spb/wp29_uqo

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It is the complete and only authoritative description of what is required: the scientific question, the inputs under `data/`, the required output files and their exact keys, and the information-availability rules.\n- There is no network access. Use the Python interpreter `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels, matplotlib are installed). Standard shell tools are available. Do not try to install packages.\n- Write every deliverable under `./out/`. The required deliverables are listed in `TASK.md`; at minimum they always include `out/results.json`, `out/report.md`, and a replication entry point `out/analysis.py` that regenerates `out/results.json` from `data/` when run with `~/wp29/venv/bin/python out/analysis.py` from the workspace root.\n- You are working alone and unattended; nobody will answer questions. Make reasonable, documented decisions.\n\nIntegrity rules (identical for every task):\n- Never fabricate numbers, data, results, or references. Every number in `out/results.json` and `out/report.md` must be produced by code you ran on the provided inputs.\n- Respect the information-availability rules in `TASK.md` exactly (for example, never use information that would not have been available at the stated decision time).\n- If part of the task cannot be completed as specified, say so explicitly in `out/report.md`, explain why, and still write every required file (use `null` for values you could not legitimately produce). An honest statement of a limitation is always preferred to a fabricated or guessed value.\n- Do not modify anything under `data/`.\n- When you are done, end with a brief plain-text summary of what you produced and any limitations.\n\nComplete the task described in `TASK.md` by following this research protocol. The protocol adds no scientific information to the task; it organizes how you work and what evidence you leave behind.\n\nPHASES (execute in order; a phase is eligible only when its dependencies are satisfied):\n\nP0 Scope and contract (depends on: nothing)\n- Read `TASK.md` completely. In `out/state/contract.md`, restate in your own words: the scientific question; the quantity or quantities to be estimated (the estimands) and the assumptions under which they are meaningful; every required output file and key; the information-availability rules; what would make the task impossible or the result invalid.\n- Write the initial phase ledger `out/state/phases.json`: a JSON object mapping each phase id (P0 … P5) to {\"status\": \"pending\"|\"running\"|\"passed\"|\"failed\"|\"blocked\"|\"stale\"|\"skipped_optional\", \"checks\": [], \"notes\": \"\"}. Keep it current as you work. A phase may only be set to \"passed\" when the checks listed for it in this protocol have actually been executed and their outcome recorded in \"checks\".\n\nP1 Data audit and provenance (depends on: P0)\n- Inspect every input file: compute and record its SHA-256, row and column counts, schema, units, date ranges, missing values, duplicates and anomalies in `out/state/data_audit.md`.\n- Keep an exclusion ledger in `out/exclusions.csv` (columns: step, rule, n_before, n_after, n_removed, rationale) for every filtering step you apply, so that n_raw − total removed = n_analysed.\n- Identify any input that violates the information-availability rules and decide, in writing, how you will handle it.\n\nP2 Baseline (depends on: P1)\n- Before any elaborate method, compute the simplest valid baseline that answers the question (for example a naïve or unconditional estimate), with the same evaluation rule used later. Record it in `out/results.json` under the keys the task requires, or under `baseline_*` keys when the task does not name them.\n\nP3 Method and computation (depends on: P2)\n- Implement the analysis in `out/analysis.py` so that it reads only `data/`, writes `out/results.json` deterministically (fix every random seed you use and record it), and prints nothing that contradicts the written results. Any figure or table must be generated by this script.\n\nP4 Verification (depends on: P3)\n- Re-run `out/analysis.py` from a clean state and confirm it regenerates `out/results.json` with identical values. Record the check in `out/state/phases.json` under P4.\n- Check internal consistency: identities that must hold (for example counts that must add up, standard errors that must be positive, confidence intervals that must contain their estimates, date orderings that must respect the information rules), units, and magnitudes against the baseline. Record every check and its outcome in `out/state/checks.md`. A failed check must be fixed or honestly reported, never silently ignored.\n\nP5 Reporting (depends on: P4)\n- Write `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. Every quantitative statement must cite the key of `out/results.json` it comes from.\n- Write `out/claims.json`: a list of the central claims of your report, each as {\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}. Do not state a claim in the report that is not in this ledger.\n- Set the final statuses in `out/state/phases.json`.\n\nSTOPPING RULES\n- Stop and declare the task complete only when every phase P0–P5 is \"passed\" with recorded checks. If a phase is \"blocked\" (missing information, impossible requirement, violated availability rule), stop, set the status, explain in `out/report.md` (section Limitations and open issues) and still write every required file with `null` for values you could not legitimately produce.\n- Do not spend effort on extensions that the task does not require.\n\nRECOVERY RULES\n- Append a short dated entry to `out/state/log.md` after each phase transition and after any important decision, so that work can be resumed by reading `out/state/`.\n- If you discover that an upstream input or decision changed after a downstream phase passed, mark the downstream phases \"stale\" and redo them; do not reuse stale results.\n- If you are interrupted and later resumed, first read `out/state/` and continue from the last consistent state; never re-run expensive steps that already have recorded, unchanged outputs.