2$ | 26/19 |\n| $\\varepsilon_1 \\cdot \\varepsilon_3$ | 11/25 |\n| $\\varepsilon_1 \\cdot \\varepsilon_4$ | 8/9 |\n| $\\varepsilon_1 \\cdot \\varepsilon_5$ | 17/16 |\n| $\\varepsilon_2 \\cdot \\varepsilon_3$ | 5/4 |\n| $\\varepsilon_2 \\cdot \\varepsilon_4$ | 5/2 |\n| $\\varepsilon_2 \\cdot \\varepsilon_5$ | 1/28 |\n| $\\varepsilon_3 \\cdot \\varepsilon_4$ | 2/3 |\n| $\\varepsilon_3 \\cdot \\varepsilon_5$ | 4/23 |\n| $\\varepsilon_4 \\cdot \\varepsilon_5$ | 11/21 |\n\n**Polarization-momentum dot products** $\\varepsilon_i \\cdot p_j$:\n\n| Variable | Value |\n| -------- | ----- |\n| $\\varepsilon_1 \\cdot p_2$ | 7 |\n| $\\varepsilon_1 \\cdot p_3$ | 9/13 |\n| $\\varepsilon_1 \\cdot p_4$ | 13/7 |\n| $\\varepsilon_2 \\cdot p_1$ | 21/11 |\n| $\\varepsilon_2 \\cdot p_3$ | 1 |\n| $\\varepsilon_2 \\cdot p_4$ | 27/29 |\n| $\\varepsilon_3 \\cdot p_1$ | 10 |\n| $\\varepsilon_3 \\cdot p_2$ | 13/11 |\n| $\\varepsilon_3 \\cdot p_4$ | 1/3 |\n| $\\varepsilon_4 \\cdot p_1$ | 13/25 |\n| $\\varepsilon_4 \\cdot p_2$ | 14/11 |\n| $\\varepsilon_4 \\cdot p_3$ | 28/11 |\n| $\\varepsilon_5 \\cdot p_1$ | 23/14 |\n| $\\varepsilon_5 \\cdot p_2$ | 2 |\n| $\\varepsilon_5 \\cdot p_3$ | 8/13 |\n\n**Momentum dot products** $p_i \\cdot p_j$:\n\n| Variable | Value |\n| -------- | ----- |\n| $p_1 \\cdot p_2$ | 12/17 |\n| $p_1 \\cdot p_3$ | 24/23 |\n| $p_1 \\cdot p_4$ | 19/22 |\n| $p_2 \\cdot p_3$ | 7/5 |\n| $p_2 \\cdot p_4$ | 30/7 |\n\n**Note**: The above are independent kinematic variables. Other variables can be derived using momentum conservation and on-shell conditions.\n\n**Output**: Write the numerical result to `./data/5p_ddim_num.csv`. \n\n### Task 4: Squared Amplitude with Specific Helicities\nFor the 5-point full-color amplitude, compute the squared amplitude $|\\mathcal{M}_5|^2$ with the following helicity configuration:\n- Particles 1, 2: negative helicity (−)\n- Particles 3, 4, 5: positive helicity (+)\n\nThis corresponds to $|\\mathcal{M}_5(--+++)|^2$.\n\n**Spinor product values** (independent basis):\n| Variable | Value |\n| -------- | ----- |\n| $\\langle 12 \\rangle$ | 33/28 |\n| $\\langle 13 \\rangle$ | 23/4 |\n| $\\langle 14 \\rangle$ | 17/91 |\n| $\\langle 15 \\rangle$ | 51/50 |\n| $\\langle 23 \\rangle$ | 11/30 |\n| $\\langle 24 \\rangle$ | 31/28 |\n| $\\langle 25 \\rangle$ | 60/11 |\n| $[34]$ | 67/84 |\n| $[35]$ | 92/91 |\n| $[45]$ | 6/23 |\n\n**Note**: The above values form an independent basis of spinor products for 5-point amplitudes. Other spinor products (e.g., $\\langle 34 \\rangle$, $\\langle 45 \\rangle$, $[12]$, $[13]$, etc.) can be derived using the Schouten identities (Eq. B.5, C.4) and momentum conservation constraints (Eq. C.6, C.7).\n\n**Color parameter**: $N_c = 5/11$\n\n**Important**: The squared amplitude must be computed from the full-color amplitude obtained in Task 1, not by directly using the known Parke-Taylor formula (Eq. 3).\n\n**Output**: Write the numerical result to `./data/5p_square_num.csv`.\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category              | Banned                                                        | Allowed Alternative         |\n| --------------------- | ------------------------------------------------------------- | --------------------------- |\n| **QFT Libraries**     | `FeynCalc`, `FORM`, `MadGraph`, `CompHEP`, `FeynArts`        | Implement from scratch      |\n| **Amplitude Packages**| `S@M`, `SpinorHelicity`, `Amplitudes`                        | Build amplitude computation manually |\n| **Symbolic Math**     | Using pre-built amplitude results                             | Derive amplitudes from Feynman rules |\n\n---\n\n## 5. Data Files to Produce\n\n### File 1: Color-Ordered Amplitude Numerical Value\n**File**: `data/5p_ddim_num.csv`\n\n| Property | Value                                              |\n| -------- | -------------------------------------------------- |\n| Content  | Numerical value of tr(1,2,3,4,5) color-ordered amplitude |\n| Format   | Single numerical value (rational or decimal)       |\n| Note     | Use `varepsilon` instead of `ee` in output notation |\n\n---\n\n### File 2: Squared Amplitude Numerical Value\n**File**: `data/5p_square_num.csv`\n\n| Property | Value                                              |\n| -------- | -------------------------------------------------- |\n| Content  | Numerical value of $\\|\\mathcal{M}_5(--+++)\\|^2$    |\n| Format   | Single numerical value (rational or decimal)       |\n| Note     | Must be computed from full-color amplitude, not from Parke-Taylor formula |\n\n---\n\n## 6. Code Structure Requirements\n\n**Note**: All code should be implemented using Mathematica (`.wl` or `.nb` files).\n\n### 6.1 Core Modules\n**Path**: `reproduction/`\n\n| File               | Description                                              |\n| ------------------ | -------------------------------------------------------- |\n| `FeynmanRules.wl`  | Gluon propagator, 3-gluon vertex, 4-gluon vertex        |\n| `ColorAlgebra.wl`  | Color factor computation, trace basis, SU(N) generators |\n| `Kinematics.wl`    | Momentum and polarization vector handling               |\n| `SpinorHelicity.wl`| Spinor products, polarization vectors in spinor basis   |\n| `Amplitude5g.wl`   | 5-gluon amplitude computation                           |\n\n### 6.2 Computation Scripts\n| Task     | Script Path                            |\n| -------- | -------------------------------------- |\n| Task 1-2 | `reproduction/ComputeAmplitude.wl`     |\n| Task 3   | `reproduction/EvaluateDdim.wl`         |\n| Task 4   | `reproduction/EvaluateSquare.wl`       |\n\n### 6.3 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\nMust contain your analysis of the paper's methodology and all formulas needed for reproduction.\n\n### 6.4 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Your methodology and formula analysis\n2. `reproduction/FeynmanRules.wl` through `reproduction/Amplitude5g.wl` — Core modules\n3. `reproduction/ComputeAmplitude.wl` through `reproduction/EvaluateSquare.wl` — Computation scripts\n4. `data/5p_ddim_num.csv` — Color-ordered amplitude numerical value\n5. `data/5p_square_num.csv` — Squared amplitude numerical value\n\n---\n\n## 8. Technical Notes\n\n### 8.1 Feynman Diagrams for 5-Gluon Scattering\nAt tree level, the 5-gluon amplitude receives contributions from:\n- Diagrams with three 3-gluon vertices (various topologies)\n- Diagrams with one 3-gluon vertex and one 4-gluon vertex\n\n### 8.2 Color Decomposition\nThe full-color amplitude can be decomposed as:\n$$\n\\mathcal{A}_5^{\\text{full}} = g^3 \\sum_{\\sigma \\in S_5/Z_5} \\mathrm{tr}(T^{a_{\\sigma(1)}} T^{a_{\\sigma(2)}} T^{a_{\\sigma(3)}} T^{a_{\\sigma(4)}} T^{a_{\\sigma(5)}}) A_5(\\sigma(1), \\sigma(2), \\sigma(3), \\sigma(4), \\sigma(5))\n$$\nwhere $A_5$ are the color-ordered (partial) amplitudes.\n\n### 8.3 Spinor Helicity for Squared Amplitude\nFor the squared amplitude computation:\n- Use polarization vectors in spinor helicity basis (Eq. B.6)\n- Momentum dot products: $2p_i \\cdot p_j = \\langle i\\,j\\rangle [j\\,i]$\n- Sum over colors using the completeness relation (Eq. D.1)\n\n### 8.4 Independent Kinematic Variables\nFor 5-point amplitudes, the independent spinor products form a basis of dimension $4n - 10 = 10$ (see Appendix C).\n\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the computation scripts or generate data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/FeynmanRules.wl", "reproduction/ColorAlgebra.wl", "reproduction/Kinematics.wl", "reproduction/SpinorHelicity.wl", "reproduction/Amplitude5g.wl", "reproduction/ComputeAmplitude.wl", "reproduction/EvaluateDdim.wl", "reproduction/EvaluateSquare.wl"], "data": ["data/5p_ddim_num.csv", "data/5p_square_num.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/FeynmanRules.wl", "reproduction/ColorAlgebra.wl", "reproduction/Kinematics.wl", "reproduction/SpinorHelicity.wl", "reproduction/Amplitude5g.wl", "reproduction/ComputeAmplitude.wl", "reproduction/EvaluateDdim.wl", "reproduction/EvaluateSquare.wl"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib", "sympy"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.2}, {"name": "data_accuracy", "weight": 0.45}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_ratti_2006", "title": "Phases of QCD: Lattice thermodynamics and a field theoretical model", "authors": "Claudia Ratti, Michael A. Thaler, Wolfram Weise", "year": 2006, "doi": "10.1103/PhysRevD.73.014019", "arxiv": null, "paper_files": ["Ratti.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a PNJL (Polyakov-loop extended Nambu--Jona-Lasinio) model to reproduce 10 key figures.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Phases of QCD: Lattice thermodynamics and a field theoretical model |\n| **Authors** | Claudia Ratti, Michael A. Thaler, Wolfram Weise |\n| **DOI** | 10.1103/PhysRevD.73.014019 |\n| **Year** | 2006 |\n| **Paper File** | `Ratti.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `Ratti.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the PNJL model combining the NJL chiral sector with a Polyakov loop effective potential\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - The Polyakov loop potential $\\mathcal{U}(\\Phi, \\bar\\Phi, T)$ with temperature-dependent coefficients\n   - The NJL gap equation and vacuum parameters\n   - The PNJL thermodynamic potential with color-traced fermionic factors\n   - Mean-field equations for $(m, \\Phi, \\bar\\Phi)$\n   - Equation of state: pressure, quark number density, interaction measure\n   - Stefan-Boltzmann limit\n3. **Algorithm Details**: Describe the self-consistent solver using `fsolve` with continuation\n4. **Physical Observables**: Explain order parameters, EOS quantities, and lattice data comparison\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduction/`. You need:\n- A core PNJL model library at `reproduction/pnjl_model.py`\n- Individual scripts for figure groups (see Section 5 below)\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n### 3.1 NJL Vacuum Parameters (Table 2)\n| Parameter | Symbol | Value | Description |\n|-----------|--------|-------|-------------|\n| 3-momentum cutoff | $\\Lambda$ | 651 MeV | UV regulator |\n| Four-quark coupling | $G$ | 10.08 GeV$^{-2}$ | Scalar-pseudoscalar channel |\n| Current quark mass | $m_0$ | 5.5 MeV | $u/d$ average |\n| Constituent mass | $m_\\mathrm{vac}$ | 325.5 MeV | From gap equation |\n| Pion decay constant | $f_\\pi$ | 94.0 MeV | Validation target |\n| Pion mass | $m_\\pi$ | 140.5 MeV | Validation target |\n| Chiral condensate | $|\\langle\\bar\\psi\\psi\\rangle|^{1/3}$ | 251.3 MeV | Validation target |\n\n### 3.2 Polyakov Loop Potential Parameters (Table 1)\n| Parameter | Value |\n|-----------|-------|\n| $a_0$ | 6.75 |\n| $a_1$ | −1.95 |\n| $a_2$ | 2.625 |\n| $a_3$ | −7.44 |\n| $b_3$ | 0.75 |\n| $b_4$ | 7.5 |\n| $T_0$ (pure gauge) | 270 MeV |\n| $T_0$ (with quarks) | 190 MeV |\n\n### 3.3 Figure-Specific Parameters\n| Figure | Key Parameters |\n|--------|---------------|\n| Fig. 1 (pure gauge Polyakov potential) | $T_0 = 270$ MeV; $T/T_0 = 0.8$–$1.3$ |\n| Fig. 2 (Polyakov potential surface) | 3D surface plot of $\\mathcal{U}/T^4$ vs $(\\Phi, T)$ |\n| Fig. 3 (pure gauge $\\Phi$ vs $T$) | $T_0 = 270$ MeV; first-order transition at $T_c = 270$ MeV |\n| Fig. 4 (order params at $\\mu=0$) | $T_0 = 190$ MeV; $\\sigma/\\sigma_0 = m/m_\\mathrm{vac}$, $\\Phi$, $\\bar\\Phi$ |\n| Fig. 5 ($\\Phi$, $\\bar\\Phi$ at $\\mu \\neq 0$) | $\\mu = 0, 100, 200, 300$ MeV |\n| Fig. 6 ($m$, $\\Phi$ vs $T$ at fixed $\\mu$) | $\\mu/T_c = 0, 0.2, 0.4, 0.6, 0.8, 1.0$ |\n| Fig. 7 (EOS at $\\mu=0$) | $p/p_\\mathrm{SB}$ and $(\\varepsilon-3p)/T^4$ vs $T/T_c$; lattice comparison |\n| Fig. 8 ($\\Delta p/T^4$ vs $\\mu$) | $\\mu = 0.2, 0.4, 0.6, 0.8, 1.0\\,T_c$; Allton lattice data |\n| Fig. 9 ($n_q/T^3$ vs $\\mu$) | Same $\\mu$ values as Fig. 8 |\n| Fig. 10 (PNJL vs NJL) | $\\mu = 0.6\\,T_c$; NJL = PNJL mass with $\\Phi=\\bar\\Phi=1$ |\n\n---\n\n## 4. Banned Libraries\n\n| Banned | Reason |\n|--------|--------|\n| Pre-packaged NJL/PNJL solvers | Must implement from scratch |\n| GPU-accelerated libraries for core physics | Keep in NumPy/SciPy |\n\n**Allowed**: `numpy`, `scipy` (integrate, optimize, interpolate), `matplotlib`\n\n---\n\n## 5. Data Files to Reproduce\n\nGenerate CSV data files for all 10 figures. Each figure script should save its data to `data/` directory. The exact column specifications should be determined from your analysis of the paper.