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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\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\nSEPARATE REVIEW (additional)\n- After the gate passes, a separate reviewer session that has not seen your work in progress will examine `TASK.md` and everything under `out/` and may return a list of issues (file `out/review/review.json`). You will then be resumed once to address them: fix what is justified, explain in `out/report.md` (Limitations and open issues) what you disagree with, re-run the gate, and update `out/claims.json` and `out/state/phases.json`. 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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.\nbundle.json\ndata\ngate_spec.json\nTASK.md\n\n./data:\ndesign.csv","is_error":true,"tool_use_id":"toolu_01HVjgbmRKTNSan2SF5FRAE9"}]},"uuid":"9959275c-2335-4846-a19d-e7bdbd572901","timestamp":"2026-10-30T04:14:54.753Z","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). 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question:** Do nominal 95% t-intervals for the OLS slope achieve 95% coverage in a fixed design (n=30) with heteroskedastic errors y_i = 1 + 0.5 x_i + sigma_i eps_i, eps_i iid N(0,1)?\n\n**Estimands** (conditional on the fixed x, sigma in data/design.csv; only eps redrawn):\n- (a) P(beta in beta_hat ± t_.975(28) se_conv), se_conv = conventional OLS SE with s^2 = RSS/(n-2). MC, R=2000.\n- (b) same with se_HC1 = sqrt(n/(n-2)) * HC0 sandwich SE. MC, R=2000.\n- (c) exact SD of beta_hat = sqrt(sum w_i^2 sigma_i^2), w_i = (x_i - xbar)/Sxx. Analytic.\n- (d) E[se_conv], MC average.\nMeaningful under model as stated (normal errors, known 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, n_replications, n_obs_per_replication, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed), out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues), out/analysis.py, out/claims.json.\nUndercovers flag: coverage_conventional < 0.95 - 3*sqrt(0.95*0.05/2000).\n\n**Information rules:** only data/design.csv plus given constants; do not redraw x or sigma.\n\n**Invalidity:** missing/malformed design (not 30 rows, non-positive sigma), wrong R, 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.describe()); print(d.isna().sum().sum(), d.duplicated().sum(), d.i.is_unique, (d.sigma>0).all())\nimport numpy as np; print(np.corrcoef(d.x**2,d.sigma**2))\"","description":"Write P0 files and audit data"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1169,"cache_read_input_tokens":6077,"output_tokens":1185,"output_tokens_details":{"thinking_tokens":80},"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":1169},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmnFTUwnA45rwF8p4Dg","requestRef":"daba3d71-90d1-4f12-aff0-77b0984958e4","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"67b1356a-e45f-4656-80bc-41cded3d63fa","timestamp":"2026-10-30T04:15:07.282Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}25{"parentUuid":"67b1356a-e45f-4656-80bc-41cded3d63fa","isSidechain":false,"promptId":"243b3c48-ceb9-4b7b-bf23-06d59c147137","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_013MBcZMNYGjrCQA7tZAQMAH","type":"tool_result","content":" 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\n[[1. 0.98667734]\n [0.98667734 1. ]]","is_error":false}]},"uuid":"b1676162-3774-49ce-9285-418fc99cfa08","timestamp":"2026-10-30T04:15:07.588Z","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\n[[1. 0.98667734]\n [0.98667734 1. ]]","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"67b1356a-e45f-4656-80bc-41cded3d63fa","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}26{"type":"api-request-blob","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","hash":"3d8e576ade3d90e544f7c7476ae0b7f14e6a9732968e4ceaed3456a948453e6a","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_013MBcZMNYGjrCQA7tZAQMAH","name":"Bash","input":{"command":"mkdir -p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question:** Do nominal 95% t-intervals for the OLS slope achieve 95% coverage in a fixed design (n=30) with heteroskedastic errors y_i = 1 + 0.5 x_i + sigma_i eps_i, eps_i iid N(0,1)?\n\n**Estimands** (conditional on the fixed x, sigma in data/design.csv; only eps redrawn):\n- (a) P(beta in beta_hat ± t_.975(28) se_conv), se_conv = conventional OLS SE with s^2 = RSS/(n-2). MC, R=2000.\n- (b) same with se_HC1 = sqrt(n/(n-2)) * HC0 sandwich SE. MC, R=2000.\n- (c) exact SD of beta_hat = sqrt(sum w_i^2 sigma_i^2), w_i = (x_i - xbar)/Sxx. 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Now the analysis script."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1374,"cache_read_input_tokens":7246,"output_tokens":2081,"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":1374},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXmo5JKos7xXA45yCReg","requestRef":"c461e644-7e58-4f44-b663-2ee151990326","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"397ee110-9253-4548-b824-12f944e63e08","timestamp":"2026-10-30T04:15:08.748Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}29{"parentUuid":"397ee110-9253-4548-b824-12f944e63e08","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmo5aStgjycVVxSxVn8","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01KYgmkQpBW4JrXQ8jHEzA6T","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n- File: data/design.csv, SHA-256 b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0\n- 30 rows x 3 columns: i (int, 1..30, unique), x (float, dimensionless, range -1.3942..1.9919, mean 0.2823), sigma (float, dimensionless, range 0.6034..1.7903, all > 0).