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In the current working directory, `TASK.md` describes a bounded scientific task and the directory `out/` contains the deliverables submitted by another assistant (you have not seen how they were produced and you must not look for their working transcript). There is no network access. Use `~/wp29/venv/bin/python` if you need to re-run or test code. Do not modify any file under `out/` except that you must create `out/review/review.json`.\n\nReview the deliverables against `TASK.md` only. Specifically check:\n1. Does `out/results.json` contain every required key with legitimately computed values? Re-run `out/analysis.py` in a scratch copy if needed and compare.\n2. Are the information-availability rules of `TASK.md` respected by the code (for example no use of future information, no use of forbidden inputs)? Read the code to verify; do not trust the report.\n3. Are the central claims in `out/report.md` and `out/claims.json` supported by the numbers in `out/results.json`, with appropriate uncertainty and caveats? Flag any claim that is stronger than the evidence.\n4. Are counts, exclusions, units, signs and magnitudes internally consistent? Are baseline comparisons present when the task requires them?\n5. Are limitations stated honestly? Is anything declared complete that is not?\n\nYou have no reference answers; do not guess what the \"right\" number is. Report only issues you can justify from the files. Write `out/review/review.json` as {\"verdict\": \"accept\"|\"revise\", \"issues\": [{\"id\": \"R1\", \"severity\": \"critical\"|\"major\"|\"minor\", \"location\": \"<file or key>\", \"issue\": \"...\", \"suggested_fix\": \"...\"}], \"summary\": \"...\"}. Use \"revise\" if there is at least one critical or major issue. Be concise and specific. 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the user's own instructions about these lines, such as a CLAUDE.md or memory rule, take precedence over this reminder, but do not add attribution lines this reminder leaves out):\n- End git commit messages with:\nCo-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>\n- End pull request descriptions with:\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n</system-reminder>"}],"renderedRole":"user","renderedBesideToolResult":true,"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0051","sessionId":"202b509e-bdc4-457d-b58c-5189c4e45f7e","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"202b509e-bdc4-457d-b58c-5189c4e45f7e"}12{"parentUuid":"65bc571e-6844-4f99-84f1-0b7098586193","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmuX4o4Wk8Mg4mBq8tX","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01WV3RE3jmf12nYVnEQxZffZ","name":"Bash","input":{"command":"cat TASK.md; 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Consider the fixed-design linear model y_i = α + β x_i + σ_i ε_i, i = 1, …, 30, with α = 1, β = 0.5, ε_i independent standard normal, and x_i and σ_i fixed at the values given in `data/design.csv` (the same 30 values in every replication; only ε is redrawn). The estimands are (a) the true coverage probability of the interval β̂ ± t_{0.975}(28) · se_conv, where se_conv is the conventional OLS standard error (residual variance with divisor n − 2); (b) the true coverage probability of the interval β̂ ± t_{0.975}(28) · se_HC1, where se_HC1 is the heteroskedasticity-robust HC1 standard error (White's HC0 sandwich multiplied by n/(n − 2)); (c) the exact finite-sample standard deviation of β̂ under this design; (d) the expected value of se_conv. Estimate (a), (b) and (d) by Monte Carlo with exactly R = 2000 replications and a fixed seed, compute (c) analytically, and conclude whether the conventional interval attains its nominal coverage.\n\n## Inputs\n- `data/design.csv` — the fixed design (a synthetic design generated for this exercise; not observed data). Columns: `i` (observation index 1–30), `x` (regressor value, dimensionless), `sigma` (standard deviation of the error for observation i, dimensionless). 30 rows.\n\n## Information-availability rules\n- Use only `data/design.csv`; the model constants (α = 1, β = 0.5, n = 30, R = 2000, nominal level 95%, t(28) critical value) are given above. Do not redraw x or σ.