1{"type":"atis-latch","atis":"","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167"}2{"type":"queue-operation","operation":"enqueue","timestamp":"2026-10-30T04:15:36.926Z","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","content":"Begin"}3{"type":"queue-operation","operation":"dequeue","timestamp":"2026-10-30T04:15:36.932Z","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167"}4{"parentUuid":null,"isSidechain":false,"promptId":"1aebd786-e531-4647-a9e1-ba1578700938","type":"user","message":{"role":"user","content":"Begin"},"uuid":"2120ed0f-f748-43b1-88ef-8ea107e77d4f","timestamp":"2026-10-30T04:15:36.937Z","permissionMode":"default","promptSource":"sdk","turnOrigin":"sdk","turnPosition":{"promptIndex":0,"turnIndex":1},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}5{"type":"api-request-shape","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","shapeHash":"aa57bdbb1073466ded2da08e0f587c11ec83cb89d43e91439134bd37ac4c0122","timestamp":"2026-10-30T04:15:36.951Z","version":"2.1.314","shape":{"system":[{"type":"text","text":"You are Claude Code, Anthropic's official CLI for Claude, running within the Claude Agent SDK."},{"type":"text","text":"CWD: /Users/simon-pierreboucher/wp29/runs/RC0054\nDate: 2026-10-30\n\nYou are a research assistant executing one bounded scientific task inside the current working directory, which is your workspace.\n\nEnvironment facts (identical for every task):\n- The task statement is the file `TASK.md` in the workspace. 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\nEXECUTABLE GATES (additional, mandatory)\n- A read-only gate program is provided at `~/wp29/gates/pgar_gate.py`. Run it from the workspace root as `~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .` It checks the output contract of `TASK.md` (required files, keys, types, finite values, report sections, the claims ledger, the phase ledger, the exclusion ledger) and reproducibility (it re-runs `out/analysis.py` in a temporary copy and compares the regenerated `out/results.json` with yours). It never checks scientific correctness and it contains no reference answers.\n- You must run the gate at the end of P4 and again at the end of P5, and record each run's receipt (the gate writes `out/state/gate_receipts/<timestamp>.json`) in `out/state/phases.json`. You may not declare the task complete while the latest gate receipt reports `\"passed\": false`. Fix the reported problems and re-run the gate.\n- The controller will run the same gate after your session ends. If it fails, you will be resumed with the gate output and asked to fix the problems; each such cycle consumes your remaining budget.\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/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167"}12{"parentUuid":"63ac64bd-b75a-4498-b649-7521aae2cf53","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmqHtR8cYLQ6RDt2Doo","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":2603,"cache_read_input_tokens":1504,"output_tokens":124,"output_tokens_details":{"thinking_tokens":22},"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":2603},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":418,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmqHd45vMLt9AZajugH","requestRef":"701bc8fe-a391-4b0c-99db-e56e56abc627","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"df4371ca-c3db-4476-b868-c58ab1a1683d","timestamp":"2026-10-30T04:15:38.972Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"df4371ca-c3db-4476-b868-c58ab1a1683d","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmqHtR8cYLQ6RDt2Doo","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Tey5WUZLnTDpDAqatry1zf","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 45 simon-pierreboucher staff 1440 oct. 30 00:15 ..\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:\ntotal 8\ndrwxr-xr-x 3 simon-pierreboucher staff 96 oct. 29 23:33 .\ndrwxr-xr-x 6 simon-pierreboucher staff 192 oct. 29 23:35 ..\n-rw-r--r-- 1 simon-pierreboucher staff 519 oct. 29 23:33 design.csv","is_error":true,"tool_use_id":"toolu_01Tey5WUZLnTDpDAqatry1zf"}]},"uuid":"f8039126-c3ac-4186-8d65-dc2dc6f21856","timestamp":"2026-10-30T04:15:39.604Z","toolUseResult":"Error: Exit code 1\n# 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 45 simon-pierreboucher staff 1440 oct. 30 00:15 ..\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:\ntotal 8\ndrwxr-xr-x 3 simon-pierreboucher staff 96 oct. 29 23:33 .\ndrwxr-xr-x 6 simon-pierreboucher staff 192 oct. 29 23:35 ..\n-rw-r--r-- 1 simon-pierreboucher staff 519 oct. 29 23:33 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** In a fixed-design small sample (n=30) with heteroskedastic errors, y_i = 1 + 0.5 x_i + sigma_i e_i, e_i iid N(0,1), x and sigma fixed from data/design.csv, do nominal 95% t(28) CIs for the OLS slope attain 95% coverage?\n\n**Estimands.**\n(a) P(beta in betahat ± t_{.975,28} se_conv), se_conv = conventional OLS SE with s^2 = RSS/(n-2).\n(b) Same with se_HC1 = sqrt(n/(n-2) * HC0 sandwich).\n(c) Exact SD of betahat: sqrt(sum w_i^2 sigma_i^2), w_i = (x_i - xbar)/Sxx (analytical).\n(d) E[se_conv], by MC.\n(a),(b),(d) estimated by Monte Carlo with exactly R=2000, fixed seed. Meaningful under the stated DGP (normal errors, fixed design).\n\n**Outputs.** out/results.json keys: task_id, coverage_conventional, coverage_hc1, sd_beta_exact, sd_beta_mc, mean_se_conventional, conventional_ci_undercovers (cov_conv < 0.95 - 3*sqrt(0.95*0.05/2000)), n_replications, n_obs_per_replication, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed. Also out/report.md (6 sections incl. MC SEs of coverages), out/analysis.py, out/claims.json (incl. claim on conventional nominal coverage).\n\n**Information rules.** Only data/design.csv; never redraw x or sigma; constants given in TASK.md.\n\n**Invalidity conditions.** Design file not 30 rows / missing or nonpositive sigma / constant x; R != 2000; non-reproducible seed.\nEOF\ncat > phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"pending\",\"checks\":[],\"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 P0 passed: contract written.