\n- Missing values: 0. Duplicate rows: 0. No dates (not applicable).\n- Anomalies: none. Note: sigma^2 is strongly correlated with x^2 (r = 0.987), i.e. error variance is largest at high-leverage points -> the setting in which conventional SEs are expected to be biased downward. This is a design feature, not a data issue.\n- Information-availability: the only input is the permitted design file; no violations.\n- Exclusions: none (see out/exclusions.csv).\nEOF\ncat > out/exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n1,none (all design rows retained),30,30,0,design is complete and valid; task forbids altering x or sigma\nEOF\ncat > out/analysis.py <<'EOF'\n\"\"\"F2-conf-03: Monte Carlo coverage of OLS CIs under heteroskedasticity.\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\nSEED = 20261030\nALPHA, BETA, N, R, LEVEL = 1.0, 0.5, 30, 2000, 0.95\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\n# exact SD of beta_hat: beta_hat - beta = sum w_i sigma_i eps_i\nxc = x - x.mean(); Sxx = np.sum(xc**2); w = xc / Sxx\nsd_exact = float(np.sqrt(np.sum(w**2 * sig**2)))\n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, N))\nY = ALPHA + BETA * x[None, :] + sig[None, :] * eps\nybar = Y.mean(axis=1, keepdims=True)\nb = (Y - ybar) @ xc / Sxx\na = ybar[:, 0] - b * x.mean()\nE = Y - a[:, None] - b[:, None] * x[None, :]\ns2 = np.sum(E**2, axis=1) / (N - 2)\nse_conv = np.sqrt(s2 / Sxx)\nse_hc0 = np.sqrt(np.sum((xc[None, :] ** 2) * E**2, axis=1)) / Sxx\nse_hc1 = se_hc0 * np.sqrt(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))\nmcse0 = np.sqrt(LEVEL * (1 - LEVEL) / R)\nundercovers = bool(cov_conv < LEVEL - 3 * mcse0)\n\n# cross-check one replication against statsmodels\nimport statsmodels.api as sm\nm = sm.OLS(Y[0], sm.add_constant(x)).fit()\nassert np.isclose(m.bse[1], se_conv[0]) and np.isclose(m.HC1_se[1], se_hc1[0])\n\nres = {\n \"task_id\": \"F2-conf-03\",\n \"coverage_conventional\": cov_conv,\n \"coverage_hc1\": cov_hc1,\n \"sd_beta_exact\": sd_exact,\n \"sd_beta_mc\": float(np.std(b, ddof=1)),\n \"mean_se_conventional\": float(se_conv.mean()),\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\": int(n_rows)},\n \"random_seed\": SEED,\n # supplementary\n \"t_critical\": 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\": float(mcse0),\n \"undercoverage_threshold\": float(LEVEL - 3 * mcse0),\n \"mean_se_hc1\": float(se_hc1.mean()),\n \"se_conv_exact_expected_s2_based\": float(np.sqrt((np.sum(sig**2) - np.sum((1/N + xc**2/Sxx) * sig**2)) / (N - 2) / Sxx)),\n \"baseline_coverage_conventional\": cov_conv,\n}\nos.makedirs(\"out\", exist_ok=True)\nwith open(\"out/results.json\", \"w\") as f:\n json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write audit files and analysis script, run it"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1374,"cache_read_input_tokens":7246,"output_tokens":2081,"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":1374},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmo5JKos7xXA45yCReg","requestRef":"c461e644-7e58-4f44-b663-2ee151990326","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"0252d822-c1a5-4a81-851d-e65f0122c370","timestamp":"2026-10-30T04:15:24.480Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}30{"parentUuid":"0252d822-c1a5-4a81-851d-e65f0122c370","isSidechain":false,"promptId":"243b3c48-ceb9-4b7b-bf23-06d59c147137","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01KYgmkQpBW4JrXQ8jHEzA6T","type":"tool_result","content":"{\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_coverage_conventional\": 0.00811369213120636,\n \"mcse_coverage_hc1\": 0.006648157639526908,\n \"mcse_at_nominal\": 0.004873397172404485,\n \"undercoverage_threshold\": 0.9353798084827865,\n \"mean_se_hc1\": 0.24080977065103962,\n \"se_conv_exact_expected_s2_based\": 0.19318017740129878,\n \"baseline_coverage_conventional\": 0.844\n}","is_error":false}]},"uuid":"65c8b262-eafe-469b-ba5c-3a4da4b2ed57","timestamp":"2026-10-30T04:15:25.552Z","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\": 0.19026231012152658,\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_coverage_conventional\": 0.00811369213120636,\n \"mcse_coverage_hc1\": 0.006648157639526908,\n \"mcse_at_nominal\": 0.004873397172404485,\n \"undercoverage_threshold\": 0.9353798084827865,\n \"mean_se_hc1\": 0.24080977065103962,\n \"se_conv_exact_expected_s2_based\": 0.19318017740129878,\n \"baseline_coverage_conventional\": 0.844\n}","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"0252d822-c1a5-4a81-851d-e65f0122c370","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}31{"type":"api-request-blob","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","hash":"eb3271d889c7fc98c511f98b5f3c6020fea6f778023f0af6c70c66efdbf1d582","message":{"role":"assistant","content":[{"type":"text","text":"Data are clean. Now the analysis script."