\n\nKey output files expected:\n- Pure gauge Polyakov potential and order parameter data (Figs. 1–3)\n- PNJL order parameters at various $\\mu$ (Figs. 4–6)\n- Equation of state quantities (Figs. 7–10)\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Module\n**Path**: `reproduction/pnjl_model.py`\n\nMust contain:\n- Vacuum NJL integrals with cutoff $\\Lambda$\n- Vacuum gap equation solver\n- Polyakov loop potential $\\mathcal{U}(\\Phi, \\bar\\Phi, T)/T^4$\n- Full PNJL thermodynamic potential\n- Mean-field gradient functions\n- Self-consistent solver with continuation\n- Pressure and quark number density computations\n\n### 6.2 Figure Scripts\n| Figures | Script Path |\n|---------|-------------|\n| Figs. 1–3 (pure gauge) | `reproduction/fig1_2_3_pure_gauge.py` |\n| Figs. 4–6 (order parameters) | `reproduction/fig4_5_6_order_parameters.py` |\n| Figs. 7–10 (equation of state) | `reproduction/fig7_10_eos.py` |\n\n### 6.3 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\n### 6.4 Output Directories\n- Data files: `data/`\n- Plot files: `plots/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Your methodology and formula analysis\n2. `reproduction/pnjl_model.py` — Core PNJL model library\n3. `reproduction/fig1_2_3_pure_gauge.py` — Pure gauge figures\n4. `reproduction/fig4_5_6_order_parameters.py` — Order parameter figures\n5. `reproduction/fig7_10_eos.py` — Equation of state figures\n6. CSV data files in `data/` for all 10 figures\n\nExport all data with 8 decimal places.\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/pnjl_model.py", "reproduction/fig1_2_3_pure_gauge.py", "reproduction/fig4_5_6_order_parameters.py", "reproduction/fig7_10_eos.py"], "data": []}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/pnjl_model.py", "reproduction/fig1_2_3_pure_gauge.py", "reproduction/fig4_5_6_order_parameters.py", "reproduction/fig7_10_eos.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 7200, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_roothaan_1960", "title": "Self-Consistent Field Theory for Atomic Systems", "authors": "Clemens C. J. Roothaan", "year": 1960, "doi": "10.1103/RevModPhys.32.186", "arxiv": null, "paper_files": ["SCF theory.md", "SCF example.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a Self-Consistent Field (SCF) solver to reproduce tables and wave functions for atomic systems.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Self-Consistent Field Theory for Atomic Systems |\n| **Author** | Clemens C. J. Roothaan |\n| **DOI** | 10.1103/RevModPhys.32.186 |\n| **Year** | 1960 |\n| **Paper Files** | `SCF theory.md`, `SCF example.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full papers at `SCF theory.md` and `SCF example.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the Hartree-Fock SCF approach for atomic systems using Slater-type orbitals (STOs)\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - Hartree-Fock equations and Fock operator\n   - STO basis functions and LCAO expansion\n   - Generalized eigenvalue problem **FC = SC**ε\n   - Total energy expression for closed-shell and open-shell systems\n   - Cusp condition\n   - Self-consistent field iteration procedure\n3. **Algorithm Details**: Describe the step-by-step SCF iteration\n4. **Physical Observables**: Explain total energy, orbital energies, and radial wave functions\n\n### Step 2: Implement the SCF Solver\nWrite all code under `reproduction/`. You need:\n- A core SCF library at `reproduction/scf_solver.py`\n- Individual scripts for each table (see Section 5 below)\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n### 3.1 Physical Parameters\n| Parameter | Symbol | Typical Values | Description |\n|-----------|--------|----------------|-------------|\n| Nuclear charge | $Z$ | 2–10 | Atomic number |\n| Orbital exponents | $\\zeta$ | System-dependent | Optimized per orbital |\n| Fractional occupation | $f$ | 0.5, 1.0 | For open-shell systems |\n| Convergence threshold | $\\epsilon$ | $10^{-8}$ | Energy change for SCF convergence |\n\n### 3.2 Atomic Systems to Reproduce\n- **Helium-like**: He(1s²), Li⁺(1s²), Be²⁺(1s²), B³⁺(1s²)\n- **Lithium series**: Li(1s²2s¹), Li⁻(1s²2s²)\n- **Beryllium series**: Be⁺(1s²2s¹), Be(1s²2s²)\n- And additional systems from the Ne isoelectronic series\n\n### 3.3 Basis Set Specifications\n- **2-term basis** (\"compromise\" functions): n=0,1 for each orbital type (Table V)\n- **4-term basis**: n=0,1,2,3 for each orbital type (Tables VII–IX)\n- Use the exact $\\zeta$ values specified in the paper for each system\n\n### 3.4 Convergence\n- Maximum iterations: 100\n- Should converge within 15 iterations for all systems\n\n---\n\n## 4. Banned Libraries\n\n| Banned | Reason |\n|--------|--------|\n| Pre-built quantum chemistry packages (PySCF, Psi4, etc.) | Must implement SCF from scratch |\n| Built-in Hartree-Fock solvers | Implement matrix formulation manually |\n| External integral evaluation libraries | Compute STO integrals analytically |\n| Pre-computed orbital databases | Generate orbitals algorithmically |\n\n**Allowed**: `numpy`, `scipy` (linalg, special), `matplotlib`\n\n---\n\n## 5. Data Files to Reproduce\n\n### 5.1 Table II: Li⁺ Parameter Optimization\n**File**: `data/table_ii_li_plus.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Total energy vs orbital exponents for Li⁺(1s²) |\n| Format | Grid search results: energy vs $\\zeta$ values |\n\n**Columns**: `zeta1, zeta2, energy` (and additional zeta columns as needed)\n\n---\n\n### 5.2 Table III: Li Parameter Optimization\n**File**: `data/table_iii_li.csv`\n\n**Columns**: `zeta1, zeta2, energy`\n\n---\n\n### 5.3 Table IV: Li⁻ Parameter Optimization\n**File**: `data/table_iv_li_minus.csv`\n\n**Columns**: `zeta1, zeta2, energy`\n\n---\n\n### 5.4 Table V: Compromise Functions\n**File**: `data/table_v_compromise.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Total energies and properties using 2-term basis (compromise) functions |\n| Systems | He, Li⁺, Li, Li⁻, Be²⁺, Be⁺, Be, B³⁺, B²⁺, B⁺, C⁴⁺, C³⁺, C²⁺, N⁵⁺, N⁴⁺, N³⁺, O⁶⁺, O⁵⁺, O⁴⁺, F⁷⁺, F⁶⁺, F⁵⁺, Ne⁸⁺, Ne⁷⁺, Ne⁶⁺ |\n\n**Columns**: `system, total_energy, orbit_energy, cusp_values, zeta_parameters, iterations`\n\n---\n\n### 5.5 Table VII: Li Wave Function\n**File**: `data/table_vii_li.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Radial wave function $P(r) = r \\cdot R(r)$ for Li(1s²2s¹) |\n| Basis | 3 zeta values, n=0–3 |\n| X-axis | Radial distance $r$ in atomic units |\n\n**Columns**: `r, P_1s, P_2s`\n\n---\n\n### 5.6 Table VIII: Be Wave Function\n**File**: `data/table_viii_be.csv`\n\n**Columns**: `r, P_1s, P_2s`\n\n---\n\n### 5.7 Table IX: Li⁻ Wave Function\n**File**: `data/table_ix_li_minus.csv`\n\n**Columns**: `r, P_1s, P_2s`\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Module\n**Path**: `reproduction/scf_solver.py`\n\nMust contain:\n- `SCFParameters` class: SCF parameters with all basis information\n- `AtomicSCF` class: SCF iteration with convergence checking\n- Matrix computation functions (overlap, kinetic, nuclear attraction, Coulomb, exchange)\n- Wave function calculation from orbital coefficients\n\n### 6.2 Table Scripts\n| Table | Script Path |\n|-------|-------------|\n| Table II | `reproduction/table_ii_li_plus.py` |\n| Table III | `reproduction/table_iii_li.py` |\n| Table IV | `reproduction/table_iv_li_minus.py` |\n| Table V | `reproduction/table_v_compromise.py` |\n| Table VII | `reproduction/table_vii_li_wavefunction.py` |\n| Table VIII | `reproduction/table_viii_be_wavefunction.py` |\n| Table IX | `reproduction/table_ix_li_minus_wavefunction.py` |\n\n### 6.3 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\n### 6.4 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Methodology and formula analysis\n2. `reproduction/scf_solver.py` — Core SCF library\n3. All 7 table scripts under `reproduction/`\n4. `data/table_ii_li_plus.csv` through `data/table_ix_li_minus.csv` — 7 output data files\n\nExport energies with 6 decimal places, radii with 4 decimal places.\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the papers\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the SCF computations or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/scf_solver.py", "reproduction/table_ii_li_plus.py", "reproduction/table_iii_li.py", "reproduction/table_iv_li_minus.py", "reproduction/table_v_compromise.py", "reproduction/table_vii_li_wavefunction.py", "reproduction/table_viii_be_wavefunction.py", "reproduction/table_ix_li_minus_wavefunction.py"], "data": ["data/table_ii_li_plus.csv", "data/table_iii_li.csv", "data/table_iv_li_minus.csv", "data/table_v_compromise.csv", "data/table_vii_li.csv", "data/table_viii_be.csv", "data/table_ix_li_minus.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/scf_solver.py", "reproduction/table_ii_li_plus.py", "reproduction/table_iii_li.py", "reproduction/table_iv_li_minus.py", "reproduction/table_v_compromise.py", "reproduction/table_vii_li_wavefunction.py", "reproduction/table_viii_be_wavefunction.py", "reproduction/table_ix_li_minus_wavefunction.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "2g", "timeout": 3600, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_rosenbluth_1998", "title": "Poloidal Flow Driven by Ion-Temperature-Gradient Turbulence in Tokamaks", "authors": "M. N. Rosenbluth, F. L. Hinton", "year": 1998, "doi": "10.1103/PhysRevLett.80.724", "arxiv": null, "paper_files": ["rosenbluth_1998.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a landmark theoretical physics paper to reproduce. Your goal is to read the paper, thoroughly understand its gyrokinetic methodology, and write a script to numerically evaluate the exact phase-space integrals that yield its famous residual flow coefficient.\n\n---\n\n## 1. Article Information\n\n| Field               | Value                                                                 |\n| ------------------- | --------------------------------------------------------------------- |\n| **Title**           | Poloidal Flow Driven by Ion-Temperature-Gradient Turbulence in Tokamaks |\n| **Author**          | M. N. Rosenbluth, F. L. Hinton                                        |\n| **DOI**             | 10.1103/PhysRevLett.80.724                                            |\n| **Paper File**      | `rosenbluth_1998.md` (in the same task directory)                     |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `rosenbluth_1998.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the multi-scale expansion and bounce-averaging technique used to isolate the long-time memory of the distribution function.\n2. **Proof of Non-Damping**: Explain the construction of the integral operator $\\mathcal{L}$ and how the Cauchy-Schwarz inequality rigorously proves its positive-definiteness (forcing the collisionless linear damping $B_k \\equiv 0$).\n3. **Geometric Cancellation**: Describe the Initial Value Problem of rotational relaxation and how the toroidal flow perfectly decouples from the residual poloidal flow.\n4. **Phase-Space Mapping**: Detail how the neoclassical polarization shielding integral is mapped to the trapping parameter space $y=k^2$ and expressed via complete elliptic integrals of the first and second kinds ($K(y)$ and $E(y)$).\n\n### Step 2: Implement the Numerical Integration\nWrite the implementation script under `reproduction/compute_rh_factor.py`. You must:\n- Implement the exact integrands for trapped ($J_T$) and passing ($J_P$) particles.\n- **CRITICALLY IMPORTANT**: Analytically expand and mathematically handle the integrable singularity for passing particles at $y \\to 0$ using a Taylor expansion to prevent numerical divergence.\n- Numerically integrate these functions to compute the Rosenbluth-Hinton constant $C_{\\text{RH}}$.\n\n### Step 3: Save Results to CSV\nAfter computing all quantities, write the results to `data/results.csv` using the following exact format:\n\n```\nquantity,value\nJ_T,<computed value>\nJ_P,<computed value>\nsum,<computed value>\nC_RH,<computed value>\n```\n\nWhere:\n- `J_T` is the trapped particle integral\n- `J_P` is the passing particle integral\n- `sum` is $J_T + J_P$\n- `C_RH` is the Rosenbluth-Hinton constant $\\frac{6\\sqrt{2}}{\\pi}(J_T + J_P)$\n\n*(Note: Since this is a theoretical letter, there are no data figures to digitize. The CSV captures the four key scalar outputs of your numerical integration.)*\n\n---\n\n## 3. Key Variables & Parameters\n\n| Parameter     | Symbol      | Description / Range          |\n| ------------- | ----------- | ---------------------------- |\n| Trapping param| $y$ or $k^2$| $0 \\le y \\le 1$              |\n| Trapped domain| $J_T$       | $y \\in [0, 1]$               |\n| Passing domain| $J_P$       | $y = 1/k^2 \\in[0, 1]$       |\n| Singularity   | $y \\to 0$   | Handled via Taylor expansion near 0 |\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category              | Banned                                                        | Allowed Alternative         |\n| --------------------- | ------------------------------------------------------------- | --------------------------- |\n| **Hardcoding**        | Directly writing the known answer into the CSV without computing | Numerical evaluation via `scipy.integrate.quad` |\n| **Symbolic Math**     | `SymPy` for the final numerical output                        | Use `scipy.special.ellipk` and `ellipe` |\n\n---\n\n## 5. Code Structure Requirements\n\n### 5.1 Core Modules\n**Path**: `reproduction/`\n\n| File                     | Description                                              |\n| ------------------------ | -------------------------------------------------------- |\n| `compute_rh_factor.py`   | The Python script containing the integrands, singularity handling, numerical quadrature using `scipy`, and CSV output. |\n\n### 5.2 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\nMust contain your comprehensive, step-by-step mathematical derivation of the paper's core results, proving the undamped nature of Zonal Flows and the derivation of the $1.6$ factor.