\" > log.md\ncd ../.. && ~/wp29/venv/bin/python -c \"\nimport pandas as pd; d=pd.read_csv('data/design.csv'); print(d.shape, d.dtypes.to_dict()); 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3) {'i': dtype('int64'), 'x': dtype('float64'), 'sigma': dtype('float64')}\n 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\nna 0 dup i 0 dup rows 0\ni 1..30 True\ncorr |x-mean|,sigma 0.8371553430740877 corr x^2 0.9999999949659686","is_error":false}]},"uuid":"0d0fd9d5-4428-43f1-a7d3-43524b7b6183","timestamp":"2026-10-30T04:15:53.290Z","toolUseResult":{"stdout":"(30, 3) {'i': dtype('int64'), 'x': dtype('float64'), 'sigma': dtype('float64')}\n 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\nna 0 dup i 0 dup rows 0\ni 1..30 True\ncorr |x-mean|,sigma 0.8371553430740877 corr x^2 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** In a fixed-design small sample (n=30) with heteroskedastic errors, y_i = 1 + 0.5 x_i + sigma_i e_i, e_i iid N(0,1), x and sigma fixed from data/design.csv, do nominal 95% t(28) CIs for the OLS slope attain 95% coverage?\n\n**Estimands.**\n(a) P(beta in betahat ± t_{.975,28} se_conv), se_conv = conventional OLS SE with s^2 = RSS/(n-2).\n(b) Same with se_HC1 = sqrt(n/(n-2) * HC0 sandwich).\n(c) Exact SD of betahat: sqrt(sum w_i^2 sigma_i^2), w_i = (x_i - xbar)/Sxx (analytical).\n(d) E[se_conv], by MC.\n(a),(b),(d) estimated by Monte Carlo with exactly R=2000, fixed seed. Meaningful under the stated DGP (normal errors, fixed design).\n\n**Outputs.** out/results.json keys: task_id, coverage_conventional, coverage_hc1, sd_beta_exact, sd_beta_mc, mean_se_conventional, conventional_ci_undercovers (cov_conv < 0.95 - 3*sqrt(0.95*0.05/2000)), n_replications, n_obs_per_replication, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed. Also out/report.md (6 sections incl. MC SEs of coverages), out/analysis.py, out/claims.json (incl. claim on conventional nominal coverage).\n\n**Information rules.** Only data/design.csv; never redraw x or sigma; constants given in TASK.md.\n\n**Invalidity conditions.** Design file not 30 rows / missing or nonpositive sigma / constant x; R != 2000; non-reproducible seed.\nEOF\ncat > phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"pending\",\"checks\":[],\"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 P0 passed: contract written.\" > log.md\ncd ../.. && ~/wp29/venv/bin/python -c \"\nimport pandas as pd; d=pd.read_csv('data/design.csv'); print(d.shape, d.dtypes.to_dict()); print(d.describe()); print('na',d.isna().sum().sum(),'dup i',d.i.duplicated().sum(),'dup rows',d.duplicated().sum()); print('i 1..30', (d.i.values==range(1,31)).all()); print('corr |x-mean|,sigma', d.sigma.corr((d.x-d.x.mean()).abs()), 'corr x^2', d.sigma.corr(d.x**2))\"","description":"Write P0 files and audit data"}}]}}27{"type":"api-request","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","id":"6ad02b96-1e03-4234-8865-5aa52c8921bd","timestamp":"2026-10-30T04:15:53.293Z","version":"2.1.314","querySource":"sdk","shapeHash":"aa57bdbb1073466ded2da08e0f587c11ec83cb89d43e91439134bd37ac4c0122","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":"fd559b61-acef-4456-b710-e36b8486c758","keep":6,"tail":["cbcbaa4a069166a9c9f7e2dcc2cd1e5a9443c67ef2c0945370d08e0af987cd2d","732aceb98cdd98a2b3d2959317f47a0362cc691b23fd62ac362b0783a649794a"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"205137c1bc305a0174748ebb009b4d88d1da46c2c8b57ca0491fe81d13ddbffc"}28{"parentUuid":"0d0fd9d5-4428-43f1-a7d3-43524b7b6183","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmrSyPrvcs15JUisTwZ","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_014oyzi2w3hjZjhmPnq1GYyG","name":"Bash","input":{"command":"cd out && cat > state/data_audit.md <<'EOF'\n# Data audit (P1)\nFile: data/design.csv — SHA-256 b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0 (matches bundle.json).\n- 30 rows × 3 columns: i (int64, 1..30, unique, contiguous), x (float64, dimensionless, range -1.3942..1.9919, mean 0.2823, sd 0.8212), sigma (float64, dimensionless, range 0.6034..1.7903, all > 0).\n- Missing values: 0. 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> out/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\nReads only data/design.csv; writes out/results.json deterministically.\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\nfrom scipy import stats\n\nSEED = 20261030\nR = 2000\nALPHA, BETA = 1.0, 0.5\nLEVEL = 0.95\n\nd = pd.read_csv(\"data/design.csv\")\nn_rows = int(len(d))\ndata_issues = []\nassert n_rows == 30 and d[[\"x\", \"sigma\"]].notna().all().all() and (d.sigma > 0).all()\nx = d[\"x\"].to_numpy(float)\nsig = d[\"sigma\"].to_numpy(float)\nn = len(x)\ndf = n - 2\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, df)\n\n# (c) exact SD of betahat: betahat - beta = sum w_i sigma_i eps_i, w_i = (x_i - xbar)/Sxx\nxc = x - x.mean()\nSxx = np.sum(xc ** 2)\nw = xc / Sxx\nsd_exact = float(np.sqrt(np.sum(w ** 2 * sig ** 2)))\n\n# Monte Carlo\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x[None, :] + sig[None, :] * eps\nX = np.column_stack([np.ones(n), x])\nXtX_inv = np.linalg.inv(X.T @ X)\nB = Y @ (XtX_inv @ X.T).T # R x 2 coefficients\nresid = Y - B @ X.T # R x n\ns2 = np.sum(resid ** 2, axis=1) / df\nse_conv = np.sqrt(s2 * XtX_inv[1, 1])\n# HC0 slope variance: sum (a_i^2 e_i^2), a = row 2 of (X'X)^-1 X' (equals w_i)\na = (XtX_inv @ X.T)[1]\nvar_hc0 = np.sum((a[None, :] ** 2) * resid ** 2, axis=1)\nse_hc1 = np.sqrt(var_hc0 * n / df)\nbhat = B[:, 1]\n\ncov_conv = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_conv))\ncov_hc1 = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_hc1))\nmcse_nominal = float(np.sqrt(LEVEL * (1 - LEVEL) / R))\nundercovers = bool(cov_conv < LEVEL - 3 * mcse_nominal)\n\n# Cross-check against statsmodels on replication 0\nimport statsmodels.api as sm\nm0 = sm.OLS(Y[0], X).fit()\nassert np.isclose(m0.bse[1], se_conv[0]) and np.isclose(m0.get_robustcov_results(\"HC1\").bse[1], se_hc1[0])\n\nresults = {\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(bhat, 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\": data_issues,\n \"n_input_rows\": {\"design.csv\": n_rows},\n \"random_seed\": SEED,\n # supplementary diagnostics\n \"t_critical_28\": float(tcrit),\n \"mcse_coverage_conventional\": float(np.sqrt(cov_conv * (1 - cov_conv) / R)),\n \"mcse_coverage_hc1\": float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R)),\n \"mcse_at_nominal_095\": mcse_nominal,\n \"undercoverage_threshold\": float(LEVEL - 3 * mcse_nominal),\n \"mean_se_hc1\": float(np.mean(se_hc1)),\n \"mean_beta_hat\": float(np.mean(bhat)),\n \"expected_se_conv_sq_exact\": float(XtX_inv[1, 1] * np.sum(sig ** 2 * (1 - np.diag(X @ XtX_inv @ X.T))) / df),\n}\nos.makedirs(\"out\", exist_ok=True)\nwith open(\"out/results.json\", \"w\") as f:\n json.dump(results, f, indent=2)\nprint(json.dumps(results, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis 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n))\nY = ALPHA + BETA * x[None, :] + sig[None, :] * eps\nX = np.column_stack([np.ones(n), x])\nXtX_inv = np.linalg.inv(X.T @ X)\nB = Y @ (XtX_inv @ X.T).T # R x 2 coefficients\nresid = Y - B @ X.T # R x n\ns2 = np.sum(resid ** 2, axis=1) / df\nse_conv = np.sqrt(s2 * XtX_inv[1, 1])\n# HC0 slope variance: sum (a_i^2 e_i^2), a = row 2 of (X'X)^-1 X' (equals w_i)\na = (XtX_inv @ X.T)[1]\nvar_hc0 = np.sum((a[None, :] ** 2) * resid ** 2, axis=1)\nse_hc1 = np.sqrt(var_hc0 * n / df)\nbhat = B[:, 1]\n\ncov_conv = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_conv))\ncov_hc1 = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_hc1))\nmcse_nominal = float(np.sqrt(LEVEL * (1 - LEVEL) / R))\nundercovers = bool(cov_conv < LEVEL - 3 * mcse_nominal)\n\n# Cross-check against statsmodels on replication 0\nimport statsmodels.api as sm\nm0 = sm.OLS(Y[0], X).fit()\nassert np.isclose(m0.bse[1], se_conv[0]) and np.isclose(m0.get_robustcov_results(\"HC1\").bse[1], se_hc1[0])\n\nresults = {\n \"task_id\": 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/Users/simon-pierreboucher/wp29/runs/RC0054 && cat > out/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\nReads only data/design.csv; writes out/results.json deterministically.\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\nfrom scipy import stats\nimport statsmodels.api as sm\n\nSEED = 20261030\nR = 2000\nALPHA, BETA = 1.0, 0.5\nLEVEL = 0.95\n\nd = pd.read_csv(\"data/design.csv\")\nn_rows = int(len(d))\ndata_issues = []\nassert n_rows == 30 and d[[\"x\", \"sigma\"]].notna().all().all() and (d.sigma > 0).all()\nx = d[\"x\"].to_numpy(float)\nsig = d[\"sigma\"].to_numpy(float)\nn = len(x)\ndf = n - 2\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, df)\n\n# (c) exact SD of betahat: betahat - beta = sum w_i sigma_i eps_i, w_i = (x_i - xbar)/Sxx\nxc = x - x.mean()\nSxx = np.sum(xc ** 2)\nw = xc / Sxx\nsd_exact = float(np.sqrt(np.sum(w ** 2 * sig ** 2)))\n\n# Monte Carlo (only eps redrawn; x, sigma fixed)\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x[None, :] + sig[None, :] * eps\nX = np.column_stack([np.ones(n), x])\nXtX_inv = np.linalg.inv(X.T @ X)\nP = XtX_inv @ X.T # 2 x n\nB = Y @ P.T # R x 2 coefficients\nresid = Y - B @ X.T # R x n\ns2 = np.sum(resid ** 2, axis=1) / df\nse_conv = np.sqrt(s2 * XtX_inv[1, 1])\na = P[1] # slope row of (X'X)^-1 X'\nvar_hc0 = np.sum((a[None, :] ** 2) * resid ** 2, axis=1)\nse_hc1 = np.sqrt(var_hc0 * n / df)\nbhat = B[:, 1]\n\ncov_conv = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_conv))\ncov_hc1 = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_hc1))\nmcse_nominal = float(np.sqrt(LEVEL * (1 - LEVEL) / R))\nundercovers = bool(cov_conv < LEVEL - 3 * mcse_nominal)\n\n# Cross-check against statsmodels on replication 0\nm0 = sm.OLS(Y[0], X).fit()\nassert np.isclose(m0.bse[1], se_conv[0])\nassert np.isclose(m0.get_robustcov_results(\"HC1\").bse[1], se_hc1[0])\nassert np.isclose(np.sqrt(np.sum(a ** 2 * sig ** 2)), sd_exact)\n\nH = np.diag(X @ XtX_inv @ X.T)\nresults = {\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(bhat, 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\": data_issues,\n \"n_input_rows\": {\"design.csv\": n_rows},\n \"random_seed\": SEED,\n # supplementary diagnostics\n \"t_critical_28\": float(tcrit),\n \"mcse_coverage_conventional\": float(np.sqrt(cov_conv * (1 - cov_conv) / R)),\n \"mcse_coverage_hc1\": float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R)),\n \"mcse_at_nominal_095\": mcse_nominal,\n \"undercoverage_threshold\": float(LEVEL - 3 * mcse_nominal),\n \"mean_se_hc1\": float(np.mean(se_hc1)),\n \"mean_beta_hat\": float(np.mean(bhat)),\n \"sd_se_conventional_mc\": float(np.std(se_conv, ddof=1)),\n \"sqrt_expected_se_conv_sq_exact\": float(np.sqrt(XtX_inv[1, 1] * np.sum(sig ** 2 * (1 - H)) / df)),\n}\nos.makedirs(\"out\", exist_ok=True)\nwith open(\"out/results.json\", \"w\") as f:\n json.dump(results, f, indent=2)\nprint(json.dumps(results, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis 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\"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_095\": 0.004873397172404485,\n \"undercoverage_threshold\": 0.9353798084827865,\n \"mean_se_hc1\": 0.24080977065103962,\n \"mean_beta_hat\": 0.4961965063446237,\n \"sd_se_conventional_mc\": 0.031210119871760807,\n \"sqrt_expected_se_conv_sq_exact\": 0.19318017740129875\n}","is_error":false}]},"uuid":"52d57be9-ab58-46ac-8940-8ba3702e3a5f","timestamp":"2026-10-30T04:16:31.100Z","toolUseResult":{"stdout":"{\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_095\": 0.004873397172404485,\n \"undercoverage_threshold\": 0.9353798084827865,\n \"mean_se_hc1\": 0.24080977065103962,\n \"mean_beta_hat\": 0.4961965063446237,\n \"sd_se_conventional_mc\": 0.031210119871760807,\n \"sqrt_expected_se_conv_sq_exact\": 0.19318017740129875\n}","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"b068f4fe-e93d-49eb-9713-2da5f3be38e4","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}47{"type":"api-request-blob","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","hash":"8f24b89eba210b466caeaaf1a94e8252113095c0bd50d65ad4f22090d618d4d2","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_0165sYFPatkJSBvJ9DQYdpqg","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0054 && cat > out/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\nReads only data/design.csv; writes out/results.json deterministically.\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\nfrom scipy import stats\nimport statsmodels.api as sm\n\nSEED = 20261030\nR = 2000\nALPHA, BETA = 1.0, 0.5\nLEVEL = 0.95\n\nd = pd.read_csv(\"data/design.csv\")\nn_rows = int(len(d))\ndata_issues = []\nassert n_rows == 30 and d[[\"x\", \"sigma\"]].notna().all().all() and (d.sigma > 0).all()\nx = d[\"x\"].to_numpy(float)\nsig = d[\"sigma\"].to_numpy(float)\nn = len(x)\ndf = n - 2\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, df)\n\n# (c) exact SD of betahat: betahat - beta = sum w_i sigma_i eps_i, w_i = (x_i - xbar)/Sxx\nxc = x - x.mean()\nSxx = np.sum(xc ** 2)\nw = xc / Sxx\nsd_exact = float(np.sqrt(np.sum(w ** 2 * sig ** 2)))\n\n# Monte Carlo (only eps redrawn; x, sigma fixed)\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x[None, :] + sig[None, :] * eps\nX = np.column_stack([np.ones(n), x])\nXtX_inv = np.linalg.inv(X.T @ X)\nP = XtX_inv @ X.T # 2 x n\nB = Y @ P.T # R x 2 coefficients\nresid = Y - B @ X.T # R x n\ns2 = np.sum(resid ** 2, axis=1) / df\nse_conv = np.sqrt(s2 * XtX_inv[1, 1])\na = P[1] # slope row of (X'X)^-1 X'\nvar_hc0 = np.sum((a[None, :] ** 2) * resid ** 2, axis=1)\nse_hc1 = np.sqrt(var_hc0 * n / df)\nbhat = B[:, 1]\n\ncov_conv = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_conv))\ncov_hc1 = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_hc1))\nmcse_nominal = float(np.sqrt(LEVEL * (1 - LEVEL) / R))\nundercovers = bool(cov_conv < LEVEL - 3 * mcse_nominal)\n\n# Cross-check against statsmodels on replication 0\nm0 = sm.OLS(Y[0], X).fit()\nassert np.isclose(m0.bse[1], se_conv[0])\nassert np.isclose(m0.get_robustcov_results(\"HC1\").bse[1], se_hc1[0])\nassert np.isclose(np.sqrt(np.sum(a ** 2 * sig ** 2)), sd_exact)\n\nH = np.diag(X @ XtX_inv @ X.T)\nresults = {\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(bhat, 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\": data_issues,\n \"n_input_rows\": {\"design.csv\": n_rows},\n \"random_seed\": SEED,\n # supplementary diagnostics\n \"t_critical_28\": float(tcrit),\n \"mcse_coverage_conventional\": float(np.sqrt(cov_conv * (1 - cov_conv) / R)),\n \"mcse_coverage_hc1\": float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R)),\n \"mcse_at_nominal_095\": mcse_nominal,\n \"undercoverage_threshold\": float(LEVEL - 3 * mcse_nominal),\n \"mean_se_hc1\": float(np.mean(se_hc1)),\n \"mean_beta_hat\": float(np.mean(bhat)),\n \"sd_se_conventional_mc\": float(np.std(se_conv, ddof=1)),\n \"sqrt_expected_se_conv_sq_exact\": float(np.sqrt(XtX_inv[1, 1] * np.sum(sig ** 2 * (1 - H)) / df)),\n}\nos.makedirs(\"out\", exist_ok=True)\nwith open(\"out/results.json\", \"w\") as f:\n json.dump(results, f, indent=2)\nprint(json.dumps(results, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis 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vs exact sd z-ish 0.39327452124298634\nmean bhat z -0.6347377827316656\nmean se_conv vs sqrt E se^2 0.1902623101215266 0.19318017740129875\ncov in [0,1] True True\nundercover logic True True","is_error":false}]},"uuid":"9b56fd7e-6345-452d-b4fb-b3bbc78ac1eb","timestamp":"2026-10-30T04:16:36.993Z","toolUseResult":{"stdout":"IDENTICAL\nmc vs exact sd z-ish 0.39327452124298634\nmean bhat z -0.6347377827316656\nmean se_conv vs sqrt E se^2 0.1902623101215266 0.19318017740129875\ncov in [0,1] True True\nundercover logic True 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consistency"}}]}}53{"type":"api-request","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","id":"5d4e85cb-a486-4a1c-b8ed-bd28be040b5a","timestamp":"2026-10-30T04:16:36.996Z","version":"2.1.314","querySource":"sdk","shapeHash":"aa57bdbb1073466ded2da08e0f587c11ec83cb89d43e91439134bd37ac4c0122","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":"3ea034fe-6192-45c9-89a7-988a6003177e","keep":16,"tail":["387eb50c84799636bfeb52f6896da4d16202ee351e12d642bd5a138f4a1469d2","3e09be401830f2e56b9364ffd99702f255bd1d3a29c8aef5693c0d15e0ea8cae"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",17,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"8e757916c9b99160c6ba4ca9bc4e8989c8abbaafbf49642fbbeeab878312d4ae"}54{"parentUuid":"9b56fd7e-6345-452d-b4fb-b3bbc78ac1eb","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmufrNnEwGe1tCqfR6z","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":2,"cache_creation_input_tokens":606,"cache_read_input_tokens":14414,"output_tokens":1176,"output_tokens_details":{"thinking_tokens":42},"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":606},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":288,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmufZGbusFRz3ADBb2Q","requestRef":"5d4e85cb-a486-4a1c-b8ed-bd28be040b5a","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"ecbf4ef6-c323-470d-96a0-eee57a067c50","timestamp":"2026-10-30T04:16:38.541Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}55{"parentUuid":"ecbf4ef6-c323-470d-96a0-eee57a067c50","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmufrNnEwGe1tCqfR6z","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01RDc16axQzETxukHFo8eMr1","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Clean re-run: deleted out/results.json, re-ran out/analysis.py → byte-identical (cmp). PASS\n2. statsmodels cross-check (asserted in script): conventional and HC1 slope SE for replication 0 match statsmodels OLS / HC1. PASS\n3. Exact SD identity: sqrt(sum a_i^2 sigma_i^2) with a = slope row of (X'X)^-1X' equals sqrt(sum w_i^2 sigma_i^2). PASS (assert)\n4. sd_beta_mc (0.26965) vs sd_beta_exact (0.26798): difference ≈ 0.39 approximate SEs of an SD estimate (sd/sqrt(2(R-1))). PASS\n5. mean_beta_hat (0.4962) vs beta 0.5: z ≈ -0.63 (unbiasedness). PASS\n6. mean_se_conventional (0.19026) ≤ sqrt(E[se_conv^2]) exact (0.19318), as Jensen requires; both well below sd_beta_exact → conventional SE is downward biased. PASS\n7. Coverages in [0,1]; all positive keys (sd_beta_exact, sd_beta_mc, mean_se_conventional) > 0. PASS\n8. Undercoverage flag: 0.844 < threshold 0.95 − 3·0.004873 = 0.93538 → true; flag equals rule. PASS\n9. Counts: n_input_rows 30 = n analysed 30 per replication; exclusions ledger removes 0. R = 2000. PASS\n10. Baseline comparison: HC1 coverage (0.902) > conventional (0.844), consistent with mean_se_hc1 (0.2408) being closer to sd_beta_exact than mean_se_conventional. PASS\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P1']={\"status\":\"passed\",\"checks\":[\"sha256 matches bundle\",\"30x3, no NA, no dups, sigma>0\",\"exclusions.csv written (0 removed)\"],\"notes\":\"\"}\np['P2']={\"status\":\"passed\",\"checks\":[\"naive baseline coverage_conventional computed = 0.844 with same evaluation rule\"],\"notes\":\"task defines conventional CI as baseline\"}\np['P3']={\"status\":\"passed\",\"checks\":[\"analysis.py runs, seed 20261030 recorded\",\"statsmodels cross-check asserts pass\"],\"notes\":\"\"}\np['P4']={\"status\":\"running\",\"checks\":[\"clean re-run byte-identical\",\"checks.md items 1-10 PASS\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P2, P3 passed (cov_conv 0.844, cov_hc1 0.902). P4 checks done; running gate.