spb/wp29_uqo

1{"type":"atis-latch","atis":"","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3"}2{"type":"queue-operation","operation":"enqueue","timestamp":"2026-10-30T04:16:59.645Z","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","content":"Begin"}3{"type":"queue-operation","operation":"dequeue","timestamp":"2026-10-30T04:16:59.649Z","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3"}4{"parentUuid":null,"isSidechain":false,"promptId":"21423356-3126-41ac-b89b-265abd7af27a","type":"user","message":{"role":"user","content":"Begin"},"uuid":"31a733e4-668e-4a15-b600-d6a629398077","timestamp":"2026-10-30T04:16:59.652Z","permissionMode":"default","promptSource":"sdk","turnOrigin":"sdk","turnPosition":{"promptIndex":0,"turnIndex":1},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}5{"type":"api-request-shape","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","shapeHash":"b938085ee2de3a6034f0fc54cf7efbd722a6862ccf97adbfd88fb3a1bcedda83","timestamp":"2026-10-30T04:16:59.661Z","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/RC0060\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/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3"}12{"parentUuid":"0cc6ec49-cd74-475c-a031-17c6f9621df3","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmweY4cuEABwi84Avdn","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":117,"output_tokens_details":{"thinking_tokens":15},"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":466,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmweKucfS8drpksEjth","requestRef":"3d743fa6-e292-4495-861e-52aaae4c9f59","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"74ac0fa0-4960-42f0-8801-5015502cc118","timestamp":"2026-10-30T04:17:04.781Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"74ac0fa0-4960-42f0-8801-5015502cc118","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmweY4cuEABwi84Avdn","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_018qgMaGMq6iUHYAMcy7v4zc","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  46 simon-pierreboucher  staff  1472 oct.  30 00:16 ..\n-rw-r--r--   1 simon-pierreboucher  staff   420 oct.  29 23:35 bundle.json\ndrwxr-xr-x   3 simon-pierreboucher  staff    96 oct.  29 23:33 data\n-rw-r--r--   1 simon-pierreboucher  staff  1456 oct.  29 23:35 gate_spec.json\n-rw-r--r--   1 simon-pierreboucher  staff  4161 oct.  29 23:35 TASK.md\ndata:\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_018qgMaGMq6iUHYAMcy7v4zc"}]},"uuid":"14d6728a-3ffa-4c16-9389-89bb671e2825","timestamp":"2026-10-30T04:17:05.309Z","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  46 simon-pierreboucher  staff  1472 oct.  30 00:16 ..\n-rw-r--r--   1 simon-pierreboucher  staff   420 oct.  29 23:35 bundle.json\ndrwxr-xr-x   3 simon-pierreboucher  staff    96 oct.  29 23:33 data\n-rw-r--r--   1 simon-pierreboucher  staff  1456 oct.  29 23:35 gate_spec.json\n-rw-r--r--   1 simon-pierreboucher  staff  4161 oct.  29 23:35 TASK.md\ndata:\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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 \"task_id\": \"F2-conf-03\",\n  \"required_files\": [\"out/results.json\", \"out/report.md\", \"out/analysis.py\", \"out/claims.json\"],\n  \"results_keys\": {\n    \"task_id\": {\"type\": \"string\", \"nullable\": false},\n    \"coverage_conventional\": {\"type\": \"number\", \"nullable\": false},\n    \"coverage_hc1\": {\"type\": \"number\", \"nullable\": false},\n    \"sd_beta_exact\": {\"type\": \"number\", \"nullable\": false},\n    \"sd_beta_mc\": {\"type\": \"number\", \"nullable\": false},\n    \"mean_se_conventional\": {\"type\": \"number\", \"nullable\": false},\n    \"conventional_ci_undercovers\": {\"type\": \"boolean\", \"nullable\": false},\n    \"n_replications\": {\"type\": \"integer\", \"nullable\": false},\n    \"n_obs_per_replication\": {\"type\": \"integer\", \"nullable\": false},\n    \"feasibility\": {\"type\": \"string\", \"nullable\": false},\n    \"feasibility_reason\": {\"type\": \"string\", \"nullable\": true},\n    \"data_issues\": {\"type\": \"array\", 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question:** In a fixed-design linear model y_i = 1 + 0.5 x_i + sigma_i eps_i (n=30, x and sigma from data/design.csv, eps iid N(0,1)), do nominal 95% t(28) intervals for the OLS slope achieve 95% coverage, using (i) conventional OLS SE and (ii) HC1 robust SE?\n\n**Estimands**\n- (a) P(beta in betahat ± t_.975(28) se_conv) — MC, R=2000, fixed seed.\n- (b) same with se_HC1 = sqrt(n/(n-2) * HC0) — MC.\n- (c) exact SD of betahat = sqrt(sum w_i^2 sigma_i^2), w_i = (x_i - xbar)/Sxx — analytic.\n- (d) E[se_conv] — MC average.\n- Also sd_beta_mc (ddof=1) and conventional_ci_undercovers = (0.95 - cov_conv) > 3*sqrt(0.95*0.05/2000).\nAssumptions: model is correctly specified as stated; x, sigma fixed; only eps redrawn.\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 (sections Question, Data and exclusions, Method, Results, Uncertainty, Limitations and open issues); out/analysis.py; out/claims.json; plus state files and out/exclusions.csv.\n\n**Information rules:** only data/design.csv; constants given; do not redraw x or sigma.\n\n**Invalidity conditions:** design file missing/malformed (not 30 rows, nonpositive sigma, missing values, constant x); non-reproducible simulation; R != 2000.\n\n**MC SE choice for the undercoverage rule:** the binomial SE at the nominal level, sqrt(0.95*0.05/2000) (test of H0 coverage=0.95). The SE at the estimated coverage is also reported in the report.\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(d.isna().sum().sum(),d.duplicated().sum(),d.i.is_unique,(d.i==range(1,31)).all())\"","description":"Write P0 state files and audit 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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\n0 0 True True","is_error":false}]},"uuid":"ef49a3c3-85a6-440c-a70b-6ce46818f873","timestamp":"2026-10-30T04:17:17.240Z","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\n0 0 True 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question:** In a fixed-design linear model y_i = 1 + 0.5 x_i + sigma_i eps_i (n=30, x and sigma from data/design.csv, eps iid N(0,1)), do nominal 95% t(28) intervals for the OLS slope achieve 95% coverage, using (i) conventional OLS SE and (ii) HC1 robust SE?\n\n**Estimands**\n- (a) P(beta in betahat ± t_.975(28) se_conv) — MC, R=2000, fixed seed.\n- (b) same with se_HC1 = sqrt(n/(n-2) * HC0) — MC.\n- (c) exact SD of betahat = sqrt(sum w_i^2 sigma_i^2), w_i = (x_i - xbar)/Sxx — analytic.\n- (d) E[se_conv] — MC average.\n- Also sd_beta_mc (ddof=1) and conventional_ci_undercovers = (0.95 - cov_conv) > 3*sqrt(0.95*0.05/2000).\nAssumptions: model is correctly specified as stated; x, sigma fixed; only eps redrawn.\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 (sections Question, Data and exclusions, Method, Results, Uncertainty, Limitations and open issues); out/analysis.py; out/claims.json; plus state files and out/exclusions.csv.