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It is the complete and only authoritative description of what is required: the scientific question, the inputs under `data/`, the required output files and their exact keys, and the information-availability rules.\n- There is no network access. Use the Python interpreter `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels, matplotlib are installed). Standard shell tools are available. Do not try to install packages.\n- Write every deliverable under `./out/`. The required deliverables are listed in `TASK.md`; at minimum they always include `out/results.json`, `out/report.md`, and a replication entry point `out/analysis.py` that regenerates `out/results.json` from `data/` when run with `~/wp29/venv/bin/python out/analysis.py` from the workspace root.\n- You are working alone and unattended; nobody will answer questions. Make reasonable, documented decisions.\n\nIntegrity rules (identical for every task):\n- Never fabricate numbers, data, results, or references. Every number in `out/results.json` and `out/report.md` must be produced by code you ran on the provided inputs.\n- Respect the information-availability rules in `TASK.md` exactly (for example, never use information that would not have been available at the stated decision time).\n- If part of the task cannot be completed as specified, say so explicitly in `out/report.md`, explain why, and still write every required file (use `null` for values you could not legitimately produce). An honest statement of a limitation is always preferred to a fabricated or guessed value.\n- Do not modify anything under `data/`.\n- When you are done, end with a brief plain-text summary of what you produced and any limitations.\n\nComplete the task described in `TASK.md` by following this research protocol. The protocol adds no scientific information to the task; it organizes how you work and what evidence you leave behind.\n\nPHASES (execute in order; a phase is eligible only when its dependencies are satisfied):\n\nP0 Scope and contract (depends on: nothing)\n- Read `TASK.md` completely. In `out/state/contract.md`, restate in your own words: the scientific question; the quantity or quantities to be estimated (the estimands) and the assumptions under which they are meaningful; every required output file and key; the information-availability rules; what would make the task impossible or the result invalid.\n- Write the initial phase ledger `out/state/phases.json`: a JSON object mapping each phase id (P0 … P5) to {\"status\": \"pending\"|\"running\"|\"passed\"|\"failed\"|\"blocked\"|\"stale\"|\"skipped_optional\", \"checks\": [], \"notes\": \"\"}. Keep it current as you work. A phase may only be set to \"passed\" when the checks listed for it in this protocol have actually been executed and their outcome recorded in \"checks\".\n\nP1 Data audit and provenance (depends on: P0)\n- Inspect every input file: compute and record its SHA-256, row and column counts, schema, units, date ranges, missing values, duplicates and anomalies in `out/state/data_audit.md`.\n- Keep an exclusion ledger in `out/exclusions.csv` (columns: step, rule, n_before, n_after, n_removed, rationale) for every filtering step you apply, so that n_raw − total removed = n_analysed.\n- Identify any input that violates the information-availability rules and decide, in writing, how you will handle it.\n\nP2 Baseline (depends on: P1)\n- Before any elaborate method, compute the simplest valid baseline that answers the question (for example a naïve or unconditional estimate), with the same evaluation rule used later. Record it in `out/results.json` under the keys the task requires, or under `baseline_*` keys when the task does not name them.\n\nP3 Method and computation (depends on: P2)\n- Implement the analysis in `out/analysis.py` so that it reads only `data/`, writes `out/results.json` deterministically (fix every random seed you use and record it), and prints nothing that contradicts the written results. Any figure or table must be generated by this script.