\n"}],"tools":[{"name":"Bash","description":"execute shell commands","input_schema":{"$schema":"https://json-schema.org/draft/2020-12/schema","type":"object","properties":{"command":{"description":"The command to execute","type":"string"},"timeout":{"description":"Optional timeout in milliseconds (max 600000 for a foreground command)","type":"number"},"description":{"description":"Clear, concise description of what this command does in active voice. 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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/RC0057","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"c3b76191-8236-4887-be14-0a8ded55b545"}12{"parentUuid":"7fc43388-77d4-4ccf-afa8-e991fa3ac35d","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmudtp7Sb9Sd5pdYFWD","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":4,"cache_creation_input_tokens":2209,"cache_read_input_tokens":1504,"output_tokens":126,"output_tokens_details":{"thinking_tokens":20},"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":2209},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":498,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmudbgzmmhffU3VTogq","requestRef":"84e44633-9d8b-4b51-bebb-1e9369c1ceb9","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"ffa2d9e9-0cfa-492b-9848-b872e43ddbc3","timestamp":"2026-10-30T04:16:37.781Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0057","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"ffa2d9e9-0cfa-492b-9848-b872e43ddbc3","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmudtp7Sb9Sd5pdYFWD","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01P5YiU9H6dKib5RThXRCwqy","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 32\ndrwxr-xr-x   6 simon-pierreboucher  staff   192 oct.  29 23:35 .\ndrwxr-xr-x  47 simon-pierreboucher  staff  1504 oct.  30 00:16 ..\n-rw-r--r--   1 simon-pierreboucher  staff   420 oct.  29 23:35 bundle.json\ndrwxr-xr-x   3 simon-pierreboucher  staff    96 oct.  29 23:33 data\n-rw-r--r--   1 simon-pierreboucher  staff  1456 oct.  29 23:35 gate_spec.json\n-rw-r--r--   1 simon-pierreboucher  staff  4161 oct.  29 23:35 TASK.md\ndata:\ndesign.csv","is_error":false}]},"uuid":"e2e29537-2f6d-46ec-b8cc-d9f8f564c1af","timestamp":"2026-10-30T04:16:38.411Z","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 32\ndrwxr-xr-x   6 simon-pierreboucher  staff   192 oct.  29 23:35 .\ndrwxr-xr-x  47 simon-pierreboucher  staff  1504 oct.  30 00:16 ..\n-rw-r--r--   1 simon-pierreboucher  staff   420 oct.  29 23:35 bundle.json\ndrwxr-xr-x   3 simon-pierreboucher  staff    96 oct.  29 23:33 data\n-rw-r--r--   1 simon-pierreboucher  staff  1456 oct.  29 23:35 gate_spec.json\n-rw-r--r--   1 simon-pierreboucher  staff  4161 oct.  29 23:35 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0) — F2-conf-03\n**Question.** In the fixed-design model y_i = 1 + 0.5 x_i + sigma_i e_i (n=30, e_i iid N(0,1), x and sigma fixed from data/design.csv), do nominal 95% t(28) intervals for the OLS slope reach 95% coverage, using (a) conventional OLS SE and (b) HC1 robust SE?\n**Estimands.** (a) P(beta in b̂ ± t.975(28) se_conv); (b) same with se_HC1 = sqrt(n/(n-2) * HC0); (c) exact SD of b̂ = sqrt(sum w_i^2 sigma_i^2), w_i=(x_i-x̄)/Sxx (analytic, valid because design is fixed and errors independent); (d) E[se_conv]. (a),(b),(d) by Monte Carlo, R=2000, fixed seed.\n**Outputs.** out/results.json keys: task_id, coverage_conventional, coverage_hc1, sd_beta_exact, sd_beta_mc (ddof=1), mean_se_conventional, conventional_ci_undercovers (cov_conv < 0.95 - 3*MCSE), n_replications=2000, n_obs_per_replication=30, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed. Also out/report.md (6 sections incl. MCSE per coverage), out/analysis.py, out/claims.json (incl. claim on nominal coverage).\n**Information rules.** Use only design.csv; never redraw x or sigma; only eps redrawn.\n**Invalidity.** Design not 30 rows / missing or nonpositive sigma / constant x; R != 2000; unseeded simulation.\n**Decision on MCSE.** \"Binomial standard error at R=2000\" is evaluated at the nominal p=0.95 (the null being tested): sqrt(0.95*0.05/2000). The SE at the estimated p is also reported; conclusion checked under both.\nEOF\ncat > log.md <<'EOF'\n# Log\n- 2026-10-30 P0: contract written.\nEOF\ncd ../..; ~/wp29/venv/bin/python - <<'EOF'\nimport pandas as pd\nd=pd.read_csv('data/design.csv');print(d.describe());print(d.isna().sum().sum(),d.duplicated().sum(),d.i.is_unique,(d.i==range(1,31)).all(),(d.sigma>0).all(), d.x.is_monotonic_increasing)\nEOF","description":"Write contract and audit 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              i          x      sigma\ncount  30.000000  30.000000  30.000000\nmean   15.500000   0.282297   0.819457\nstd     8.803408   0.821180   0.290442\nmin     1.000000  -1.394200   0.603400\n25%     8.250000  -0.231900   0.617025\n50%    15.500000   0.231150   0.735150\n75%    22.750000   0.765550   0.869300\nmax    30.000000   1.991900   1.790300\n0 0 True True True True","is_error":false}]},"uuid":"5b60f6e0-fec3-4fa2-8f4a-1e1e285abc01","timestamp":"2026-10-30T04:16:51.719Z","toolUseResult":{"stdout":"               i          x      sigma\ncount  30.000000  30.000000  30.000000\nmean   15.500000   0.282297   0.819457\nstd     8.803408   0.821180   0.290442\nmin     1.000000  -1.394200   0.603400\n25%     8.250000  -0.231900   0.617025\n50%    15.500000   0.231150   0.735150\n75%    22.750000   0.765550   0.869300\nmax    30.000000   1.991900   1.790300\n0 0 True True True 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0) — F2-conf-03\n**Question.** In the fixed-design model y_i = 1 + 0.5 x_i + sigma_i e_i (n=30, e_i iid N(0,1), x and sigma fixed from data/design.csv), do nominal 95% t(28) intervals for the OLS slope reach 95% coverage, using (a) conventional OLS SE and (b) HC1 robust SE?\n**Estimands.** (a) P(beta in b̂ ± t.975(28) se_conv); (b) same with se_HC1 = sqrt(n/(n-2) * HC0); (c) exact SD of b̂ = sqrt(sum w_i^2 sigma_i^2), w_i=(x_i-x̄)/Sxx (analytic, valid because design is fixed and errors independent); (d) E[se_conv]. (a),(b),(d) by Monte Carlo, R=2000, fixed seed.\n**Outputs.** out/results.json keys: task_id, coverage_conventional, coverage_hc1, sd_beta_exact, sd_beta_mc (ddof=1), mean_se_conventional, conventional_ci_undercovers (cov_conv < 0.95 - 3*MCSE), n_replications=2000, n_obs_per_replication=30, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed. Also out/report.md (6 sections incl. MCSE per coverage), out/analysis.py, out/claims.json (incl. claim on nominal coverage).