\n\n**Information rules:** only data/design.csv; constants given; do not redraw x or sigma.\n\n**Invalidity conditions:** design file missing/malformed (not 30 rows, nonpositive sigma, missing values, constant x); non-reproducible simulation; R != 2000.\n\n**MC SE choice for the undercoverage rule:** the binomial SE at the nominal level, sqrt(0.95*0.05/2000) (test of H0 coverage=0.95). The SE at the estimated coverage is also reported in the report.\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(d.isna().sum().sum(),d.duplicated().sum(),d.i.is_unique,(d.i==range(1,31)).all())\"","description":"Write P0 state files and audit data"}}]}}27{"type":"api-request","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","id":"bc4e55f4-6506-4c33-beef-778ba4547634","timestamp":"2026-10-30T04:17:17.243Z","version":"2.1.314","querySource":"sdk","shapeHash":"b938085ee2de3a6034f0fc54cf7efbd722a6862ccf97adbfd88fb3a1bcedda83","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":"037dfe68-0006-40ec-ab4b-8c4f63d292b3","keep":6,"tail":["e3fd18230f55324f1dad82a2e5ed87bf74cc61b866cc85109e5a40ba302f6629","7090359557252928c9ecc035aceacf678a356948a79c86fdcf8a5d5a8ac92868"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"053fe7e865dce26732252e09bf6744b588df1c963513a3f803edbca87ab5194e"}28{"parentUuid":"ef49a3c3-85a6-440c-a70b-6ce46818f873","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmxdyr4eRxsiyMcjLjP","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_019a8FHihMqPpvF2Fkrmjepg","name":"Bash","input":{"command":"cd out && cat > state/data_audit.md <<'EOF'\n# Data audit (P1)\n| file | SHA-256 | rows | cols |\n|---|---|---|---|\n| data/design.csv | b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0 (matches bundle.json) | 30 | 3 |\n\nSchema: i (int64, 1..30, unique, sequential), x (float64, dimensionless, range -1.3942..1.9919, mean 0.2823, sd 0.8212), sigma (float64, dimensionless, range 0.6034..1.7903, all > 0).\nNo dates (synthetic fixed design). Missing values: 0. Duplicate rows: 0.\nAnomalies: none. Note: sigma increases with |x - c| (roughly quadratic in x; largest at extreme x), i.e. heteroskedasticity is concentrated at high-leverage points — the setting where conventional SEs understate variability.\nAvailability: the file is the only permitted input; no violation. No exclusions applied.\nEOF\nprintf 'step,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\\n' > exclusions.csv\necho \"- 2026-10-30 P1 passed: audit done, no issues, no exclusions.\" >> state/log.md","description":"Write data audit and exclusion ledger"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1489,"cache_read_input_tokens":7614,"output_tokens":559,"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":1489},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXmxdgk4WdynExEyPVmn","requestRef":"bc4e55f4-6506-4c33-beef-778ba4547634","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"1574da38-031b-4e92-bdc6-7f4668a525c6","timestamp":"2026-10-30T04:17:22.734Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}29{"parentUuid":"1574da38-031b-4e92-bdc6-7f4668a525c6","isSidechain":false,"promptId":"21423356-3126-41ac-b89b-265abd7af27a","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_019a8FHihMqPpvF2Fkrmjepg","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"0ec06bb1-0562-48f9-b07b-c4fe0145cfc7","timestamp":"2026-10-30T04:17:22.780Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"1574da38-031b-4e92-bdc6-7f4668a525c6","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060/out","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}30{"type":"api-request-blob","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","hash":"6b00ae32a8d43b76227708f9498ebea02ea99028ce20f60851a5c231e60b572c","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_019a8FHihMqPpvF2Fkrmjepg","name":"Bash","input":{"command":"cd out && cat > state/data_audit.md <<'EOF'\n# Data audit (P1)\n| file | SHA-256 | rows | cols |\n|---|---|---|---|\n| data/design.csv | b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0 (matches bundle.json) | 30 | 3 |\n\nSchema: i (int64, 1..30, unique, sequential), x (float64, dimensionless, range -1.3942..1.9919, mean 0.2823, sd 0.8212), sigma (float64, dimensionless, range 0.6034..1.7903, all > 0).\nNo dates (synthetic fixed design). 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> out/analysis.py <<'EOF'\n\"\"\"F2-conf-03: Monte Carlo coverage of OLS slope CIs under heteroskedasticity.\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\nALPHA, BETA, R, LEVEL = 1.0, 0.5, 2000, 0.95\n\nd = pd.read_csv(\"data/design.csv\")\nissues = []\nassert d.shape[0] == 30 and d[[\"x\", \"sigma\"]].notna().all().all() and (d.sigma > 0).all()\nx = d[\"x\"].to_numpy(float); s = d[\"sigma\"].to_numpy(float); n = len(x); df = n - 2\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, df)\n\nxc = x - x.mean(); Sxx = np.sum(xc ** 2); w = xc / Sxx\nsd_exact = float(np.sqrt(np.sum(w ** 2 * s ** 2)))          # (c) analytic\n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x + s * eps                               # R x n\nbhat = (Y - Y.mean(axis=1, keepdims=True)) @ xc / Sxx\nahat = Y.mean(axis=1) - bhat * x.mean()\ne = Y - ahat[:, None] - bhat[:, None] * x\nse_conv = np.sqrt(np.sum(e ** 2, axis=1) / df / Sxx)\nhc0 = np.sum((xc ** 2) * e ** 2, axis=1) / Sxx ** 2\nse_hc1 = np.sqrt(hc0 * n / df)\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((LEVEL - cov_conv) > 3 * mcse_nominal)\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(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\": issues,\n    \"n_input_rows\": {\"design.csv\": int(d.shape[0])},\n    \"random_seed\": SEED,\n    # supplementary diagnostics\n    \"t_crit_28\": float(tcrit),\n    \"mcse_at_nominal\": mcse_nominal,\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    \"mean_se_hc1\": float(np.mean(se_hc1)),\n    \"mean_bhat_mc\": float(np.mean(bhat)),\n    \"sd_beta_conv_formula_homosk\": float(np.sqrt(np.mean(s ** 2) / Sxx)),\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 and run analysis 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> out/analysis.py <<'EOF'\n\"\"\"F2-conf-03: Monte Carlo coverage of OLS slope CIs under heteroskedasticity.