\n\nP4 Verification (depends on: P3)\n- Re-run `out/analysis.py` from a clean state and confirm it regenerates `out/results.json` with identical values. Record the check in `out/state/phases.json` under P4.\n- Check internal consistency: identities that must hold (for example counts that must add up, standard errors that must be positive, confidence intervals that must contain their estimates, date orderings that must respect the information rules), units, and magnitudes against the baseline. Record every check and its outcome in `out/state/checks.md`. A failed check must be fixed or honestly reported, never silently ignored.\n\nP5 Reporting (depends on: P4)\n- Write `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. Every quantitative statement must cite the key of `out/results.json` it comes from.\n- Write `out/claims.json`: a list of the central claims of your report, each as {\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}. Do not state a claim in the report that is not in this ledger.\n- Set the final statuses in `out/state/phases.json`.\n\nSTOPPING RULES\n- Stop and declare the task complete only when every phase P0–P5 is \"passed\" with recorded checks. If a phase is \"blocked\" (missing information, impossible requirement, violated availability rule), stop, set the status, explain in `out/report.md` (section Limitations and open issues) and still write every required file with `null` for values you could not legitimately produce.\n- Do not spend effort on extensions that the task does not require.\n\nRECOVERY RULES\n- Append a short dated entry to `out/state/log.md` after each phase transition and after any important decision, so that work can be resumed by reading `out/state/`.\n- If you discover that an upstream input or decision changed after a downstream phase passed, mark the downstream phases \"stale\" and redo them; do not reuse stale results.\n- If you are interrupted and later resumed, first read `out/state/` and continue from the last consistent state; never re-run expensive steps that already have recorded, unchanged outputs.\n\nEXECUTABLE GATES (additional, mandatory)\n- A read-only gate program is provided at `~/wp29/gates/pgar_gate.py`. Run it from the workspace root as `~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .` It checks the output contract of `TASK.md` (required files, keys, types, finite values, report sections, the claims ledger, the phase ledger, the exclusion ledger) and reproducibility (it re-runs `out/analysis.py` in a temporary copy and compares the regenerated `out/results.json` with yours). It never checks scientific correctness and it contains no reference answers.\n- You must run the gate at the end of P4 and again at the end of P5, and record each run's receipt (the gate writes `out/state/gate_receipts/<timestamp>.json`) in `out/state/phases.json`. You may not declare the task complete while the latest gate receipt reports `\"passed\": false`. Fix the reported problems and re-run the gate.\n- The controller will run the same gate after your session ends. If it fails, you will be resumed with the gate output and asked to fix the problems; each such cycle consumes your remaining budget.\n"}],"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/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c"}12{"parentUuid":"66818ffb-4751-4186-9a7c-2547b6aafc6f","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmmz3nGH3FN5mo7NA6x","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":145,"output_tokens_details":{"thinking_tokens":23},"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":476,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmmyqPhVguawwMQQrCN","requestRef":"4b97a59b-a924-4812-bb95-587a4b0df966","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"44d041db-30a3-4680-b175-d2e697fc91e3","timestamp":"2026-10-30T04:14:54.024Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"44d041db-30a3-4680-b175-d2e697fc91e3","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmmz3nGH3FN5mo7NA6x","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_015LLtC9Etg33ucaxUJUC46b","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 43 simon-pierreboucher staff 1376 oct. 30 00:14 ..