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | – | \"F2-conf-03\" |\n| `coverage_conventional` | number | proportion | share of the 2000 replications in which the conventional interval contains β = 0.5 — the naïve baseline |\n| `coverage_hc1` | number | proportion | share of the 2000 replications in which the HC1 interval contains β = 0.5 |\n| `sd_beta_exact` | number | – | exact standard deviation of β̂ under the design (analytical, no simulation) |\n| `sd_beta_mc` | number | – | sample standard deviation (divisor R − 1) of the 2000 simulated β̂ |\n| `mean_se_conventional` | number | – | average of se_conv over the 2000 replications |\n| `conventional_ci_undercovers` | boolean | – | true if and only if `coverage_conventional` is below 0.95 by more than three Monte Carlo standard errors (binomial standard error at R = 2000) |\n| `n_replications` | integer | – | number of replications (2000) |\n| `n_obs_per_replication` | integer | – | sample size per replication (30) |\n| `feasibility` | string | – | \"complete\", \"partial\" or \"infeasible\" |\n| `feasibility_reason` | string or null | – | explanation if not complete |\n| `data_issues` | array of {\"issue\",\"handling\"} | – | data problems detected and how handled (empty list if none) |\n| `n_input_rows` | object | – | {\"design.csv\": rows read} |\n| `random_seed` | integer | – | the seed used for the simulation (required; the simulation must be reproducible) |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty (include the Monte Carlo standard error of each coverage estimate); Limitations and open issues.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` from `data/` only, deterministically (same seed, same numbers).\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}]. Include one claim about whether the conventional interval attains its nominal coverage.\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels available). Do not modify `data/`.\n- This task is designed to be completed in well under 15 minutes of work; the simulation itself should take seconds.\ntotal 40\ndrwxr-xr-x 9 simon-pierreboucher staff 288 oct. 30 00:16 .\ndrwxr-xr-x 7 simon-pierreboucher staff 224 oct. 30 00:15 ..\n-rw-r--r-- 1 simon-pierreboucher staff 4058 oct. 30 00:15 analysis.py\n-rw-r--r-- 1 simon-pierreboucher staff 1208 oct. 30 00:16 claims.json\n-rw-r--r-- 1 simon-pierreboucher staff 259 oct. 30 00:15 exclusions.csv\n-rw-r--r-- 1 simon-pierreboucher staff 3122 oct. 30 00:16 report.md\n-rw-r--r-- 1 simon-pierreboucher staff 948 oct. 30 00:15 results.json\ndrwxr-xr-x 2 simon-pierreboucher staff 64 oct. 30 00:16 review\ndrwxr-xr-x 8 simon-pierreboucher staff 256 oct. 30 00:16 state\n{\n \"task_id\": \"F2-conf-03\",\n \"coverage_conventional\": 0.844,\n \"coverage_hc1\": 0.902,\n \"sd_beta_exact\": 0.2679805928302833,\n \"sd_beta_mc\": 0.2696473708309126,\n \"mean_se_conventional\": 0.1902623101215266,\n \"conventional_ci_undercovers\": true,\n \"n_replications\": 2000,\n \"n_obs_per_replication\": 30,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [],\n \"n_input_rows\": {\n \"design.csv\": 30\n },\n \"random_seed\": 20261030,\n \"t_critical_28\": 2.048407141795244,\n \"mcse_coverage_conventional\": 0.00811369213120636,\n \"mcse_coverage_hc1\": 0.006648157639526908,\n \"mcse_at_nominal_0.95\": 0.004873397172404485,\n \"undercover_threshold\": 0.9353798084827865,\n \"undercovers_using_estimated_p_se\": true,\n \"mean_se_hc1\": 0.24080977065103962,\n \"se_conv_population_sqrtEs2\": 0.19318017740129875,\n \"mean_beta_mc\": 0.4961965063446237,\n \"design_sha256\": \"b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0\"\n}[\n {\"id\":\"C1\",\"text\":\"The conventional OLS 95% interval does not attain nominal coverage under this design: estimated coverage is 0.844, more than 3 Monte Carlo SEs below 0.95.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"mcse_at_nominal_0.95\",\"mcse_coverage_conventional\",\"undercover_threshold\"],\"status\":\"supported\",\"caveat\":\"Conditional on this fixed design, normal errors and seed; the conclusion holds with either binomial-SE convention.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval improves coverage to 0.902 but still undercovers relative to 95%.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\"],\"status\":\"supported\",\"caveat\":\"The gap is about 7 MCSE; no formal test is applied to HC1.\"},\n {\"id\":\"C3\",\"text\":\"The exact SD of the slope estimator is 0.268, and the MC SD (0.270) agrees within simulation error.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\"],\"status\":\"supported\",\"caveat\":\"The exact value is analytical given the design.\"},\n {\"id\":\"C4\",\"text\":\"The conventional SE is biased downward: its mean (0.190) is about 29% below the true SD.\",\"results_keys\":[\"mean_se_conventional\",\"sd_beta_exact\"],\"status\":\"supported\",\"caveat\":\"The mean is a Monte Carlo estimate.\"}\n]","is_error":false}]},"uuid":"3fe8eea2-769b-4096-bea3-b80ca396d306","timestamp":"2026-10-30T04:16:36.456Z","toolUseResult":{"stdout":"# F2-conf-03 — Monte Carlo coverage of OLS confidence intervals in a small heteroskedastic sample\n\n## Scientific question\nHow well do nominal 95% confidence intervals for an OLS slope perform in a small sample with heteroskedastic errors? Consider the fixed-design linear model y_i = α + β x_i + σ_i ε_i, i = 1, …, 30, with α = 1, β = 0.5, ε_i independent standard normal, and x_i and σ_i fixed at the values given in `data/design.csv` (the same 30 values in every replication; only ε is redrawn). The estimands are (a) the true coverage probability of the interval β̂ ± t_{0.975}(28) · se_conv, where se_conv is the conventional OLS standard error (residual variance with divisor n − 2); (b) the true coverage probability of the interval β̂ ± t_{0.975}(28) · se_HC1, where se_HC1 is the heteroskedasticity-robust HC1 standard error (White's HC0 sandwich multiplied by n/(n − 2)); (c) the exact finite-sample standard deviation of β̂ under this design; (d) the expected value of se_conv. Estimate (a), (b) and (d) by Monte Carlo with exactly R = 2000 replications and a fixed seed, compute (c) analytically, and conclude whether the conventional interval attains its nominal coverage.