\n\n### 5.3 Output Directories\n- Code and Analysis: `reproduction/`\n- Data: `data/`\n\n---\n\n## 6. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Your methodology, non-damping proof, and formula analysis.\n2. `reproduction/compute_rh_factor.py` — The numerical integration script.\n3. `data/results.csv` — The computed values in CSV format.\n\n---\n\n## 7. Reproduction Requirements\n\n### 7.1 Computational Resources\n\n| Requirement          | Value        | Notes                              |\n| -------------------- | ------------ | ---------------------------------- |\n| **Total time limit** | ~10 minutes  | 1D numerical quadrature is very fast |\n| **Memory limit**     | < 1 GB       | Minimal memory overhead required   |\n| **CPU**              | 1 Core       | No parallelization required        |\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement the numerical integration script `reproduction/compute_rh_factor.py`\n4. **DO NOT** execute the script to print outputs\n5. Focus on writing correct, mathematically rigorous, and well-structured code\n\nYour deliverables are ONLY the analysis document and the code file.\nYou do NOT need to produce `data/results.csv` in code-only mode.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/compute_rh_factor.py"], "data": ["data/results.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/compute_rh_factor.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 1800, "pip_install": ["numpy", "scipy"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.35}, {"name": "numerical_accuracy", "weight": 0.35}, {"name": "code_correctness", "weight": 0.2}, {"name": "completeness", "weight": 0.1}]}
{"task_id": "task_shvetsov_2016", "title": "Semiclassical two-step model for strong-field ionization", "authors": "N. I. Shvetsov-Shilovski et al.", "year": 2016, "doi": "10.1103/PhysRevA.94.013415", "arxiv": null, "paper_files": ["shvetsov2016.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a semiclassical two-step model for strong-field ionization to reproduce key figures.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Semiclassical two-step model for strong-field ionization |\n| **Authors** | N. I. Shvetsov-Shilovski, M. Lein, L. B. Madsen, E. Räsänen, C. Lemell, J. Burgdörfer, D. G. Arbó, K. Tőkési |\n| **DOI** | 10.1103/PhysRevA.94.013415 |\n| **Journal** | Physical Review A **94**, 013415 (2016) |\n| **Paper File** | `shvetsov2016.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `shvetsov2016.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the SCTS two-step model combining tunneling ionization with classical propagation and semiclassical phase accumulation\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - Tunneling ionization rate (EQ-9)\n   - Tunnel exit coordinate (EQ-11, EQ-12, EQ-13)\n   - Newton's equations of motion (EQ-14)\n   - Semiclassical phase with factor-2 Coulomb correction (EQ-22)\n   - Coulomb mapping to asymptotic momentum (EQ-26-29)\n   - Post-pulse Coulomb phase (EQ-40)\n   - Coherent sum for observables (EQ-41)\n   - Laser pulse vector potential (EQ-42)\n   - SFA parallel velocity (EQ-47, EQ-48)\n3. **Physical Interpretation**: Explain what each figure shows and the significance of the SCTS model vs QTMC\n4. **Parameters**: Identify all atomic and laser parameters needed\n\n### Step 2: Implement the Computation\nWrite all code under `reproduction/`. You need:\n- A core module at `reproduction/scts_core.py` with the SCTS model implementation\n- Figure scripts for Figures 1, 2, 4 (energy + angular), 6, and 7 (energy + angular)\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 6 for exact specifications.\n\n---\n\n## 3. Main Formulas Used in Reproduction\n\n### 3.1 Hamiltonian (EQ-3)\n$$\nH[\\vec{r}(t), \\vec{p}(t)] = \\frac{p^2(t)}{2} + \\vec{F}(t) \\cdot \\vec{r}(t) - \\frac{Z}{r(t)}\n$$\n\n### 3.2 Tunneling Ionization Rate (EQ-9)\n$$\nw(t_0, v_{0,\\perp}) \\sim \\exp\\left(-\\frac{2\\kappa^3}{3F(t_0)}\\right) \\exp\\left(-\\frac{\\kappa v_{0,\\perp}^2}{F(t_0)}\\right)\n$$\nwhere $\\kappa = \\sqrt{2 I_p}$.\n\n### 3.3 Tunnel Exit Coordinate (EQ-11)\n$$\n-\\frac{\\beta^2(F)}{2\\eta} + \\frac{m^2 - 1}{8\\eta^2} - \\frac{F\\eta}{8} = -\\frac{I_p(F)}{4}\n$$\n\n### 3.4 Separation Constant (EQ-12)\n$$\n\\beta^2(F) = Z - (1 + |m|)\\frac{\\sqrt{2 I_p(F)}}{2}\n$$\n\n### 3.5 Stark-Shifted Ionization Potential (EQ-13)\n$$\nI_p(F) = I_p + \\frac{1}{2}(\\alpha_N - \\alpha_I) F^2\n$$\n\n### 3.6 Newton's Equation of Motion (EQ-14)\n$$\n\\frac{d^2 \\vec{r}(t)}{dt^2} = -\\vec{F}(t) - \\frac{Z \\vec{r}(t)}{r^3(t)}\n$$\n\n### 3.7 Semiclassical Phase — SCTS (EQ-22)\n$$\n\\Phi(t_0^j, \\vec{v}_0^j) = -\\vec{v}_0^j \\cdot \\vec{r}(t_0^j) + I_p t_0^j - \\int_{t_0^j}^{\\infty} dt\\left[\\frac{p^2(t)}{2} - \\frac{2Z}{r(t)}\\right]\n$$\n**Key:** Factor of **2** on Coulomb term distinguishes SCTS from QTMC.\n\n### 3.8 Asymptotic Energy (EQ-26)\n$$\n\\frac{k^2}{2} = \\frac{p^2(\\tau_f)}{2} - \\frac{Z}{r(\\tau_f)}\n$$\n\n### 3.9 Angular Momentum (EQ-27)\n$$\n\\vec{L} = \\vec{r}(\\tau_f) \\times \\vec{p}(\\tau_f)\n$$\n\n### 3.10 Runge-Lenz Vector (EQ-28)\n$$\n\\vec{a} = \\vec{p}(\\tau_f) \\times \\vec{L} - \\frac{\\vec{r}(\\tau_f)}{r(\\tau_f)}\n$$\n\n### 3.11 Asymptotic Momentum (EQ-29)\n$$\n\\vec{k} = k \\frac{k(\\vec{L} \\times \\vec{a}) - \\vec{a}}{1 + k^2 L^2}\n$$\n\n### 3.12 Post-Pulse Coulomb Phase (EQ-40)\n$$\n\\tilde{\\Phi}_f^C(\\tau_f) = -Z\\sqrt{b}\\left[\\ln g + \\text{arsinh}\\left(\\frac{\\vec{r}(\\tau_f) \\cdot \\vec{p}(\\tau_f)}{g\\sqrt{b}}\\right)\\right]\n$$\nwhere $b = 1/(2E)$, $g = \\sqrt{1 + 2EL^2}$.\n\n### 3.13 Ionization Probability — Coherent Sum (EQ-41)\n$$\nR(\\vec{k}) = \\left|\\sum_{j=1}^{n_p} \\exp\\left[i\\Phi(t_0^j, \\vec{v}_0^j)\\right]\\right|^2\n$$\n\n### 3.14 Laser Pulse Vector Potential (EQ-42)\n$$\n\\vec{A}(t) = (-1)^{n+1} \\frac{c F_0}{\\omega} \\sin^2\\left(\\frac{\\omega t}{2n}\\right) \\sin(\\omega t)\\, \\vec{e}_z\n$$\nElectric field: $\\vec{F}(t) = -(1/c)\\, d\\vec{A}/dt$\n\n### 3.15 SFA Parallel Velocity (EQ-47, EQ-48)\n$$\nv_{z,0}(t_0) = -\\frac{1}{c} A_z(t_0)\\left[\\sqrt{1 + \\gamma^2(t_0, v_{0,\\perp})} - 1\\right]\n$$\n$$\n\\gamma(t_0, v_{0,\\perp}) = \\frac{\\omega\\sqrt{2I_p + v_{0,\\perp}^2}}{F_0 \\sin^2\\!\\left(\\frac{\\omega t_0}{2n}\\right)|\\cos(\\omega t_0)|}\n$$\n\n---\n\n## 4. Main Methodology\n\n### 4.1 Two-Step Semiclassical Model\n1. **Step 1 — Tunneling Ionization:**\n   - Sample ionization time $t_0$ from ADK-type rate (EQ-9)\n   - Compute tunnel exit position from parabolic coordinate equation (EQ-11, EQ-12, EQ-13)\n   - Sample transverse velocity from Gaussian distribution\n   - Optionally compute SFA parallel velocity (EQ-47, EQ-48)\n   - Use importance sampling: trajectories distributed as $\\sqrt{w(t_0, v_{0,\\perp})}$\n\n2. **Step 2 — Classical Propagation:**\n   - Integrate Newton's equations (EQ-14) with adaptive RK4\n   - Accumulate semiclassical phase along trajectory (EQ-22)\n   - At pulse end, apply Coulomb mapping to get asymptotic momentum (EQ-26-29)\n   - Compute post-pulse Coulomb phase correction (EQ-40)\n   - Filter recaptured trajectories ($E < 0$)\n\n3. **Observable Computation:**\n   - Bin ionized trajectories by asymptotic momentum\n   - Compute coherent sum within each bin (EQ-41)\n   - Generate 2D momentum distribution, energy spectrum, angular distribution\n\n### 4.2 Coordinate System\n- Atomic units throughout: $\\hbar = m_e = e = 4\\pi\\epsilon_0 = 1$\n- Length gauge for laser-matter interaction\n- Cylindrical symmetry: 2D simulation in $(z, r_\\perp)$ plane\n\n---\n\n## 5. Input Parameters\n\n### 5.1 Atomic Parameters (Hydrogen)\n| Parameter | Symbol | Value | Units | Notes |\n|-----------|--------|-------|-------|-------|\n| Ionization potential | $I_p$ | 0.5 | a.u. | H ground state |\n| Ionic charge | $Z$ | 1 | — | H$^+$ |\n| Magnetic quantum number | $m$ | 0 | — | H(1s) |\n| Atomic polarizability | $\\alpha_N$ | 4.5 | a.u. | For Stark shift |\n| Ionic polarizability | $\\alpha_I$ | 0 | a.u. | H$^+$ |\n| $\\kappa = \\sqrt{2I_p}$ | $\\kappa$ | 1.0 | a.u. | Derived |\n\n### 5.2 Laser Parameters (800 nm benchmark)\n| Parameter | Symbol | Value | Units | Notes |\n|-----------|--------|-------|-------|-------|\n| Wavelength | $\\lambda$ | 800 | nm | Primary benchmark |\n| Peak intensity | $I$ | $0.9 \\times 10^{14}$ | W/cm² | |\n| Peak field | $F_0$ | 0.0507 | a.u. | $\\sqrt{I / 3.51 \\times 10^{16}}$ |\n| Angular frequency | $\\omega$ | 0.057 | a.u. | $2\\pi c / \\lambda$ |\n| Number of cycles | $n$ | 8 | — | |\n| Pulse duration | $\\tau_f$ | 882.6 | a.u. | $2\\pi n / \\omega$ |\n| Ponderomotive energy | $U_p$ | 0.198 | a.u. | $F_0^2 / (4\\omega^2)$ |\n| Keldysh parameter | $\\gamma$ | 1.12 | — | $\\omega\\kappa / F_0$ |\n\n### 5.3 Numerical Parameters\n| Parameter | Value | Units | Notes |\n|-----------|-------|-------|-------|\n| Trajectories | $10^6$–$10^7$ | — | Production quality |\n| Momentum bin size | 0.01 | a.u. | $\\Delta k_z = \\Delta k_\\perp$ |\n| Energy bin size | 0.005 | a.u. | |\n| Angular bin size | 1.0 | degrees | |\n| Integrator tolerance | $10^{-8}$ | — | Adaptive RK4 |\n| Coulomb softening radius | 0.01 | a.u. | |\n| Random seed | 42 | — | Base seed |\n\n---\n\n## 6. Banned Libraries\n\n| Banned | Reason |\n|--------|--------|\n| Pre-built strong-field ionization libraries | Must implement SCTS from scratch |\n| GPU-accelerated computation (cupy, pytorch) | Keep in pure NumPy for clarity |\n| External Monte Carlo frameworks | Implement trajectory sampling directly |\n| Pre-built ODE solvers (scipy.integrate) | Implement RK4 integrator explicitly |\n\n**Allowed:** `numpy`, `matplotlib` (plotting only), standard library.\n\n---\n\n## 7. Data Files to Reproduce\n\n### 7.1 Figure 1: 2D Momentum Distribution (SCTS, $v_z = 0$)\n**File**: `data/fig1_momentum_distribution.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | $R(k_z, k_\\perp)$ ionization probability distribution |\n| Parameters | 800 nm, $0.9 \\times 10^{14}$ W/cm², 8 cycles, $v_{z,0} = 0$ |\n| k_z range | $[-1.5, 1.5]$ a.u. |\n| k_perp range | $[0, 1.5]$ a.u. |\n| Grid size | 300 × 150 bins |\n| Format | Flattened R matrix with metadata |\n\n**Columns**: `R_flat, n_z, n_perp` (first row contains grid dimensions)\n\n---\n\n### 7.2 Figure 2: Low-Energy Momentum Distribution\n**File**: `data/fig2_lowenergy_momentum.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Low-energy magnification of Fig. 1, showing fanlike interference |\n| Region | $|k_z| < 0.3$ a.u., $k_\\perp < 0.3$ a.u. |\n| Grid size | 60 × 30 bins |\n| Format | Same as Fig. 1 with additional k range metadata |\n\n**Columns**: `R_flat, n_z, n_perp, k_z_min, k_z_max, k_perp_min, k_perp_max`\n\n---\n\n### 7.3 Figure 4: Energy Spectrum (800 nm, $v_z = 0$)\n**File**: `data/fig4_energy_spectrum.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Energy spectrum $dR/dE$ showing ATI peaks |\n| X-axis | Energy $E$ (a.u.), range $[0, 2U_p]$ |\n| Y-axis | $dR/dE$ (arbitrary units) |\n| Energy bin size | 0.005 a.u. |\n| Number of points | ~80 |\n\n**Columns**: `E, dR_dE`\n\n---\n\n### 7.4 Figure 4: Angular Distribution (800 nm, $v_z = 0$)\n**File**: `data/fig4_angular_distribution.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Angular distribution $dR/(\\sin\\theta\\, d\\theta)$ for $E < U_p$ |\n| X-axis | $\\theta$ (degrees), range $[0, 180]$ |\n| Y-axis | $dR/(\\sin\\theta\\, d\\theta)$ (arbitrary units) |\n| Angular bin size | 1.0 degree |\n| Number of points | 180 |\n\n**Columns**: `theta_deg, dR_dtheta`\n\n---\n\n### 7.5 Figure 6: 2D Momentum Distribution (SFA $v_z$)\n**File**: `data/fig6_sfa_momentum.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Same as Fig. 1 but with SFA parallel velocity (EQ-47) |\n| Parameters | 800 nm, same intensity, $v_{z,0}$ from SFA |\n| Grid size | 300 × 150 bins |\n| Format | Same as Fig. 1 |\n\n**Columns**: `R_flat, n_z, n_perp`\n\n---\n\n### 7.6 Figure 7: Energy Spectrum with SFA $v_z$\n**File**: `data/fig7_sfa_energy_spectrum.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Energy spectrum with nonzero initial parallel velocity |\n| Parameters | 800 nm, SFA $v_{z,0}$ |\n\n**Columns**: `E, dR_dE`\n\n---\n\n### 7.7 Figure 7: Angular Distribution with SFA $v_z$\n**File**: `data/fig7_sfa_angular_distribution.