},{"type":"tool_use","id":"toolu_01KYgmkQpBW4JrXQ8jHEzA6T","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n- File: data/design.csv, SHA-256 b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0\n- 30 rows x 3 columns: i (int, 1..30, unique), x (float, dimensionless, range -1.3942..1.9919, mean 0.2823), sigma (float, dimensionless, range 0.6034..1.7903, all > 0).\n- Missing values: 0. Duplicate rows: 0. No dates (not applicable).\n- Anomalies: none. Note: sigma^2 is strongly correlated with x^2 (r = 0.987), i.e. error variance is largest at high-leverage points -> the setting in which conventional SEs are expected to be biased downward. This is a design feature, not a data issue.\n- Information-availability: the only input is the permitted design file; no violations.\n- Exclusions: none (see out/exclusions.csv).\nEOF\ncat > out/exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n1,none (all design rows retained),30,30,0,design is complete and valid; task forbids altering x or sigma\nEOF\ncat > out/analysis.py <<'EOF'\n\"\"\"F2-conf-03: Monte Carlo coverage of OLS CIs under heteroskedasticity.\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\nSEED = 20261030\nALPHA, BETA, N, R, LEVEL = 1.0, 0.5, 30, 2000, 0.95\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\n# exact SD of beta_hat: beta_hat - beta = sum w_i sigma_i eps_i\nxc = x - x.mean(); Sxx = np.sum(xc**2); w = xc / Sxx\nsd_exact = float(np.sqrt(np.sum(w**2 * sig**2)))\n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, N))\nY = ALPHA + BETA * x[None, :] + sig[None, :] * eps\nybar = Y.mean(axis=1, keepdims=True)\nb = (Y - ybar) @ xc / Sxx\na = ybar[:, 0] - b * x.mean()\nE = Y - a[:, None] - b[:, None] * x[None, :]\ns2 = np.sum(E**2, axis=1) / (N - 2)\nse_conv = np.sqrt(s2 / Sxx)\nse_hc0 = np.sqrt(np.sum((xc[None, :] ** 2) * E**2, axis=1)) / Sxx\nse_hc1 = se_hc0 * np.sqrt(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))\nmcse0 = np.sqrt(LEVEL * (1 - LEVEL) / R)\nundercovers = bool(cov_conv < LEVEL - 3 * mcse0)\n\n# cross-check one replication against statsmodels\nimport statsmodels.api as sm\nm = sm.OLS(Y[0], sm.add_constant(x)).fit()\nassert np.isclose(m.bse[1], se_conv[0]) and np.isclose(m.HC1_se[1], se_hc1[0])\n\nres = {\n \"task_id\": \"F2-conf-03\",\n \"coverage_conventional\": cov_conv,\n \"coverage_hc1\": cov_hc1,\n \"sd_beta_exact\": sd_exact,\n \"sd_beta_mc\": float(np.std(b, ddof=1)),\n \"mean_se_conventional\": float(se_conv.mean()),\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\": int(n_rows)},\n \"random_seed\": SEED,\n # supplementary\n \"t_critical\": 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\": float(mcse0),\n \"undercoverage_threshold\": float(LEVEL - 3 * mcse0),\n \"mean_se_hc1\": float(se_hc1.mean()),\n \"se_conv_exact_expected_s2_based\": float(np.sqrt((np.sum(sig**2) - np.sum((1/N + xc**2/Sxx) * sig**2)) / (N - 2) / Sxx)),\n \"baseline_coverage_conventional\": cov_conv,\n}\nos.makedirs(\"out\", exist_ok=True)\nwith open(\"out/results.json\", \"w\") as f:\n json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write audit files and analysis script, run it"}}]}}32{"type":"api-request","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","id":"309f625e-0309-48d1-9804-bc6d10fc2033","timestamp":"2026-10-30T04:15:25.556Z","version":"2.1.314","querySource":"sdk","shapeHash":"70d77a7de77f059bf051febed9b41785f87945454de098e28add14503d432686","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":"c461e644-7e58-4f44-b663-2ee151990326","keep":8,"tail":["eb3271d889c7fc98c511f98b5f3c6020fea6f778023f0af6c70c66efdbf1d582","f92fda854bd72ed3592d9d663c27833bdd14800f1adf54a8dfedf15d2b0c239d"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",9,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"a13b7a31a1fa8c19c8a156a4734165c5803141933db04759854e5514298365d6"}33{"parentUuid":"65c8b262-eafe-469b-ba5c-3a4da4b2ed57","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmpQJMk2wdV5H1Mw98m","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":2503,"cache_read_input_tokens":8620,"output_tokens":648,"output_tokens_details":{"thinking_tokens":108},"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":2503},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":681,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmpQ5hp2dZacRkXPaJM","requestRef":"309f625e-0309-48d1-9804-bc6d10fc2033","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"ff0a5c9c-143e-42a1-93e3-f55d2fa2389f","timestamp":"2026-10-30T04:15:27.503Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}34{"parentUuid":"ff0a5c9c-143e-42a1-93e3-f55d2fa2389f","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmpQJMk2wdV5H1Mw98m","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01RYyucDRHUEVFHVDtJt9CFh","name":"Bash","input":{"command":"sed -i '' 's/se_conv_exact_expected_s2_based/sqrt_E_s2_over_Sxx_analytic/' out/analysis.py\ncp out/results.json /tmp/r1.json && rm out/results.json && ~/wp29/venv/bin/python out/analysis.py >/dev/null && ~/wp29/venv/bin/python out/analysis.py > /dev/null && cp out/results.json /tmp/r2.json && rm out/results.json && ~/wp29/venv/bin/python out/analysis.py >/dev/null && cmp /tmp/r2.json out/results.json && echo IDENTICAL\n~/wp29/venv/bin/python -c \"\nimport json;r=json.load(open('out/results.json'))\nprint(abs(r['sd_beta_mc']-r['sd_beta_exact'])/r['sd_beta_exact'], 'rel diff sd; expected MC rel se ~', 1/(2*1999)**.5)\nprint(r['mean_se_conventional']<=r['sqrt_E_s2_over_Sxx_analytic'])\nprint((0.95-r['coverage_conventional'])/r['mcse_at_nominal'],(0.95-r['coverage_hc1'])/r['mcse_at_nominal'])\nprint(r['coverage_conventional']*2000, r['coverage_hc1']*2000)\"","description":"Reproducibility and consistency 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rel diff sd; expected MC rel se ~ 0.015815342630852665\nTrue\n21.75074106420525 9.84939218001746\n1688.0 1804.0","is_error":false}]},"uuid":"9af6bd94-7cff-4286-bdba-10480de50b95","timestamp":"2026-10-30T04:15:34.487Z","toolUseResult":{"stdout":"IDENTICAL\n0.006219771301442373 rel diff sd; expected MC rel se ~ 0.015815342630852665\nTrue\n21.75074106420525 9.84939218001746\n1688.0 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-i '' 's/se_conv_exact_expected_s2_based/sqrt_E_s2_over_Sxx_analytic/' out/analysis.py\ncp out/results.json /tmp/r1.json && rm out/results.json && ~/wp29/venv/bin/python out/analysis.py >/dev/null && ~/wp29/venv/bin/python out/analysis.py > /dev/null && cp out/results.json /tmp/r2.json && rm out/results.json && ~/wp29/venv/bin/python out/analysis.py >/dev/null && cmp /tmp/r2.json out/results.json && echo IDENTICAL\n~/wp29/venv/bin/python -c \"\nimport json;r=json.load(open('out/results.json'))\nprint(abs(r['sd_beta_mc']-r['sd_beta_exact'])/r['sd_beta_exact'], 'rel diff sd; expected MC rel se ~', 1/(2*1999)**.5)\nprint(r['mean_se_conventional']<=r['sqrt_E_s2_over_Sxx_analytic'])\nprint((0.95-r['coverage_conventional'])/r['mcse_at_nominal'],(0.95-r['coverage_hc1'])/r['mcse_at_nominal'])\nprint(r['coverage_conventional']*2000, r['coverage_hc1']*2000)\"","description":"Reproducibility and consistency 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> out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Reproducibility: results.json deleted and regenerated twice; byte-identical (cmp) -> PASS.\n2. Statsmodels cross-check (inside analysis.py, assert): replication 1 se_conv and HC1 se match statsmodels OLS bse / HC1_se -> PASS.\n3. sd_beta_mc vs sd_beta_exact: relative difference 0.62%, within one MC relative SE of an SD (~1/sqrt(2(R-1)) = 1.58%) -> PASS.\n4. Jensen: mean_se_conventional (0.1903) <= sqrt(E[s^2]/Sxx) analytic (0.1932) -> PASS.\n5. Positivity: sd_beta_exact, sd_beta_mc, mean_se_conventional, MC SEs all > 0 -> PASS.\n6. Counts: coverage*R integers (1688, 1804); n_obs=30=n_input_rows; exclusions 30-0=30 -> PASS.\n7. Undercoverage rule: threshold 0.95 - 3*0.004873 = 0.93538; coverage_conventional 0.844 < threshold -> flag true, consistent -> PASS.\n8. Magnitudes: mean_se_conventional (0.190) well below sd_beta_exact (0.268), consistent with observed undercoverage; HC1 mean SE 0.241 also below 0.268, consistent with HC1 also undercovering (0.902) -> PASS (plausible).\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P1']={\"status\":\"passed\",\"checks\":[\"sha256 computed\",\"schema/missing/duplicates/sigma>0 checked\",\"exclusions.csv sums 30-0=30\"],\"notes\":\"no issues\"}\np['P2']={\"status\":\"passed\",\"checks\":[\"baseline conventional coverage computed = 0.844 (coverage_conventional, baseline_coverage_conventional)\"],\"notes\":\"\"}\np['P3']={\"status\":\"passed\",\"checks\":[\"analysis.py runs, seed 20261030, statsmodels cross-check assert passed\"],\"notes\":\"\"}\np['P4']={\"status\":\"running\",\"checks\":[\"clean re-run byte-identical\",\"checks.md items 1-8 PASS\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P1-P3 passed (data clean, seed 20261030, 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, 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":724,"cache_read_input_tokens":11123,"output_tokens":1034,"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":724},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXmq4J74iJ1mVuSNiuJZ","requestRef":"b8aae211-7da1-411b-adb1-36cb21f38197","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6e69c98e-5be3-42d4-910f-3b03e18d6b42","timestamp":"2026-10-30T04:15:43.301Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}41{"parentUuid":"6e69c98e-5be3-42d4-910f-3b03e18d6b42","isSidechain":false,"promptId":"243b3c48-ceb9-4b7b-bf23-06d59c147137","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: 0.19026231012152658\n [ok] reproducibility: regenerated in 1.1s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0050/out/state/gate_receipts/20261030T041544.527834Z.json","is_error":true,"tool_use_id":"toolu_01XN8TUgxx6GsAJ6KtTiSKAY"}]},"uuid":"dd88c97e-0302-46bd-a714-77a5d09def31","timestamp":"2026-10-30T04:15:44.536Z","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: 0.19026231012152658\n [ok] reproducibility: regenerated in 1.1s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0050/out/state/gate_receipts/20261030T041544.527834Z.json","sandboxed":false,"sourceToolAssistantUUID":"6e69c98e-5be3-42d4-910f-3b03e18d6b42","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}42{"type":"api-request-blob","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","hash":"640010a967dc09c6422f375d8cde2926609a4e7fb11c15bd95f3218ae1f91adc","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01XN8TUgxx6GsAJ6KtTiSKAY","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Reproducibility: results.json deleted and regenerated twice; byte-identical (cmp) -> PASS.