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Record checks and run gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":606,"cache_read_input_tokens":14414,"output_tokens":1176,"output_tokens_details":{"thinking_tokens":42},"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":606},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmufZGbusFRz3ADBb2Q","requestRef":"5d4e85cb-a486-4a1c-b8ed-bd28be040b5a","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"687f725c-e0aa-4807-a0fe-545a8331aca6","timestamp":"2026-10-30T04:16:47.041Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}56{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"687f725c-e0aa-4807-a0fe-545a8331aca6","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167"}57{"type":"atis-latch","atis":"","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167"}58{"parentUuid":"687f725c-e0aa-4807-a0fe-545a8331aca6","isSidechain":false,"promptId":"1aebd786-e531-4647-a9e1-ba1578700938","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 1\nPGAR GATE pgar_gate/1.0 — FAILED (10 of 32 checks failed)\n [ok] file:out/results.json: present\n [FAIL] file:out/report.md: missing or empty\n [ok] file:out/analysis.py: present\n [FAIL] file:out/claims.json: missing or empty\n [ok] results_json: parsed\n [ok] key:task_id: ok\n [ok] key:coverage_conventional: ok\n [ok] key:coverage_hc1: ok\n [ok] key:sd_beta_exact: ok\n [ok] key:sd_beta_mc: ok\n [ok] key:mean_se_conventional: ok\n [ok] key:conventional_ci_undercovers: ok\n [ok] key:n_replications: ok\n [ok] key:n_obs_per_replication: ok\n [ok] key:feasibility: ok\n [ok] key:feasibility_reason: ok\n [ok] key:data_issues: ok\n [ok] key:n_input_rows: ok\n [ok] key:random_seed: ok\n [FAIL] section:Question: heading not found\n [FAIL] section:Data and exclusions: heading not found\n [FAIL] section:Method: heading not found\n [FAIL] section:Results: heading not found\n [FAIL] section:Uncertainty: heading not found\n [FAIL] section:Limitations and open issues: heading not found\n [FAIL] claims_json: out/claims.json missing\n [FAIL] phase_ledger: phases not terminal: ['P4', 'P5']\n [ok] exclusion_ledger: 1 steps consistent\n [ok] positive:sd_beta_exact: 0.2679805928302833\n [ok] positive:sd_beta_mc: 0.2696473708309126\n [ok] positive:mean_se_conventional: 0.1902623101215266\n [ok] reproducibility: regenerated in 0.9s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0054/out/state/gate_receipts/20261030T041648.056767Z.json","is_error":true,"tool_use_id":"toolu_01RDc16axQzETxukHFo8eMr1"}]},"uuid":"a73e66cc-c896-4eac-8433-9200c197524f","timestamp":"2026-10-30T04:16:48.065Z","toolUseResult":"Error: Exit code 1\nPGAR GATE pgar_gate/1.0 — FAILED (10 of 32 checks failed)\n [ok] file:out/results.json: present\n [FAIL] file:out/report.md: missing or empty\n [ok] file:out/analysis.py: present\n [FAIL] file:out/claims.json: missing or empty\n [ok] results_json: parsed\n [ok] key:task_id: ok\n [ok] key:coverage_conventional: ok\n [ok] key:coverage_hc1: ok\n [ok] key:sd_beta_exact: ok\n [ok] key:sd_beta_mc: ok\n [ok] key:mean_se_conventional: ok\n [ok] key:conventional_ci_undercovers: ok\n [ok] key:n_replications: ok\n [ok] key:n_obs_per_replication: ok\n [ok] key:feasibility: ok\n [ok] key:feasibility_reason: ok\n [ok] key:data_issues: ok\n [ok] key:n_input_rows: ok\n [ok] key:random_seed: ok\n [FAIL] section:Question: heading not found\n [FAIL] section:Data and exclusions: heading not found\n [FAIL] section:Method: heading not found\n [FAIL] section:Results: heading not found\n [FAIL] section:Uncertainty: heading not found\n [FAIL] section:Limitations and open issues: heading not found\n [FAIL] claims_json: out/claims.json missing\n [FAIL] phase_ledger: phases not terminal: ['P4', 'P5']\n [ok] exclusion_ledger: 1 steps consistent\n [ok] positive:sd_beta_exact: 0.2679805928302833\n [ok] positive:sd_beta_mc: 0.2696473708309126\n [ok] positive:mean_se_conventional: 0.1902623101215266\n [ok] reproducibility: regenerated in 0.9s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0054/out/state/gate_receipts/20261030T041648.056767Z.json","sandboxed":false,"sourceToolAssistantUUID":"687f725c-e0aa-4807-a0fe-545a8331aca6","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}59{"type":"api-request-blob","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","hash":"7814cd2824d6aceee6981ef96f14d8458761db4eaa056dd8970d8431d04fe39a","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01RDc16axQzETxukHFo8eMr1","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Clean re-run: deleted out/results.json, re-ran out/analysis.py → byte-identical (cmp). PASS\n2. statsmodels cross-check (asserted in script): conventional and HC1 slope SE for replication 0 match statsmodels OLS / HC1. PASS\n3. Exact SD identity: sqrt(sum a_i^2 sigma_i^2) with a = slope row of (X'X)^-1X' equals sqrt(sum w_i^2 sigma_i^2). PASS (assert)\n4. sd_beta_mc (0.26965) vs sd_beta_exact (0.26798): difference ≈ 0.39 approximate SEs of an SD estimate (sd/sqrt(2(R-1))). PASS\n5. mean_beta_hat (0.4962) vs beta 0.5: z ≈ -0.63 (unbiasedness). PASS\n6. mean_se_conventional (0.19026) ≤ sqrt(E[se_conv^2]) exact (0.19318), as Jensen requires; both well below sd_beta_exact → conventional SE is downward biased. PASS\n7. Coverages in [0,1]; all positive keys (sd_beta_exact, sd_beta_mc, mean_se_conventional) > 0. PASS\n8. Undercoverage flag: 0.844 < threshold 0.95 − 3·0.004873 = 0.93538 → true; flag equals rule. PASS\n9. Counts: n_input_rows 30 = n analysed 30 per replication; exclusions ledger removes 0. R = 2000. PASS\n10. Baseline comparison: HC1 coverage (0.902) > conventional (0.844), consistent with mean_se_hc1 (0.2408) being closer to sd_beta_exact than mean_se_conventional. PASS\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P1']={\"status\":\"passed\",\"checks\":[\"sha256 matches bundle\",\"30x3, no NA, no dups, sigma>0\",\"exclusions.csv written (0 removed)\"],\"notes\":\"\"}\np['P2']={\"status\":\"passed\",\"checks\":[\"naive baseline coverage_conventional computed = 0.844 with same evaluation rule\"],\"notes\":\"task defines conventional CI as baseline\"}\np['P3']={\"status\":\"passed\",\"checks\":[\"analysis.py runs, seed 20261030 recorded\",\"statsmodels cross-check asserts pass\"],\"notes\":\"\"}\np['P4']={\"status\":\"running\",\"checks\":[\"clean re-run byte-identical\",\"checks.md items 1-10 PASS\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P2, P3 passed (cov_conv 0.844, cov_hc1 0.902). P4 checks done; running gate.