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Angular distribution with nonzero initial parallel velocity |\n| Parameters | 800 nm, SFA $v_{z,0}$, $E < U_p$ |\n\n**Columns**: `theta_deg, dR_dtheta`\n\n---\n\n## 8. Code Structure\n\n### 8.1 Core Module\n**Path**: `reproduction/scts_core.py`\n\nContains:\n- `Config`, `LaserConfig`, `AtomicConfig`, `NumericalConfig`: Configuration dataclasses\n- `LaserPulse`: Laser field evaluation (EQ-42)\n- `AtomicParams`, `InitialCondition`: Tunneling parameters and sampling (EQ-9, EQ-11-13)\n- `propagate_trajectory()`: Adaptive RK4 integrator with phase (EQ-14, EQ-22)\n- `coulomb_map_to_asymptotic()`: Coulomb mapping (EQ-26-29, EQ-40)\n- `compute_momentum_distribution()`, `compute_energy_spectrum()`, `compute_angular_distribution()`: Observable computation (EQ-41)\n- `run_simulation()`: End-to-end simulation runner\n\n### 8.2 Figure Scripts\n| Figure | Script Path |\n|--------|-------------|\n| Fig 1 | `reproduction/fig1_momentum_distribution.py` |\n| Fig 2 | `reproduction/fig2_lowenergy_momentum.py` |\n| Fig 4 (energy) | `reproduction/fig4_energy_spectrum.py` |\n| Fig 4 (angular) | `reproduction/fig4_angular_distribution.py` |\n| Fig 6 | `reproduction/fig6_sfa_momentum.py` |\n| Fig 7 (energy) | `reproduction/fig7_sfa_energy_spectrum.py` |\n| Fig 7 (angular) | `reproduction/fig7_sfa_angular_distribution.py` |\n\n### 8.3 Output Directory\n- Data files: `data/`\n\n---\n\n## 9. Reproduction Requirements\n\n### 9.1 Computational Resources\n| Requirement | Value | Notes |\n|-------------|-------|-------|\n| **Total time limit** | 3 hours | All figures |\n| **Memory limit** | 4 GB | |\n| **CPU** | Single-threaded | No parallelization required for reproduction scripts |\n\n### 9.2 Numerical Precision\n- Export data with 8 decimal places\n- Use double precision (float64) throughout\n\n### 9.3 Expected Results\n| Metric | Expected Value |\n|--------|---------------|\n| Ionization fraction ($v_z = 0$) | ~70-80% |\n| Ionization fraction (SFA $v_z$) | ~80-85% (higher than $v_z = 0$) |\n| ATI peak spacing | ~$\\omega = 0.057$ a.u. |\n| Fanlike nodal lines | 6-8 in low-energy region |\n\n---\n\n## 10. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` -- Methodology and formula analysis\n2. `reproduction/scts_core.py` -- Core SCTS model implementation\n3. `reproduction/fig1_momentum_distribution.py` -- Figure 1 script\n4. `reproduction/fig2_lowenergy_momentum.py` -- Figure 2 script\n5. `reproduction/fig4_energy_spectrum.py` -- Figure 4 energy spectrum script\n6. `reproduction/fig4_angular_distribution.py` -- Figure 4 angular distribution script\n7. `reproduction/fig6_sfa_momentum.py` -- Figure 6 script\n8. `reproduction/fig7_sfa_energy_spectrum.py` -- Figure 7 energy spectrum script\n9. `reproduction/fig7_sfa_angular_distribution.py` -- Figure 7 angular distribution script\n10. `data/fig1_momentum_distribution.csv` -- 2D momentum distribution\n11. `data/fig2_lowenergy_momentum.csv` -- Low-energy momentum distribution\n12. `data/fig4_energy_spectrum.csv` -- Energy spectrum\n13. `data/fig4_angular_distribution.csv` -- Angular distribution\n14. `data/fig6_sfa_momentum.csv` -- SFA momentum distribution\n15. `data/fig7_sfa_energy_spectrum.csv` -- SFA energy spectrum\n16. `data/fig7_sfa_angular_distribution.csv` -- SFA angular distribution\n\nExport all data with 8 decimal places.\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/scts_core.py", "reproduction/fig1_momentum_distribution.py", "reproduction/fig2_lowenergy_momentum.py", "reproduction/fig4_energy_spectrum.py", "reproduction/fig4_angular_distribution.py", "reproduction/fig6_sfa_momentum.py", "reproduction/fig7_sfa_energy_spectrum.py", "reproduction/fig7_sfa_angular_distribution.py"], "data": ["data/fig1_momentum_distribution.csv", "data/fig2_lowenergy_momentum.csv", "data/fig4_energy_spectrum.csv", "data/fig4_angular_distribution.csv", "data/fig6_sfa_momentum.csv", "data/fig7_sfa_energy_spectrum.csv", "data/fig7_sfa_angular_distribution.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/scts_core.py", "reproduction/fig1_momentum_distribution.py", "reproduction/fig2_lowenergy_momentum.py", "reproduction/fig4_energy_spectrum.py", "reproduction/fig4_angular_distribution.py", "reproduction/fig6_sfa_momentum.py", "reproduction/fig7_sfa_energy_spectrum.py", "reproduction/fig7_sfa_angular_distribution.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_vautherin_1972", "title": "Hartree-Fock Calculations with Skyrme's Interaction. I. Spherical Nuclei", "authors": "D. Vautherin and D. M. Brink", "year": 1972, "doi": "10.1103/PhysRevC.5.626", "arxiv": null, "paper_files": ["Vautherin1972Phys.Rev.C626.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a Skyrme-Hartree-Fock (HF) code to reproduce ground-state properties of spherical nuclei.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Hartree-Fock Calculations with Skyrme's Interaction. I. Spherical Nuclei |\n| **Authors** | D. Vautherin and D. M. Brink |\n| **DOI** | 10.1103/PhysRevC.5.626 |\n| **Year** | 1972 |\n| **Paper File** | `Vautherin1972Phys.Rev.C626.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `Vautherin1972Phys.Rev.C626.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the Skyrme-Hartree-Fock approach for spherical nuclei\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - Skyrme two-body and three-body interaction (Eqs. 2, 6, 7)\n   - Energy density functional (Eq. 12)\n   - Effective mass (Eq. 21)\n   - Central and spin-orbit mean fields (Eqs. 22a, 22b)\n   - Radial densities: number density, kinetic density, spin-orbit density (Eqs. 27, 30)\n   - Coulomb direct potential (Eq. 13)\n   - Radial HF equation (Eq. 35)\n   - Appendix E: eigenvalue solver with Newton-Raphson and logarithmic derivative matching\n3. **Algorithm Details**: Describe the SCF iteration with outward/inward integration and matching\n4. **Physical Observables**: Total energy, binding energy per nucleon, RMS radii, single-particle energies\n\n### Step 2: Implement the Skyrme-HF Code\nWrite all code under `reproduction/`. You need separate modules for each component of the calculation.\n\n### Step 3: Generate Data Files\nRun your code to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n### 3.1 Skyrme Force Parameters (Table II)\n| Parameter | Force I | Force II | Unit |\n|-----------|---------|----------|------|\n| $t_0$ | -1057.3 | -1169.9 | MeV·fm³ |\n| $t_1$ | 235.9 | 585.6 | MeV·fm⁵ |\n| $t_2$ | -100.0 | -27.1 | MeV·fm⁵ |\n| $t_3$ | 14463.5 | 9331.1 | MeV·fm⁶ |\n| $x_0$ | 0.56 | 0.34 | dimensionless |\n| $W_0$ | 120.0 | 105.0 | MeV·fm⁵ |\n\n### 3.2 Physical Constants\n| Constant | Value | Unit |\n|----------|-------|------|\n| $\\hbar^2/(2m)$ | 20.73553 | MeV·fm² |\n| $e^2$ | 1.4399764 | MeV·fm |\n\n### 3.3 Numerical Parameters\n| Parameter | Value | Description |\n|-----------|-------|-------------|\n| $r_{\\max}$ | 25 fm | Outer boundary for inward integration |\n| $\\Delta r$ | 0.05–0.1 fm | Radial grid spacing |\n| Grid points | 250–500 | Radial mesh |\n| Convergence | $10^{-4}$ | Relative change in single-particle energies |\n| Mixing parameter | 0.2–0.4 | Wavefunction mixing for SCF stability |\n\n### 3.4 Target Nuclei\n| Nucleus | Z | N | A |\n|---------|---|---|---|\n| $^{16}$O | 8 | 8 | 16 |\n| $^{40}$Ca | 20 | 20 | 40 |\n| $^{48}$Ca | 20 | 28 | 48 |\n\n---\n\n## 4. Banned Libraries\n\n| Banned | Reason |\n|--------|--------|\n| Pre-built HF libraries (PySCF, etc.) | Must implement Skyrme-HF from scratch |\n| Nuclear structure codes (HFBTHO, Sky3D) | Core algorithm must be self-implemented |\n| Automatic differentiation for $F'(E)$ | Use analytic formula Eq. (E8) |\n| ODE solvers for eigenvalue search | Implement RK4 + Newton-Raphson directly |\n\n**Allowed**: `numpy`, `scipy` (interpolation, integration), `matplotlib`\n\n---\n\n## 5. Data Files to Reproduce\n\n### 5.1 Bulk Properties\n**File**: `data/bulk_properties.csv`\n\n| Property | Value |\n|----------|-------|\n| Description | Ground state energies and radii from Table IV |\n| Nuclei | O-16, Ca-40, Ca-48 |\n| Quantities | E/A (MeV), $r_p$ (fm), $r_n$ (fm) |\n\n**Columns**: `nucleus, Z, N, A, E_per_A_MeV, r_p_rms_fm, r_n_rms_fm`\n\n**Benchmark Values (Force I)**:\n| Nucleus | E/A (MeV) | $r_p$ (fm) |\n|---------|-----------|------------|\n| $^{16}$O | -8.22 | 2.56 |\n| $^{40}$Ca | -8.64 | 3.31 |\n| $^{48}$Ca | -8.54 | 3.41 |\n\n---\n\n### 5.2 Single-Particle Energies — O-16\n**File**: `data/single_particle_energies_O16.csv`\n\n**Columns**: `orbital, n, l, j, proton_energy_MeV, neutron_energy_MeV`\n\n---\n\n### 5.3 Single-Particle Energies — Ca-40\n**File**: `data/single_particle_energies_Ca40.csv`\n\n**Columns**: `orbital, n, l, j, proton_energy_MeV, neutron_energy_MeV`\n\n---\n\n### 5.4 Single-Particle Energies — Ca-48\n**File**: `data/single_particle_energies_Ca48.csv`\n\n**Columns**: `orbital, n, l, j, proton_energy_MeV, neutron_energy_MeV`\n\n---\n\n### 5.5 Skyrme Parameters (Input Reference)\n**File**: `data/skyrme_parameters.csv`\n\n**Columns**: `force, t0, t1, t2, t3, x0, W0`\n\n---\n\n### 5.6 Physical Constants (Input Reference)\n**File**: `data/physical_constants.csv`\n\n**Columns**: `name, value, unit`\n\n---\n\n### 5.7 Shell Configurations\n**File**: `data/shell_configurations.csv`\n\n**Columns**: `nucleus, Z, N, particle_type, orbital, n, l, j, degeneracy, occupied`\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Modules\n| Module | Path | Description |\n|--------|------|-------------|\n| Constants | `reproduction/constants.py` | Physical constants and Skyrme parameters |\n| Grid | `reproduction/grid.py` | Radial grid and numerical derivatives |\n| Orbitals | `reproduction/orbitals.py` | Orbital definitions and shell configurations |\n| Densities | `reproduction/densities.py` | Compute $\\rho_q$, $\\tau_q$, $J_q$ from wavefunctions |\n| Mean fields | `reproduction/meanfields.py` | Compute $A_q$, $U_q$, $W_q$, $V_C$ from densities |\n| Solver | `reproduction/solver.py` | Radial eigenvalue solver (Appendix E algorithm) |\n| SCF | `reproduction/scf.py` | Self-consistent field iteration loop |\n| Main | `reproduction/main.py` | Main driver script |\n\n### 6.2 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\n### 6.3 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Methodology and formula analysis\n2. All 8 module files under `reproduction/`\n3. 7 CSV data files under `data/`\n\nExport energies with 6 decimal places, radii with 4 decimal places.\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the Skyrme-HF computations or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/constants.py", "reproduction/grid.py", "reproduction/orbitals.py", "reproduction/densities.py", "reproduction/meanfields.py", "reproduction/solver.py", "reproduction/scf.py", "reproduction/main.py"], "data": ["data/bulk_properties.csv", "data/single_particle_energies_O16.csv", "data/single_particle_energies_Ca40.csv", "data/single_particle_energies_Ca48.csv", "data/skyrme_parameters.csv", "data/physical_constants.csv", "data/shell_configurations.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/constants.py", "reproduction/grid.py", "reproduction/orbitals.py", "reproduction/densities.py", "reproduction/meanfields.py", "reproduction/solver.py", "reproduction/scf.py", "reproduction/main.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "2g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_wang_2015", "title": "Quantum Computation under Micromotion in a Planar Ion Crystal", "authors": "S.-T. Wang, C. Shen, L.-M. Duan", "year": 2015, "doi": "10.1038/srep08555", "arxiv": null, "paper_files": ["MicroOf2DTrap.md"], "input_files": [], "instruction": "# Reproduction Instructions for AI Agent\n\nThis document provides complete instructions for an AI agent to reproduce all figures from the referenced physics paper.\n\n**Note**: The paper contains figures as images. These image files are available at `/workspace/_paper_images/` (JPEG files like `_page_*.jpeg`). You can read them using the Read tool if you need to inspect figures from the paper for reference.\n\n---\n\n## 1. Article Information\n\n| Field               | quamtum computing                                            |\n| ------------------- | ------------------------------------------------------------ |\n| **Title**           | Quantum Computation under Micromotion in a Planar Ion Crystal |\n| **Author**          | S.-T. Wang<sup>1,2</sup>, C. Shen<sup>1,3</sup> & L.