\n**Information rules.** Use only design.csv; never redraw x or sigma; only eps redrawn.\n**Invalidity.** Design not 30 rows / missing or nonpositive sigma / constant x; R != 2000; unseeded simulation.\n**Decision on MCSE.** \"Binomial standard error at R=2000\" is evaluated at the nominal p=0.95 (the null being tested): sqrt(0.95*0.05/2000). The SE at the estimated p is also reported; conclusion checked under both.\nEOF\ncat > log.md <<'EOF'\n# Log\n- 2026-10-30 P0: contract written.\nEOF\ncd ../..; ~/wp29/venv/bin/python - <<'EOF'\nimport pandas as pd\nd=pd.read_csv('data/design.csv');print(d.describe());print(d.isna().sum().sum(),d.duplicated().sum(),d.i.is_unique,(d.i==range(1,31)).all(),(d.sigma>0).all(), d.x.is_monotonic_increasing)\nEOF","description":"Write contract and audit data"}}]}}27{"type":"api-request","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","id":"e9cf4467-0bb8-42ee-bf38-a6f64c2519e9","timestamp":"2026-10-30T04:16:51.723Z","version":"2.1.314","querySource":"sdk","shapeHash":"f700157f4d0195718816c4ddcaae81c64cf79395b988c095a19642618115b4bc","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":"7d08a77c-51b6-4baa-aa57-2c6a9201b163","keep":6,"tail":["495f09330f4e445aad1ece39a06176e6d2ba9a9bddda786301fb58887c177378","12f0fefbdb9069edc1e91d49be68418866ff669e1901787996cdaaa1c2dc269a"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"8e230d2c566743e0e6d63531f1864b006cab850d250aed62e2515540df7c97ea"}28{"parentUuid":"5b60f6e0-fec3-4fa2-8f4a-1e1e285abc01","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmvko4Y1JLqZSHkzv8j","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01RdM9ezJDHRqbZAXGmPsgKr","name":"Bash","input":{"command":"cd out && cat > state/data_audit.md <<'EOF'\n# Data audit (P1)\n- File: data/design.csv, SHA-256 b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0 (matches bundle.json).\n- 30 rows x 3 columns: i (int, 1..30, unique, consecutive), x (float, dimensionless, min -1.3942, max 1.9919, mean 0.2823, sd 0.8212), sigma (float, dimensionless, min 0.6034, max 1.7903, all > 0).\n- No date columns (synthetic fixed design). Missing values: 0. Duplicate rows: 0. Rows sorted by x.\n- Anomalies: none. Note (feature, not defect): sigma increases with |x - ~0| (smallest near x≈0, largest at extreme x, esp. x=1.99) — heteroskedasticity linked to leverage, which is the setting where conventional SE is expected to be biased.\n- Information-availability: only input is design.csv, allowed. No violations.\n- Exclusions: none (all 30 rows used); see out/exclusions.csv.\nEOF\ncat > exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n0,read data/design.csv (no filtering applied),30,30,0,all rows valid: no missing values, duplicates, or nonpositive sigma\nEOF\ncat > state/phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n \"P1\":{\"status\":\"passed\",\"checks\":[\"sha256 matches bundle.json\",\"30 rows, 3 cols, 0 NA, 0 duplicates, sigma>0, i=1..30\",\"exclusion ledger 30-0=30\"],\"notes\":\"\"},\n \"P2\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n \"P3\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n \"P4\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n \"P5\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"}}\nEOF\necho \"- 2026-10-30 P1 passed: data clean, no exclusions.\" >> state/log.md","description":"Write audit, exclusions, phase ledger"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1332,"cache_read_input_tokens":7096,"output_tokens":858,"output_tokens_details":{"thinking_tokens":0},"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":1332},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXmvkYgwMPeB8QNNpaSc","requestRef":"e9cf4467-0bb8-42ee-bf38-a6f64c2519e9","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"55a578de-2575-45df-b737-9938b43ddeff","timestamp":"2026-10-30T04:16:59.659Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0057","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","version":"2.1.314","gitBranch":"HEAD"}29{"parentUuid":"55a578de-2575-45df-b737-9938b43ddeff","isSidechain":false,"promptId":"dbeb1549-6a10-461e-a215-202293e2a3f0","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01RdM9ezJDHRqbZAXGmPsgKr","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"5c9f6222-901b-465e-b9ce-8053d9a049ad","timestamp":"2026-10-30T04:16:59.702Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"55a578de-2575-45df-b737-9938b43ddeff","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0057/out","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","version":"2.1.314","gitBranch":"HEAD"}30{"type":"api-request-blob","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","hash":"c0c5290e5ef1b146d74067d6910046934e21f73284becab9763ef0c708ffa1c3","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01RdM9ezJDHRqbZAXGmPsgKr","name":"Bash","input":{"command":"cd out && cat > state/data_audit.md <<'EOF'\n# Data audit (P1)\n- File: data/design.csv, SHA-256 b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0 (matches bundle.json).\n- 30 rows x 3 columns: i (int, 1..30, unique, consecutive), x (float, dimensionless, min -1.3942, max 1.9919, mean 0.2823, sd 0.8212), sigma (float, dimensionless, min 0.6034, max 1.7903, all > 0).\n- No date columns (synthetic fixed design). Missing values: 0. Duplicate rows: 0. Rows sorted by x.\n- Anomalies: none. Note (feature, not defect): sigma increases with |x - ~0| (smallest near x≈0, largest at extreme x, esp. x=1.99) — heteroskedasticity linked to leverage, which is the setting where conventional SE is expected to be biased.\n- Information-availability: only input is design.csv, allowed. No violations.\n- Exclusions: none (all 30 rows used); see out/exclusions.csv.\nEOF\ncat > exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n0,read data/design.csv (no filtering applied),30,30,0,all rows valid: no missing values, duplicates, or nonpositive sigma\nEOF\ncat > state/phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n \"P1\":{\"status\":\"passed\",\"checks\":[\"sha256 matches bundle.json\",\"30 rows, 3 cols, 0 NA, 0 duplicates, sigma>0, i=1..30\",\"exclusion ledger 30-0=30\"],\"notes\":\"\"},\n \"P2\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n \"P3\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n \"P4\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n \"P5\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"}}\nEOF\necho \"- 2026-10-30 P1 passed: data clean, no exclusions.