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Record checks and run gate"}}]}}60{"type":"api-request","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","id":"42ec4c91-fe4b-445f-8b26-fc1a48efd284","timestamp":"2026-10-30T04:16:48.070Z","version":"2.1.314","querySource":"sdk","shapeHash":"aa57bdbb1073466ded2da08e0f587c11ec83cb89d43e91439134bd37ac4c0122","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":"5d4e85cb-a486-4a1c-b8ed-bd28be040b5a","keep":18,"tail":["7814cd2824d6aceee6981ef96f14d8458761db4eaa056dd8970d8431d04fe39a","4aecf25633ee0c62f07952f1ac7281eee4b872852d7409ef94c8c1939954b7e9"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",19,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"ca1b2e67f823105dcccb18d234a59067c29c1a65b1f82add9738829a911031e6"}61{"parentUuid":"a73e66cc-c896-4eac-8433-9200c197524f","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmvVAioqCU4D6NY8daX","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":2,"cache_creation_input_tokens":1920,"cache_read_input_tokens":15020,"output_tokens":3066,"output_tokens_details":{"thinking_tokens":57},"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":1920},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":876,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmvUtbo6Yj6WVqNohmv","requestRef":"42ec4c91-fe4b-445f-8b26-fc1a48efd284","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"e97d02dd-4505-495b-b09b-6af3136c6721","timestamp":"2026-10-30T04:16:50.458Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}62{"parentUuid":"e97d02dd-4505-495b-b09b-6af3136c6721","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmvVAioqCU4D6NY8daX","type":"message","role":"assistant","content":[{"type":"text","text":"The P4 gate run passes every check that belongs to P4 (keys, positivity, exclusion ledger, reproducibility). The remaining failures are the P5 deliverables, which I write next."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1920,"cache_read_input_tokens":15020,"output_tokens":3066,"output_tokens_details":{"thinking_tokens":57},"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":1920},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmvUtbo6Yj6WVqNohmv","requestRef":"42ec4c91-fe4b-445f-8b26-fc1a48efd284","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6570ccbc-9499-47f4-9eb0-2bc23eba093f","timestamp":"2026-10-30T04:16:50.458Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}63{"parentUuid":"6570ccbc-9499-47f4-9eb0-2bc23eba093f","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmvVAioqCU4D6NY8daX","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01M4wqjV2TQVgpT8Tx7NDqVC","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F2-conf-03 — Coverage of OLS slope CIs in a small heteroskedastic fixed design\n\n## Question\nIn the fixed design y_i = 1 + 0.5 x_i + σ_i ε_i (n = 30, ε_i iid N(0,1), x_i and σ_i taken from `data/design.csv`), how often do nominal 95% intervals β̂ ± t_{0.975}(28)·se cover β = 0.5 when se is (a) the conventional OLS SE or (b) the HC1 robust SE? Also: (c) the exact SD of β̂ and (d) E[se_conv]. Does the conventional interval attain nominal coverage?\n\n## Data and exclusions\nOne input, `data/design.csv` (SHA-256 b1a17a52…e74f0), 30 rows (`n_input_rows`), columns i, x, σ. No missing values, duplicates or invalid σ; `data_issues` is empty and no rows were excluded (`out/exclusions.csv`: 30 → 30). σ_i rises with |x_i| (it is almost exactly a function of x²), so the noise is largest at the high-leverage design points. This pattern makes the conventional SE too small. Full audit: `out/state/data_audit.md`.\n\n## Method\n- Exact SD (c): β̂ − β = Σ w_i σ_i ε_i with w_i = (x_i − x̄)/Σ(x_j − x̄)², so SD(β̂) = sqrt(Σ w_i² σ_i²). No simulation is used.\n- Monte Carlo: R = 2000 replications (`n_replications`), n = 30 (`n_obs_per_replication`). In each replication only ε is redrawn (numpy `default_rng`, seed `random_seed` = 20261030). Each replication fits OLS and computes se_conv = sqrt(s²·[(X'X)⁻¹]₂₂) with s² = RSS/28, and se_HC1 = sqrt(30/28 · Σ a_i² e_i²), where a is the slope row of (X'X)⁻¹X'. The critical value is t_{0.975}(28) = 2.0484 (`t_critical_28`). Coverage is the share of replications with |β̂ − 0.5| ≤ t·se.\n- Decision rule: `conventional_ci_undercovers` is true iff the conventional coverage is below 0.95 − 3·sqrt(0.95·0.05/2000) = 0.9354 (`undercoverage_threshold`).\n- For replication 1, statsmodels gives the same conventional and HC1 SEs as the script (asserted in `out/analysis.py`).\n\n## Results\n| quantity | value | key |\n|---|---|---|\n| Coverage, conventional CI (naïve baseline) | 0.844 | `coverage_conventional` |\n| Coverage, HC1 CI | 0.902 | `coverage_hc1` |\n| Exact SD of β̂ | 0.2680 | `sd_beta_exact` |\n| MC SD of β̂ | 0.2696 | `sd_beta_mc` |\n| Mean se_conv | 0.1903 | `mean_se_conventional` |\n| Mean se_HC1 | 0.2408 | `mean_se_hc1` |\n| Mean β̂ | 0.4962 | `mean_beta_hat` |\n| Conventional CI undercovers? | true | `conventional_ci_undercovers` |\n\nThe conventional interval does **not** reach its nominal 95% coverage. Its estimated coverage of 0.844 (`coverage_conventional`) is far below the 0.9354 threshold (`undercoverage_threshold`). The cause is visible in the SEs: on average se_conv is 0.190 (`mean_se_conventional`), about 29% below the true SD of 0.268 (`sd_beta_exact`). As a check, the exact value of sqrt(E[se_conv²]) is 0.193 (`sqrt_expected_se_conv_sq_exact`), in line with the MC mean. HC1 does much better, at 0.902 (`coverage_hc1`), but it still falls short of 95% at n = 30: its average SE of 0.241 (`mean_se_hc1`) is still below the true SD. The MC SD of β̂ agrees with the exact value (`sd_beta_mc` vs `sd_beta_exact`), and β̂ is unbiased (`mean_beta_hat`).\n\n## Uncertainty\nBinomial Monte Carlo standard errors with R = 2000:\n- conventional coverage: 0.0081 (`mcse_coverage_conventional`), giving an approximate 95% MC interval of 0.828–0.860;\n- HC1 coverage: 0.0066 (`mcse_coverage_hc1`), giving an approximate 95% MC interval of 0.889–0.915;\n- MC SE at the nominal level 0.95: 0.0049 (`mcse_at_nominal_095`).\nThe conventional shortfall is 0.106, which is about 22 nominal MC SEs, so the undercoverage verdict does not depend on simulation noise. HC1's shortfall of 0.048 is also many MC SEs, so HC1 undercovers here as well. That statement goes beyond the required outputs and was not tested with a formal rule. sd_beta_exact is analytical and has no MC error.\n\n## Limitations and open issues\n- The results are specific to this one fixed design and to normal errors. With a different design or error distribution, coverage would differ.\n- Only the HC1 robust interval is assessed. Small-sample variants (HC2, HC3, wild bootstrap) were not studied because the task did not ask for them.\n- The coverage estimates depend on the seed (20261030) only through MC error, which is quantified above.\n- No part of the task was infeasible (`feasibility` = \"complete\").\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The conventional nominal 95% OLS interval does not attain nominal coverage: estimated coverage 0.844, below 0.95 by more than three binomial MC standard errors.