-M. Duan<sup>1,2</sup> |\n| **DOI**             | https://doi.org/10.1038/srep08555                            |\n| **arXiv**           | Not available (predates arXiv)                               |\n| **Source Markdown** | `MicroOf2DTrap.md`                                           |\n\n---\n\n## 2. Main Formulas Used in Reproduction\n\nAll the formulas should be extracted from the article\n\n## 3. Main Methodology\n\nAll the methods used should be mentioned in the article\n\n---\n\n## 4. Input Parameters\n\n| Parameter                              | Symbol   | Typical Values | Description               |\n| -------------------------------------- | -------- | -------------- | ------------------------- |\n| number of ions                         | $N$      | 127            |                           |\n| mass of ion                            | $m$      | 2.874e-15      | mass of ion,usually Yb    |\n| ratio of transverse to longitude field | $\\alpha$ | 1              | Sweeps before measurement |\n| unit of length                         | $l_0$    | 8um            | Sweeps for averaging      |\n|                                        |          |                |                           |\n| number of the first selected ion       | $i_1$    | 4              |                           |\n| number of the second selected ion      | $i_2$    | 6              |                           |\n\nBesides,you can use any constant in scipy.const.\n\n---\n\n## 5. Banned Libraries\n\nThe following libraries/approaches are **NOT allowed** for the core physics simulation:\n\n| Banned                                    | Reason           |\n| ----------------------------------------- | ---------------- |\n| use the result of the article before code | prevent cheating |\n|                                           |                  |\n|                                           |                  |\n|                                           |                  |\n\n\n---\n\n## 6. Data Files to Reproduce\n\n### 6.1 Balance_place_of_ions.csv\n\n**File**: `data/Balance_place_of_ions.csv`\n\n**Columns**: `number of ions,x,y,z`\n\nMeaning of x,y,z means the balance place. Parameters are the same as in the article.\n\nThe ion numbers are arranged based on the increasing order of u.\n\nIn this part,you need to plot the balance place with 2 kinds of situation mentioned in the article but the data only need to save the best one in the file.\n\n\n---\n\n### 6.2 normal frequency\n\n**File**: `data/normal_frequancy.csv`\n\n**Columns**: `frequency,b1x,b1y,b1z,...,bNx,bNy,bNz`\n\nbix, biy, biz are the normal modes of the i-th ion corresponding to this frequency.\n\nfrequency are sorted in descending order.\n\nIn this part, you do not need to plot a figure.\n\n### 6.3 Raman Frequency of Typical couples of ions\n\n**File**: `data/Segments.csv`\n\n**Columns**: `Segment1,Segment2`\n\nlist your results of 2 Segments shown in the article.\n\nIn this part you need to plot 2 figures to show the results above like the article.\n\n\n---\n\nIf you can give me the right segments,you can draw other pictures easily.So you don’t need to draw them.\n\nAll the figures is also placed in the \\data\n\n---\n\n## 7. Code Structure\n\n### 7.1 Main Code\n\n**Path**: `reproduction/GateOfLinearTrap.py`\n\nContains:\n\n* Basic information and parameters\n\n- `balance_place` function: input with N,A,Q,output the balance place of ions \n- `normal_mode` function: input with balance place of ions and omegax, output the normal frequency and normal modes. \n- `Segment`function: input normal frequency, normal modes,couple of ions and other parameters shown in the article. Output the Segment of the parameter. \n- And other functions if you need.\n\n### 7.2 execution code\n\n| Part | Script Path                             |\n| ---- | --------------------------------------- |\n| 1    | `reproduction/Balance_place_of_ions.py` |\n| 2    | `reproduction/normal_frequancy.py`      |\n|      |                                         |\n| 3    | `reproduction/Raman_Segments.py`        |\n\n### 7.3 Output Directories\n\n- Data files: `data/`\n\n---\n\n## 8. Reproduction Requirements\n\n### 8.1 Computational Resources\n\nD:\\python310\\python.exe\n\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/GateOfLinearTrap.py", "reproduction/Balance_place_of_ions.py", "reproduction/normal_frequancy.py", "reproduction/Raman_Segments.py"], "data": ["data/Balance_place_of_ions.csv", "data/normal_frequancy.csv", "data/Segments.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/GateOfLinearTrap.py", "reproduction/Balance_place_of_ions.py", "reproduction/normal_frequancy.py", "reproduction/Raman_Segments.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.15}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.55}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_white_1993", "title": "Density-matrix algorithms for quantum renormalization groups", "authors": "Steven R. White", "year": 1993, "doi": "10.1103/PhysRevB.48.10345", "arxiv": null, "paper_files": ["white1993.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement a DMRG simulation to reproduce 7 key figures.\n\n---\n\n## 1. Article Information\n\n| Field               | Value                                                        |\n| ------------------- | ------------------------------------------------------------ |\n| **Title**           | Density-matrix algorithms for quantum renormalization groups |\n| **Author**          | Steven R. White                                              |\n| **DOI**             | 10.1103/PhysRevB.48.10345                                    |\n| **Paper File**      | `white1993.md` (in the same task directory)                  |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `white1993.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the DMRG algorithm (both infinite and finite system versions)\n2. **Key Formulas**: List and explain every formula needed for the reproduction, including:\n   - The Heisenberg Hamiltonian (OBC and PBC)\n   - Superblock construction\n   - Density matrix and truncation\n   - SVD-based truncation\n   - Multi-target state density matrix\n   - Measurement formulas for observables\n3. **Algorithm Details**: Describe the infinite system algorithm (Table II) and finite system algorithm (Table III) step by step\n4. **Physical Observables**: Explain what each figure measures and its physical significance\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduction/`. You need:\n- Core DMRG modules (see Section 6 below)\n- Individual scripts for each figure\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n| Parameter     | Symbol      | Values         |\n| ------------- | ----------- | -------------- |\n| Spin          | $S$         | 1/2, 1         |\n| Coupling      | $J$         | 0.236, 1.0     |\n| Length        | $L$         | 4–100          |\n| States kept   | $m$         | 4–200          |\n| Target states | $k$         | 1–5            |\n| $S_z$ sector  | $S_z^{tot}$ | 0, 1           |\n| Boundary      | BCs         | OBC, PBC, Soft |\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category              | Banned                                                        | Allowed Alternative         |\n| --------------------- | ------------------------------------------------------------- | --------------------------- |\n| **DMRG/TN Libraries** | `TeNPy`, `ITensor`, `ALPS`, `TenPy`, `quimb`, `tensornetwork` | Implement from scratch      |\n| **ED Packages**       | `QuSpin`, `EDKit`, `exact_diag`                               | Build Hamiltonians manually |\n| **GPU Libraries**     | `cupy`, `PyTorch`, `JAX`, `TensorFlow`                        | `NumPy`, `SciPy`            |\n| **Symbolic Math**     | `SymPy` for numerical computation                             | Use for verification only   |\n| **Auto-diff**         | `autograd`, `JAX`                                             | Manual derivatives          |\n\n---\n\n## 5. Data Files to Reproduce\n\n### Figure 2: Density-Matrix Eigenvalues\n**File**: `data/fig2.csv`\n\n| Property | Value                                              |\n| -------- | -------------------------------------------------- |\n| X-axis   | $\\alpha$ (eigenvalue index)                        |\n| Y-axis   | $w_\\alpha$ (log, $10^0$–$10^{-10}$)                |\n| System   | $L=32$, $S_z=0$                                    |\n| Series   | Open S=1/2, Open S=1, Periodic S=1/2, Periodic S=1 |\n\n**X values**: 1, 2, 3, ..., 50\n\n**Columns**: `alpha,\"Open, S=1/2\",\"Open, S=1\",\"Periodic, S=1/2\",\"Periodic, S=1\"`\n\n---\n\n### Figure 3: Energy Convergence (S=1/2)\n**File**: `data/fig3.csv`\n\n| Property | Value                                        |\n| -------- | -------------------------------------------- |\n| X-axis   | $m$ (states kept)                            |\n| Y-axis   | $\\Delta E/\\|E\\|$ (log, $10^{-1}$–$10^{-11}$) |\n| System   | $L=28$, $S=1/2$                              |\n| Series   | Open BCs, Periodic BCs                       |\n\n**X values**: 4, 6, 8, 10, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80, 90, 100, 110, 120\n\n**Columns**: `m,Open BCs,Periodic BCs`\n\n---\n\n### Figure 4: Energy Convergence (S=1)\n**File**: `data/fig4.csv`\n\n| Property | Value                                        |\n| -------- | -------------------------------------------- |\n| X-axis   | $m$ (states kept)                            |\n| Y-axis   | $\\Delta E/\\|E\\|$ (log, $10^{-1}$–$10^{-10}$) |\n| System   | $L=16$, $S=1$                                |\n| Series   | Open BCs, Periodic BCs                       |\n\n**X values**: 4, 6, 8, 10, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80, 90, 100, 110, 120\n\n**Columns**: `m,Open BCs,Periodic BCs`\n\n---\n\n### Figure 5: Energy Gap vs 1/L\n**File**: `data/fig5.csv`\n\n| Property | Value                        |\n| -------- | ---------------------------- |\n| X-axis   | $1/L$ (inverse chain length) |\n| Y-axis   | $\\Delta_L$ (0–1.0)           |\n| System   | PBC                          |\n| Series   | S=1/2 (→0), S=1 (→0.41)      |\n\n**X values (L)**: 4, 6, 8, 10, 12, 14, 16, 20, 24, 32, 40, 50, 64, 80, 100\n\n**Columns**: `L,1/L,Gap S=1/2,Gap S=1`\n\n---\n\n### Figure 6: Local Bond Strength (S=1/2)\n**File**: `data/fig6.csv`\n\n| Property | Value                                             |\n| -------- | ------------------------------------------------- |\n| X-axis   | $i$ (site index)                                  |\n| Y-axis   | $\\langle S_i \\cdot S_{i+1}\\rangle$ (−0.7 to −0.3) |\n| System   | $S=1/2$, OBC                                      |\n| Series   | (a) $L$=60, (b) $L$=61, (c) $L$=60 soft           |\n\n**X values**: 1, 2, 3, ..., 59 (panels a, c); 1, 2, 3, ..., 60 (panel b)\n\n**Columns**: `i,Panel (a),Panel (b),Panel (c)`\n\n---\n\n### Figure 7: Local Observables (S=1)\n**File**: `data/fig7.csv`\n\n| Property | Value                                                  |\n| -------- | ------------------------------------------------------ |\n| X-axis   | $i$ (site index)                                       |\n| Y-axis   | Bond: −1.7 to −1.3; $S_z$: −0.4 to 0.6                 |\n| System   | $L$=60, $S=1$, OBC                                     |\n| Series   | (a) Bond ($S_z$=0), (b) $\\langle S_z\\rangle$ ($S_z$=1) |\n\n**X values**: 1, 2, 3, ..., 59 (bond strength); 1, 2, 3, ..., 60 (local $S_z$)\n\n**Columns**: `i,Bond Strength,Local Sz`\n\n---\n\n### Figure 8: Multi-Target Eigenvalues\n**File**: `data/fig8.csv`\n\n| Property | Value                               |\n| -------- | ----------------------------------- |\n| X-axis   | $\\alpha$ (eigenvalue index)         |\n| Y-axis   | $w_\\alpha$ (log, $10^0$–$10^{-10}$) |\n| System   | $L$=32, $S=1/2$, OBC                |\n| Series   | $k$=1, 2, 3, 4, 5 targets           |\n\n**X values**: 1, 2, 3, ..., 50\n\n**Columns**: `alpha,1 Target,2 Targets,3 Targets,4 Targets,5 Targets`\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Modules\n**Path**: `reproduction/`\n\n| File               | Description                                              |\n| ------------------ | -------------------------------------------------------- |\n| `operators.py`     | Spin matrices $S^z, S^+, S^-$ for $S=1/2$ and $S=1$     |\n| `block.py`         | Block class with Hamiltonian and boundary operators      |\n| `superblock.py`    | Superblock construction, diagonalization, density matrix |\n| `dmrg_infinite.py` | Infinite System Algorithm                                |\n| `dmrg_finite.py`   | Finite System Algorithm                                  |\n\n### 6.2 Figure Scripts\n| Figure | Script Path                    |\n| ------ | ------------------------------ |\n| Fig 2  | `reproduction/fig2_compute.py` |\n| Fig 3  | `reproduction/fig3_compute.py` |\n| Fig 4  | `reproduction/fig4_compute.py` |\n| Fig 5  | `reproduction/fig5_compute.py` |\n| Fig 6  | `reproduction/fig6_compute.py` |\n| Fig 7  | `reproduction/fig7_compute.py` |\n| Fig 8  | `reproduction/fig8_compute.py` |\n\n### 6.3 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\nMust contain your analysis of the paper's methodology and all formulas needed for reproduction.