\n2. Statsmodels cross-check (inside analysis.py, assert): replication 1 se_conv and HC1 se match statsmodels OLS bse / HC1_se -> PASS.\n3. sd_beta_mc vs sd_beta_exact: relative difference 0.62%, within one MC relative SE of an SD (~1/sqrt(2(R-1)) = 1.58%) -> PASS.\n4. Jensen: mean_se_conventional (0.1903) <= sqrt(E[s^2]/Sxx) analytic (0.1932) -> PASS.\n5. Positivity: sd_beta_exact, sd_beta_mc, mean_se_conventional, MC SEs all > 0 -> PASS.\n6. Counts: coverage*R integers (1688, 1804); n_obs=30=n_input_rows; exclusions 30-0=30 -> PASS.\n7. Undercoverage rule: threshold 0.95 - 3*0.004873 = 0.93538; coverage_conventional 0.844 < threshold -> flag true, consistent -> PASS.\n8. Magnitudes: mean_se_conventional (0.190) well below sd_beta_exact (0.268), consistent with observed undercoverage; HC1 mean SE 0.241 also below 0.268, consistent with HC1 also undercovering (0.902) -> PASS (plausible).\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P1']={\"status\":\"passed\",\"checks\":[\"sha256 computed\",\"schema/missing/duplicates/sigma>0 checked\",\"exclusions.csv sums 30-0=30\"],\"notes\":\"no issues\"}\np['P2']={\"status\":\"passed\",\"checks\":[\"baseline conventional coverage computed = 0.844 (coverage_conventional, baseline_coverage_conventional)\"],\"notes\":\"\"}\np['P3']={\"status\":\"passed\",\"checks\":[\"analysis.py runs, seed 20261030, statsmodels cross-check assert passed\"],\"notes\":\"\"}\np['P4']={\"status\":\"running\",\"checks\":[\"clean re-run byte-identical\",\"checks.md items 1-8 PASS\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P1-P3 passed (data clean, seed 20261030, 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, update ledger, run gate"}}]}}43{"type":"api-request","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","id":"5b134bd2-6b87-4669-93d3-a1bb3cfcfe6a","timestamp":"2026-10-30T04:15:44.539Z","version":"2.1.314","querySource":"sdk","shapeHash":"70d77a7de77f059bf051febed9b41785f87945454de098e28add14503d432686","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":"b8aae211-7da1-411b-adb1-36cb21f38197","keep":12,"tail":["640010a967dc09c6422f375d8cde2926609a4e7fb11c15bd95f3218ae1f91adc","8d48c351386ee133651faa8b9a072fb0285d8048b6a6bd5690388dc2dba83e5e"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",13,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"728e9ae514d69affb2964de6d7033de4bf3620a77747e59b85db49ab70511b35"}44{"parentUuid":"dd88c97e-0302-46bd-a714-77a5d09def31","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmqobrS7u6PRuG7ZnFR","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":1778,"cache_read_input_tokens":11847,"output_tokens":2571,"output_tokens_details":{"thinking_tokens":47},"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":1778},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":819,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmqoG19mWei489cadXb","requestRef":"5b134bd2-6b87-4669-93d3-a1bb3cfcfe6a","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"78221136-bd7e-4576-833d-77396c465781","timestamp":"2026-10-30T04:15:46.657Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}45{"parentUuid":"78221136-bd7e-4576-833d-77396c465781","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmqobrS7u6PRuG7ZnFR","type":"message","role":"assistant","content":[{"type":"text","text":"P4-scope checks pass (contract keys, reproducibility, positivity, exclusions); remaining failures are P5 deliverables. Writing report and claims."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1778,"cache_read_input_tokens":11847,"output_tokens":2571,"output_tokens_details":{"thinking_tokens":47},"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":1778},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmqoG19mWei489cadXb","requestRef":"5b134bd2-6b87-4669-93d3-a1bb3cfcfe6a","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"2711ccda-335c-4d18-9b69-9826dd6bb609","timestamp":"2026-10-30T04:15:46.657Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}46{"parentUuid":"2711ccda-335c-4d18-9b69-9826dd6bb609","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmqobrS7u6PRuG7ZnFR","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01JKwnYNBnuRLX8fLo75Gt5i","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F2-conf-03 — Monte Carlo coverage of OLS confidence intervals (n = 30, heteroskedastic)\n\n## Question\nIn the fixed-design model y_i = 1 + 0.5 x_i + σ_i ε_i (i = 1..30, ε_i iid N(0,1), x_i and σ_i fixed from `data/design.csv`), do nominal 95% t(28) intervals for the slope based on (a) the conventional OLS SE and (b) the HC1 robust SE reach 95% coverage? We also report (c) the exact SD of β̂ and (d) E[se_conv].