\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\nALPHA, BETA, R, LEVEL = 1.0, 0.5, 2000, 0.95\n\nd = pd.read_csv(\"data/design.csv\")\nissues = []\nassert d.shape[0] == 30 and d[[\"x\", \"sigma\"]].notna().all().all() and (d.sigma > 0).all()\nx = d[\"x\"].to_numpy(float); s = d[\"sigma\"].to_numpy(float); n = len(x); df = n - 2\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, df)\n\nxc = x - x.mean(); Sxx = np.sum(xc ** 2); w = xc / Sxx\nsd_exact = float(np.sqrt(np.sum(w ** 2 * s ** 2)))          # (c) analytic\n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x + s * eps                               # R x n\nbhat = (Y - Y.mean(axis=1, keepdims=True)) @ xc / Sxx\nahat = Y.mean(axis=1) - bhat * x.mean()\ne = Y - ahat[:, None] - bhat[:, None] * x\nse_conv = np.sqrt(np.sum(e ** 2, axis=1) / df / Sxx)\nhc0 = np.sum((xc ** 2) * e ** 2, axis=1) / Sxx ** 2\nse_hc1 = np.sqrt(hc0 * n / df)\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((LEVEL - cov_conv) > 3 * mcse_nominal)\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(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\": issues,\n    \"n_input_rows\": {\"design.csv\": 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> out/analysis.py <<'EOF'\n\"\"\"F2-conf-03: Monte Carlo coverage of OLS slope CIs under heteroskedasticity.\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\nALPHA, BETA, R, LEVEL = 1.0, 0.5, 2000, 0.95\n\nd = pd.read_csv(\"data/design.csv\")\nissues = []\nassert d.shape[0] == 30 and d[[\"x\", \"sigma\"]].notna().all().all() and (d.sigma > 0).all()\nx = d[\"x\"].to_numpy(float); s = d[\"sigma\"].to_numpy(float); n = len(x); df = n - 2\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, df)\n\nxc = x - x.mean(); Sxx = np.sum(xc ** 2); w = xc / Sxx\nsd_exact = float(np.sqrt(np.sum(w ** 2 * s ** 2)))          # (c) analytic\n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x + s * eps                               # R x n\nbhat = (Y - Y.mean(axis=1, keepdims=True)) @ xc / Sxx\nahat = Y.mean(axis=1) - bhat * x.mean()\ne = Y - ahat[:, None] - bhat[:, None] * x\nse_conv = np.sqrt(np.sum(e ** 2, axis=1) / df / Sxx)\nhc0 = np.sum((xc ** 2) * e ** 2, axis=1) / Sxx ** 2\nse_hc1 = np.sqrt(hc0 * n / df)\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((LEVEL - cov_conv) > 3 * mcse_nominal)\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(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\": issues,\n    \"n_input_rows\": {\"design.csv\": int(d.shape[0])},\n    \"random_seed\": SEED,\n    # supplementary diagnostics\n    \"t_crit_28\": float(tcrit),\n    \"mcse_at_nominal\": mcse_nominal,\n    \"undercoverage_threshold\": float(LEVEL - 3 * mcse_nominal),\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    \"mean_se_hc1\": float(np.mean(se_hc1)),\n    \"mean_bhat_mc\": float(np.mean(bhat)),\n    \"sd_beta_homoskedastic_formula\": float(np.sqrt(np.mean(s ** 2) / Sxx)),\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 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\": 0.19026231012152658,\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_crit_28\": 2.048407141795244,\n  \"mcse_at_nominal\": 0.004873397172404485,\n  \"undercoverage_threshold\": 0.9353798084827865,\n  \"mcse_coverage_conventional\": 0.00811369213120636,\n  \"mcse_coverage_hc1\": 0.006648157639526908,\n  \"mean_se_hc1\": 0.24080977065103962,\n  \"mean_bhat_mc\": 0.4961965063446237,\n  \"sd_beta_homoskedastic_formula\": 0.19623471734704753\n}","is_error":false}]},"uuid":"45052eb9-3287-459f-a9ff-b2b3d88796d3","timestamp":"2026-10-30T04:17:46.581Z","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_crit_28\": 2.048407141795244,\n  \"mcse_at_nominal\": 0.004873397172404485,\n  \"undercoverage_threshold\": 0.9353798084827865,\n  \"mcse_coverage_conventional\": 0.00811369213120636,\n  \"mcse_coverage_hc1\": 0.006648157639526908,\n  \"mean_se_hc1\": 0.24080977065103962,\n  \"mean_bhat_mc\": 0.4961965063446237,\n  \"sd_beta_homoskedastic_formula\": 0.19623471734704753\n}","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"e44a2f66-f014-4060-9909-ca4a30596cfd","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}46{"type":"api-request-blob","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","hash":"aaed72ba878bfa7ba4ab22e83cf8acb5db5c9e08e9ed1c752b6987e026dad02f","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_019MVgXWUQ52pVCs3iDeWgZV","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F2-conf-03: Monte Carlo coverage of OLS slope CIs under heteroskedasticity.\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\nALPHA, BETA, R, LEVEL = 1.0, 0.5, 2000, 0.95\n\nd = pd.read_csv(\"data/design.csv\")\nissues = []\nassert d.shape[0] == 30 and d[[\"x\", \"sigma\"]].notna().all().all() and (d.sigma > 0).all()\nx = d[\"x\"].to_numpy(float); s = d[\"sigma\"].to_numpy(float); n = len(x); df = n - 2\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, df)\n\nxc = x - x.mean(); Sxx = np.sum(xc ** 2); w = xc / Sxx\nsd_exact = float(np.sqrt(np.sum(w ** 2 * s ** 2)))          # (c) analytic\n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x + s * eps                               # R x n\nbhat = (Y - Y.mean(axis=1, keepdims=True)) @ xc / Sxx\nahat = Y.mean(axis=1) - bhat * x.mean()\ne = Y - ahat[:, None] - bhat[:, None] * x\nse_conv = np.sqrt(np.sum(e ** 2, axis=1) / df / Sxx)\nhc0 = np.sum((xc ** 2) * e ** 2, axis=1) / Sxx ** 2\nse_hc1 = np.sqrt(hc0 * n / df)\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((LEVEL - cov_conv) > 3 * mcse_nominal)\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(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\": issues,\n    \"n_input_rows\": {\"design.csv\": int(d.shape[0])},\n    \"random_seed\": SEED,\n    # supplementary diagnostics\n    \"t_crit_28\": float(tcrit),\n    \"mcse_at_nominal\": mcse_nominal,\n    \"undercoverage_threshold\": float(LEVEL - 3 * mcse_nominal),\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    \"mean_se_hc1\": float(np.mean(se_hc1)),\n    \"mean_bhat_mc\": float(np.mean(bhat)),\n    \"sd_beta_homoskedastic_formula\": float(np.sqrt(np.mean(s ** 2) / Sxx)),\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 and run analysis script"}}]}}47{"type":"api-request","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","id":"9ef6d9fa-f635-4ca8-a7d3-2b7612ce823b","timestamp":"2026-10-30T04:17:46.584Z","version":"2.1.314","querySource":"sdk","shapeHash":"b938085ee2de3a6034f0fc54cf7efbd722a6862ccf97adbfd88fb3a1bcedda83","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":"b66a944c-f1af-4788-8a61-24f497a1843c","keep":14,"tail":["aaed72ba878bfa7ba4ab22e83cf8acb5db5c9e08e9ed1c752b6987e026dad02f","1c98c2744eb194bebdf20b6558bd9db1cd795f6e55f1cebdf700159828702032"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",15,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"ec642a6335d5ae396cb86eadb1a11dce5afe014a0bf78a5b23a37024b057262f"}48{"parentUuid":"45052eb9-3287-459f-a9ff-b2b3d88796d3","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmzoSRsG16vdSqpt2dK","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":1925,"cache_read_input_tokens":11533,"output_tokens":997,"output_tokens_details":{"thinking_tokens":71},"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":1925},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":824,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmzoAJkpgsERamg6gKm","requestRef":"9ef6d9fa-f635-4ca8-a7d3-2b7612ce823b","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"08393a1d-bf70-4f64-b884-4a0e3f100339","timestamp":"2026-10-30T04:17:48.437Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}49{"parentUuid":"08393a1d-bf70-4f64-b884-4a0e3f100339","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmzoSRsG16vdSqpt2dK","type":"message","role":"assistant","content":[{"type":"text","text":"Now P4 verification: clean re-run, statsmodels cross-check, identities."