\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\n(eval):1: no matches found: out/state/*","is_error":false}]},"uuid":"285222e5-3ef4-4949-a7e0-284682dfdbe9","timestamp":"2026-10-30T04:14:54.843Z","toolUseResult":{"stdout":"# F2-conf-03 — Monte Carlo coverage of OLS confidence intervals in a small heteroskedastic sample\n\n## Scientific question\nHow well do nominal 95% confidence intervals for an OLS slope perform in a small sample with heteroskedastic errors? Consider the fixed-design linear model y_i = α + β x_i + σ_i ε_i, i = 1, …, 30, with α = 1, β = 0.5, ε_i independent standard normal, and x_i and σ_i fixed at the values given in `data/design.csv` (the same 30 values in every replication; only ε is redrawn). The estimands are (a) the true coverage probability of the interval β̂ ± t_{0.975}(28) · se_conv, where se_conv is the conventional OLS standard error (residual variance with divisor n − 2); (b) the true coverage probability of the interval β̂ ± t_{0.975}(28) · se_HC1, where se_HC1 is the heteroskedasticity-robust HC1 standard error (White's HC0 sandwich multiplied by n/(n − 2)); (c) the exact finite-sample standard deviation of β̂ under this design; (d) the expected value of se_conv. Estimate (a), (b) and (d) by Monte Carlo with exactly R = 2000 replications and a fixed seed, compute (c) analytically, and conclude whether the conventional interval attains its nominal coverage.\n\n## Inputs\n- `data/design.csv` — the fixed design (a synthetic design generated for this exercise; not observed data). Columns: `i` (observation index 1–30), `x` (regressor value, dimensionless), `sigma` (standard deviation of the error for observation i, dimensionless). 30 rows.\n\n## Information-availability rules\n- Use only `data/design.csv`; the model constants (α = 1, β = 0.5, n = 30, R = 2000, nominal level 95%, t(28) critical value) are given above. Do not redraw x or σ.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | – | \"F2-conf-03\" |\n| `coverage_conventional` | number | proportion | share of the 2000 replications in which the conventional interval contains β = 0.5 — the naïve baseline |\n| `coverage_hc1` | number | proportion | share of the 2000 replications in which the HC1 interval contains β = 0.5 |\n| `sd_beta_exact` | number | – | exact standard deviation of β̂ under the design (analytical, no simulation) |\n| `sd_beta_mc` | number | – | sample standard deviation (divisor R − 1) of the 2000 simulated β̂ |\n| `mean_se_conventional` | number | – | average of se_conv over the 2000 replications |\n| `conventional_ci_undercovers` | boolean | – | true if and only if `coverage_conventional` is below 0.95 by more than three Monte Carlo standard errors (binomial standard error at R = 2000) |\n| `n_replications` | integer | – | number of replications (2000) |\n| `n_obs_per_replication` | integer | – | sample size per replication (30) |\n| `feasibility` | string | – | \"complete\", \"partial\" or \"infeasible\" |\n| `feasibility_reason` | string or null | – | explanation if not complete |\n| `data_issues` | array of {\"issue\",\"handling\"} | – | data problems detected and how handled (empty list if none) |\n| `n_input_rows` | object | – | {\"design.csv\": rows read} |\n| `random_seed` | integer | – | the seed used for the simulation (required; the simulation must be reproducible) |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty (include the Monte Carlo standard error of each coverage estimate); Limitations and open issues.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` from `data/` only, deterministically (same seed, same numbers).\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}]. Include one claim about whether the conventional interval attains its nominal coverage.\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels available). Do not modify `data/`.