\n\n## Data and exclusions\n`data/design.csv` (SHA-256 b1a17a52…3e74f0): 30 rows, columns i, x, sigma; no missing values, no duplicates, all σ_i > 0 (`n_input_rows`, `data_issues` = []). No rows excluded (`out/exclusions.csv`: 30 → 30). Design feature: σ_i² is strongly correlated with x_i² (r = 0.987, computed in the audit), so error variance is largest at high-leverage points.\n\n## Method\nAnalytic: 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). Monte Carlo: R = 2000 replications (`n_replications`), n = 30 (`n_obs_per_replication`), numpy `default_rng` seed 20261030 (`random_seed`); only ε redrawn. In each replication OLS is fitted; se_conv = sqrt(s²/S_xx), s² = RSS/(n−2); se_HC1 = sqrt(n/(n−2)) · sqrt(Σ (x_i−x̄)² e_i²)/S_xx. Intervals β̂ ± t_{0.975}(28)·se with t = 2.0484 (`t_critical`). Both SE formulas were cross-checked against statsmodels for one replication. Undercoverage rule: coverage_conventional < 0.95 − 3·sqrt(0.95·0.05/2000) = 0.9354 (`undercoverage_threshold`). The conventional interval's coverage is the naïve baseline (`baseline_coverage_conventional`).\n\n## Results\n- Conventional interval coverage: **0.844** (`coverage_conventional`), far below 95%.\n- HC1 interval coverage: **0.902** (`coverage_hc1`) — better, but still below 95%.\n- Exact SD of β̂: **0.2680** (`sd_beta_exact`); Monte Carlo SD: 0.2696 (`sd_beta_mc`), agreeing within MC error.\n- Mean conventional SE: **0.1903** (`mean_se_conventional`), about 29% below the true SD of 0.2680; mean HC1 SE is 0.2408 (`mean_se_hc1`), also below the true SD. Analytic check: sqrt(E[s²]/S_xx) = 0.1932 (`sqrt_E_s2_over_Sxx_analytic`), consistent with the MC mean SE (Jensen).\n- Conclusion: the conventional interval does **not** attain its nominal coverage (`conventional_ci_undercovers` = true).\n\n## Uncertainty\nBinomial Monte Carlo standard errors: conventional coverage 0.844 ± 0.0081 (`mcse_coverage_conventional`); HC1 coverage 0.902 ± 0.0067 (`mcse_coverage_hc1`); MC SE at the nominal 0.95 is 0.0049 (`mcse_at_nominal`). The conventional shortfall (0.106) is about 22 nominal-level MC SEs; the HC1 shortfall (0.048) is about 10. The sd_beta_exact value is analytic (no MC error); sd_beta_mc differs from it by 0.6%, below its approximate MC relative SE of 1.6%.\n\n## Limitations and open issues\n- Results are conditional on this one synthetic fixed design and normal errors; they do not generalise to other designs.\n- Coverage estimates depend on the seed at the level of the reported MC SEs; R = 2000 is fixed by the task.\n- HC1 also undercovers in this n = 30 high-leverage design; small-sample refinements (HC2/HC3, wild bootstrap) were not evaluated because the task does not require them.\n- No data problems were found; feasibility is \"complete\".\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The conventional 95% interval does not attain nominal coverage: estimated coverage 0.844, more than three MC standard errors below 0.95.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"mcse_coverage_conventional\",\"undercoverage_threshold\"],\"status\":\"supported\",\"caveat\":\"Conditional on this fixed design, normal errors and seed; MC SE about 0.008.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval covers better (0.902) than the conventional interval but still falls below 95%.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\",\"mcse_at_nominal\"],\"status\":\"supported\",\"caveat\":\"MC SE about 0.007; small-sample HC variants not evaluated.\"},\n {\"id\":\"C3\",\"text\":\"The exact SD of the slope estimator is 0.268, and the Monte Carlo SD (0.270) agrees with it.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\"],\"status\":\"supported\",\"caveat\":\"Exact value is analytic, given the design.\"},\n {\"id\":\"C4\",\"text\":\"The conventional SE is biased downward: its mean (0.190) is about 29% below the true SD of the slope estimator.\",\"results_keys\":[\"mean_se_conventional\",\"sd_beta_exact\",\"sqrt_E_s2_over_Sxx_analytic\"],\"status\":\"supported\",\"caveat\":\"MC average; consistent with the analytic sqrt(E[s^2]/Sxx).\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P4']['status']='passed'; p['P4']['checks'].append(\"gate run 20261030T041544.527834Z: all P4-scope checks ok (keys, positivity, exclusions, reproducibility); failures only for P5 deliverables not yet written\")\np['P5']={\"status\":\"passed\",\"checks\":[\"report.md with 6 sections written\",\"claims.json 4 claims referencing existing keys\",\"final gate run (see log)\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P4 passed; P5 report and claims written; running final gate.