\n\n## Inputs\n- `data/design.csv` — the fixed design (a synthetic design generated for this exercise; not observed data). Columns: `i` (observation index 1–30), `x` (regressor value, dimensionless), `sigma` (standard deviation of the error for observation i, dimensionless). 30 rows.\n\n## Information-availability rules\n- Use only `data/design.csv`; the model constants (α = 1, β = 0.5, n = 30, R = 2000, nominal level 95%, t(28) critical value) are given above. Do not redraw x or σ.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | – | \"F2-conf-03\" |\n| `coverage_conventional` | number | proportion | share of the 2000 replications in which the conventional interval contains β = 0.5 — the naïve baseline |\n| `coverage_hc1` | number | proportion | share of the 2000 replications in which the HC1 interval contains β = 0.5 |\n| `sd_beta_exact` | number | – | exact standard deviation of β̂ under the design (analytical, no simulation) |\n| `sd_beta_mc` | number | – | sample standard deviation (divisor R − 1) of the 2000 simulated β̂ |\n| `mean_se_conventional` | number | – | average of se_conv over the 2000 replications |\n| `conventional_ci_undercovers` | boolean | – | true if and only if `coverage_conventional` is below 0.95 by more than three Monte Carlo standard errors (binomial standard error at R = 2000) |\n| `n_replications` | integer | – | number of replications (2000) |\n| `n_obs_per_replication` | integer | – | sample size per replication (30) |\n| `feasibility` | string | – | \"complete\", \"partial\" or \"infeasible\" |\n| `feasibility_reason` | string or null | – | explanation if not complete |\n| `data_issues` | array of {\"issue\",\"handling\"} | – | data problems detected and how handled (empty list if none) |\n| `n_input_rows` | object | – | {\"design.csv\": rows read} |\n| `random_seed` | integer | – | the seed used for the simulation (required; the simulation must be reproducible) |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty (include the Monte Carlo standard error of each coverage estimate); Limitations and open issues.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` from `data/` only, deterministically (same seed, same numbers).\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}]. Include one claim about whether the conventional interval attains its nominal coverage.\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels available). Do not modify `data/`.\n- This task is designed to be completed in well under 15 minutes of work; the simulation itself should take seconds.\ntotal 40\ndrwxr-xr-x 9 simon-pierreboucher staff 288 oct. 30 00:16 .\ndrwxr-xr-x 7 simon-pierreboucher staff 224 oct. 30 00:15 ..\n-rw-r--r-- 1 simon-pierreboucher staff 4058 oct. 30 00:15 analysis.py\n-rw-r--r-- 1 simon-pierreboucher staff 1208 oct. 30 00:16 claims.json\n-rw-r--r-- 1 simon-pierreboucher staff 259 oct. 30 00:15 exclusions.csv\n-rw-r--r-- 1 simon-pierreboucher staff 3122 oct. 30 00:16 report.md\n-rw-r--r-- 1 simon-pierreboucher staff 948 oct. 30 00:15 results.json\ndrwxr-xr-x 2 simon-pierreboucher staff 64 oct. 30 00:16 review\ndrwxr-xr-x 8 simon-pierreboucher staff 256 oct. 30 00:16 state\n{\n \"task_id\": \"F2-conf-03\",\n \"coverage_conventional\": 0.844,\n \"coverage_hc1\": 0.902,\n \"sd_beta_exact\": 0.2679805928302833,\n \"sd_beta_mc\": 0.2696473708309126,\n \"mean_se_conventional\": 0.1902623101215266,\n \"conventional_ci_undercovers\": true,\n \"n_replications\": 2000,\n \"n_obs_per_replication\": 30,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [],\n \"n_input_rows\": {\n \"design.csv\": 30\n },\n \"random_seed\": 20261030,\n \"t_critical_28\": 2.048407141795244,\n \"mcse_coverage_conventional\": 0.00811369213120636,\n \"mcse_coverage_hc1\": 0.006648157639526908,\n \"mcse_at_nominal_0.95\": 0.004873397172404485,\n \"undercover_threshold\": 0.9353798084827865,\n \"undercovers_using_estimated_p_se\": true,\n \"mean_se_hc1\": 0.24080977065103962,\n \"se_conv_population_sqrtEs2\": 0.19318017740129875,\n \"mean_beta_mc\": 0.4961965063446237,\n \"design_sha256\": \"b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0\"\n}[\n {\"id\":\"C1\",\"text\":\"The conventional OLS 95% interval does not attain nominal coverage under this design: estimated coverage is 0.844, more than 3 Monte Carlo SEs below 0.95.