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1925,"cache_read_input_tokens":11533,"output_tokens":997,"output_tokens_details":{"thinking_tokens":71},"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":1925},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmzoAJkpgsERamg6gKm","requestRef":"9ef6d9fa-f635-4ca8-a7d3-2b7612ce823b","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"2e24dbd3-5a0f-4f11-9a93-831001c3e7e7","timestamp":"2026-10-30T04:17:48.439Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}50{"parentUuid":"2e24dbd3-5a0f-4f11-9a93-831001c3e7e7","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmzoSRsG16vdSqpt2dK","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_017sG69UG5RXg3SVCyveyKmY","name":"Bash","input":{"command":"cp out/results.json /tmp/r1.json && rm out/results.json && ~/wp29/venv/bin/python out/analysis.py >/dev/null && cmp out/results.json /tmp/r1.json && echo IDENTICAL\n~/wp29/venv/bin/python - <<'EOF'\nimport numpy as np, pandas as pd, statsmodels.api as sm, json\nd=pd.read_csv(\"data/design.csv\"); x=d.x.values; s=d.sigma.values\nrng=np.random.default_rng(20261030); eps=rng.standard_normal((2000,30))\nX=sm.add_constant(x); bs=[];c1=[];c2=[];sec=[]\nfrom scipy import stats; t=stats.t.ppf(.975,28)\nfor r in range(2000):\n    y=1+0.5*x+s*eps[r]; m=sm.OLS(y,X).fit(); h=m.get_robustcov_results(\"HC1\")\n    b=m.params[1]; bs.append(b); sec.append(m.bse[1])\n    c1.append(abs(b-.5)<=t*m.bse[1]); c2.append(abs(b-.5)<=t*h.bse[1])\nres=json.load(open(\"out/results.json\"))\nprint(\"conv\",np.mean(c1),res[\"coverage_conventional\"]); print(\"hc1\",np.mean(c2),res[\"coverage_hc1\"])\nprint(\"meanse\",np.mean(sec),res[\"mean_se_conventional\"]); print(\"sdmc\",np.std(bs,ddof=1),res[\"sd_beta_mc\"])\n# exact sd via matrix formula\nXtXi=np.linalg.inv(X.T@X); V=XtXi@X.T@np.diag(s**2)@X@XtXi; print(\"sd exact\",np.sqrt(V[1,1]),res[\"sd_beta_exact\"])\n# z-score of MC sd vs exact: se of sd approx sd/sqrt(2(R-1))\nprint(\"z sd\", (res[\"sd_beta_mc\"]-res[\"sd_beta_exact\"])/(res[\"sd_beta_exact\"]/np.sqrt(2*1999)))\nprint(\"z mean bhat\",(res[\"mean_bhat_mc\"]-.5)/(res[\"sd_beta_exact\"]/np.sqrt(2000)))\nprint(\"gap conv\", 0.95-res[\"coverage_conventional\"], 3*res[\"mcse_at_nominal\"])\nEOF","description":"Reproducibility and statsmodels cross-check"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1925,"cache_read_input_tokens":11533,"output_tokens":997,"output_tokens_details":{"thinking_tokens":71},"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":1925},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXmzoAJkpgsERamg6gKm","requestRef":"9ef6d9fa-f635-4ca8-a7d3-2b7612ce823b","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"24aaf691-29b9-44f3-b578-f47daf768b2f","timestamp":"2026-10-30T04:17:54.789Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}51{"parentUuid":"24aaf691-29b9-44f3-b578-f47daf768b2f","isSidechain":false,"promptId":"21423356-3126-41ac-b89b-265abd7af27a","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_017sG69UG5RXg3SVCyveyKmY","type":"tool_result","content":"IDENTICAL\nconv 0.844 0.844\nhc1 0.902 0.902\nmeanse 0.19026231012152658 0.19026231012152658\nsdmc 0.2696473708309126 0.2696473708309126\nsd exact 0.2679805928302833 0.2679805928302833\nz sd 0.39327452124298634\nz mean bhat -0.6347377827316656\ngap conv 0.10599999999999998 0.014620191517213454","is_error":false}]},"uuid":"8b886f27-2191-4b0a-a071-021ef3f876b5","timestamp":"2026-10-30T04:17:55.997Z","toolUseResult":{"stdout":"IDENTICAL\nconv 0.844 0.844\nhc1 0.902 0.902\nmeanse 0.19026231012152658 0.19026231012152658\nsdmc 0.2696473708309126 0.2696473708309126\nsd exact 0.2679805928302833 0.2679805928302833\nz sd 0.39327452124298634\nz mean bhat -0.6347377827316656\ngap conv 0.10599999999999998 0.014620191517213454","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"24aaf691-29b9-44f3-b578-f47daf768b2f","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}52{"type":"api-request-blob","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","hash":"d5410c3a932452f918db0f5883877f5c3e470958336ea3fd69fa64bfc4f51712","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"Now P4 verification: clean re-run, statsmodels cross-check, identities."},{"type":"tool_use","id":"toolu_017sG69UG5RXg3SVCyveyKmY","name":"Bash","input":{"command":"cp out/results.json /tmp/r1.json && rm out/results.json && ~/wp29/venv/bin/python out/analysis.py >/dev/null && cmp out/results.json /tmp/r1.json && echo IDENTICAL\n~/wp29/venv/bin/python - <<'EOF'\nimport numpy as np, pandas as pd, statsmodels.api as sm, json\nd=pd.read_csv(\"data/design.csv\"); x=d.x.values; s=d.sigma.values\nrng=np.random.default_rng(20261030); eps=rng.standard_normal((2000,30))\nX=sm.add_constant(x); bs=[];c1=[];c2=[];sec=[]\nfrom scipy import stats; t=stats.t.ppf(.975,28)\nfor r in range(2000):\n    y=1+0.5*x+s*eps[r]; m=sm.OLS(y,X).fit(); h=m.get_robustcov_results(\"HC1\")\n    b=m.params[1]; bs.append(b); sec.append(m.bse[1])\n    c1.append(abs(b-.5)<=t*m.bse[1]); c2.append(abs(b-.5)<=t*h.bse[1])\nres=json.load(open(\"out/results.json\"))\nprint(\"conv\",np.mean(c1),res[\"coverage_conventional\"]); print(\"hc1\",np.mean(c2),res[\"coverage_hc1\"])\nprint(\"meanse\",np.mean(sec),res[\"mean_se_conventional\"]); print(\"sdmc\",np.std(bs,ddof=1),res[\"sd_beta_mc\"])\n# exact sd via matrix formula\nXtXi=np.linalg.inv(X.T@X); V=XtXi@X.T@np.diag(s**2)@X@XtXi; print(\"sd exact\",np.sqrt(V[1,1]),res[\"sd_beta_exact\"])\n# z-score of MC sd vs exact: se of sd approx sd/sqrt(2(R-1))\nprint(\"z sd\", (res[\"sd_beta_mc\"]-res[\"sd_beta_exact\"])/(res[\"sd_beta_exact\"]/np.sqrt(2*1999)))\nprint(\"z mean bhat\",(res[\"mean_bhat_mc\"]-.5)/(res[\"sd_beta_exact\"]/np.sqrt(2000)))\nprint(\"gap conv\", 0.95-res[\"coverage_conventional\"], 3*res[\"mcse_at_nominal\"])\nEOF","description":"Reproducibility and statsmodels cross-check"}}]}}53{"type":"api-request","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","id":"6436cf4d-8df3-4b5c-bac8-b80cfcd09b61","timestamp":"2026-10-30T04:17:55.999Z","version":"2.1.314","querySource":"sdk","shapeHash":"b938085ee2de3a6034f0fc54cf7efbd722a6862ccf97adbfd88fb3a1bcedda83","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":"9ef6d9fa-f635-4ca8-a7d3-2b7612ce823b","keep":16,"tail":["d5410c3a932452f918db0f5883877f5c3e470958336ea3fd69fa64bfc4f51712","0387593989e1a9fd3e8e712bbdb4698b6de752ee429768d4b0f5f2f45ceaf256"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",17,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"0485e8e0dfc9c34f4bf8c0f5f3b16c9f808ecf42c6a8f620269443e2738d3de1"}54{"parentUuid":"8b886f27-2191-4b0a-a071-021ef3f876b5","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXn1Vi6NMbYpQxGxykiu","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01RwnxnCh7jqFXtyQecNUX9U","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Clean