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v '\\[ok\\]'","description":"Write report, claims, update ledger, rerun gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1778,"cache_read_input_tokens":11847,"output_tokens":2571,"output_tokens_details":{"thinking_tokens":47},"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":1778},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXmqoG19mWei489cadXb","requestRef":"5b134bd2-6b87-4669-93d3-a1bb3cfcfe6a","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"5e4c8839-f48d-4831-8402-9e813a86b10a","timestamp":"2026-10-30T04:16:05.778Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}47{"parentUuid":"5e4c8839-f48d-4831-8402-9e813a86b10a","isSidechain":false,"promptId":"243b3c48-ceb9-4b7b-bf23-06d59c147137","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01JKwnYNBnuRLX8fLo75Gt5i","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 32 checks failed)\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0050/out/state/gate_receipts/20261030T041606.746456Z.json","is_error":false}]},"uuid":"697b8fa0-1a23-4434-bf66-a99633bc1399","timestamp":"2026-10-30T04:16:06.755Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 32 checks failed)\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0050/out/state/gate_receipts/20261030T041606.746456Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"5e4c8839-f48d-4831-8402-9e813a86b10a","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0050","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","version":"2.1.314","gitBranch":"HEAD"}48{"type":"api-request-blob","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","hash":"07244d0832f99f46aef9f657b0c734f30c2cf8cc5f9eae22df48456cd35f4386","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQS5AYKEAgTGAI4AUIIdGhpbmtpbmcSDEo1qi3aOjANdwuf2BoMYRnDf42tc19fck7sIjCrG5JpxkH50HmOb6R8qlaNU1CUmgbrNOVaTQTh6+PfWlJqT5t4gekJHK/1eSukx/4qgQb+Jry0poXP9jdR+iS5DXxHjaq2cjBQmpP7YU02LeHlmcml3s3jybEKvFS/ZaoG3MN1PRfjOF7HzjzZZiRg/ctbV8dMZbWrzGwzLWteNhQ4AucP9xxGHRXorLk6KuvPj/BRMEKFr713wNREHDBV7Tb0nUdYmfkJrmIEdzoH0MeM+IdA5EbBGXL0bV3jVLaUBBw/tpaYPAvyaWERpZgtUD4RpDlOrZqSF3b8TPKUYamEmdG6kvk3fA053OvvtGgmMHCve9r+DB+9lMSqVRoEEXmSxcLpUVcLMFt61pz+K58bDn3B/XRXMo9OeiRaNhgd2AbiOyCA9l7BRTl1hrfyW9LFE1gnzkxlg3iOLXnt0T1jO+aG9IbpWyRqxnmJiLrlwvvVH4IKqKXDBziBZIHLVmZ7O/BGB+xB01R4Uh4NfWHXwm/lYtbzbs6O5aBMb/ZbtcQtVzLlYKw04+7uftzyzzbYnxvxP+f86d3HOBT/r8bmdfIZ1UpCGVfzl8Q5l5LofrMTpTW4EUn5UcaOywDBE69ujj0hzq2yjz/KmvO1l7ZDMh667eGrS6JDhcjiIcpLGrUCOXyrlPbvKYswj4mUGB3Lw5oP0dNy6MuKnfKwAWIr6DUv6PiF1t4RUmEVVEwffig7O2H3TcLpqYnhh2aNfsmePQAK8WjWijq/P45LOr+X1JSttftLE/YFzDLVihLNbqbnkp6Oki28kjkImXqXLOHM92pZDDjFUNiK6HPX3Mb2wEDEfhO6rMp2caebzJ2+4vks3y21ZQrv4ZMCy2QG1kfM0t0Xe3pJFaaAvrFIRDPBBFX0CqQXzGkt0ihbjYICBy5vQZhGmNMFBak4yTaBgBKNghJKioa3ImkdIyKxOJFGLgZ7urRkET65fD1IN/a6UERvWX0LtW7UygJW/6XJQ3ff4mHnku6V/YoHPLaY5mhUpPIBzBg1GTZX4zSB8/Ck+ERvoTpcfEDeo9JdVVVDYuQ+vmMRtz5OdxTqxI/4SToc4qDbUuO7Dda+YUIrrlQeTBE/GAE="},{"type":"text","text":"P4-scope checks pass (contract keys, reproducibility, positivity, exclusions); remaining failures are P5 deliverables. Writing report and claims."},{"type":"tool_use","id":"toolu_01JKwnYNBnuRLX8fLo75Gt5i","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F2-conf-03 — Monte Carlo coverage of OLS confidence intervals (n = 30, heteroskedastic)\n\n## Question\nIn the fixed-design model y_i = 1 + 0.5 x_i + σ_i ε_i (i = 1..30, ε_i iid N(0,1), x_i and σ_i fixed from `data/design.csv`), do nominal 95% t(28) intervals for the slope based on (a) the conventional OLS SE and (b) the HC1 robust SE reach 95% coverage? We also report (c) the exact SD of β̂ and (d) E[se_conv].\n\n## Data and exclusions\n`data/design.csv` (SHA-256 b1a17a52…3e74f0): 30 rows, columns i, x, sigma; no missing values, no duplicates, all σ_i > 0 (`n_input_rows`, `data_issues` = []). No rows excluded (`out/exclusions.csv`: 30 → 30). Design feature: σ_i² is strongly correlated with x_i² (r = 0.987, computed in the audit), so error variance is largest at high-leverage points.\n\n## Method\nAnalytic: 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). Monte Carlo: R = 2000 replications (`n_replications`), n = 30 (`n_obs_per_replication`), numpy `default_rng` seed 20261030 (`random_seed`); only ε redrawn. In each replication OLS is fitted; se_conv = sqrt(s²/S_xx), s² = RSS/(n−2); se_HC1 = sqrt(n/(n−2)) · sqrt(Σ (x_i−x̄)² e_i²)/S_xx. Intervals β̂ ± t_{0.975}(28)·se with t = 2.0484 (`t_critical`). Both SE formulas were cross-checked against statsmodels for one replication. Undercoverage rule: coverage_conventional < 0.95 − 3·sqrt(0.95·0.05/2000) = 0.9354 (`undercoverage_threshold`). The conventional interval's coverage is the naïve baseline (`baseline_coverage_conventional`).\n\n## Results\n- Conventional interval coverage: **0.844** (`coverage_conventional`), far below 95%.\n- HC1 interval coverage: **0.902** (`coverage_hc1`) — better, but still below 95%.\n- Exact SD of β̂: **0.2680** (`sd_beta_exact`); Monte Carlo SD: 0.2696 (`sd_beta_mc`), agreeing within MC error.\n- Mean conventional SE: **0.1903** (`mean_se_conventional`), about 29% below the true SD of 0.2680; mean HC1 SE is 0.2408 (`mean_se_hc1`), also below the true SD. Analytic check: sqrt(E[s²]/S_xx) = 0.1932 (`sqrt_E_s2_over_Sxx_analytic`), consistent with the MC mean SE (Jensen).\n- Conclusion: the conventional interval does **not** attain its nominal coverage (`conventional_ci_undercovers` = true).