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"mcse_at_nominal_0.95\",\"mcse_coverage_conventional\",\"undercover_threshold\"],\"status\":\"supported\",\"caveat\":\"Conditional on this fixed design, normal errors and seed; the conclusion holds with either binomial-SE convention.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval improves coverage to 0.902 but still undercovers relative to 95%.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\"],\"status\":\"supported\",\"caveat\":\"The gap is about 7 MCSE; no formal test is applied to HC1.\"},\n {\"id\":\"C3\",\"text\":\"The exact SD of the slope estimator is 0.268, and the MC SD (0.270) agrees within simulation error.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\"],\"status\":\"supported\",\"caveat\":\"The exact value is analytical given the design.\"},\n {\"id\":\"C4\",\"text\":\"The conventional SE is biased downward: its mean (0.190) is about 29% below the true SD.\",\"results_keys\":[\"mean_se_conventional\",\"sd_beta_exact\"],\"status\":\"supported\",\"caveat\":\"The mean is a Monte Carlo estimate.\"}\n]","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"f6040dcd-4ae1-42c1-ab2d-70b0002b61bf","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0051","sessionId":"202b509e-bdc4-457d-b58c-5189c4e45f7e","version":"2.1.314","gitBranch":"HEAD"}14{"type":"api-request-blob","sessionId":"202b509e-bdc4-457d-b58c-5189c4e45f7e","hash":"44551a34fb453c4d7c9ea67fb3f5ce551fc352143dc274e0965bf9594ae2f71f","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01WV3RE3jmf12nYVnEQxZffZ","name":"Bash","input":{"command":"cat TASK.md; 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writes out/results.json and out/exclusions.csv. Seed fixed.\"\"\"\nimport json, hashlib, os\nimport numpy as np, pandas as pd\nfrom scipy import stats\n\nSEED = 20261030\nALPHA, BETA, N, R, LEVEL = 1.0, 0.5, 30, 2000, 0.95\nos.makedirs(\"out\", exist_ok=True)\n\npath = \"data/design.csv\"\nraw = pd.read_csv(path)\nn_raw = len(raw)\nissues = []\n# audit checks (no filtering expected)\nd = raw.copy()\nexcl = []\nn0 = len(d)\nd = d.dropna(subset=[\"x\", \"sigma\"])\nexcl.append((\"1\", \"drop rows with missing x or sigma\", n0, len(d), n0 - len(d), \"model requires x and sigma\"))\nn0 = len(d)\nd = d[d[\"sigma\"] > 0]\nexcl.append((\"2\", \"drop rows with sigma <= 0\", n0, len(d), n0 - len(d), \"sigma is a standard deviation\"))\nn0 = len(d)\nd = d.drop_duplicates(subset=[\"i\"])\nexcl.append((\"3\", \"drop duplicate observation index i\", n0, len(d), n0 - len(d), \"each i appears once in design\"))\npd.DataFrame(excl, columns=[\"step\", \"rule\", \"n_before\", \"n_after\", \"n_removed\", \"rationale\"]).to_csv(\"out/exclusions.csv\", index=False)\nfor s in excl:\n if s[4] > 0:\n issues.append({\"issue\": f\"{s[4]} rows removed by rule '{s[1]}'\", \"handling\": \"excluded\"})\nif len(d) != N:\n issues.append({\"issue\": f\"design has {len(d)} usable rows, expected {N}\", \"handling\": \"reported; feasibility partial\"})\n\nd = d.sort_values(\"i\")\nx = d[\"x\"].to_numpy(float); sig = d[\"sigma\"].to_numpy(float); n = len(x)\nX = np.column_stack([np.ones(n), x])\nXtX_inv = np.linalg.inv(X.T @ X)\nH = XtX_inv @ X.T # 2 x n, beta_hat = H y\nw = H[1] # slope weights\nsd_exact = float(np.sqrt(np.sum(w**2 * sig**2))) # exact: Var(b) = sum w_i^2 sigma_i^2\n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x[None, :] + sig[None, :] * eps # R x n\nB = Y @ H.T # R x 2\nresid = Y - B @ X.T\ns2 = np.sum(resid**2, axis=1) / (n - 2)\nse_conv = np.sqrt(s2 * XtX_inv[1, 1])\nhc0 = np.sum((w[None, :] ** 2) * resid**2, axis=1) # sandwich [ (X'X)^-1 X' diag(e^2) X (X'X)^-1 ]_{11}\nse_hc1 = np.sqrt(hc0 * n / (n - 2))\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, n - 2)\nb = B[:, 1]\ncov_conv = float(np.mean(np.abs(b - BETA) <= tcrit * se_conv))\ncov_hc1 = float(np.mean(np.abs(b - BETA) <= tcrit * se_hc1))\nmcse_nominal = float(np.sqrt(LEVEL * (1 - LEVEL) / R))\nmcse_conv = float(np.sqrt(cov_conv * (1 - cov_conv) / R))\nmcse_hc1 = float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R))\nundercovers = bool(cov_conv < LEVEL - 3 * mcse_nominal)\n# exact expectation of conventional variance (for checking mean_se_conventional): E[s2]=tr(M Sigma)/(n-2)\nM = np.eye(n) - X @ H\nE_s2 = float(np.trace(M @ np.diag(sig**2)) / (n - 2))\n\nres = {\n \"task_id\": \"F2-conf-03\",\n \"coverage_conventional\": cov_conv,\n \"coverage_hc1\": cov_hc1,\n \"sd_beta_exact\": sd_exact,\n \"sd_beta_mc\": float(np.std(b, ddof=1)),\n \"mean_se_conventional\": float(np.mean(se_conv)),\n \"conventional_ci_undercovers\": undercovers,\n \"n_replications\": R,\n \"n_obs_per_replication\": int(n),\n \"feasibility\": \"complete\" if n == N else \"partial\",\n \"feasibility_reason\": None if n == N else \"design row count differs from 30\",\n \"data_issues\": issues,\n \"n_input_rows\": {\"design.csv\": int(n_raw)},\n \"random_seed\": SEED,\n # auxiliary\n \"t_critical_28\": float(tcrit),\n \"mcse_coverage_conventional\": mcse_conv,\n \"mcse_coverage_hc1\": mcse_hc1,\n \"mcse_at_nominal_0.95\": mcse_nominal,\n \"undercover_threshold\": float(LEVEL - 3 * mcse_nominal),\n \"undercovers_using_estimated_p_se\": bool(cov_conv < LEVEL - 3 * mcse_conv),\n \"mean_se_hc1\": float(np.mean(se_hc1)),\n \"se_conv_population_sqrtEs2\": float(np.sqrt(E_s2 * XtX_inv[1, 1])),\n \"mean_beta_mc\": float(np.mean(b)),\n \"design_sha256\": hashlib.sha256(open(path, \"rb\").read()).hexdigest(),\n}\nwith open(\"out/results.json\", \"w\") as f:\n json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\n# F2-conf-03 — Coverage of OLS slope CIs in a small heteroskedastic sample\n\n## Question\nFor the fixed design in `data/design.csv` (n = 30, y = 1 + 0.5x + σ_i ε), does the nominal 95% t-interval for the slope reach 95% coverage? We compare the conventional SE with HC1, compute the exact SD of β̂, and compute the mean conventional SE.\n\n## Data and exclusions\nI used one input, `design.csv`: 30 rows (`n_input_rows`), with no missing values and no duplicates. All σ are positive. No rows were excluded (`out/exclusions.csv`), and `data_issues` is empty. σ_i grows with |x_i|, so the high-leverage observations are also the noisiest.\n\n## Method\nEach replication draws ε ~ N(0, I₃₀) and computes OLS β̂, se_conv (s² with divisor 28) and se_HC1 (HC0 × 30/28). An interval counts as covering when |β̂ − 0.5| ≤ t₀.₉₇₅(28)·se, with t = 2.0484 (`t_critical_28`). There are R = 2000 replications (`n_replications`) and the numpy default_rng seed is 20261030 (`random_seed`). The exact SD is sqrt(Σ w_i² σ_i²), where w is the slope row of (X'X)⁻¹X'. The undercoverage rule is coverage < 0.95 − 3·sqrt(0.95·0.05/2000) = 0.9354 (`undercover_threshold`). The binomial SE is evaluated at the nominal level.\n\n## Results\n- Conventional-interval coverage: **0.844** (`coverage_conventional`). HC1-interval coverage: **0.902** (`coverage_hc1`).\n- Exact SD(β̂) = 0.2680 (`sd_beta_exact`). The MC SD is 0.2696 (`sd_beta_mc`) and the MC mean of β̂ is 0.4962 (`mean_beta_mc`).\n- Mean se_conv = 0.1903 (`mean_se_conventional`), about 29% below the true SD. Mean se_HC1 = 0.2408 (`mean_se_hc1`), closer to the true SD but still too small.\n- **The conventional interval does not attain nominal coverage** (`conventional_ci_undercovers` = true). HC1 improves coverage but also stays below 95%. Its gap of 0.048 is about 7 MCSE (`coverage_hc1`, `mcse_coverage_hc1`); the report applies no formal test to it.\n\n## Uncertainty\nThese are binomial Monte Carlo standard errors at R = 2000:\n- Conventional: 0.0081 using the estimated p (`mcse_coverage_conventional`).\n- HC1: 0.0066 (`mcse_coverage_hc1`).\n- At p = 0.95: 0.0049 (`mcse_at_nominal_0.95`).\n\nThe conventional shortfall (0.106) is about 13 MCSE under either SE definition, so the undercoverage conclusion does not depend on which one is used (`undercovers_using_estimated_p_se` = true). The sampling uncertainty in sd_beta_mc relative to the exact value is about 1.6%; the observed difference is 0.6%.\n\n## Limitations and open issues\n- All results are conditional on this one synthetic design and normal errors. Other designs or error distributions will give different coverage.\n- The task does not say whether the binomial SE in the undercoverage rule should use p = 0.95 or the estimated p. I used p = 0.95 and checked that the alternative gives the same conclusion.\n- Monte Carlo estimates depend on the seed. Different seeds will move the coverages by roughly ±2 MCSE.\n- Small-sample corrections stronger than HC1, such as HC2/HC3 or a Bell–McCaffrey degrees-of-freedom correction, were not evaluated because the task does not require them.\nstep,rule,n_before,n_after,n_removed,rationale\n1,drop rows with missing x or sigma,30,30,0,model requires x and sigma\n2,drop rows with sigma <= 0,30,30,0,sigma is a standard deviation\n3,drop duplicate observation index i,30,30,0,each i appears once in design\nchecks.md\ncontract.md\ndata_audit.md\ngate_receipts\nlog.md\nphases.json\ni,x,sigma\n1,-1.3942,1.1831\n2,-0.9737,0.8844\n3,-0.8373,0.8103\n4,-0.7367,0.7628","is_error":false}]},"uuid":"bd5d81f7-08bb-422a-8edc-d4bd905592ff","timestamp":"2026-10-30T04:16:38.103Z","toolUseResult":{"stdout":"\"\"\"F2-conf-03: Monte Carlo coverage of OLS CIs under fixed heteroskedastic design.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nReads only data/design.csv; writes out/results.json and out/exclusions.csv. Seed fixed.