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"undercoverage_threshold\",\"mcse_coverage_conventional\"],\"status\":\"supported\",\"caveat\":\"Specific to this fixed design, normal errors, R=2000 and seed 20261030.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval covers much better (0.902) but remains below 95% at n=30.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\"],\"status\":\"supported\",\"caveat\":\"No formal threshold test was required for HC1; the shortfall is many MC SEs.\"},\n {\"id\":\"C3\",\"text\":\"The conventional SE is downward biased: mean se_conv 0.190 vs exact SD of beta-hat 0.268.\",\"results_keys\":[\"mean_se_conventional\",\"sd_beta_exact\",\"sqrt_expected_se_conv_sq_exact\"],\"status\":\"supported\",\"caveat\":\"mean_se_conventional is a MC estimate.\"},\n {\"id\":\"C4\",\"text\":\"The Monte Carlo SD of beta-hat (0.2696) agrees with the analytical exact SD (0.2680).\",\"results_keys\":[\"sd_beta_mc\",\"sd_beta_exact\"],\"status\":\"supported\",\"caveat\":\"Agreement within MC error of an SD estimate (~0.4 SE).\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json,glob\np=json.load(open('out/state/phases.json'))\nr=sorted(glob.glob('out/state/gate_receipts/*.json'))\np['P4']={\"status\":\"passed\",\"checks\":p['P4']['checks']+[f\"gate run {r[-1]}: all results/reproducibility/positivity/exclusion checks ok; only failures were P5 deliverables (report, claims) not yet written and non-terminal phases\"],\"notes\":\"\"}\np['P5']={\"status\":\"passed\",\"checks\":[\"report.md written with 6 sections citing keys\",\"claims.json written (4 claims incl. nominal coverage claim)\",\"final gate run recorded below\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P4 passed; P5 report and claims written; final gate run.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Write report, claims, update ledger, run gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1920,"cache_read_input_tokens":15020,"output_tokens":3066,"output_tokens_details":{"thinking_tokens":57},"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":1920},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXmvUtbo6Yj6WVqNohmv","requestRef":"42ec4c91-fe4b-445f-8b26-fc1a48efd284","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"ccc30d07-54db-448b-9f77-669c227dc0fe","timestamp":"2026-10-30T04:17:13.935Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}64{"parentUuid":"ccc30d07-54db-448b-9f77-669c227dc0fe","isSidechain":false,"promptId":"1aebd786-e531-4647-a9e1-ba1578700938","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01M4wqjV2TQVgpT8Tx7NDqVC","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 32 checks failed)\n [ok] file:out/results.json: present\n [ok] file:out/report.md: present\n [ok] file:out/analysis.py: present\n [ok] file:out/claims.json: present\n [ok] results_json: parsed\n [ok] key:task_id: ok\n [ok] key:coverage_conventional: ok\n [ok] key:coverage_hc1: ok\n [ok] key:sd_beta_exact: ok\n [ok] key:sd_beta_mc: ok\n [ok] key:mean_se_conventional: ok\n [ok] key:conventional_ci_undercovers: ok\n [ok] key:n_replications: ok\n [ok] key:n_obs_per_replication: ok\n [ok] key:feasibility: ok\n [ok] key:feasibility_reason: ok\n [ok] key:data_issues: ok\n [ok] key:n_input_rows: ok\n [ok] key:random_seed: ok\n [ok] section:Question: present\n [ok] section:Data and exclusions: present\n [ok] section:Method: present\n [ok] section:Results: present\n [ok] section:Uncertainty: present\n [ok] section:Limitations and open issues: present\n [ok] claims_json: 4 claims, all keys resolve\n [ok] phase_ledger: consistent\n [ok] exclusion_ledger: 1 steps consistent\n [ok] positive:sd_beta_exact: 0.2679805928302833\n [ok] positive:sd_beta_mc: 0.2696473708309126\n [ok] positive:mean_se_conventional: 0.1902623101215266\n [ok] reproducibility: regenerated in 0.9s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0054/out/state/gate_receipts/20261030T041714.943382Z.json","is_error":false}]},"uuid":"5e202e1c-6d03-4f05-88ec-9303213ee3a0","timestamp":"2026-10-30T04:17:14.951Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 32 checks failed)\n [ok] file:out/results.json: present\n [ok] file:out/report.md: present\n [ok] file:out/analysis.py: present\n [ok] file:out/claims.json: present\n [ok] results_json: parsed\n [ok] key:task_id: ok\n [ok] key:coverage_conventional: ok\n [ok] key:coverage_hc1: ok\n [ok] key:sd_beta_exact: ok\n [ok] key:sd_beta_mc: ok\n [ok] key:mean_se_conventional: ok\n [ok] key:conventional_ci_undercovers: ok\n [ok] key:n_replications: ok\n [ok] key:n_obs_per_replication: ok\n [ok] key:feasibility: ok\n [ok] key:feasibility_reason: ok\n [ok] key:data_issues: ok\n [ok] key:n_input_rows: ok\n [ok] key:random_seed: ok\n [ok] section:Question: present\n [ok] section:Data and exclusions: present\n [ok] section:Method: present\n [ok] section:Results: present\n [ok] section:Uncertainty: present\n [ok] section:Limitations and open issues: present\n [ok] claims_json: 4 claims, all keys resolve\n [ok] phase_ledger: consistent\n [ok] exclusion_ledger: 1 steps consistent\n [ok] positive:sd_beta_exact: 0.2679805928302833\n [ok] positive:sd_beta_mc: 0.2696473708309126\n [ok] positive:mean_se_conventional: 0.1902623101215266\n [ok] reproducibility: regenerated in 0.9s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0054/out/state/gate_receipts/20261030T041714.943382Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"ccc30d07-54db-448b-9f77-669c227dc0fe","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0054","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","version":"2.1.314","gitBranch":"HEAD"}65{"type":"api-request-blob","sessionId":"58a1d6e7-5814-47a3-8350-78d2614a1167","hash":"c54aa8ec09da9a861e717c4f9bdc8861ec0ceb6b5e758ce2c2e8b98a5f5010b8","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"The P4 gate run passes every check that belongs to P4 (keys, positivity, exclusion ledger, reproducibility). The remaining failures are the P5 deliverables, which I write next."},{"type":"tool_use","id":"toolu_01M4wqjV2TQVgpT8Tx7NDqVC","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F2-conf-03 — Coverage of OLS slope CIs in a small heteroskedastic fixed design\n\n## Question\nIn the fixed design y_i = 1 + 0.5 x_i + σ_i ε_i (n = 30, ε_i iid N(0,1), x_i and σ_i taken from `data/design.csv`), how often do nominal 95% intervals β̂ ± t_{0.975}(28)·se cover β = 0.5 when se is (a) the conventional OLS SE or (b) the HC1 robust SE? Also: (c) the exact SD of β̂ and (d) E[se_conv]. Does the conventional interval attain nominal coverage?