re-run: deleted out/results.json, re-ran analysis.py; byte-identical to previous output (cmp). PASS\n2. Independent cross-check with statsmodels OLS (conventional bse and HC1 robust cov) on the same 2000 draws: coverage_conventional 0.844, coverage_hc1 0.902, mean_se_conventional, sd_beta_mc all identical. PASS\n3. sd_beta_exact equals sqrt([(X'X)^-1 X' diag(sigma^2) X (X'X)^-1]_22) from matrix formula = 0.26798. PASS\n4. sd_beta_mc (0.26965) vs exact: z = 0.39 using approx SE sd/sqrt(2(R-1)). Consistent. PASS\n5. mean betahat 0.4962 vs 0.5: z = -0.63; unbiasedness consistent. PASS\n6. Positive SEs: sd_beta_exact, sd_beta_mc, mean_se_conventional > 0. PASS\n7. Coverages in [0,1]; n_replications=2000, n_obs=30; exclusion ledger 30-0=30. PASS\n8. Undercoverage rule: 0.95-0.844=0.106 > 3*0.004873=0.0146 -> true. PASS\n9. Magnitude sanity: mean_se_conventional (0.190) < sd_beta_exact (0.268), consistent with the homoskedastic-formula SD 0.196 — explains the undercoverage of the baseline; HC1 mean se 0.241 closer but still below. 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\",\"30 rows x 3 cols, no NA, no dups, sigma>0\",\"exclusions.csv written (0 removed)\"],\"notes\":\"\"}\np[\"P2\"]={\"status\":\"passed\",\"checks\":[\"baseline coverage_conventional=0.844 computed with the same coverage rule\"],\"notes\":\"conventional interval is the task-named naive baseline\"}\np[\"P3\"]={\"status\":\"passed\",\"checks\":[\"analysis.py runs, seed 20261030 recorded, writes results.json\"],\"notes\":\"\"}\np[\"P4\"]={\"status\":\"running\",\"checks\":[\"clean rerun byte-identical\",\"statsmodels cross-check identical\",\"exact sd matrix check\",\"see checks.md\"],\"notes\":\"\"}\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\necho \"- 2026-10-30 P2/P3 passed: baseline cov_conv 0.844, HC1 0.902, seed 20261030. 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 (P4)"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1152,"cache_read_input_tokens":13458,"output_tokens":1082,"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":1152},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXn1VTDpwVAiUDXMTQKi","requestRef":"6436cf4d-8df3-4b5c-bac8-b80cfcd09b61","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"397a79eb-bbd9-453f-b1a3-ad1835cc3bbc","timestamp":"2026-10-30T04:18:05.098Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}55{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"397a79eb-bbd9-453f-b1a3-ad1835cc3bbc","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3"}56{"type":"atis-latch","atis":"","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3"}57{"parentUuid":"397a79eb-bbd9-453f-b1a3-ad1835cc3bbc","isSidechain":false,"promptId":"21423356-3126-41ac-b89b-265abd7af27a","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 0.4s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0060/out/state/gate_receipts/20261030T041805.646278Z.json","is_error":true,"tool_use_id":"toolu_01RwnxnCh7jqFXtyQecNUX9U"}]},"uuid":"9924cfa9-364f-4049-bfef-75b7fe818f96","timestamp":"2026-10-30T04:18:05.651Z","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 0.4s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0060/out/state/gate_receipts/20261030T041805.646278Z.json","sandboxed":false,"sourceToolAssistantUUID":"397a79eb-bbd9-453f-b1a3-ad1835cc3bbc","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}58{"type":"api-request-blob","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","hash":"910018eea5ca061d8fce8caa7494dec2b11351998d5dbf8a893cbfa8b6ec9768","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01RwnxnCh7jqFXtyQecNUX9U","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Clean re-run: deleted out/results.json, re-ran analysis.py; byte-identical to previous output (cmp). PASS\n2. Independent cross-check with statsmodels OLS (conventional bse and HC1 robust cov) on the same 2000 draws: coverage_conventional 0.844, coverage_hc1 0.902, mean_se_conventional, sd_beta_mc all identical. PASS\n3. sd_beta_exact equals sqrt([(X'X)^-1 X' diag(sigma^2) X (X'X)^-1]_22) from matrix formula = 0.26798. PASS\n4. sd_beta_mc (0.26965) vs exact: z = 0.39 using approx SE sd/sqrt(2(R-1)). Consistent. PASS\n5. mean betahat 0.4962 vs 0.5: z = -0.63; unbiasedness consistent. PASS\n6. Positive SEs: sd_beta_exact, sd_beta_mc, mean_se_conventional > 0. PASS\n7. Coverages in [0,1]; n_replications=2000, n_obs=30; exclusion ledger 30-0=30. PASS\n8. Undercoverage rule: 0.95-0.844=0.106 > 3*0.004873=0.0146 -> true. PASS\n9. Magnitude sanity: mean_se_conventional (0.190) < sd_beta_exact (0.268), consistent with the homoskedastic-formula SD 0.196 — explains the undercoverage of the baseline; HC1 mean se 0.241 closer but still below. 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\",\"30 rows x 3 cols, no NA, no dups, sigma>0\",\"exclusions.csv written (0 removed)\"],\"notes\":\"\"}\np[\"P2\"]={\"status\":\"passed\",\"checks\":[\"baseline coverage_conventional=0.844 computed with the same coverage rule\"],\"notes\":\"conventional interval is the task-named naive baseline\"}\np[\"P3\"]={\"status\":\"passed\",\"checks\":[\"analysis.py runs, seed 20261030 recorded, writes results.json\"],\"notes\":\"\"}\np[\"P4\"]={\"status\":\"running\",\"checks\":[\"clean rerun byte-identical\",\"statsmodels cross-check identical\",\"exact sd matrix check\",\"see checks.md\"],\"notes\":\"\"}\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\necho \"- 2026-10-30 P2/P3 passed: baseline cov_conv 0.844, HC1 0.902, seed 20261030. 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 (P4)"}}]}}59{"type":"api-request","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","id":"b47f88c8-9cbd-4848-80ab-709694686970","timestamp":"2026-10-30T04:18:05.653Z","version":"2.1.314","querySource":"sdk","shapeHash":"b938085ee2de3a6034f0fc54cf7efbd722a6862ccf97adbfd88fb3a1bcedda83","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":"6436cf4d-8df3-4b5c-bac8-b80cfcd09b61","keep":18,"tail":["910018eea5ca061d8fce8caa7494dec2b11351998d5dbf8a893cbfa8b6ec9768","00696268c7d965f34b6566d5460832e0e04051689262ff1f54a146dfec8a6cbd"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",19,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"49a74269124bba9429e4483a67be4695aacfaa83e6aadca1845752d9793025b4"}60{"parentUuid":"9924cfa9-364f-4049-bfef-75b7fe818f96","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXn2CsrZehf6dPMpSAyc","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":1826,"cache_read_input_tokens":14610,"output_tokens":3153,"output_tokens_details":{"thinking_tokens":66},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1826},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1266,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXn2CgwRubnSZeA1PrEi","requestRef":"b47f88c8-9cbd-4848-80ab-709694686970","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"38370230-a18a-4a11-8854-8b84999f8026","timestamp":"2026-10-30T04:18:08.086Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}61{"parentUuid":"38370230-a18a-4a11-8854-8b84999f8026","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXn2CsrZehf6dPMpSAyc","type":"message","role":"assistant","content":[{"type":"text","text":"At P4, the only gate failures are for P5 deliverables that don't exist yet. Every P4-relevant check passes, including reproducibility. Next I'll write the report and claims."