\" >> state/log.md","description":"Write audit, exclusions, phase 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out && cat > exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n0,read data/design.csv (no filtering applied),30,30,0,\"all rows valid: no missing values, duplicates, or nonpositive sigma\"\nEOF\ncat > analysis.py <<'EOF'\n\"\"\"F2-conf-03: Monte Carlo coverage of OLS slope CIs under fixed heteroskedastic design.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\n\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\nfrom scipy import stats\n\nALPHA, BETA, N, R, LEVEL, SEED = 1.0, 0.5, 30, 2000, 0.95, 20261030\n\nd = pd.read_csv(\"data/design.csv\")\nn_rows = len(d)\nissues = []\nassert n_rows == N and d[[\"x\", \"sigma\"]].notna().all().all() and (d.sigma > 0).all()\nx = d[\"x\"].to_numpy(float); sig = d[\"sigma\"].to_numpy(float)\n\nxc = x - x.mean(); Sxx = np.sum(xc**2)\nw = xc / Sxx                       # beta_hat = beta + sum w_i sigma_i eps_i\nsd_beta_exact = float(np.sqrt(np.sum(w**2 * sig**2)))\n# exact E[s^2] (not E[se]): trace(M Sigma)/(n-2), reported as a diagnostic\nX = np.column_stack([np.ones(N), x])\nH = X @ np.linalg.solve(X.T @ X, X.T); M = np.eye(N) - H\nse_conv_sqrt_Es2 = float(np.sqrt(np.trace(M * sig**2) / (N - 2) / Sxx))\n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, N))          # only eps redrawn; x, sigma fixed\nY = ALPHA + BETA * x + sig * eps           # R x N\nyc = Y - Y.mean(axis=1, keepdims=True)\nb = yc @ xc / Sxx\na = Y.mean(axis=1) - b * x.mean()\ne = Y - a[:, None] - b[:, None] * x\nse_conv = np.sqrt(np.sum(e**2, axis=1) / (N - 2) / Sxx)\nhc0 = np.sum((xc**2) * e**2, axis=1) / Sxx**2   # slope element of HC0 sandwich\nse_hc1 = np.sqrt(hc0 * N / (N - 2))\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, N - 2)\ncov_conv = float(np.mean(np.abs(b - BETA) <= tcrit * se_conv))\ncov_hc1 = float(np.mean(np.abs(b - BETA) <= tcrit * se_hc1))\n\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\n# cross-check one replication with statsmodels\ntry:\n    import statsmodels.api as sm\n    f = sm.OLS(Y[0], X).fit()\n    assert abs(f.bse[1] - se_conv[0]) < 1e-10\n    assert abs(f.get_robustcov_results(\"HC1\").bse[1] - se_hc1[0]) < 1e-10\n    sm_check = True\nexcept ImportError:\n    sm_check = None\n\nres = {\n    \"task_id\": \"F2-conf-03\",\n    \"coverage_conventional\": cov_conv,\n    \"coverage_hc1\": cov_hc1,\n    \"sd_beta_exact\": sd_beta_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\": N,\n    \"feasibility\": \"complete\",\n    \"feasibility_reason\": None,\n    \"data_issues\": issues,\n    \"n_input_rows\": {\"design.csv\": n_rows},\n    \"random_seed\": SEED,\n    # supplementary\n    \"t_critical\": float(tcrit),\n    \"mcse_at_nominal\": mcse_nominal,\n    \"mcse_coverage_conventional\": mcse_conv,\n    \"mcse_coverage_hc1\": mcse_hc1,\n    \"undercover_threshold\": LEVEL - 3 * mcse_nominal,\n    \"conventional_ci_undercovers_using_estimated_mcse\": bool(cov_conv < LEVEL - 3 * mcse_conv),\n    \"hc1_ci_undercovers\": bool(cov_hc1 < LEVEL - 3 * mcse_nominal),\n    \"mean_se_hc1\": float(np.mean(se_hc1)),\n    \"mean_beta_hat\": float(np.mean(b)),\n    \"sqrt_expected_conv_variance_exact\": se_conv_sqrt_Es2,\n    \"ratio_mean_se_conv_to_sd_exact\": float(np.mean(se_conv) / sd_beta_exact),\n    \"statsmodels_crosscheck_passed\": sm_check,\n}\nos.makedirs(\"out\", exist_ok=True)\nwith open(\"out/results.json\", \"w\") as fh:\n    json.dump(res, fh, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\ncd .. && ~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis script"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":873,"cache_read_input_tokens":8428,"output_tokens":2150,"output_tokens_details":{"thinking_tokens":66},"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":873},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmwLfH74pxV9LVzLNnE","requestRef":"b2c9e0c4-658b-4e23-a631-0eec1e99bb30","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"298e34b8-4b2b-4c08-8c32-1eede119df5c","timestamp":"2026-10-30T04:17:16.120Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0057/out","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","version":"2.1.314","gitBranch":"HEAD"}34{"parentUuid":"298e34b8-4b2b-4c08-8c32-1eede119df5c","isSidechain":false,"promptId":"dbeb1549-6a10-461e-a215-202293e2a3f0","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01JMWb67w2UX7Z7YHLJqDrmY","type":"tool_result","content":"(eval):cd:1: no such file or directory: out\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\": 0.19026231012152658,\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\": 2.048407141795244,\n  \"mcse_at_nominal\": 0.004873397172404485,\n  \"mcse_coverage_conventional\": 0.00811369213120636,\n  \"mcse_coverage_hc1\": 0.006648157639526908,\n  \"undercover_threshold\": 0.9353798084827865,\n  \"conventional_ci_undercovers_using_estimated_mcse\": true,\n  \"hc1_ci_undercovers\": true,\n  \"mean_se_hc1\": 0.24080977065103962,\n  \"mean_beta_hat\": 0.4961965063446237,\n  \"sqrt_expected_conv_variance_exact\": 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Sigma)/(n-2), reported as a diagnostic\nX = np.column_stack([np.ones(N), x])\nH = X @ np.linalg.solve(X.T @ X, X.T); M = np.eye(N) - H\nse_conv_sqrt_Es2 = float(np.sqrt(np.trace(M * sig**2) / (N - 2) / Sxx))\n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, N))          # only eps redrawn; x, sigma fixed\nY = ALPHA + BETA * x + sig * eps           # R x N\nyc = Y - Y.mean(axis=1, keepdims=True)\nb = yc @ xc / Sxx\na = Y.mean(axis=1) - b * x.mean()\ne = Y - a[:, None] - b[:, None] * x\nse_conv = np.sqrt(np.sum(e**2, axis=1) / (N - 2) / Sxx)\nhc0 = np.sum((xc**2) * e**2, axis=1) / Sxx**2   # slope element of HC0 sandwich\nse_hc1 = np.sqrt(hc0 * N / (N - 2))\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, N - 2)\ncov_conv = float(np.mean(np.abs(b - BETA) <= tcrit * se_conv))\ncov_hc1 = float(np.mean(np.abs(b - BETA) <= tcrit * se_hc1))\n\nmcse_nominal = float(np.sqrt(LEVEL * (1 - LEVEL) / R))\nmcse_conv = float(np.sqrt(cov_conv * (1 - cov_conv) / R))\nmcse_hc1 = 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> out/state/checks.md <<'EOF'\n# Verification checks (P4)\n| # | check | outcome |\n|---|---|---|\n| 1 | Clean re-run (results.json deleted, script re-run) reproduces byte-identical results.json | PASS (cmp identical) |\n| 2 | data/design.csv SHA-256 unchanged after runs | PASS |\n| 3 | n_replications=2000, n_obs=30, n_input_rows=30; exclusions 30-0=30 | PASS |\n| 4 | sd_beta_exact, sd_beta_mc, mean_se_conventional > 0 | PASS (0.2680, 0.2696, 0.1903) |\n| 5 | sd_beta_mc vs sd_beta_exact: diff 0.0017 vs MC SE of SD ≈ 0.268/sqrt(2*1999)=0.0042 | PASS (within 0.4 SE) |\n| 6 | mean_beta_hat 0.4962 vs beta=0.5: diff -0.0038 vs MC SE 0.0060 | PASS (unbiased as expected) |\n| 7 | mean_se_conventional 0.1903 ≤ exact sqrt(E[s²]/Sxx)=0.1932 (Jensen) and close | PASS |\n| 8 | se_conv and se_HC1 of replication 1 match statsmodels to 1e-10 | PASS |\n| 9 | Coverages in [0,1]; t crit = t.975(28)=2.0484 | PASS |\n| 10 | Undercoverage flag: 0.844 < 0.95-3*0.004873=0.9354 → true; same conclusion with MCSE at estimated p (0.00811) | PASS (robust to MCSE definition) |\n| 11 | Magnitude vs baseline: mean se_conv / exact SD = 0.71, consistent with coverage well below 0.95; HC1 mean SE 0.241 closer to 0.268, coverage 0.902 higher than baseline 0.844 | PASS (coherent) |\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P2']={\"status\":\"passed\",\"checks\":[\"baseline coverage_conventional=0.844 computed with same evaluation rule (|b-beta|<=t*se) as HC1\"],\"notes\":\"conventional interval is the task-defined naive baseline\"}\np['P3']={\"status\":\"passed\",\"checks\":[\"analysis.py reads only data/, seed 20261030 recorded, vectorized R=2000 simulation\",\"statsmodels cross-check passed\"],\"notes\":\"\"}\np['P4']={\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical results.json\",\"11 consistency checks in checks.md all PASS\"],\"notes\":\"\"}\np['P5']={\"status\":\"running\",\"checks\":[],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P2/P3 passed (baseline cov_conv=0.844; HC1 0.902). P4 passed: reproducible, checks OK. Decision: MCSE for flag at nominal p=0.95; robust to alternative.\" >> out/state/log.md","description":"Record checks and update ledger"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":498,"cache_read_input_tokens":12337,"output_tokens":1336,"output_tokens_details":{"thinking_tokens":156},"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":498},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmyDKZShqTbXBm4Hn4J","requestRef":"838f3869-d6fb-446c-8250-0a75c2b3e3a8","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"15ae052b-3820-4adb-943c-1c4ee3fda0a8","timestamp":"2026-10-30T04:17:36.964Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0057","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","version":"2.1.314","gitBranch":"HEAD"}51{"parentUuid":"15ae052b-3820-4adb-943c-1c4ee3fda0a8","isSidechain":false,"promptId":"dbeb1549-6a10-461e-a215-202293e2a3f0","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01Cye72du3q71vLRTiDshpsZ","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"b8f960d4-b742-4cdc-b860-625aeb8ba8de","timestamp":"2026-10-30T04:17:37.026Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"15ae052b-3820-4adb-943c-1c4ee3fda0a8","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0057","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","version":"2.1.314","gitBranch":"HEAD"}52{"type":"api-request-blob","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","hash":"3b9089fee9ea1d7e48a78b48dd5cb13ba0f89be57dc1867433856dc7ac5c4b87","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01Cye72du3q71vLRTiDshpsZ","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n| # | check | outcome |\n|---|---|---|\n| 1 | Clean re-run (results.json deleted, script re-run) reproduces byte-identical results.json | PASS (cmp identical) |\n| 2 | data/design.csv SHA-256 unchanged after runs | PASS |\n| 3 | n_replications=2000, n_obs=30, n_input_rows=30; exclusions 30-0=30 | PASS |\n| 4 | sd_beta_exact, sd_beta_mc, mean_se_conventional > 0 | PASS (0.2680, 0.2696, 0.1903) |\n| 5 | sd_beta_mc vs sd_beta_exact: diff 0.0017 vs MC SE of SD ≈ 0.268/sqrt(2*1999)=0.0042 | PASS (within 0.4 SE) |\n| 6 | mean_beta_hat 0.4962 vs beta=0.5: diff -0.0038 vs MC SE 0.0060 | PASS (unbiased as expected) |\n| 7 | mean_se_conventional 0.1903 ≤ exact sqrt(E[s²]/Sxx)=0.1932 (Jensen) and close | PASS |\n| 8 | se_conv and se_HC1 of replication 1 match statsmodels to 1e-10 | PASS |\n| 9 | Coverages in [0,1]; t crit = t.975(28)=2.0484 | PASS |\n| 10 | Undercoverage flag: 0.844 < 0.95-3*0.004873=0.9354 → true; same conclusion with MCSE at estimated p (0.00811) | PASS (robust to MCSE definition) |\n| 11 | Magnitude vs baseline: mean se_conv / exact SD = 0.71, consistent with coverage well below 0.95; HC1 mean SE 0.241 closer to 0.268, coverage 0.902 higher than baseline 0.844 | PASS (coherent) |\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P2']={\"status\":\"passed\",\"checks\":[\"baseline coverage_conventional=0.844 computed with same evaluation rule (|b-beta|<=t*se) as HC1\"],\"notes\":\"conventional interval is the task-defined naive baseline\"}\np['P3']={\"status\":\"passed\",\"checks\":[\"analysis.py reads only data/, seed 20261030 recorded, vectorized R=2000 simulation\",\"statsmodels cross-check passed\"],\"notes\":\"\"}\np['P4']={\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical results.json\",\"11 consistency checks in checks.md all PASS\"],\"notes\":\"\"}\np['P5']={\"status\":\"running\",\"checks\":[],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P2/P3 passed (baseline cov_conv=0.844; HC1 0.902). P4 passed: reproducible, checks OK. Decision: MCSE for flag at nominal p=0.95; robust to alternative.