\n- This task is designed to be completed in well under 15 minutes of work; the simulation itself should take seconds.\ntotal 32\ndrwxr-xr-x 6 simon-pierreboucher staff 192 oct. 29 23:35 .\ndrwxr-xr-x 43 simon-pierreboucher staff 1376 oct. 30 00:14 ..\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\n(eval):1: no matches found: 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> out/state/contract.md <<'EOF'\n# Contract (P0)\n**Question:** In the fixed-design 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 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 mean.\n- Also sd_beta_mc (divisor R-1) and decision conventional_ci_undercovers = cov_conv < 0.95 - 3*sqrt(0.95*0.05/2000).\nMeaningful under: fixed design, normal errors, known sigma_i only used by the DGP (not by estimators).\n\n**Outputs:** out/results.json (task_id, coverage_conventional, coverage_hc1, sd_beta_exact, sd_beta_mc, mean_se_conventional, conventional_ci_undercovers, n_replications, n_obs_per_replication, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed), out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues), out/analysis.py, out/claims.json, plus protocol files.\n\n**Information rules:** only data/design.csv; never redraw x or sigma; constants as given.\n\n**Invalidity:** design file missing/malformed (not 30 rows, non-positive sigma, constant x), R != 2000, non-reproducible seed.\nEOF\ncat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\nFile: data/design.csv — SHA-256 b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0 (matches bundle.json).\n- 30 rows × 3 columns: i (int64, 1..30, unique, consecutive), x (float64, dimensionless, range −1.3942..1.9919, mean 0.2823, sd 0.8212), sigma (float64, dimensionless, range 0.6034..1.7903, all > 0).\n- Missing values: 0. Duplicate rows: 0. Duplicate x: 0. No dates (synthetic design).\n- Notable feature (not an error): sigma is strongly increasing in |x| (corr(x², sigma²) = 0.987), i.e. heteroskedasticity loaded on high-leverage points — the setting where conventional SE is expected to be biased downward.\n- Availability: the only input; it is the design itself, no rule violations. No exclusions applied (exclusions.csv records a no-op step).\nEOF\nprintf 'step,rule,n_before,n_after,n_removed,rationale\\n1,none (all design rows retained; no missing/invalid values),30,30,0,fixed design must be used as given\\n' > out/exclusions.csv","description":"Write contract, audit, exclusions"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":577,"cache_read_input_tokens":7648,"output_tokens":1225,"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":577},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmnZHYAVf3xHCmP3DaU","requestRef":"709d4015-435b-4886-8683-3b72dc0a4713","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"22182da4-5983-4eb0-991a-5570713b8d67","timestamp":"2026-10-30T04:15:12.077Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}30{"parentUuid":"22182da4-5983-4eb0-991a-5570713b8d67","isSidechain":false,"promptId":"6a467718-f2b4-4f12-aa3d-7bee6edb5c9d","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_016tHYhcZoYVfWqMAMi6ZUqh","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"f3debb47-e142-44c1-b898-1f2c4e9ab141","timestamp":"2026-10-30T04:15:12.132Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"22182da4-5983-4eb0-991a-5570713b8d67","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}31{"type":"api-request-blob","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","hash":"c4bc445a690b40b0ffb41efc9a641d67080765f983d97a96c26ec875bbd53c98","message":{"role":"assistant","content":[{"type":"text","text":"Now the contract, audit, and analysis script."},{"type":"tool_use","id":"toolu_016tHYhcZoYVfWqMAMi6ZUqh","name":"Bash","input":{"command":"cat > out/state/contract.md <<'EOF'\n# Contract (P0)\n**Question:** In the fixed-design 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 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 mean.\n- Also sd_beta_mc (divisor R-1) and decision conventional_ci_undercovers = cov_conv < 0.95 - 3*sqrt(0.95*0.05/2000).