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1826,"cache_read_input_tokens":14610,"output_tokens":3153,"output_tokens_details":{"thinking_tokens":66},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1826},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXn2CgwRubnSZeA1PrEi","requestRef":"b47f88c8-9cbd-4848-80ab-709694686970","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6ebd21e7-d94a-41df-83f1-b64572af0110","timestamp":"2026-10-30T04:18:08.089Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}62{"parentUuid":"6ebd21e7-d94a-41df-83f1-b64572af0110","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXn2CsrZehf6dPMpSAyc","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01T9ouQJ2FtCKxPkzdwA2t3b","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F2-conf-03 — Coverage of OLS slope confidence intervals under heteroskedasticity\n\n## Question\nIn the fixed-design model y_i = 1 + 0.5 x_i + σ_i ε_i (n = 30, with x_i and σ_i from `data/design.csv` and ε_i iid N(0,1)), do nominal 95% intervals β̂ ± t_0.975(28)·se cover β = 0.5 with probability 0.95? The question is asked for (i) the conventional OLS standard error and (ii) the HC1 robust standard error.\n\n## Data and exclusions\nThe only input is `data/design.csv`: 30 rows, columns i, x, sigma. Its SHA-256 matches the bundle manifest. It has no missing values and no duplicate rows, and every σ is positive (`n_input_rows`). No rows were excluded (`out/exclusions.csv`: 30 → 30), and no data issues were found (`data_issues` = []). σ_i is largest at the extreme x values, so the heteroskedasticity sits on the high-leverage points. Full audit: `out/state/data_audit.md`.\n\n## Method\n- **Exact SD of β̂ (computed analytically):** sqrt(Σ w_i² σ_i²), with w_i = (x_i − x̄)/S_xx. I confirmed it against the sandwich matrix formula.\n- **Monte Carlo:** R = 2000 replications (`n_replications`), n = 30 (`n_obs_per_replication`), numpy `default_rng` with seed 20261030 (`random_seed`). Only ε is redrawn; x and σ are held fixed.\n- **Standard errors in each replication:**\n  - se_conv = sqrt(s²/S_xx), where s² uses divisor n − 2.\n  - se_HC1 = sqrt(n/(n−2) · Σ(x_i−x̄)² e_i² / S_xx²).\n- **Critical value:** t_0.975(28) = 2.0484 (`t_crit_28`).\n- **Coverage:** the share of replications with |β̂ − 0.5| ≤ t·se.\n- **Undercoverage decision:** the conventional interval is declared to undercover if 0.95 − coverage > 3 × sqrt(0.95·0.05/2000). This uses the binomial MC standard error at the nominal level (`mcse_at_nominal` = 0.00487), which gives a threshold of 0.9354 (`undercoverage_threshold`).\n- **Baseline:** the conventional interval is the naïve baseline.\n- **Cross-check:** statsmodels OLS/HC1 on the same draws reproduced every number exactly.\n\n## Results\n| quantity | value | key |\n|---|---|---|\n| Coverage, conventional interval | 0.844 | `coverage_conventional` |\n| Coverage, HC1 interval | 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_bhat_mc` |\n| Conventional CI undercovers | true | `conventional_ci_undercovers` |\n\n**The conventional interval does not reach its nominal 95% coverage.**\n- Its coverage of 0.844 is about 10.6 points below 0.95, far beyond the three-MC-SE threshold of 0.9354.\n- On average, se_conv (0.190) understates the true sampling SD (0.268) by about 29%. Its mean is close to the homoskedastic-formula SD (0.196, `sd_beta_homoskedastic_formula`), which ignores the fact that error variance is concentrated at high-leverage x.\n\n**HC1 helps but also undercovers in this small sample.**\n- HC1 coverage is 0.902 and its mean SE is 0.241. Both are better than the conventional interval but still below nominal.\n- No formal three-SE test was specified for HC1. Even so, 0.902 is about 7 binomial MC SEs at the estimate (≈ 0.0066) below 0.95.\n\nThe MC SD of β̂ agrees with the exact SD (z ≈ 0.39), and mean β̂ is consistent with unbiasedness (`out/state/checks.md`).\n\n## Uncertainty\n- **Conventional coverage:** MC standard error at the estimate is sqrt(p(1−p)/R) = 0.0081 (`mcse_coverage_conventional`), giving an approximate 95% MC interval of 0.828–0.860.\n- **HC1 coverage:** MC standard error is 0.0066 (`mcse_coverage_hc1`), giving an approximate interval of 0.889–0.915.\n- **At the nominal level:** the MC SE is 0.0049 (`mcse_at_nominal`).\n- **SD estimate:** sd_beta_mc has a sampling SE of about sd/sqrt(2(R−1)) ≈ 0.0042.\n- **Other sources:** the results depend on the single seed 20261030. Under the stated model the analytic SD has no uncertainty.\n\n## Limitations and open issues\n- The results apply only to this specific synthetic design (n = 30, these x and σ) with normal errors. They should not be generalised to other designs or error distributions.\n- I used one seed and R = 2000, as the task specifies. Coverage figures are therefore accurate only to about ±0.016 (2 MC SEs).\n- The undercoverage rule uses the binomial SE at the nominal 0.95. Using the SE at the estimate (0.0081) gives the same conclusion.\n- Small-sample HC variants (HC2, HC3, wild bootstrap) were outside scope and were not evaluated.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The conventional OLS 95% interval does not attain nominal coverage: estimated coverage 0.844, more than three Monte Carlo SEs below 0.95.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"mcse_at_nominal\",\"undercoverage_threshold\"],\"status\":\"supported\",\"caveat\":\"Specific to this fixed design, normal errors, single seed, R=2000.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval covers better (0.902) but still below nominal in this n=30 sample.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\"],\"status\":\"supported\",\"caveat\":\"No formal test specified for HC1; judged by ~7 MC SEs gap.\"},\n {\"id\":\"C3\",\"text\":\"The exact SD of the slope estimator is 0.268, matched by the Monte Carlo SD 0.270.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\"],\"status\":\"supported\",\"caveat\":\"MC SD has sampling SE ~0.004.\"},\n {\"id\":\"C4\",\"text\":\"The conventional SE understates the true sampling SD on average (mean 0.190 vs 0.268), which explains the undercoverage.\",\"results_keys\":[\"mean_se_conventional\",\"sd_beta_exact\",\"sd_beta_homoskedastic_formula\"],\"status\":\"supported\",\"caveat\":\"Mechanism inferred from SE magnitudes; heteroskedasticity is concentrated at high-leverage x.