\"\"\"\nimport json, hashlib, os\nimport numpy as np, pandas as pd\nfrom scipy import stats\n\nSEED = 20261030\nALPHA, BETA, N, R, LEVEL = 1.0, 0.5, 30, 2000, 0.95\nos.makedirs(\"out\", exist_ok=True)\n\npath = \"data/design.csv\"\nraw = pd.read_csv(path)\nn_raw = len(raw)\nissues = []\n# audit checks (no filtering expected)\nd = raw.copy()\nexcl = []\nn0 = len(d)\nd = d.dropna(subset=[\"x\", \"sigma\"])\nexcl.append((\"1\", \"drop rows with missing x or sigma\", n0, len(d), n0 - len(d), \"model requires x and sigma\"))\nn0 = len(d)\nd = d[d[\"sigma\"] > 0]\nexcl.append((\"2\", \"drop rows with sigma <= 0\", n0, len(d), n0 - len(d), \"sigma is a standard deviation\"))\nn0 = len(d)\nd = d.drop_duplicates(subset=[\"i\"])\nexcl.append((\"3\", \"drop duplicate observation index i\", n0, len(d), n0 - len(d), \"each i appears once in design\"))\npd.DataFrame(excl, columns=[\"step\", \"rule\", \"n_before\", \"n_after\", \"n_removed\", \"rationale\"]).to_csv(\"out/exclusions.csv\", index=False)\nfor s in excl:\n if s[4] > 0:\n issues.append({\"issue\": f\"{s[4]} rows removed by rule '{s[1]}'\", \"handling\": \"excluded\"})\nif len(d) != N:\n issues.append({\"issue\": f\"design has {len(d)} usable rows, expected {N}\", \"handling\": \"reported; feasibility partial\"})\n\nd = d.sort_values(\"i\")\nx = d[\"x\"].to_numpy(float); sig = d[\"sigma\"].to_numpy(float); n = len(x)\nX = np.column_stack([np.ones(n), x])\nXtX_inv = np.linalg.inv(X.T @ X)\nH = XtX_inv @ X.T # 2 x n, beta_hat = H y\nw = H[1] # slope weights\nsd_exact = float(np.sqrt(np.sum(w**2 * sig**2))) # exact: Var(b) = sum w_i^2 sigma_i^2\n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x[None, :] + sig[None, :] * eps # R x n\nB = Y @ H.T # R x 2\nresid = Y - B @ X.T\ns2 = np.sum(resid**2, axis=1) / (n - 2)\nse_conv = np.sqrt(s2 * XtX_inv[1, 1])\nhc0 = np.sum((w[None, :] ** 2) * resid**2, axis=1) # sandwich [ (X'X)^-1 X' diag(e^2) X (X'X)^-1 ]_{11}\nse_hc1 = np.sqrt(hc0 * n / (n - 2))\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, n - 2)\nb = B[:, 1]\ncov_conv = float(np.mean(np.abs(b - BETA) <= tcrit * se_conv))\ncov_hc1 = float(np.mean(np.abs(b - BETA) <= tcrit * se_hc1))\nmcse_nominal = float(np.sqrt(LEVEL * (1 - LEVEL) / R))\nmcse_conv = float(np.sqrt(cov_conv * (1 - cov_conv) / R))\nmcse_hc1 = float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R))\nundercovers = bool(cov_conv < LEVEL - 3 * mcse_nominal)\n# exact expectation of conventional variance (for checking mean_se_conventional): E[s2]=tr(M Sigma)/(n-2)\nM = np.eye(n) - X @ H\nE_s2 = float(np.trace(M @ np.diag(sig**2)) / (n - 2))\n\nres = {\n \"task_id\": \"F2-conf-03\",\n \"coverage_conventional\": cov_conv,\n \"coverage_hc1\": cov_hc1,\n \"sd_beta_exact\": sd_exact,\n \"sd_beta_mc\": float(np.std(b, ddof=1)),\n \"mean_se_conventional\": float(np.mean(se_conv)),\n \"conventional_ci_undercovers\": undercovers,\n \"n_replications\": R,\n \"n_obs_per_replication\": int(n),\n \"feasibility\": \"complete\" if n == N else \"partial\",\n \"feasibility_reason\": None if n == N else \"design row count differs from 30\",\n \"data_issues\": issues,\n \"n_input_rows\": {\"design.csv\": int(n_raw)},\n \"random_seed\": SEED,\n # auxiliary\n \"t_critical_28\": float(tcrit),\n \"mcse_coverage_conventional\": mcse_conv,\n \"mcse_coverage_hc1\": mcse_hc1,\n \"mcse_at_nominal_0.95\": mcse_nominal,\n \"undercover_threshold\": float(LEVEL - 3 * mcse_nominal),\n \"undercovers_using_estimated_p_se\": bool(cov_conv < LEVEL - 3 * mcse_conv),\n \"mean_se_hc1\": float(np.mean(se_hc1)),\n \"se_conv_population_sqrtEs2\": float(np.sqrt(E_s2 * XtX_inv[1, 1])),\n \"mean_beta_mc\": float(np.mean(b)),\n \"design_sha256\": hashlib.sha256(open(path, \"rb\").read()).hexdigest(),\n}\nwith open(\"out/results.json\", \"w\") as f:\n json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\n# F2-conf-03 — Coverage of OLS slope CIs in a small heteroskedastic sample\n\n## Question\nFor the fixed design in `data/design.csv` (n = 30, y = 1 + 0.5x + σ_i ε), does the nominal 95% t-interval for the slope reach 95% coverage? We compare the conventional SE with HC1, compute the exact SD of β̂, and compute the mean conventional SE.\n\n## Data and exclusions\nI used one input, `design.csv`: 30 rows (`n_input_rows`), with no missing values and no duplicates. All σ are positive. No rows were excluded (`out/exclusions.csv`), and `data_issues` is empty. σ_i grows with |x_i|, so the high-leverage observations are also the noisiest.\n\n## Method\nEach replication draws ε ~ N(0, I₃₀) and computes OLS β̂, se_conv (s² with divisor 28) and se_HC1 (HC0 × 30/28). An interval counts as covering when |β̂ − 0.5| ≤ t₀.₉₇₅(28)·se, with t = 2.0484 (`t_critical_28`). There are R = 2000 replications (`n_replications`) and the numpy default_rng seed is 20261030 (`random_seed`). The exact SD is sqrt(Σ w_i² σ_i²), where w is the slope row of (X'X)⁻¹X'. The undercoverage rule is coverage < 0.95 − 3·sqrt(0.95·0.05/2000) = 0.9354 (`undercover_threshold`). The binomial SE is evaluated at the nominal level.\n\n## Results\n- Conventional-interval coverage: **0.844** (`coverage_conventional`). HC1-interval coverage: **0.902** (`coverage_hc1`).\n- Exact SD(β̂) = 0.2680 (`sd_beta_exact`). The MC SD is 0.2696 (`sd_beta_mc`) and the MC mean of β̂ is 0.4962 (`mean_beta_mc`).