\" >> out/state/log.md","description":"Record checks and update ledger"}}]}}53{"type":"api-request","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","id":"6c73c5a2-53b2-4df1-846a-1f017bf419e8","timestamp":"2026-10-30T04:17:37.031Z","version":"2.1.314","querySource":"sdk","shapeHash":"f700157f4d0195718816c4ddcaae81c64cf79395b988c095a19642618115b4bc","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":"838f3869-d6fb-446c-8250-0a75c2b3e3a8","keep":16,"tail":["3b9089fee9ea1d7e48a78b48dd5cb13ba0f89be57dc1867433856dc7ac5c4b87","3f4fb2835701e8a026fe0a0c4ed1d92a17601f0db637f313d66cb9ef99713254"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",17,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"5c4226ead1156e25d6640dc1c2aa2711533e9beacbab6616ee7656c3c6d09625"}54{"parentUuid":"b8f960d4-b742-4cdc-b860-625aeb8ba8de","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmz6XYxML3a82eWQQPw","type":"message","role":"assistant","content":[{"type":"text","text":"Now the report and claims."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1351,"cache_read_input_tokens":12835,"output_tokens":2961,"output_tokens_details":{"thinking_tokens":0},"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":1351},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXmz6FCARLvWBmbNjVJP","requestRef":"6c73c5a2-53b2-4df1-846a-1f017bf419e8","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"504a739f-7640-417a-af16-0fac4cd63eed","timestamp":"2026-10-30T04:17:37.822Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0057","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","version":"2.1.314","gitBranch":"HEAD"}55{"parentUuid":"504a739f-7640-417a-af16-0fac4cd63eed","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmz6XYxML3a82eWQQPw","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_015gpbNj5nxKDkHNBM7GB9Qv","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F2-conf-03 — Coverage of OLS slope confidence intervals in a small heteroskedastic fixed design\n\n## Question\nModel: y_i = 1 + 0.5 x_i + σ_i ε_i, with i = 1…30, ε_i iid N(0,1), and x_i, σ_i held fixed at the values in `data/design.csv`. Do nominal 95% intervals β̂ ± t_{0.975}(28)·se reach 95% coverage when se is (a) the conventional OLS standard error, or (b) the HC1 robust standard error? The task also asks for (c) the exact SD of β̂ and (d) E[se_conv].\n\n## Data and exclusions\n`data/design.csv` has 30 rows (`n_input_rows`) and SHA-256 b1a17a52…74f0. It has no missing values, no duplicates, and every σ is positive. No rows were excluded (`out/exclusions.csv`: 30 − 0 = 30). No data issues were found, so `data_issues` = []. In this design σ_i is smallest near x = 0 and largest at the extreme x values (largest of all at x = 1.99). That means the error variance is highest at the high-leverage points. See `out/state/data_audit.md`.\n\n## Method\n- **Exact SD.** β̂ − β = Σ w_i σ_i ε_i, with w_i = (x_i − x̄)/S_xx. So SD(β̂) = sqrt(Σ w_i² σ_i²) (`sd_beta_exact`). No simulation is involved.\n- **Monte Carlo.** R = 2000 replications (`n_replications`), using numpy `default_rng` with seed 20261030 (`random_seed`). Only ε is redrawn in each replication; x and σ stay fixed. Each replication fits OLS and computes:\n  - se_conv = sqrt(s²/S_xx), where s² = RSS/(n − 2);\n  - se_HC1 = sqrt(n/(n−2) · Σ(x_i − x̄)² e_i² / S_xx²).\n- **Coverage** is the share of replications with |β̂ − 0.5| ≤ t_{0.975}(28)·se, where t = 2.0484 (`t_critical`).\n- **Checks.** For replication 1, both SEs match statsmodels to within 1e-10 (`statsmodels_crosscheck_passed`).\n- **Decision rule.** `conventional_ci_undercovers` is true if coverage_conventional < 0.95 − 3·sqrt(0.95·0.05/2000). The binomial standard error here is evaluated at the nominal level, which is the null hypothesis being tested. I also checked the conclusion using the SE evaluated at the estimated coverage.\n\n## Results\n- **Conventional interval (baseline).** Coverage is **0.844** (`coverage_conventional`), well short of the nominal 0.95.\n- **HC1 interval.** Coverage is **0.902** (`coverage_hc1`). This is better than the conventional interval but still below 0.95 (`hc1_ci_undercovers` = true).\n- **SD of β̂.** The exact value is 0.2680 (`sd_beta_exact`). The Monte Carlo SD is 0.2696 (`sd_beta_mc`), which agrees with it. The mean of β̂ across replications is 0.4962 (`mean_beta_hat`), consistent with β̂ being unbiased.\n- **Conventional SE.** Its average is 0.1903 (`mean_se_conventional`), only 0.71 of the true SD (`ratio_mean_se_conv_to_sd_exact`). The exact value of sqrt(E[s²]/S_xx) is 0.1932 (`sqrt_expected_conv_variance_exact`). So the conventional SE is biased downward by design, not by sampling noise: it ignores the fact that the error variance is largest at high-leverage x values. The mean HC1 SE is 0.2408 (`mean_se_hc1`), closer to the true value but still too small.\n- **Conclusion.** The conventional interval does **not** attain its nominal coverage (`conventional_ci_undercovers` = true). The threshold is 0.9354 (`undercover_threshold`).\n\n## Uncertainty\n- **Coverage estimates (binomial Monte Carlo standard errors):**\n  - conventional: 0.844 ± 0.0081 (`mcse_coverage_conventional`);\n  - HC1: 0.902 ± 0.0066 (`mcse_coverage_hc1`);\n  - at the nominal level: 0.0049 (`mcse_at_nominal`).\n- **Size of the shortfall.** The conventional coverage falls about 22 nominal-level MCSEs below 0.95. The conclusion is the same if the MCSE at the estimated coverage is used instead (`conventional_ci_undercovers_using_estimated_mcse` = true).\n- **SD estimate.** The Monte Carlo standard error of `sd_beta_mc` is about 0.0042. The gap from the exact value (0.0017) is within that noise.\n- **What the numbers depend on.** All values are for this seed and this R. A different seed would shift the coverages by roughly ±1–2 MCSE.\n\n## Limitations and open issues\n- The results apply only to this fixed design, this σ pattern, n = 30 and Gaussian errors. They should not be generalised to other designs.\n- E[se_conv] is estimated by simulation, as the task specifies. Only E[s²] is available in closed form, and it is reported as a diagnostic.\n- The undercoverage flag depends on how \"binomial standard error\" is defined, so I checked two definitions: SE at p = 0.95 and SE at the estimated p. Both give the same conclusion.\n- HC1 also undercovers in this small, high-leverage sample. Alternatives such as HC2/HC3 or wild bootstrap were not evaluated because the task does not ask for them.\n- Feasibility: complete.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The conventional 95% OLS interval does not attain nominal coverage: estimated coverage 0.844, more than three Monte Carlo SEs below 0.95.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"mcse_at_nominal\",\"undercover_threshold\",\"conventional_ci_undercovers_using_estimated_mcse\"],\"status\":\"supported\",\"caveat\":\"Specific to this fixed design, n=30, Gaussian errors, seed 20261030.