\n\n### 6.4 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Your methodology and formula analysis\n2. `reproduction/operators.py` through `reproduction/dmrg_finite.py` — Core DMRG modules\n3. `reproduction/fig2_compute.py` through `reproduction/fig8_compute.py` — Figure scripts\n4. `data/fig2.csv` through `data/fig8.csv` — Output data files (7 total)\n\nExport data with 10 decimal places (`%.10e`).\n\n---\n\n## 8. Reproduction Requirements\n\n### 8.1 Computational Resources\n\n| Requirement          | Value        | Notes                              |\n| -------------------- | ------------ | ---------------------------------- |\n| **Total time limit** | ~2 - 4 hours | PBC with $m=200$ and finite sweeps |\n| **Memory limit**     | 4 - 8 GB     | Superblock for $m=200$, $S=1$      |\n| **CPU**              | 1 - 4 Cores  | No parallelization required        |\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the DMRG simulations or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/operators.py", "reproduction/block.py", "reproduction/superblock.py", "reproduction/dmrg_infinite.py", "reproduction/dmrg_finite.py", "reproduction/fig2_compute.py", "reproduction/fig3_compute.py", "reproduction/fig4_compute.py", "reproduction/fig5_compute.py", "reproduction/fig6_compute.py", "reproduction/fig7_compute.py", "reproduction/fig8_compute.py"], "data": ["data/fig2.csv", "data/fig3.csv", "data/fig4.csv", "data/fig5.csv", "data/fig6.csv", "data/fig7.csv", "data/fig8.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/operators.py", "reproduction/block.py", "reproduction/superblock.py", "reproduction/dmrg_infinite.py", "reproduction/dmrg_finite.py", "reproduction/fig2_compute.py", "reproduction/fig3_compute.py", "reproduction/fig4_compute.py", "reproduction/fig5_compute.py", "reproduction/fig6_compute.py", "reproduction/fig7_compute.py", "reproduction/fig8_compute.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "8g", "timeout": 14400, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_wu_2013", "title": "Time-domain Perspective on Autler-Townes Splitting in Attosecond Transient Absorption", "authors": "Mengxi Wu, Shaohao Chen, Mette B. Gaarde, Kenneth J. Schafer", "year": 2013, "doi": "10.1103/PhysRevA.88.043416", "arxiv": null, "paper_files": ["wu2013.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand its methodology, select an appropriate numerical algorithm, write the code, and reproduce Figure 3 (a) through numerical simulation.\n\n---\n\n## 1. Article Information\n\n| Field          | Value                                                            |\n| -------------- | ---------------------------------------------------------------- |\n| **Title**      | Density-matrix algorithms for quantum renormalization groups     |\n| **Author**     | Mengxi Wu, Shaohao Chen, Mette B. Gaarde, and Kenneth J. Schafer |\n| **DOI**        | 10.1103/PhysRevA.88.043416                                       |\n| **Paper File** | `wu2013.md` (in the same task directory)                         |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\n\nRead the full paper at `wu2013.md`. Write a detailed analysis document at `reproduce/ANALYSIS.md` that covers:\n\n1. **Overview**:Provides the overall framework and logical structure of the paper, including:\n   \n   - Research Background and Motivation\n   - Research Objectives\n   - Paper Structure\n\n2. **Model Construction**:  Analyze the physical problem studied in the paper and present the physical model employed to investigate this problem.\n\n3. **Key Formulas**: List and explain every formula needed for the reproduction.\n\n4. **Algorithm Details**: Select an appropriate numerical algorithm based on the type of equation to be solved, and provide detailed steps and specifics for solving the equation using that algorithm.\n\n5. **Input Parameters**: Determine the parameters needed for the calculation. Parameters used in the calculation should be obtained from the paper or inferred based on the information provided therein.\n\n6. **Physical Observables**: Explain the detailed characteristics of the figure to be reproduced and their corresponding physical significance.\n\n### Step 2: Implement the Simulation\n\nWrite all code under `reproduce/`. You need:\n\n- Ensure all parameters are converted to atomic units before writing code in atomic units.\n- When plotting, convert required data to the desired units.\n- Separate the simulation code from the plotting code.\n- Individual codes for each figure.\n\n### Step 3: Generate Data Files and Plot\n\nRun your codes to produce CSV data files and corresponding figures under `data/`. \n\n### Step 4: Comparison and Correction\n\nCompare the reproduced figure with the original. If significant discrepancies exist, modify the numerical simulation code and plotting code accordingly based on the observed differences.\n\n---\n\n## 3. Input Parameters\n\nYou may need the following parameters:\n\n| Parameter                     | Symbol  | Values |\n| ----------------------------- | ------- | ------ |\n| the dipole transition element | $\\mu_1$ | 2.7823 |\n\nOther parameters used in the calculations can be obtained from the paper or found online.\n\n---\n\n## 4. Data Files to Reproduce\n\n### Figure 3 (a)\n\n**File**: `data/fig3a.csv`\n\nNormalize the calculated spectral data.\n\nIn the table header, the first column is ‘energy_eV’, followed by all time delays. The table data merges two arrays by column, where the first column is the energy data array and the subsequent columns are the spectral data arrays.\n\n| Property | Value                                                                           |\n| -------- | ------------------------------------------------------------------------------- |\n| X-axis   | Delay τ in units of fs (-85 to +50, 0.5fs intervals, totaling 271 time delays)  |\n| Y-axis   | Energy in eV (20.0 to 22.5 eV, 0.01eV intervals, 251 energy grid points total)) |\n| colorbar | arb. units                                                                      |\n\n---\n\n## 5. Special considerations\n\n- The function introducing decoherence adopts a cosine-squared form, with the decoherence time being its full width at half maximum (FWHM). Additionally, ensure that the time-dependent transition dipole moment smoothly transitions to zero at each time delay.\n\n---\n\n### \n\n## \n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduce/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduce/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/simulate_fig3a.py", "reproduce/plot_fig3a.py"], "data": ["data/fig3a.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/simulate_fig3a.py", "reproduce/plot_fig3a.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_wu_2018", "title": "Noise analysis for high-fidelity quantum entangling gates in an anharmonic linear Paul trap", "authors": "Yukai Wu, Sheng-Tao Wang, L.-M. Duan", "year": 2018, "doi": "10.1103/PhysRevA.97.062325", "arxiv": null, "paper_files": ["GateOfLinearTrap.md"], "input_files": [], "instruction": "# Reproduction Instructions for AI Agent\n\nThis document provides complete instructions for an AI agent to reproduce all figures from the referenced physics paper.\n\n**Note**: The paper contains figures as images. These image files are available at `/workspace/_paper_images/images1/` (JPEG files). You can read them using the Read tool if you need to inspect figures from the paper for reference.\n\n---\n\n## 1. Article Information\n\n| Field               | quamtum computing                                            |\n| ------------------- | ------------------------------------------------------------ |\n| **Title**           | Noise analysis for high-fidelity quantum entangling gates in an anharmonic linear Paul trap |\n| **Author**          | Yukai Wu                                                     |\n| **DOI**             | [10.1103/PhysRevA.97.062325](http://dx.doi.org/10.1103/PhysRevA.97.062325) |\n| **arXiv**           | Not available (predates arXiv)                               |\n| **Source Markdown** | `GateOfLinearTrap.md`                                        |\n\n---\n\n## 2. Main Formulas Used in Reproduction\n\nAll the formulas should be extracted from the article\n\n## 3. Main Methodology\n\nAll the methods used should be mentioned in the article\n\n---\n\n## 4. Input Parameters\n\n| Parameter                              | Symbol     | Typical Values | Description                   |\n| -------------------------------------- | ---------- | -------------- | ----------------------------- |\n| number of ions                         | $N$        | 19             |                               |\n| mass of ion                            | $m$        | 2.874e-15      | mass of ion,usually Yb        |\n| ratio of transverse to longitude field | $\\alpha$   | 1e4            | Sweeps before measurement     |\n| unit of length                         | $l_0$      | 40μm           | Sweeps for averaging          |\n| octupole potential coefficient         | $\\gamma_4$ | 4.3            | coefficient of part of energy |\n| number of the first selected ion       | $i_1$      | 4              |                               |\n| number of the second selected ion      | $i_2$      | 6              |                               |\n\nBesides,you can use any constant in scipy.const.\n\n---\n\n## 5. Banned Libraries\n\nThe following libraries/approaches are **NOT allowed** for the core physics simulation:\n\n| Banned                                    | Reason           |\n| ----------------------------------------- | ---------------- |\n| use the result of the article before code | prevent cheating |\n|                                           |                  |\n|                                           |                  |\n|                                           |                  |\n\n\n---\n\n## 6. Data Files to Reproduce\n\n### 6.1 Balance_place_of_ions.csv\n\n**File**: `data/Balance_place_of_ions.csv`\n\n**Columns**: `number of ions,u`\n\nMeaning of u refers to the article. Parameters are the same as in the article.\n\nThe ion numbers are arranged based on the increasing order of u.\n\nIn this part,you need to plot the balance place with 2 kinds of situation mentioned in the article but the data only need to save the best one in the file.\n\n\n---\n\n### 6.2 normal frequency\n\n**File**: `data/normal_frequancy.csv`\n\n**Columns**: `frequency,b0x,b0y,b0z,...,b18x,b18y,b18z`\n\nb_ix, b_iy, b_iz are the normal modes of the i-th ion (0-indexed, i = 0, 1, ..., 18) corresponding to this frequency.\n\nFrequencies are sorted in ascending order.\n\nIn this part, you do not need to plot a figure.\n\n\n---\n\n### 6.3 infidelity as a function of μ\n\n**File**: `data/infidelity_of_mu.csv`\n\n**Columns**: ` mu，F_Nseg_10，F_Nseg_12，F_Nseg_14`\n\nParameters are the same as in the article.\n\nIn this part you need to plot the results above like the article.\n\n\n---\n\n### 6.4 Raman Frequency of Typical couples of ions\n\n**File**: `data/Segments.csv`\n\n**Columns**: `segment1,segment2,segment3`\n\nlist your results of three Segments shown in the article between 5 and 6,1 and 4,9 and 14.\n\nIn this part you need to plot 3 figures to show the results above like the article.\n\n\n---\n\nIf you can give me the right segments,you can draw other pictures easily.So you don’t need to draw them.\n\nAll the figures is also placed in the \\data\n\n---\n\n## 7. Code Structure\n\n### 7.1 Main Code\n\n**Path**: `reproduction/GateOfLinearTrap.py`\n\nContains:\n\n* Basic information and parameters\n\n- `balance_place` function: input with N,gamma4,output the balance place of ions \n- `normal_mode` function: input with balance place of ions and omegax, output the normal frequency and normal modes. Note that omegax can be presented by $\\alpha$ and $l_0$\n- `Segment`function: input normal frequency, normal modes,couple of ions and other parameters shown in the article. Output the Segment of the parameter. \n- And other functions if you need.\n\n### 7.2 execution code\n\n| Part | Script Path                             |\n| ---- | --------------------------------------- |\n| 1    | `reproduction/Balance_place_of_ions.py` |\n| 2    | `reproduction/normal_frequancy.py`      |\n| 3    | `reproduction/infidelity_of_mu.py`      |\n| 4    | `reproduction/Raman_Segments.py`        |\n\n### 7.3 Output Directories\n\n- Data files: `data/`\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/GateOfLinearTrap.py", "reproduction/Balance_place_of_ions.py", "reproduction/normal_frequancy.py", "reproduction/infidelity_of_mu.py", "reproduction/Raman_Segments.py"], "data": ["data/Balance_place_of_ions.csv", "data/normal_frequancy.csv", "data/infidelity_of_mu.csv", "data/Segments.