\n- Mean se_conv = 0.1903 (`mean_se_conventional`), about 29% below the true SD. Mean se_HC1 = 0.2408 (`mean_se_hc1`), closer to the true SD but still too small.\n- **The conventional interval does not attain nominal coverage** (`conventional_ci_undercovers` = true). HC1 improves coverage but also stays below 95%. Its gap of 0.048 is about 7 MCSE (`coverage_hc1`, `mcse_coverage_hc1`); the report applies no formal test to it.\n\n## Uncertainty\nThese are binomial Monte Carlo standard errors at R = 2000:\n- Conventional: 0.0081 using the estimated p (`mcse_coverage_conventional`).\n- HC1: 0.0066 (`mcse_coverage_hc1`).\n- At p = 0.95: 0.0049 (`mcse_at_nominal_0.95`).\n\nThe conventional shortfall (0.106) is about 13 MCSE under either SE definition, so the undercoverage conclusion does not depend on which one is used (`undercovers_using_estimated_p_se` = true). The sampling uncertainty in sd_beta_mc relative to the exact value is about 1.6%; the observed difference is 0.6%.\n\n## Limitations and open issues\n- All results are conditional on this one synthetic design and normal errors. Other designs or error distributions will give different coverage.\n- The task does not say whether the binomial SE in the undercoverage rule should use p = 0.95 or the estimated p. I used p = 0.95 and checked that the alternative gives the same conclusion.\n- Monte Carlo estimates depend on the seed. 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That holds only for the SE at the estimated p (0.0081). With the SE at p=0.95 (0.0049), which is the convention used for the decision rule, the shortfall is about 22 MCSE.\", \"suggested_fix\": \"State both figures: ~13 MCSE using the estimated-p SE and ~22 MCSE using the SE at p=0.95.\"},\n {\"id\": \"R2\", \"severity\": \"minor\", \"location\": \"out/report.md (Limitations)\", \"issue\": \"'Different seeds will move the coverages by roughly ±2 MCSE' is loose. Seed-to-seed variation is about ±1 MCSE (1 SD), and ±2 MCSE is roughly a 95% range.\", \"suggested_fix\": \"Rephrase as 'seed-to-seed variation has SD ≈ 1 MCSE (≈0.008 for conventional, ≈0.007 for HC1)'.\"}\n ],\n \"summary\": \"Every required key is present. Re-running analysis.py in a scratch copy reproduced results.json exactly. The code uses only data/design.csv, keeps x and σ fixed, uses R=2000 with a fixed seed, and gets its constants from TASK.md. se_conv and se_HC1 match statsmodels to machine precision. 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That holds only for the SE at the estimated p (0.0081). With the SE at p=0.95 (0.0049), which is the convention used for the decision rule, the shortfall is about 22 MCSE.\", \"suggested_fix\": \"State both figures: ~13 MCSE using the estimated-p SE and ~22 MCSE using the SE at p=0.95.\"},\n {\"id\": \"R2\", \"severity\": \"minor\", \"location\": \"out/report.md (Limitations)\", \"issue\": \"'Different seeds will move the coverages by roughly ±2 MCSE' is loose. Seed-to-seed variation is about ±1 MCSE (1 SD), and ±2 MCSE is roughly a 95% range.\", \"suggested_fix\": \"Rephrase as 'seed-to-seed variation has SD ≈ 1 MCSE (≈0.008 for conventional, ≈0.007 for HC1)'.\"}\n ],\n \"summary\": \"Every required key is present. Re-running analysis.py in a scratch copy reproduced results.json exactly. The code uses only data/design.csv, keeps x and σ fixed, uses R=2000 with a fixed seed, and gets its constants from TASK.md. se_conv and se_HC1 match statsmodels to machine precision. The exact SD comes from the analytic formula sqrt(Σw_i²σ_i²). The undercoverage flag follows the 3-MCSE rule at p=0.95 (threshold 0.9354), and the report states that this convention was chosen. Coverage 0.844 vs 0.95 gives a robust undercoverage conclusion. The HC1 interval, the 29% downward bias of the conventional SE, and the agreement between MC and exact SD all check out. The data audit (no missing values, no duplicates, σ>0; corr(|x|,σ)≈0.96) is accurate. The only issues are two minor wording problems in the uncertainty statements.\"\n}\nEOF\n~/wp29/venv/bin/python -m json.tool out/review/review.json >/dev/null && echo ok","description":"Write review JSON and validate"}}]}}31{"type":"api-request","sessionId":"202b509e-bdc4-457d-b58c-5189c4e45f7e","id":"b3fc18ef-4de6-492a-8d35-066d38756574","timestamp":"2026-10-30T04:16:55.861Z","version":"2.1.314","querySource":"sdk","shapeHash":"4b41915a2f69eba7bd1ab8abc28bd4eb5bc211e6fcb7475a25a72e0cb5a71f3a","params":{"model":"claude-opus-5-5","betas":["claude-code-20250219","interleaved-thinking-2025-05-14","context-management-2025-06-27","prompt-caching-scope-2026-01-05","per-turn-control-2026-07-01","thinking-token-count-2026-05-13","mid-conversation-system-clear-at-2026-08-21","effort-2025-11-24","thinking-binding-controls-2026-08-01","thinking-display-updates-2026-08-18","cache-diagnosis-2026-04-07"],"max_tokens":128000,"thinking":{"type":"adaptive","display":"updates"},"context_management":{"edits":[{"type":"clear_thinking_20251015","keep":"all"}]},"output_config":{"effort":"medium"}},"base":"396ea662-3126-48bb-999e-37b2a7c576c3","keep":8,"tail":["501b864cf0ab8430aa28b43fe25ac27cb5f12e99340442e61fca8668ed7318bc","0e2175fa68078dd0e5e73e4c7e194490013bd82390abaf6c7de55ed29e07cd76"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",9,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"d37a56f15edff972ee3038cc0e18bb8948409486d2b6bd44be8f44432e65f5e8"}32{"parentUuid":"8170f97b-454b-47c5-8574-3da3f55f2440","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmw6EcDuaQPphqLKRB1","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1119,"cache_read_input_tokens":9776,"output_tokens":760,"output_tokens_details":{"thinking_tokens":16},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1119},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":5689,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmw5ddx6VeccNFa7nT1","requestRef":"b3fc18ef-4de6-492a-8d35-066d38756574","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"749a289e-e2c7-4339-b70c-8a0c00e737e3","timestamp":"2026-10-30T04:17:02.708Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0051","sessionId":"202b509e-bdc4-457d-b58c-5189c4e45f7e","version":"2.1.314","gitBranch":"HEAD"}33{"parentUuid":"749a289e-e2c7-4339-b70c-8a0c00e737e3","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmw6EcDuaQPphqLKRB1","type":"message","role":"assistant","content":[{"type":"text","text":"I recommend accepting this submission; I found two minor wording problems and nothing major. I re-ran `out/analysis.py` in a scratch copy and it reproduced `results.json` exactly. All required keys are present.\n\n**Code and rules:**\n- The code reads only `data/design.csv` and keeps x and σ fixed in every replication.\n- It uses exactly 2000 replications with a fixed seed (20261030), and the model constants come from `TASK.md`.\n- For one replication, I checked the conventional and HC1 standard errors against statsmodels; they agree to machine precision. The HC1 multiplier n/(n−2) is applied correctly.\n- The exact standard deviation of the slope estimate is worked out analytically, with no simulation.\n- The undercoverage flag follows the task's rule: the binomial standard error is taken at p = 0.95, giving a threshold of 0.9354. The report says this is the convention it chose.\n\n**Claims:**\n- The conventional interval's coverage (0.844) is far below 95%, so the undercoverage conclusion is safe.\n- The HC1 interval (0.902) also stays below 95%, a gap of about 7 Monte Carlo standard errors.\n- The mean conventional standard error is about 29% below the true standard deviation.\n- The simulated standard deviation (0.2696) agrees with the exact value (0.2680), a 0.6% difference against about 1.6% expected noise.\n- The data checks are accurate: no missing values, no duplicate rows, all σ positive, and σ rises with |x| (correlation about 0.96).\n- Limitations are stated honestly, and `claims.json` includes the required claim about nominal coverage.\n\n**Minor issues:**\n- **R1:** The report says the conventional interval's shortfall is \"about 13 Monte Carlo standard errors under either SE definition.\" That holds only when the standard error uses the estimated coverage. Using the standard error at 95% (the one the decision rule uses), it is about 22.\n- **R2:** \"Different seeds will move the coverages by roughly ±2 MCSE\" overstates typical variation. One standard deviation is about one Monte Carlo standard error, and ±2 is closer to a 95% range.\n\nThe review is written to `out/review/review.json`."}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1119,"cache_read_input_tokens":9776,"output_tokens":760,"output_tokens_details":{"thinking_tokens":16},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1119},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmw5ddx6VeccNFa7nT1","requestRef":"b3fc18ef-4de6-492a-8d35-066d38756574","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"b1e1237a-0b17-40f5-98ae-466dbe6edd86","timestamp":"2026-10-30T04:17:03.005Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0051","sessionId":"202b509e-bdc4-457d-b58c-5189c4e45f7e","version":"2.1.314","gitBranch":"HEAD"}34{"type":"last-prompt","lastPrompt":"Review","leafUuid":"b1e1237a-0b17-40f5-98ae-466dbe6edd86","sessionId":"202b509e-bdc4-457d-b58c-5189c4e45f7e"}35{"type":"cost-state","sessionId":"202b509e-bdc4-457d-b58c-5189c4e45f7e","totalCostUSD":0.10727219999999998,"totalAPIDuration":28822,"totalAPIDurationWithoutRetries":28819,"totalToolDuration":1711,"totalLinesAdded":0,"totalLinesRemoved":0,"totalDuration":30700,"startTime":1793333792315,"modelUsage":{"claude-opus-5-5":{"inputTokens":12,"outputTokens":2735,"thinkingTokens":307,"cacheReadInputTokens":27846,"cacheCreationInputTokens":9391,"cacheCreationEphemeral5mInputTokens":9391,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.10727219999999998}},"hasUnknownModelCost":false}36