\"}\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\":[\"clean rerun byte-identical\",\"statsmodels cross-check identical\",\"exact sd matrix check\",\"consistency checks in checks.md\",\"gate run: \"+r[0]+\" (results/keys/reproducibility/positive/exclusion ok; remaining failures were P5 deliverables not yet written)\"],\"notes\":\"\"}\np[\"P5\"]={\"status\":\"passed\",\"checks\":[\"report.md with 6 sections, keys cited\",\"claims.json with 4 claims incl. nominal-coverage claim\",\"final gate run (see log)\"],\"notes\":\"\"}\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\necho \"- 2026-10-30 P4 passed (gate receipt 1 recorded); P5 report+claims written; running final gate.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","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":1826,"cache_read_input_tokens":14610,"output_tokens":3153,"output_tokens_details":{"thinking_tokens":66},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1826},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXn2CgwRubnSZeA1PrEi","requestRef":"b47f88c8-9cbd-4848-80ab-709694686970","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f74069f9-2cab-40ff-8053-f2aad7cf5096","timestamp":"2026-10-30T04:18:32.699Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}63{"parentUuid":"f74069f9-2cab-40ff-8053-f2aad7cf5096","isSidechain":false,"promptId":"21423356-3126-41ac-b89b-265abd7af27a","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01T9ouQJ2FtCKxPkzdwA2t3b","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: 0.19026231012152658\n  [ok] reproducibility: regenerated in 0.4s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0060/out/state/gate_receipts/20261030T041833.247373Z.json","is_error":false}]},"uuid":"bacbdf28-f51b-4361-a4e3-2e43ae8a520b","timestamp":"2026-10-30T04:18:33.253Z","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: 0.19026231012152658\n  [ok] reproducibility: regenerated in 0.4s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0060/out/state/gate_receipts/20261030T041833.247373Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"f74069f9-2cab-40ff-8053-f2aad7cf5096","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}64{"type":"api-request-blob","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","hash":"76ebc2ca431330c38eef7c8f924664a89419db58ba7b45537742e34c11dc4beb","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"At P4, the only gate failures are for P5 deliverables that don't exist yet. Every P4-relevant check passes, including reproducibility. Next I'll write the report and claims."},{"type":"tool_use","id":"toolu_01T9ouQJ2FtCKxPkzdwA2t3b","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F2-conf-03 — Coverage of OLS slope confidence intervals under heteroskedasticity\n\n## Question\nIn the fixed-design model y_i = 1 + 0.5 x_i + σ_i ε_i (n = 30, with x_i and σ_i from `data/design.csv` and ε_i iid N(0,1)), do nominal 95% intervals β̂ ± t_0.975(28)·se cover β = 0.5 with probability 0.95? The question is asked for (i) the conventional OLS standard error and (ii) the HC1 robust standard error.\n\n## Data and exclusions\nThe only input is `data/design.csv`: 30 rows, columns i, x, sigma. Its SHA-256 matches the bundle manifest. It has no missing values and no duplicate rows, and every σ is positive (`n_input_rows`). No rows were excluded (`out/exclusions.csv`: 30 → 30), and no data issues were found (`data_issues` = []). σ_i is largest at the extreme x values, so the heteroskedasticity sits on the high-leverage points. Full audit: `out/state/data_audit.md`.\n\n## Method\n- **Exact SD of β̂ (computed analytically):** sqrt(Σ w_i² σ_i²), with w_i = (x_i − x̄)/S_xx. I confirmed it against the sandwich matrix formula.\n- **Monte Carlo:** R = 2000 replications (`n_replications`), n = 30 (`n_obs_per_replication`), numpy `default_rng` with seed 20261030 (`random_seed`). Only ε is redrawn; x and σ are held fixed.\n- **Standard errors in each replication:**\n  - se_conv = sqrt(s²/S_xx), where s² uses divisor n − 2.\n  - se_HC1 = sqrt(n/(n−2) · Σ(x_i−x̄)² e_i² / S_xx²).\n- **Critical value:** t_0.975(28) = 2.0484 (`t_crit_28`).\n- **Coverage:** the share of replications with |β̂ − 0.5| ≤ t·se.\n- **Undercoverage decision:** the conventional interval is declared to undercover if 0.95 − coverage > 3 × sqrt(0.95·0.05/2000). This uses the binomial MC standard error at the nominal level (`mcse_at_nominal` = 0.00487), which gives a threshold of 0.9354 (`undercoverage_threshold`).\n- **Baseline:** the conventional interval is the naïve baseline.\n- **Cross-check:** statsmodels OLS/HC1 on the same draws reproduced every number exactly.\n\n## Results\n| quantity | value | key |\n|---|---|---|\n| Coverage, conventional interval | 0.844 | `coverage_conventional` |\n| Coverage, HC1 interval | 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_bhat_mc` |\n| Conventional CI undercovers | true | `conventional_ci_undercovers` |\n\n**The conventional interval does not reach its nominal 95% coverage.**\n- Its coverage of 0.844 is about 10.6 points below 0.95, far beyond the three-MC-SE threshold of 0.9354.\n- On average, se_conv (0.190) understates the true sampling SD (0.268) by about 29%. Its mean is close to the homoskedastic-formula SD (0.196, `sd_beta_homoskedastic_formula`), which ignores the fact that error variance is concentrated at high-leverage x.\n\n**HC1 helps but also undercovers in this small sample.**\n- HC1 coverage is 0.902 and its mean SE is 0.241. Both are better than the conventional interval but still below nominal.\n- No formal three-SE test was specified for HC1. Even so, 0.902 is about 7 binomial MC SEs at the estimate (≈ 0.0066) below 0.95.\n\nThe MC SD of β̂ agrees with the exact SD (z ≈ 0.39), and mean β̂ is consistent with unbiasedness (`out/state/checks.md`).\n\n## Uncertainty\n- **Conventional coverage:** MC standard error at the estimate is sqrt(p(1−p)/R) = 0.0081 (`mcse_coverage_conventional`), giving an approximate 95% MC interval of 0.828–0.860.\n- **HC1 coverage:** MC standard error is 0.0066 (`mcse_coverage_hc1`), giving an approximate interval of 0.889–0.915.\n- **At the nominal level:** the MC SE is 0.0049 (`mcse_at_nominal`).\n- **SD estimate:** sd_beta_mc has a sampling SE of about sd/sqrt(2(R−1)) ≈ 0.0042.\n- **Other sources:** the results depend on the single seed 20261030. Under the stated model the analytic SD has no uncertainty.\n\n## Limitations and open issues\n- The results apply only to this specific synthetic design (n = 30, these x and σ) with normal errors. They should not be generalised to other designs or error distributions.\n- I used one seed and R = 2000, as the task specifies. Coverage figures are therefore accurate only to about ±0.016 (2 MC SEs).\n- The undercoverage rule uses the binomial SE at the nominal 0.95. Using the SE at the estimate (0.0081) gives the same conclusion.