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/GateOfLinearTrap.py", "reproduction/Balance_place_of_ions.py", "reproduction/normal_frequancy.py", "reproduction/infidelity_of_mu.py", "reproduction/Raman_Segments.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.15}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.55}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_wu_2021", "title": "High-fidelity entangling gates in a three-dimensional ion crystal under micromotion", "authors": "Y.-K. Wu, Z.-D. Liu, W.-D. Zhao, L.-M. Duan", "year": 2021, "doi": "10.1103/PhysRevA.103.022419", "arxiv": null, "paper_files": ["GateOf2D.md"], "input_files": [], "instruction": "# Reproduction Instructions for AI Agent\n\nThis document provides complete instructions for an AI agent to reproduce all figures from the referenced physics paper.\n\n**Note**: The paper contains figures as images. These image files are available at `/workspace/_paper_images/` (JPEG files like `_page_*.jpeg`). You can read them using the Read tool if you need to inspect figures from the paper for reference.\n\n---\n\n## 1. Article Information\n\n| Field               | quamtum computing                                            |\n| ------------------- | ------------------------------------------------------------ |\n| **Title**           | High-fidelity entangling gates in a three-dimensional ion crystal under micromotion |\n| **Author**          | Y.-K. Wu , * Z.-D. Liu,* W.-D. Zhao, and L.-M. Duan          |\n| **DOI**             | 10.1103/PhysRevA.103.022419                                  |\n| **arXiv**           | Not available (predates arXiv)                               |\n| **Source Markdown** | `GateOf2D.md`                                                |\n\n---\n\n## 2. Main Formulas Used in Reproduction\n\nAll the formulas should be extracted from the article\n\n## 3. Main Methodology\n\nAll the methods used should be mentioned in the article\n\n---\n\n## 4. Input Parameters\n\n| Parameter                              | Symbol        | Typical Values    | Description            |\n| -------------------------------------- | ------------- | ----------------- | ---------------------- |\n| number of ions                         | $N$           | 127               |                        |\n| mass of ion                            | $m$           | 2.874e-15         | mass of ion,usually Yb |\n| ratio of transverse to longitude field | $\\alpha$      | 1                 |                        |\n| Mathieu parameters                     | q             | 0.3               |                        |\n| Mathieu parameters                     | a             | 0.015             |                        |\n| rf frequency                           | $\\omega_{rf}$ | $2\\pi\\times50$MHz |                        |\n| number of the first selected ion       | $i_1$         | 4                 |                        |\n| number of the second selected ion      | $i_2$         | 6                 |                        |\n\nBesides,you can use any constant in scipy.const.\n\n---\n\n## 5. Banned Libraries\n\nThe following libraries/approaches are **NOT allowed** for the core physics simulation:\n\n| Banned                                    | Reason           |\n| ----------------------------------------- | ---------------- |\n| use the result of the article before code | prevent cheating |\n|                                           |                  |\n|                                           |                  |\n|                                           |                  |\n\n\n---\n\n## 6. Data Files to Reproduce\n\n### 6.1 Balance_place_of_ions.csv\n\n**File**: `data/Balance_place_of_ions.csv`\n\n**Columns**: `number of ions,x,y,z,x1,y1,z1`\n\nxyz are the zeroth-order terms of the ion's equilibrium position, and x1y1z1 are the first-order terms of the ion's equilibrium position.. Parameters are the same as in the article.In particular, the number of ions is set to 50 to reduce unnecessary computation time.\n\nThe ion numbers are arranged based on the increasing order of x.\n\n\n---\n\n### 6.2 normal frequency\n\n**File**: `data/normal_frequancy.csv`\n\n**Columns**: `frequency,C1x,C1y,C1z,...,CNx,CNy,CNz,C1x1,C1y1,C1z1,...,CNx1,CNy1,CNz1,C1x-1,C1y-1,C1z-1,...,CNx-1,CNy-1,CNz-1`\n\nCix, Ciy, Ciz are  zeroth-order terms of the normal modes of the i-th ion corresponding to this frequency.\n\nCix1, Ciy1, Ciz1 are  first-order terms of the normal modes of the i-th ion corresponding to this frequency.\n\nCix-1, Ciy-1, Ciz-1 are  negative first-order terms of the normal modes of the i-th ion corresponding to this frequency.\n\nfrequency are sorted in descending order.\n\nIn particular, the number of ions is set to 50 to reduce unnecessary computation time.\n\nIn this part, you do not need to plot a figure.\n\n\n---\n\n### 6.3 Raman Frequency of Typical couples of ions\n\n**File**: `data/Segments.csv`\n\n**Columns**: `Segment1`\n\nlist your results of  Segment shown in the article between the nearest ion pair.\n\nIn particular, the number of ions is set to 50 to reduce unnecessary computation time.\n\nnseg =100 is not need\n\nIn this part you need to plot 1 figure to show the results above like the article.\n\n\n---\n\nIf you can give me the right segments,you can draw other pictures easily.So you don’t need to draw them.\n\nAll the figures is also placed in the \\data\n\n---\n\n## 7. Code Structure\n\n### 7.1 Main Code\n\n**Path**: `reproduction/GateOfLinearTrap.py`\n\nContains:\n\n* Basic information and parameters\n\n- `balance_place` function: input with N,A,Q,output the balance place of ions \n- `normal_mode` function: input with balance place of ions and A,Q, output the normal frequency and normal modes.\n- `Segment`function: input normal frequency, normal modes,couple of ions and other parameters shown in the article. Output the Segment of the parameter. \n- And other functions if you need.\n\n### 7.2 execution code\n\n| Part | Script Path                             |\n| ---- | --------------------------------------- |\n| 1    | `reproduction/Balance_place_of_ions.py` |\n| 2    | `reproduction/normal_frequancy.py`      |\n| 3    | `reproduction/infidelity_of_mu.py`      |\n| 4    | `reproduction/Raman_Segments.py`        |\n\n### 7.3 Output Directories\n\n- Data files: `data/`\n\n---\n\n## 8. Reproduction Requirements\n\n### 8.1 Computational Resources\n\nD:\\python310\\python.exe\n\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/GateOfLinearTrap.py", "reproduction/Balance_place_of_ions.py", "reproduction/normal_frequancy.py", "reproduction/infidelity_of_mu.py", "reproduction/Raman_Segments.py"], "data": ["data/Balance_place_of_ions.csv", "data/normal_frequancy.csv", "data/Segments.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/GateOfLinearTrap.py", "reproduction/Balance_place_of_ions.py", "reproduction/normal_frequancy.py", "reproduction/infidelity_of_mu.py", "reproduction/Raman_Segments.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.15}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.55}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_xie_2025", "title": "Developing a linear fluid plasma model with accurate kinetic Bernstein waves: A first step", "authors": "Huasheng Xie", "year": 2025, "doi": "10.1063/5.0274495", "arxiv": null, "paper_files": ["Xie2025.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a physics paper to reproduce. Your goal is to read the paper, understand the target outputs, and implement the linear fluid plasma calculations needed to reproduce the required Xie (2025) figures.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Developing a linear fluid plasma model with accurate kinetic Bernstein waves: A first step |\n| **Author** | Huasheng Xie |\n| **DOI** | 10.1063/5.0274495 |\n| **Paper File** | `Xie2025.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `Xie2025.md`. Write the analysis document at `reproduce/ANALYSIS.md`.\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduce/`. You need:\n- Shared linear-fluid plasma helper modules\n- Figure scripts for the required ICW and ECW outputs\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n### Output Requirements\nFor both code and analysis, place everything under `reproduce/`. If the output is formulas, derivations, or a technical report, name the file `ANALYSIS.md`. For other code files, use the filenames already provided in `reproduce/`.\n\n### Methodology Constraint\nDo not provide any external implementation methodology information, except for the necessary input parameters, which should be placed only under `## 3. Input Parameters`.\n\n---\n\n## 3. Input Parameters\n\n| Parameter | Symbol | Values |\n|-----------|--------|--------|\n| Magnetic field (ICW case) | $B_0$ | 6.0 T |\n| Density (ICW case) | $n_{s0}$ | $2 \\times 10^{20}$ m$^{-3}$ |\n| Temperature (ICW case) | $T_s$ | 4.0 keV |\n| Parallel wavevector (ICW case) | $k_z$ | 10.0 m$^{-1}$ |\n| Species (ICW case) | $S$ | electron, deuterium ion |\n| Magnetic field (ECW case) | $B_0$ | 1.0 T |\n| Density (ECW case) | $n_{s0}$ | $6.075 \\times 10^{19}$ m$^{-3}$ |\n| Temperature (ECW case) | $T_s$ | 1.0 keV |\n| Parallel wavevector (ECW case) | $k_z \\rho_{ce}$ | 0.1 |\n| Species (ECW case) | $S$ | electron only |\n| Harmonic truncation (ICW) | $N_{\\max}$ | 5 |\n| Harmonic truncation (ECW) | $N_{\\max}$ | 7 |\n| Z-function pole count | $J$ | 8 |\n\n---\n\n## 4. Banned Libraries & Practices\n\n| Category | Banned | Allowed Alternative |\n|----------|--------|---------------------|\n| **Plasma Solvers** | `PDRK`, `WHAMP`, existing linear plasma-wave solvers | Build the matrix model directly |\n| **GPU Libraries** | `cupy`, `PyTorch`, `JAX`, `TensorFlow` | `NumPy`, `SciPy` |\n| **Black-box Codes** | External electromagnetic wave / accessibility solvers | Custom scripts in `reproduce/` |\n| **Symbolic Math** | `SymPy` for production numerical workflows | Direct numerical implementation |\n\n---\n\n## 5. Data Files to Reproduce\n\n### Figure 3: ICW Dispersion Sweep\n**File**: `data/fig3.csv`\n\n| Property | Value |\n|----------|-------|\n| X-axis | $\\omega / \\omega_{ci}$ |\n| Y-axis | $\\mathrm{Re}(k_\\perp)$ and $\\mathrm{Im}(k_\\perp)$ |\n| System | ICW case |\n| Series | Up to five retained branches per frequency |\n\n**Columns**: `omega_norm,re_kperp_0,im_kperp_0,...`\n\n---\n\n### Figure 3 Auxiliary Scatter Data\n**File**: `data/fig3_scatter.csv`\n\n| Property | Value |\n|----------|-------|\n| X-axis | $\\mathrm{Re}(k_\\perp)$ |\n| Y-axis | $\\mathrm{Im}(k_\\perp)$ |\n| System | ICW case at $\\omega / \\omega_{ci} = 1.5$ |\n| Series | Eigenvalue scatter points |\n\n**Columns**: `re_kx,im_kx`\n\n---\n\n### Figure 4: ECW Dispersion Sweep\n**File**: `data/fig4.csv`\n\n| Property | Value |\n|----------|-------|\n| X-axis | $\\omega / \\omega_{ce}$ |\n| Y-axis | $\\mathrm{Re}(k_\\perp)$ and $\\mathrm{Im}(k_\\perp)$ |\n| System | ECW case |\n| Series | Up to five retained branches per frequency |\n\n**Columns**: `omega_norm,re_kperp_0,im_kperp_0,...`\n\n---\n\n## 6. Code Structure Requirements\n\n### 6.1 Core Modules\n**Path**: `reproduce/`\n\n| File | Description |\n|------|-------------|\n| `params_loader.py` | Pole/residue coefficient loading utilities |\n| `fluid_matrix.py` | Fluid matrix assembly and species base quantities |\n| `solver.py` | Eigenvalue solving and physical-mode filtering |\n| `plot_dispersion.py` | Plotting utility for the generated CSV files |\n\n### 6.2 Figure Scripts\n| Figure | Script Path |\n|--------|-------------|\n| Fig 3 | `reproduce/fig3_compute.py` |\n| Fig 4 | `reproduce/fig4_compute.py` |\n\n### 6.3 Analysis Document\n**Path**: `reproduce/ANALYSIS.md`\n\nMust contain your analysis of the paper's formulas and reproduction targets.\n\n### 6.4 Output Directories\n- Data files: `data/`\n- Code files: `reproduce/`\n\n---\n\n## 7. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduce/ANALYSIS.md`\n2. `reproduce/params_loader.py`\n3. `reproduce/fluid_matrix.py`\n4. `reproduce/solver.py`\n5. `reproduce/plot_dispersion.py`\n6. `reproduce/fig3_compute.py`\n7. `reproduce/fig4_compute.py`\n8. `data/fig3.csv`\n9. `data/fig3_scatter.csv`\n10. `data/fig4.csv`\n\nExport numeric results with at least 8 decimal places.\n\n---", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduce/ANALYSIS.md`\n3. Implement all required code files under `reproduce/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Do not provide external implementation methodology information outside the required files\n\nYour deliverables are only the analysis document and code files.\nDo not produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/params_loader.py", "reproduce/fluid_matrix.py", "reproduce/solver.py", "reproduce/plot_dispersion.py", "reproduce/fig3_compute.py", "reproduce/fig4_compute.py"], "data": ["data/fig3.csv", "data/fig3_scatter.csv", "data/fig4.