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval improves coverage to 0.902 but still falls short of 0.95.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\",\"hc1_ci_undercovers\"],\"status\":\"supported\",\"caveat\":\"HC1 is known to be downward biased in small, high-leverage samples; other estimators not evaluated.\"},\n {\"id\":\"C3\",\"text\":\"The exact SD of the slope estimator is 0.268, and the Monte Carlo SD (0.270) agrees within Monte Carlo error.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\"],\"status\":\"supported\",\"caveat\":\"MC SE of the sample SD approx 0.004 (computed in checks).\"},\n {\"id\":\"C4\",\"text\":\"The conventional SE averages 0.190, about 71% of the true SD, which explains the undercoverage.\",\"results_keys\":[\"mean_se_conventional\",\"ratio_mean_se_conv_to_sd_exact\",\"sqrt_expected_conv_variance_exact\"],\"status\":\"supported\",\"caveat\":\"Attributing the undercoverage to SE bias is an interpretation, supported by the exact E[s^2] computation.\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\nr=json.load(open('out/results.json'));c=json.load(open('out/claims.json'))\nassert all(k in r for x in c for k in x['results_keys']);print(\"claims keys ok\")\np=json.load(open('out/state/phases.json'))\np['P5']={\"status\":\"passed\",\"checks\":[\"report.md has 6 required sections citing results keys\",\"claims.json keys all exist in results.json\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\ngrep '^## ' out/report.md; echo \"- 2026-10-30 P5 passed: report and claims written. 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Do nominal 95% intervals β̂ ± t_{0.975}(28)·se reach 95% coverage when se is (a) the conventional OLS standard error, or (b) the HC1 robust standard error? The task also asks for (c) the exact SD of β̂ and (d) E[se_conv].\n\n## Data and exclusions\n`data/design.csv` has 30 rows (`n_input_rows`) and SHA-256 b1a17a52…74f0. It has no missing values, no duplicates, and every σ is positive. No rows were excluded (`out/exclusions.csv`: 30 − 0 = 30). No data issues were found, so `data_issues` = []. In this design σ_i is smallest near x = 0 and largest at the extreme x values (largest of all at x = 1.99). That means the error variance is highest at the high-leverage points. See `out/state/data_audit.md`.\n\n## Method\n- **Exact SD.** β̂ − β = Σ w_i σ_i ε_i, with w_i = (x_i − x̄)/S_xx. So SD(β̂) = sqrt(Σ w_i² σ_i²) (`sd_beta_exact`). No simulation is involved.\n- **Monte Carlo.** R = 2000 replications (`n_replications`), using numpy `default_rng` with seed 20261030 (`random_seed`). Only ε is redrawn in each replication; x and σ stay fixed. Each replication fits OLS and computes:\n  - se_conv = sqrt(s²/S_xx), where s² = RSS/(n − 2);\n  - se_HC1 = sqrt(n/(n−2) · Σ(x_i − x̄)² e_i² / S_xx²).\n- **Coverage** is the share of replications with |β̂ − 0.5| ≤ t_{0.975}(28)·se, where t = 2.0484 (`t_critical`).\n- **Checks.** For replication 1, both SEs match statsmodels to within 1e-10 (`statsmodels_crosscheck_passed`).\n- **Decision rule.** `conventional_ci_undercovers` is true if coverage_conventional < 0.95 − 3·sqrt(0.95·0.05/2000). The binomial standard error here is evaluated at the nominal level, which is the null hypothesis being tested. I also checked the conclusion using the SE evaluated at the estimated coverage.\n\n## Results\n- **Conventional interval (baseline).** Coverage is **0.844** (`coverage_conventional`), well short of the nominal 0.95.\n- **HC1 interval.** Coverage is **0.902** (`coverage_hc1`). This is better than the conventional interval but still below 0.95 (`hc1_ci_undercovers` = true).\n- **SD of β̂.** The exact value is 0.2680 (`sd_beta_exact`). The Monte Carlo SD is 0.2696 (`sd_beta_mc`), which agrees with it. The mean of β̂ across replications is 0.4962 (`mean_beta_hat`), consistent with β̂ being unbiased.\n- **Conventional SE.** Its average is 0.1903 (`mean_se_conventional`), only 0.71 of the true SD (`ratio_mean_se_conv_to_sd_exact`). The exact value of sqrt(E[s²]/S_xx) is 0.1932 (`sqrt_expected_conv_variance_exact`). So the conventional SE is biased downward by design, not by sampling noise: it ignores the fact that the error variance is largest at high-leverage x values. The mean HC1 SE is 0.2408 (`mean_se_hc1`), closer to the true value but still too small.\n- **Conclusion.** The conventional interval does **not** attain its nominal coverage (`conventional_ci_undercovers` = true). The threshold is 0.9354 (`undercover_threshold`).\n\n## Uncertainty\n- **Coverage estimates (binomial Monte Carlo standard errors):**\n  - conventional: 0.844 ± 0.0081 (`mcse_coverage_conventional`);\n  - HC1: 0.902 ± 0.0066 (`mcse_coverage_hc1`);\n  - at the nominal level: 0.0049 (`mcse_at_nominal`).\n- **Size of the shortfall.** The conventional coverage falls about 22 nominal-level MCSEs below 0.95. The conclusion is the same if the MCSE at the estimated coverage is used instead (`conventional_ci_undercovers_using_estimated_mcse` = true).\n- **SD estimate.** The Monte Carlo standard error of `sd_beta_mc` is about 0.0042. The gap from the exact value (0.0017) is within that noise.\n- **What the numbers depend on.** All values are for this seed and this R. A different seed would shift the coverages by roughly ±1–2 MCSE.\n\n## Limitations and open issues\n- The results apply only to this fixed design, this σ pattern, n = 30 and Gaussian errors. They should not be generalised to other designs.\n- E[se_conv] is estimated by simulation, as the task specifies. Only E[s²] is available in closed form, and it is reported as a diagnostic.\n- The undercoverage flag depends on how \"binomial standard error\" is defined, so I checked two definitions: SE at p = 0.95 and SE at the estimated p. Both give the same conclusion.\n- HC1 also undercovers in this small, high-leverage sample. Alternatives such as HC2/HC3 or wild bootstrap were not evaluated because the task does not ask for them.\n- Feasibility: complete.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The conventional 95% OLS interval does not attain nominal coverage: estimated coverage 0.844, more than three Monte Carlo SEs below 0.95.