\n- Small-sample HC variants (HC2, HC3, wild bootstrap) were outside scope and were not evaluated.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The conventional OLS 95% interval does not attain nominal coverage: estimated coverage 0.844, more than three Monte Carlo SEs below 0.95.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"mcse_at_nominal\",\"undercoverage_threshold\"],\"status\":\"supported\",\"caveat\":\"Specific to this fixed design, normal errors, single seed, R=2000.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval covers better (0.902) but still below nominal in this n=30 sample.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\"],\"status\":\"supported\",\"caveat\":\"No formal test specified for HC1; judged by ~7 MC SEs gap.\"},\n {\"id\":\"C3\",\"text\":\"The exact SD of the slope estimator is 0.268, matched by the Monte Carlo SD 0.270.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\"],\"status\":\"supported\",\"caveat\":\"MC SD has sampling SE ~0.004.\"},\n {\"id\":\"C4\",\"text\":\"The conventional SE understates the true sampling SD on average (mean 0.190 vs 0.268), which explains the undercoverage.\",\"results_keys\":[\"mean_se_conventional\",\"sd_beta_exact\",\"sd_beta_homoskedastic_formula\"],\"status\":\"supported\",\"caveat\":\"Mechanism inferred from SE magnitudes; heteroskedasticity is concentrated at high-leverage x.\"}\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\":[\"clean rerun byte-identical\",\"statsmodels cross-check identical\",\"exact sd matrix check\",\"consistency checks in checks.md\",\"gate run: \"+r[0]+\" (results/keys/reproducibility/positive/exclusion ok; remaining failures were P5 deliverables not yet written)\"],\"notes\":\"\"}\np[\"P5\"]={\"status\":\"passed\",\"checks\":[\"report.md with 6 sections, keys cited\",\"claims.json with 4 claims incl. nominal-coverage claim\",\"final gate run (see log)\"],\"notes\":\"\"}\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\necho \"- 2026-10-30 P4 passed (gate receipt 1 recorded); P5 report+claims written; running final gate.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Write report, claims, update ledger, rerun gate"}}]}}65{"type":"api-request","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","id":"0905583b-684b-43a6-9153-edd54014cda7","timestamp":"2026-10-30T04:18:33.255Z","version":"2.1.314","querySource":"sdk","shapeHash":"b938085ee2de3a6034f0fc54cf7efbd722a6862ccf97adbfd88fb3a1bcedda83","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":"b47f88c8-9cbd-4848-80ab-709694686970","keep":20,"tail":["76ebc2ca431330c38eef7c8f924664a89419db58ba7b45537742e34c11dc4beb","6d78b297a761f17d56869075dfd6ee40d04022dcea1cb39056274031012235e7"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",21,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"4ff31c48e5952ac89fe1171b44ef5c85687fb0a99cb4944e981df598b9e47021"}66{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"bacbdf28-f51b-4361-a4e3-2e43ae8a520b","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3"}67{"type":"atis-latch","atis":"","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3"}68{"parentUuid":"bacbdf28-f51b-4361-a4e3-2e43ae8a520b","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXn4EqyUSksCQ9ZVSbJV","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01XNimpmU15m7f5kucQXQZJ4","name":"Bash","input":{"command":"~/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[\"P5\"][\"checks\"][-1]=\"final gate PASSED: \"+r[-1]\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\necho \"- 2026-10-30 P5 passed; final gate PASSED. 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All phases P0–P5 are complete and the final gate check passed.\n\n| Quantity | Result |\n|---|---|\n| Coverage, conventional interval | 0.844 (Monte Carlo SE 0.008) |\n| Coverage, HC1 robust interval | 0.902 (Monte Carlo SE 0.007) |\n| Exact SD of β̂ (analytic) | 0.2680 |\n| Simulated SD of β̂ | 0.2696 |\n| Average conventional SE | 0.1903 |\n| Conventional interval undercovers | true |\n\n- **Conventional interval:** the task's cutoff for \"undercovers\" is three Monte Carlo SEs below 95%, which is 0.9354. The observed 0.844 is far below that.\n- **Why it undercovers:** on average the conventional SE (0.190) is about 29% smaller than the true spread of β̂ (0.268). In this design the error variance is largest at the extreme x values, which have the most influence on the slope, and the conventional SE ignores that.\n- **HC1 interval:** it does better but is still below 95%. 0.902 is about seven Monte Carlo SEs short. The task set no formal test for HC1, so this is my judgement from that gap.\n- **Checks:** running statsmodels on the same random draws gave exactly the same numbers. A clean re-run of the script reproduced `results.json` byte for byte. The simulated SD agrees with the exact one.\n\n**Limitations:**\n- The results apply only to this synthetic 30-point design with normal errors.\n- They come from a single seed (20261030) and 2,000 replications as specified, so each coverage figure is accurate to roughly ±0.016.\n- Small-sample corrections beyond HC1 (HC2, HC3, bootstrap) were out of scope and not evaluated.\n\nThe data file had no problems and no rows were excluded. Besides the required keys, `results.json` also holds extra diagnostics such as the Monte Carlo SEs and the average HC1 SE.\n\nEverything is in `out/`:\n- `results.json`\n- `report.md`\n- `analysis.py` (re-run it with `~/wp29/venv/bin/python out/analysis.py`)\n- `claims.json`\n- `exclusions.csv`\n- `state/` (contract, data audit, checks, phase ledger, log, gate receipts)"}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":333,"cache_read_input_tokens":20264,"output_tokens":856,"output_tokens_details":{"thinking_tokens":19},"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":333},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXn4U2ETERLNzgqsMJXg","requestRef":"98256f3d-1444-4dcf-b720-040cec0427e4","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"1aef7d6c-29be-4374-b625-c4c588737e6b","timestamp":"2026-10-30T04:18:44.689Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0060","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","version":"2.1.314","gitBranch":"HEAD"}74{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"1aef7d6c-29be-4374-b625-c4c588737e6b","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3"}75{"type":"cost-state","sessionId":"f9377b92-96a7-4f54-8801-781959cb44b3","totalCostUSD":0.353422,"totalAPIDuration":101413,"totalAPIDurationWithoutRetries":101406,"totalToolDuration":3637,"totalLinesAdded":0,"totalLinesRemoved":0,"totalDuration":105166,"startTime":1793333819549,"modelUsage":{"claude-opus-5-5":{"inputTokens":26,"outputTokens":11634,"thinkingTokens":307,"cacheReadInputTokens":125865,"cacheCreationInputTokens":19093,"cacheCreationEphemeral5mInputTokens":19093,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.353422}},"hasUnknownModelCost":false}76