\n\n## Uncertainty\nBinomial Monte Carlo standard errors: conventional coverage 0.844 ± 0.0081 (`mcse_coverage_conventional`); HC1 coverage 0.902 ± 0.0067 (`mcse_coverage_hc1`); MC SE at the nominal 0.95 is 0.0049 (`mcse_at_nominal`). The conventional shortfall (0.106) is about 22 nominal-level MC SEs; the HC1 shortfall (0.048) is about 10. The sd_beta_exact value is analytic (no MC error); sd_beta_mc differs from it by 0.6%, below its approximate MC relative SE of 1.6%.\n\n## Limitations and open issues\n- Results are conditional on this one synthetic fixed design and normal errors; they do not generalise to other designs.\n- Coverage estimates depend on the seed at the level of the reported MC SEs; R = 2000 is fixed by the task.\n- HC1 also undercovers in this n = 30 high-leverage design; small-sample refinements (HC2/HC3, wild bootstrap) were not evaluated because the task does not require them.\n- No data problems were found; feasibility is \"complete\".\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The conventional 95% interval does not attain nominal coverage: estimated coverage 0.844, more than three MC standard errors below 0.95.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"mcse_coverage_conventional\",\"undercoverage_threshold\"],\"status\":\"supported\",\"caveat\":\"Conditional on this fixed design, normal errors and seed; MC SE about 0.008.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval covers better (0.902) than the conventional interval but still falls below 95%.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\",\"mcse_at_nominal\"],\"status\":\"supported\",\"caveat\":\"MC SE about 0.007; small-sample HC variants not evaluated.\"},\n {\"id\":\"C3\",\"text\":\"The exact SD of the slope estimator is 0.268, and the Monte Carlo SD (0.270) agrees with it.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\"],\"status\":\"supported\",\"caveat\":\"Exact value is analytic, given the design.\"},\n {\"id\":\"C4\",\"text\":\"The conventional SE is biased downward: its mean (0.190) is about 29% below the true SD of the slope estimator.\",\"results_keys\":[\"mean_se_conventional\",\"sd_beta_exact\",\"sqrt_E_s2_over_Sxx_analytic\"],\"status\":\"supported\",\"caveat\":\"MC average; consistent with the analytic sqrt(E[s^2]/Sxx).\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P4']['status']='passed'; p['P4']['checks'].append(\"gate run 20261030T041544.527834Z: all P4-scope checks ok (keys, positivity, exclusions, reproducibility); failures only for P5 deliverables not yet written\")\np['P5']={\"status\":\"passed\",\"checks\":[\"report.md with 6 sections written\",\"claims.json 4 claims referencing existing keys\",\"final gate run (see log)\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P4 passed; P5 report and claims written; running final gate.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v '\\[ok\\]'","description":"Write report, claims, update ledger, rerun gate"}}]}}49{"type":"api-request","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842","id":"e0899e10-e3e1-4e62-a73d-f142fc9b53b6","timestamp":"2026-10-30T04:16:06.758Z","version":"2.1.314","querySource":"sdk","shapeHash":"70d77a7de77f059bf051febed9b41785f87945454de098e28add14503d432686","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":"5b134bd2-6b87-4669-93d3-a1bb3cfcfe6a","keep":14,"tail":["07244d0832f99f46aef9f657b0c734f30c2cf8cc5f9eae22df48456cd35f4386","824c02a4881bf4461c83f650307778e6351c23f340567ea49b5ffadd587f530b"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",15,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"792b46d92cef129b9a5b18f48b18e026fa60efa0ba9ceea746e78bb8ce61a41f"}50{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"697b8fa0-1a23-4434-bf66-a99633bc1399","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842"}51{"type":"atis-latch","atis":"","sessionId":"28701b56-d967-44b6-8e2a-b83548a3b842"}52{"parentUuid":"697b8fa0-1a23-4434-bf66-a99633bc1399","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmsSSRWtvRVVB9j6T8h","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_017ALtV4ycfNcF4N81S6sM5m","name":"Bash","input":{"command":"~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P5']['checks'][-1]=\"final gate run 20261030T041606.746456Z: PASSED 0/32 failed\"\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 Final gate PASSED (receipt 20261030T041606.746456Z). 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Its actual coverage is about 84%. The final gate check passes with no failures, and re-running `out/analysis.py` reproduces `out/results.json` exactly.\n\n**Results** (2,000 replications, n = 30, seed 20261030):\n\n| Quantity | Value |\n|---|---|\n| Coverage, conventional interval | **0.844** (±0.008 Monte Carlo standard error) |\n| Coverage, HC1 robust interval | **0.902** (±0.007) |\n| Exact SD of β̂ (worked out by formula, not simulated) | 0.2680 |\n| Simulated SD of β̂ | 0.2696 |\n| Average conventional standard error | 0.1903 |\n| Conventional interval undercovers? | **true** |\n\n- **Why the conventional interval falls short:** its standard error averages about 29% below the true SD of β̂. 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