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduce/ANALYSIS.md"], "code": ["reproduce/params_loader.py", "reproduce/fluid_matrix.py", "reproduce/solver.py", "reproduce/plot_dispersion.py", "reproduce/fig3_compute.py", "reproduce/fig4_compute.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "2g", "timeout": 3600, "pip_install": ["numpy", "scipy", "matplotlib", "pandas"]}, "grading_dimensions": [{"name": "instruction_following", "weight": 0.15}, {"name": "code_correctness", "weight": 0.25}, {"name": "data_accuracy", "weight": 0.45}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_xue_2023", "title": "Generalized Quantum Measurements on a Higher-Dimensional System via Quantum Walks", "authors": "Peng Xue", "year": 2023, "doi": "10.1103/PhysRevLett.131.150803", "arxiv": null, "paper_files": ["2023PRL.md"], "input_files": [], "instruction": "# Project: Physics Paper Figure Reproduction\n\n## Role & Core Directives\nYou are an **Expert Computational Physicist**. Your goal is to deeply understand a paper's theoretical framework and write rigorous, production-grade Python scientific computing code to reproduce 3 key figures.\n\n\n---\n\n## 1. Article Information\n\n| Field               | Value                                                        |\n| ------------------- | ------------------------------------------------------------ |\n| **Title**           | Generalized Quantum Measurements on a Higher-Dimensional System via Quantum Walks |\n| **Author**          | Peng Xue                                             |\n| **DOI**             | 10.1103/PhysRevLett.131.15080310345                                    |\n| **Paper File**      | `2023PRL.md` (in the same task directory)                  |\n\n---\n\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `2023PRL.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Physical Observables**: Explain what each figure measures and its physical significance\n\n### Step 2: Implement the Simulation\nWrite all code under `reproduction/`. You need:\n- Individual scripts for each figure\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 5 for exact specifications.\n\n---\n\n## 3. Input Parameters\n\n| Parameter         | Symbol      | Values         |\n| -------------     | ----------- | -------------- |\n| qutrit dimension  | $d$         | 3              |\n\n---\n\n\n## 4. Data Files to Reproduce\n\n### Figure 3: Probabilities of the photons\n**File**: `data/fig3.csv`\n\n#### X-Axis (POVM outcome)\n\n- *Labels**: $E_1, E_2, E_3, E_4, E_5, E_6, E_7, E_8, E_9$ (LaTeX italic subscript format)\n- **Range**: 9 discrete categories (1 to 9)\n- **Axis title**: \"POVM outcome\" (only shown on bottom row subplots)\n\n\n#### Y-Axis (Probability)\n\n- **Range**: 0 to 0.55 (slightly above max probability ~0.5)\n- **Axis title**: \"Probability\" (only shown on left column subplots)\n\n\n---\n\n### Figure 4: Matrix forms of the elements Ej of a qutrit SIC-POVM\n**File**: `data/fig4.csv`\n\n#### X-Axis (j - Column Index)\n\n\n- **Axis title**: \"j\" (italic)\n\n#### Y-Axis (k - Row Index)\n\n\n- **Axis title**: \"k\" (italic)\n\n\n#### Z-Axis (Matrix Element Value)\n\n---\n\n### Figure 5: Infidelity versus N for two different measure methods\n**File**: `data/fig5.csv`\n\n#### X-Axis (Number of copies N)\n\n- **Axis title**: \"Number of copies $N$\" (LaTeX italic N)\n\n#### Y-Axis (Infidelity 1-F)\n\n- **Axis title**: \"Infidelity $1-F$\" (LaTeX math format)\n\n\n#### Subplot Titles\n\n- **Format**: $|\\varphi_i\\rangle$ (LaTeX ket notation)\n- **Position**: Centered above each subplot\n- **States shown**: $|\\varphi_1\\rangle$, $|\\varphi_4\\rangle$, $|\\varphi_8\\rangle$\n\n---\n\n\n\n\n## 6. Code Structure Requirements\n\n### 6.1 Figure Scripts\n| Figure | Script Path                    |\n| ------ | ------------------------------ |\n| Fig 3  | `reproduction/fig3_compute.py` |\n| Fig 4  | `reproduction/fig4_compute.py` |\n| Fig 5  | `reproduction/fig5_compute.py` |\n\n\n### 6.2 Output Directories\n- Data files: `data/`\n- Code files: `reproduction/`\n\n---\n\n## 8. Reproduction Requirements\n\n### 8.1 Computational Resources\n\n| Requirement          | Value        | Notes                              |\n| -------------------- | ------------ | ---------------------------------- |\n| **Total time limit** | ~1 - 2 hours | PBC with $m=200$ and finite sweeps |\n| **Memory limit**     | 4 - 8 GB     | Superblock for $m=200$, $S=1$      |\n| **CPU**              | 1 - 4 Cores  | No parallelization required        |\n\n\n\n\n\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate CSV data files\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/fig3_compute.py", "reproduction/fig4_compute.py", "reproduction/fig5_compute.py"], "data": ["data/fig3.csv", "data/fig4.csv", "data/fig5.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/fig3_compute.py", "reproduction/fig4_compute.py", "reproduction/fig5_compute.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "4g", "timeout": 10800, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.2}, {"name": "data_accuracy", "weight": 0.45}, {"name": "completeness", "weight": 0.15}]}
{"task_id": "task_yee_1966", "title": "Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media", "authors": "Kane S. Yee", "year": 1966, "doi": "10.1109/TAP.1966.1138693", "arxiv": null, "paper_files": ["yee1966.md"], "input_files": [], "instruction": "# Paper Reproduction Task\n\nYou are given a computational electromagnetics paper to reproduce. Your goal is to read the paper, understand its methodology, and implement an FDTD simulation to reproduce key figures.\n\n---\n\n## 1. Article Information\n\n| Field | Value |\n|-------|-------|\n| **Title** | Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media |\n| **Author** | Kane S. Yee |\n| **DOI** | 10.1109/TAP.1966.1138693 |\n| **Year** | 1966 |\n| **Journal** | IEEE Transactions on Antennas and Propagation, Vol. AP-14, No. 3 |\n| **Paper File** | `yee1966.md` (in the same task directory) |\n\n---\n\n## 2. What You Must Do\n\n### Step 1: Read and Analyze the Paper\nRead the full paper at `yee1966.md`. Write a detailed analysis document at `reproduction/ANALYSIS.md` that covers:\n\n1. **Methodology**: Describe the Yee FDTD algorithm for solving Maxwell's equations with staggered grids\n2. **Key Formulas**: List and explain the finite difference equations for TM waves (Eq. 14a-c)\n3. **Boundary Conditions**: Explain the perfectly conducting boundary conditions\n4. **Physical Observables**: Explain what each figure shows\n\n### Step 2: Implement the Computation\nWrite all code under `reproduction/`. You need:\n- A main simulation script at `reproduction/yee1966.py` implementing the 2D FDTD TM wave simulation\n\n### Step 3: Generate Data Files\nRun your scripts to produce CSV data files under `data/`. See Section 6 for exact specifications.\n\n---\n\n## 3. Main Equations\n\n### 3.1 TM Wave Finite Difference Equations (Eq. 14)\n\n$$\nE_z^{n+1}(i, j) = E_z^n(i, j) + Z\\frac{\\Delta\\tau}{\\Delta x}\\left[H_y^{n+1/2}\\left(i+\\frac{1}{2}, j\\right) - H_y^{n+1/2}\\left(i-\\frac{1}{2}, j\\right)\\right] - Z\\frac{\\Delta\\tau}{\\Delta y}\\left[H_x^{n+1/2}\\left(i, j+\\frac{1}{2}\\right) - H_x^{n+1/2}\\left(i, j-\\frac{1}{2}\\right)\\right]\n$$\n\n$$\nH_x^{n+1/2}\\left(i, j+\\frac{1}{2}\\right) = H_x^{n-1/2}\\left(i, j+\\frac{1}{2}\\right) - \\frac{1}{Z}\\frac{\\Delta\\tau}{\\Delta y}\\left[E_z^n(i, j+1) - E_z^n(i, j)\\right]\n$$\n\n$$\nH_y^{n+1/2}\\left(i+\\frac{1}{2}, j\\right) = H_y^{n-1/2}\\left(i+\\frac{1}{2}, j\\right) + \\frac{1}{Z}\\frac{\\Delta\\tau}{\\Delta x}\\left[E_z^n(i+1, j) - E_z^n(i, j)\\right]\n$$\n\n### 3.2 Incident Wave\n\n$$\nE_z(x, y, t) = \\sin\\left[\\frac{(x - 50\\alpha + ct)\\pi}{8\\alpha}\\right], \\quad 0 \\leq x - 50\\alpha + ct \\leq 8\\alpha\n$$\n\n$$\nH_y(x, y, t) = \\frac{1}{Z} E_z(x, y, t)\n$$\n\n---\n\n## 4. Boundary Conditions\n\n### 4.1 Perfect Conductor Boundaries (Domain Edges)\n$$\nE_z(0, y) = 0, \\quad E_z(\\text{max}, y) = 0, \\quad E_z(x, 0) = 0, \\quad E_z(x, \\text{max}) = 0\n$$\n\n### 4.2 Obstacle Boundary (Conducting Square)\n$E_z^n(i, j) = 0$ on the perfectly conducting square obstacle.\n\nFor the obstacle, the H-field boundary conditions are:\n- $H_x(x, y_0) = 0$ for $x_0 \\leq x \\leq x_1$\n- $H_x(x, y_1) = 0$ for $x_0 \\leq x \\leq x_1$\n- $H_y(x_0, y) = 0$ for $y_0 \\leq y \\leq y_1$\n- $H_y(x_1, y) = 0$ for $y_0 \\leq y \\leq y_1$\n\n---\n\n## 5. Input Parameters\n\n### 5.1 Grid Parameters\n\n| Parameter | Value | Notes |\n|-----------|-------|-------|\n| $\\alpha$ | 8 | Characteristic length |\n| Grid size | 100 × 100 | $N_x \\times N_y$ |\n| $\\Delta x = \\Delta y$ | 1 | $= \\alpha/8$ |\n| $\\Delta\\tau = c\\Delta t$ | 0.5 | $= \\alpha/16$ |\n| $Z$ | 376.7 | Impedance of free space |\n\n### 5.2 Obstacle Parameters (Conducting Square)\n\n| Parameter | Value |\n|-----------|-------|\n| $x_0$ | 17 |\n| $x_1$ | 49 |\n| $y_0$ | 33 |\n| $y_1$ | 65 |\n| Side length | $4\\alpha = 32$ |\n\n### 5.3 Source Injection\n- Source injected at $i = 90$, $x = 90\\Delta x$\n- Only when time satisfies the incident wave condition\n\n---\n\n## 6. Banned Libraries\n\n| Banned | Reason |\n|--------|--------|\n| Pre-built FDTD libraries | Must implement Yee algorithm from scratch |\n| Pre-built electromagnetic solvers | Implement finite difference equations directly |\n\n**Allowed**: `numpy`, `scipy`, `matplotlib`\n\n---\n\n## 7. Data Files to Reproduce\n\n### 7.1 Figure 3: Free-Space Propagation (No Obstacle)\n$E_z$ along x-axis for various time steps, no obstacle present.\n\n**Files**: `data/fig3_a.csv` through `data/fig3_d.csv`\n- Each file: one time snapshot\n- **Columns**: `x, Ez` (position along x-axis, electric field value)\n- 4 snapshots at different time steps\n\n### 7.2 Figure 4: Wave at j=30 (With Obstacle)\n$E_z$ along x-axis at $j=30$ (near but not intersecting obstacle).\n\n**Files**: `data/fig4_a.csv` through `data/fig4_j.csv`\n- **Columns**: `x, Ez`\n- 10 snapshots at different time steps\n\n### 7.3 Figure 5: Wave at j=50 (With Obstacle)\n$E_z$ along x-axis at $j=50$ (line meets the obstacle).\n\n**Files**: `data/fig5_a.csv` through `data/fig5_i.csv`\n- **Columns**: `x, Ez`\n- 9 snapshots at different time steps\n\n### 7.4 Figure 6: Wave at j=65 (Obstacle Boundary)\n$E_z$ along x-axis at $j=65$ (on obstacle boundary).\n\n**Files**: `data/fig6_a.csv` through `data/fig6_j.csv`\n- **Columns**: `x, Ez`\n- 10 snapshots at different time steps\n\n---\n\n## 8. Code Structure Requirements\n\n### 8.1 Main Script\n**Path**: `reproduction/yee1966.py`\n\nMust contain:\n- 2D FDTD TM wave simulator class/functions\n- Incident wave initialization\n- Time-stepping loop with Yee update equations (Eq. 14a-c)\n- Perfect conductor boundary conditions\n- Data extraction at specified j-lines and time steps\n- CSV output generation\n\n### 8.2 Analysis Document\n**Path**: `reproduction/ANALYSIS.md`\n\n---\n\n## 9. Deliverables Summary\n\nUpon completion, the following files must exist:\n1. `reproduction/ANALYSIS.md` — Methodology and formula analysis\n2. `reproduction/yee1966.py` — FDTD simulation code\n3. 33 CSV data files under `data/` (4 for Fig 3, 10 for Fig 4, 9 for Fig 5, 10 for Fig 6)\n\nExport all floating-point values with 8 decimal places.\n", "code_only_instruction_suffix": "## IMPORTANT: Code-Only Mode\n\nIn this task you are in **code-only mode**. You must:\n1. Read and analyze the paper\n2. Write `reproduction/ANALYSIS.md` with your methodology analysis\n3. Implement ALL code files under `reproduction/`\n4. **DO NOT** run the scripts or generate CSV data files\n5. Focus on writing correct, complete, and well-structured code\n\nYour deliverables are ONLY the analysis document and code files.\nDo NOT produce any CSV data files.\n", "expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/yee1966.py"], "data": ["data/fig3_a.csv", "data/fig3_b.csv", "data/fig3_c.csv", "data/fig3_d.csv", "data/fig4_a.csv", "data/fig4_b.csv", "data/fig4_c.csv", "data/fig4_d.csv", "data/fig4_e.csv", "data/fig4_f.csv", "data/fig4_g.csv", "data/fig4_h.csv", "data/fig4_i.csv", "data/fig4_j.csv", "data/fig5_a.csv", "data/fig5_b.csv", "data/fig5_c.csv", "data/fig5_d.csv", "data/fig5_e.csv", "data/fig5_f.csv", "data/fig5_g.csv", "data/fig5_h.csv", "data/fig5_i.csv", "data/fig6_a.csv", "data/fig6_b.csv", "data/fig6_c.csv", "data/fig6_d.csv", "data/fig6_e.csv", "data/fig6_f.csv", "data/fig6_g.csv", "data/fig6_h.csv", "data/fig6_i.csv", "data/fig6_j.csv"]}, "code_only_expected_outputs": {"analysis": ["reproduction/ANALYSIS.md"], "code": ["reproduction/yee1966.py"]}, "docker": {"image": "python:3.11-slim", "memory_limit": "2g", "timeout": 3600, "pip_install": ["numpy", "scipy", "matplotlib"]}, "grading_dimensions": [{"name": "methodology_understanding", "weight": 0.2}, {"name": "code_correctness", "weight": 0.15}, {"name": "data_accuracy", "weight": 0.5}, {"name": "completeness", "weight": 0.15}]}