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"mcse_at_nominal\",\"undercover_threshold\",\"conventional_ci_undercovers_using_estimated_mcse\"],\"status\":\"supported\",\"caveat\":\"Specific to this fixed design, n=30, Gaussian errors, seed 20261030.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval improves coverage to 0.902 but still falls short of 0.95.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\",\"hc1_ci_undercovers\"],\"status\":\"supported\",\"caveat\":\"HC1 is known to be downward biased in small, high-leverage samples; other estimators not evaluated.\"},\n {\"id\":\"C3\",\"text\":\"The exact SD of the slope estimator is 0.268, and the Monte Carlo SD (0.270) agrees within Monte Carlo error.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\"],\"status\":\"supported\",\"caveat\":\"MC SE of the sample SD approx 0.004 (computed in checks).\"},\n {\"id\":\"C4\",\"text\":\"The conventional SE averages 0.190, about 71% of the true SD, which explains the undercoverage.\",\"results_keys\":[\"mean_se_conventional\",\"ratio_mean_se_conv_to_sd_exact\",\"sqrt_expected_conv_variance_exact\"],\"status\":\"supported\",\"caveat\":\"Attributing the undercoverage to SE bias is an interpretation, supported by the exact E[s^2] computation.\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\nr=json.load(open('out/results.json'));c=json.load(open('out/claims.json'))\nassert all(k in r for x in c for k in x['results_keys']);print(\"claims keys ok\")\np=json.load(open('out/state/phases.json'))\np['P5']={\"status\":\"passed\",\"checks\":[\"report.md has 6 required sections citing results keys\",\"claims.json keys all exist in results.json\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\ngrep '^## ' out/report.md; echo \"- 2026-10-30 P5 passed: report and claims written. 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1))),|' out/analysis.py\n~/wp29/venv/bin/python out/analysis.py | grep -E 'mcse_sd|coverage_conv\"' ; ~/wp29/venv/bin/python out/analysis.py >/dev/null; cp out/results.json /tmp/r2.json; ~/wp29/venv/bin/python out/analysis.py >/dev/null; cmp out/results.json /tmp/r2.json && echo IDENTICAL\nsed -i '' 's|The Monte Carlo standard error of `sd_beta_mc` is about 0.0042|The Monte Carlo standard error of `sd_beta_mc` is about 0.0043 (`mcse_sd_beta_mc_approx`)|' out/report.md\nsed -i '' 's|\"MC SE of the sample SD approx 0.004 (computed in checks).\"|\"MC SE of the sample SD approx 0.004 (mcse_sd_beta_mc_approx).\"|; s|\"results_keys\":\\[\"sd_beta_exact\",\"sd_beta_mc\"\\]|\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\",\"mcse_sd_beta_mc_approx\"]|' out/claims.json\ngrep -n mcse_sd out/report.md out/claims.json; echo \"- 2026-10-30 added mcse_sd_beta_mc_approx key; re-ran, reproducible; other values unchanged.\" >> out/state/log.md","description":"Add SD MCSE key, rerun, update report"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":3011,"cache_read_input_tokens":14186,"output_tokens":811,"output_tokens_details":{"thinking_tokens":139},"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":3011},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXn1uoSYRB52mtaPxdGF","requestRef":"5666bd1f-56bd-4623-8c22-ceb088f2b435","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"1bbd50d0-d6f1-4b96-b00b-b3a13727861b","timestamp":"2026-10-30T04:18:08.876Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0057","sessionId":"c3b76191-8236-4887-be14-0a8ded55b545","version":"2.1.314","gitBranch":"HEAD"}63{"parentUuid":"1bbd50d0-d6f1-4b96-b00b-b3a13727861b","isSidechain":false,"promptId":"dbeb1549-6a10-461e-a215-202293e2a3f0","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01A1zL1DN2BEK5GUnRtjT6Vp","type":"tool_result","content":"  \"mcse_sd_beta_mc_approx\": 0.004264565559199469,\nIDENTICAL\nout/report.md:31:- **SD estimate.** The Monte Carlo standard error of `sd_beta_mc` is about 0.0043 (`mcse_sd_beta_mc_approx`). The gap from the exact value (0.0017) is within that noise.\nout/claims.json:4: {\"id\":\"C3\",\"text\":\"The exact SD of the slope estimator is 0.268, and the Monte Carlo SD (0.270) agrees within Monte Carlo error.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\",\"mcse_sd_beta_mc_approx\"],\"status\":\"supported\",\"caveat\":\"MC SE of the sample SD approx 0.004 (mcse_sd_beta_mc_approx).\"},","is_error":false}]},"uuid":"bc42c1b1-7eb8-4460-acc4-b38e738a90cc","timestamp":"2026-10-30T04:18:11.694Z","toolUseResult":{"stdout":"  \"mcse_sd_beta_mc_approx\": 0.004264565559199469,\nIDENTICAL\nout/report.md:31:- **SD estimate.** The Monte Carlo standard error of `sd_beta_mc` is about 0.0043 (`mcse_sd_beta_mc_approx`). 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The task is complete, and re-running `out/analysis.py` (seed 20261030) reproduces `out/results.json` exactly.\n\n| Quantity | Value | Monte Carlo standard error |\n|---|---|---|\n| Coverage, conventional interval | 0.844 | 0.0081 |\n| Coverage, HC1 interval | 0.902 | 0.0066 |\n| Exact SD of β̂ | 0.2680 | – (calculated, not simulated) |\n| Simulated SD of β̂ | 0.2696 | about 0.0043 |\n| Average conventional standard error | 0.1903 | – |\n\n- **Shortfall:** 0.844 is about 22 standard errors below 0.95, far past the task's cut-off of three. So `conventional_ci_undercovers` is true.\n- **Choice of standard error for that test:** the task doesn't say whether the binomial standard error should be taken at 0.95 or at the estimated coverage. I used 0.95 (0.0049); using the estimated coverage gives the same answer.\n- **Why it undercovers:** the conventional standard error averages only about 71% of the true SD of β̂. In this design the error variance is largest at the extreme x values, which pull hardest on the slope, and the conventional formula ignores that. The shortfall comes from the formula, not from simulation noise.\n- **HC1:** the robust interval does better (90.2%) but also falls clearly short of 95%. Its average standard error is 0.241 against the true 0.268.\n- **Checks:** the simulated SD agrees with the exact value within simulation error. Both standard errors match statsmodels for a test replication.\n\n**Limitations:** the results hold only for this design, n = 30, normal errors and this seed. The expected conventional standard error is estimated by simulation, as the task specifies. 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