\n\n## Data and exclusions\nOne input, `data/design.csv` (SHA-256 b1a17a52…e74f0), 30 rows (`n_input_rows`), columns i, x, σ. No missing values, duplicates or invalid σ; `data_issues` is empty and no rows were excluded (`out/exclusions.csv`: 30 → 30). σ_i rises with |x_i| (it is almost exactly a function of x²), so the noise is largest at the high-leverage design points. This pattern makes the conventional SE too small. Full audit: `out/state/data_audit.md`.\n\n## Method\n- Exact SD (c): β̂ − β = Σ w_i σ_i ε_i with w_i = (x_i − x̄)/Σ(x_j − x̄)², so SD(β̂) = sqrt(Σ w_i² σ_i²). No simulation is used.\n- Monte Carlo: R = 2000 replications (`n_replications`), n = 30 (`n_obs_per_replication`). In each replication only ε is redrawn (numpy `default_rng`, seed `random_seed` = 20261030). Each replication fits OLS and computes se_conv = sqrt(s²·[(X'X)⁻¹]₂₂) with s² = RSS/28, and se_HC1 = sqrt(30/28 · Σ a_i² e_i²), where a is the slope row of (X'X)⁻¹X'. The critical value is t_{0.975}(28) = 2.0484 (`t_critical_28`). Coverage is the share of replications with |β̂ − 0.5| ≤ t·se.\n- Decision rule: `conventional_ci_undercovers` is true iff the conventional coverage is below 0.95 − 3·sqrt(0.95·0.05/2000) = 0.9354 (`undercoverage_threshold`).\n- For replication 1, statsmodels gives the same conventional and HC1 SEs as the script (asserted in `out/analysis.py`).\n\n## Results\n| quantity | value | key |\n|---|---|---|\n| Coverage, conventional CI (naïve baseline) | 0.844 | `coverage_conventional` |\n| Coverage, HC1 CI | 0.902 | `coverage_hc1` |\n| Exact SD of β̂ | 0.2680 | `sd_beta_exact` |\n| MC SD of β̂ | 0.2696 | `sd_beta_mc` |\n| Mean se_conv | 0.1903 | `mean_se_conventional` |\n| Mean se_HC1 | 0.2408 | `mean_se_hc1` |\n| Mean β̂ | 0.4962 | `mean_beta_hat` |\n| Conventional CI undercovers? | true | `conventional_ci_undercovers` |\n\nThe conventional interval does **not** reach its nominal 95% coverage. Its estimated coverage of 0.844 (`coverage_conventional`) is far below the 0.9354 threshold (`undercoverage_threshold`). The cause is visible in the SEs: on average se_conv is 0.190 (`mean_se_conventional`), about 29% below the true SD of 0.268 (`sd_beta_exact`). As a check, the exact value of sqrt(E[se_conv²]) is 0.193 (`sqrt_expected_se_conv_sq_exact`), in line with the MC mean. HC1 does much better, at 0.902 (`coverage_hc1`), but it still falls short of 95% at n = 30: its average SE of 0.241 (`mean_se_hc1`) is still below the true SD. The MC SD of β̂ agrees with the exact value (`sd_beta_mc` vs `sd_beta_exact`), and β̂ is unbiased (`mean_beta_hat`).\n\n## Uncertainty\nBinomial Monte Carlo standard errors with R = 2000:\n- conventional coverage: 0.0081 (`mcse_coverage_conventional`), giving an approximate 95% MC interval of 0.828–0.860;\n- HC1 coverage: 0.0066 (`mcse_coverage_hc1`), giving an approximate 95% MC interval of 0.889–0.915;\n- MC SE at the nominal level 0.95: 0.0049 (`mcse_at_nominal_095`).\nThe conventional shortfall is 0.106, which is about 22 nominal MC SEs, so the undercoverage verdict does not depend on simulation noise. HC1's shortfall of 0.048 is also many MC SEs, so HC1 undercovers here as well. That statement goes beyond the required outputs and was not tested with a formal rule. sd_beta_exact is analytical and has no MC error.\n\n## Limitations and open issues\n- The results are specific to this one fixed design and to normal errors. With a different design or error distribution, coverage would differ.\n- Only the HC1 robust interval is assessed. Small-sample variants (HC2, HC3, wild bootstrap) were not studied because the task did not ask for them.\n- The coverage estimates depend on the seed (20261030) only through MC error, which is quantified above.\n- No part of the task was infeasible (`feasibility` = \"complete\").\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The conventional nominal 95% OLS interval does not attain nominal coverage: estimated coverage 0.844, below 0.95 by more than three binomial MC standard errors.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"undercoverage_threshold\",\"mcse_coverage_conventional\"],\"status\":\"supported\",\"caveat\":\"Specific to this fixed design, normal errors, R=2000 and seed 20261030.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval covers much better (0.902) but remains below 95% at n=30.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\"],\"status\":\"supported\",\"caveat\":\"No formal threshold test was required for HC1; the shortfall is many MC SEs.\"},\n {\"id\":\"C3\",\"text\":\"The conventional SE is downward biased: mean se_conv 0.190 vs exact SD of beta-hat 0.268.\",\"results_keys\":[\"mean_se_conventional\",\"sd_beta_exact\",\"sqrt_expected_se_conv_sq_exact\"],\"status\":\"supported\",\"caveat\":\"mean_se_conventional is a MC estimate.\"},\n {\"id\":\"C4\",\"text\":\"The Monte Carlo SD of beta-hat (0.2696) agrees with the analytical exact SD (0.2680).\",\"results_keys\":[\"sd_beta_mc\",\"sd_beta_exact\"],\"status\":\"supported\",\"caveat\":\"Agreement within MC error of an SD estimate (~0.4 SE).\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json,glob\np=json.load(open('out/state/phases.json'))\nr=sorted(glob.glob('out/state/gate_receipts/*.json'))\np['P4']={\"status\":\"passed\",\"checks\":p['P4']['checks']+[f\"gate run {r[-1]}: all results/reproducibility/positivity/exclusion checks ok; only failures were P5 deliverables (report, claims) not yet written and non-terminal phases\"],\"notes\":\"\"}\np['P5']={\"status\":\"passed\",\"checks\":[\"report.md written with 6 sections citing keys\",\"claims.json written (4 claims incl. nominal coverage claim)\",\"final gate run recorded below\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P4 passed; 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Across the 2000 simulated samples it contained the true slope 84.4% of the time, against a cut-off of 93.5% (0.95 minus three Monte Carlo standard errors). The final gate run passed all 32 checks, and re-running `out/analysis.py` reproduces `out/results.json` exactly.\n\n| Quantity | Value | Monte Carlo standard error |\n|---|---|---|\n| Coverage, conventional interval | 0.844 | 0.0081 |\n| Coverage, robust (HC1) interval | 0.902 | 0.0066 |\n| Exact SD of the slope estimate (calculated, not simulated) | 0.2680 | – |\n| SD of the slope estimate across the simulations | 0.2696 | – |\n| Average conventional standard error | 0.1903 | – |\n\n- **Why the conventional interval fails:** its standard error averages 0.190, about 29% below the true spread of 0.268. 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