\nMeaningful under: fixed design, normal errors, known sigma_i only used by the DGP (not by estimators).\n\n**Outputs:** out/results.json (task_id, coverage_conventional, coverage_hc1, sd_beta_exact, sd_beta_mc, mean_se_conventional, conventional_ci_undercovers, n_replications, n_obs_per_replication, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed), out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues), out/analysis.py, out/claims.json, plus protocol files.\n\n**Information rules:** only data/design.csv; never redraw x or sigma; constants as given.\n\n**Invalidity:** design file missing/malformed (not 30 rows, non-positive sigma, constant x), R != 2000, non-reproducible seed.\nEOF\ncat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\nFile: data/design.csv — SHA-256 b1a17a529973e7994bbedad5ec1bc73fe968c777301ca8745657ea300e3c74f0 (matches bundle.json).\n- 30 rows × 3 columns: i (int64, 1..30, unique, consecutive), x (float64, dimensionless, range −1.3942..1.9919, mean 0.2823, sd 0.8212), sigma (float64, dimensionless, range 0.6034..1.7903, all > 0).\n- Missing values: 0. Duplicate rows: 0. Duplicate x: 0. No dates (synthetic design).\n- Notable feature (not an error): sigma is strongly increasing in |x| (corr(x², sigma²) = 0.987), i.e. heteroskedasticity loaded on high-leverage points — the setting where conventional SE is expected to be biased downward.\n- Availability: the only input; it is the design itself, no rule violations. No exclusions applied (exclusions.csv records a no-op step).\nEOF\nprintf 'step,rule,n_before,n_after,n_removed,rationale\\n1,none (all design rows retained; no missing/invalid values),30,30,0,fixed design must be used as given\\n' > out/exclusions.csv","description":"Write contract, audit, exclusions"}}]}}32{"type":"api-request","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","id":"bef99ac0-dd22-439c-b4f0-c763bf53e92b","timestamp":"2026-10-30T04:15:12.136Z","version":"2.1.314","querySource":"sdk","shapeHash":"6bbd835952ff5e70d3a7334e92f6ecff4e25d57126d287d8df8169be9dafc906","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":"709d4015-435b-4886-8683-3b72dc0a4713","keep":8,"tail":["c4bc445a690b40b0ffb41efc9a641d67080765f983d97a96c26ec875bbd53c98","73bbea8855c855c50ae9b746a4aa8dcee71b59b7e5fa7210af9214c3bb54bc79"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",9,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"2c853e58dcc3d34b2e5a0a84b67fb0ed0db554253fc2bc6f4aec77c24dd93702"}33{"parentUuid":"f3debb47-e142-44c1-b898-1f2c4e9ab141","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmoQvXcGYR79nmG1x9Y","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01XSP9khq6FNYQciU45ZfG1c","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\n\"\"\"\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\")\nn_rows = len(d)\nissues = []\nassert n_rows == 30 and d[[\"x\", \"sigma\"]].notna().all().all() and (d.sigma > 0).all()\nx = d[\"x\"].to_numpy(float); sig = d[\"sigma\"].to_numpy(float); n = len(x)\nX = np.column_stack([np.ones(n), x])\nXtX_inv = np.linalg.inv(X.T @ X)\nH = XtX_inv @ X.T # 2 x n, betahat = H y\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, n - 2)\n\n# (c) exact sd of betahat: Var = sum w_i^2 sigma_i^2, w = H[1]\nw = H[1]\nsd_exact = float(np.sqrt(np.sum(w**2 * sig**2)))\n\n# Monte Carlo (vectorised): Y is R x n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x[None, :] + sig[None, :] * eps\nB = Y @ H.T # R x 2\nresid = Y - B @ X.T\ns2 = (resid**2).sum(1) / (n - 2)\nse_conv = np.sqrt(s2 * XtX_inv[1, 1])\n# HC0 slope variance = sum_i w_i^2 e_i^2 ; HC1 = n/(n-2) * HC0\nse_hc1 = np.sqrt(n / (n - 2) * (resid**2 @ (w**2)))\nbhat = B[:, 1]\ncov_conv = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_conv))\ncov_hc1 = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_hc1))\nmcse_nominal = float(np.sqrt(LEVEL * (1 - LEVEL) / R))\nundercovers = bool(cov_conv < LEVEL - 3 * mcse_nominal)\n\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(se_conv.mean()),\n \"conventional_ci_undercovers\": undercovers,\n \"n_replications\": R,\n \"n_obs_per_replication\": n,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": None,\n \"data_issues\": issues,\n \"n_input_rows\": {\"design.csv\": n_rows},\n \"random_seed\": SEED,\n # supplementary diagnostics\n \"t_critical_28\": float(tcrit),\n \"mcse_coverage_conventional\": float(np.sqrt(cov_conv * (1 - cov_conv) / R)),\n \"mcse_coverage_hc1\": float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R)),\n \"mcse_at_nominal_095\": mcse_nominal,\n \"undercoverage_threshold\": LEVEL - 3 * mcse_nominal,\n \"mean_se_hc1\": float(se_hc1.mean()),\n \"mean_beta_hat\": float(bhat.mean()),\n \"sd_conv_exact_naive\": float(np.sqrt(XtX_inv[1, 1] * np.mean(sig**2) * 1.0)),\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"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1240,"cache_read_input_tokens":8225,"output_tokens":1560,"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":1240},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXmoQk7xq8NegS6stb2R","requestRef":"bef99ac0-dd22-439c-b4f0-c763bf53e92b","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f02c3ad1-d24f-4873-b837-8c0f929b1229","timestamp":"2026-10-30T04:15:24.197Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}34{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"f02c3ad1-d24f-4873-b837-8c0f929b1229","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c"}35{"type":"atis-latch","atis":"","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c"}36{"parentUuid":"f02c3ad1-d24f-4873-b837-8c0f929b1229","isSidechain":false,"promptId":"6a467718-f2b4-4f12-aa3d-7bee6edb5c9d","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01XSP9khq6FNYQciU45ZfG1c","type":"tool_result","content":"{\n \"task_id\": \"F2-conf-03\",\n \"coverage_conventional\": 0.844,\n \"coverage_hc1\": 0.902,\n \"sd_beta_exact\": 0.2679805928302833,\n \"sd_beta_mc\": 0.2696473708309126,\n \"mean_se_conventional\": 0.1902623101215266,\n \"conventional_ci_undercovers\": true,\n \"n_replications\": 2000,\n \"n_obs_per_replication\": 30,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [],\n \"n_input_rows\": {\n \"design.csv\": 30\n },\n \"random_seed\": 20261030,\n \"t_critical_28\": 2.048407141795244,\n \"mcse_coverage_conventional\": 0.00811369213120636,\n \"mcse_coverage_hc1\": 0.006648157639526908,\n \"mcse_at_nominal_095\": 0.004873397172404485,\n \"undercoverage_threshold\": 0.9353798084827865,\n \"mean_se_hc1\": 0.24080977065103962,\n \"mean_beta_hat\": 0.4961965063446237,\n \"sd_conv_exact_naive\": 0.19623471734704753\n}","is_error":false}]},"uuid":"f8aa323b-9483-43ee-bf4c-619c9930914d","timestamp":"2026-10-30T04:15:24.902Z","toolUseResult":{"stdout":"{\n \"task_id\": \"F2-conf-03\",\n \"coverage_conventional\": 0.844,\n \"coverage_hc1\": 0.902,\n \"sd_beta_exact\": 0.2679805928302833,\n \"sd_beta_mc\": 0.2696473708309126,\n \"mean_se_conventional\": 0.1902623101215266,\n \"conventional_ci_undercovers\": true,\n \"n_replications\": 2000,\n \"n_obs_per_replication\": 30,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [],\n \"n_input_rows\": {\n \"design.csv\": 30\n },\n \"random_seed\": 20261030,\n \"t_critical_28\": 2.048407141795244,\n \"mcse_coverage_conventional\": 0.00811369213120636,\n \"mcse_coverage_hc1\": 0.006648157639526908,\n \"mcse_at_nominal_095\": 0.004873397172404485,\n \"undercoverage_threshold\": 0.9353798084827865,\n \"mean_se_hc1\": 0.24080977065103962,\n \"mean_beta_hat\": 0.4961965063446237,\n \"sd_conv_exact_naive\": 0.19623471734704753\n}","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"f02c3ad1-d24f-4873-b837-8c0f929b1229","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}37{"type":"api-request-blob","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","hash":"635f5d69dfb1ac7badf7a831cbf4c467745196d489223abdb68088b59a4cfd95","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01XSP9khq6FNYQciU45ZfG1c","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\n\"\"\"\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\")\nn_rows = len(d)\nissues = []\nassert n_rows == 30 and d[[\"x\", \"sigma\"]].notna().all().all() and (d.sigma > 0).all()\nx = d[\"x\"].to_numpy(float); sig = d[\"sigma\"].to_numpy(float); n = len(x)\nX = np.column_stack([np.ones(n), x])\nXtX_inv = np.linalg.inv(X.T @ X)\nH = XtX_inv @ X.T # 2 x n, betahat = H y\ntcrit = stats.t.ppf(0.5 + LEVEL / 2, n - 2)\n\n# (c) exact sd of betahat: Var = sum w_i^2 sigma_i^2, w = H[1]\nw = H[1]\nsd_exact = float(np.sqrt(np.sum(w**2 * sig**2)))\n\n# Monte Carlo (vectorised): Y is R x n\nrng = np.random.default_rng(SEED)\neps = rng.standard_normal((R, n))\nY = ALPHA + BETA * x[None, :] + sig[None, :] * eps\nB = Y @ H.T # R x 2\nresid = Y - B @ X.T\ns2 = (resid**2).sum(1) / (n - 2)\nse_conv = np.sqrt(s2 * XtX_inv[1, 1])\n# HC0 slope variance = sum_i w_i^2 e_i^2 ; HC1 = n/(n-2) * HC0\nse_hc1 = np.sqrt(n / (n - 2) * (resid**2 @ (w**2)))\nbhat = B[:, 1]\ncov_conv = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_conv))\ncov_hc1 = float(np.mean(np.abs(bhat - BETA) <= tcrit * se_hc1))\nmcse_nominal = float(np.sqrt(LEVEL * (1 - LEVEL) / R))\nundercovers = bool(cov_conv < LEVEL - 3 * mcse_nominal)\n\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(se_conv.mean()),\n \"conventional_ci_undercovers\": undercovers,\n \"n_replications\": R,\n \"n_obs_per_replication\": n,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": None,\n \"data_issues\": issues,\n \"n_input_rows\": {\"design.csv\": n_rows},\n \"random_seed\": SEED,\n # supplementary diagnostics\n \"t_critical_28\": float(tcrit),\n \"mcse_coverage_conventional\": float(np.sqrt(cov_conv * (1 - cov_conv) / R)),\n \"mcse_coverage_hc1\": float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R)),\n \"mcse_at_nominal_095\": mcse_nominal,\n \"undercoverage_threshold\": LEVEL - 3 * mcse_nominal,\n \"mean_se_hc1\": float(se_hc1.mean()),\n \"mean_beta_hat\": float(bhat.mean()),\n \"sd_conv_exact_naive\": float(np.sqrt(XtX_inv[1, 1] * np.mean(sig**2) * 1.0)),\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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np.sqrt(30/28*(r**2*w**2).sum()))\nEOF","description":"Update diagnostic, rerun, cross-check with 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\"mean_beta_hat\": 0.4961965063446237,\n \"rms_se_conventional_exact\": 0.19318017740129875\n}\n0.15933017823041823 0.15393737845216712\n0.1593301782304182 0.1539373784521671","is_error":false}]},"uuid":"e06a800b-3805-488a-a7c1-e420f25f807e","timestamp":"2026-10-30T04:15:34.529Z","toolUseResult":{"stdout":" \"mean_beta_hat\": 0.4961965063446237,\n \"rms_se_conventional_exact\": 0.19318017740129875\n}\n0.15933017823041823 0.15393737845216712\n0.1593301782304182 0.1539373784521671","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"6949b637-1ffd-4c70-abf6-21da0310062f","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}43{"type":"api-request-blob","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","hash":"411207300c10ace9dd43a5ec72fc33a48543e78f3be89cf57c21e4648bfd4eef","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"Let me replace the loose diagnostic with an exact one (√E[s²]·(X'X)⁻¹₁₁, an upper bound for E[se_conv] by Jensen) and cross-check SEs against statsmodels."},{"type":"tool_use","id":"toolu_018UsNHxEFUXsTevuR71sPwW","name":"Bash","input":{"command":"cd out && ~/wp29/venv/bin/python - <<'EOF'\ns=open('analysis.py').read()\ns=s.replace(''' \"sd_conv_exact_naive\": float(np.sqrt(XtX_inv[1, 1] * np.mean(sig**2) * 1.0)),''',''' # sqrt(E[s^2] * (X'X)^-1_11), E[s^2] = sum sigma_i^2 (1 - h_ii) / (n-2); >= E[se_conv] by Jensen\n \"rms_se_conventional_exact\": float(np.sqrt(XtX_inv[1, 1] * np.sum(sig**2 * (1 - np.einsum(\"ij,ji->i\", X, H))) / (n - 2))),''')\nopen('analysis.py','w').write(s)\nEOF\ncd .. && ~/wp29/venv/bin/python out/analysis.py | tail -3 && cp out/results.json /tmp/r1.json && ~/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); e=rng.standard_normal((2000,30))[0]\ny=1+0.5*x+s*e; X=sm.add_constant(x)\nm=sm.OLS(y,X).fit(); print(m.bse[1], m.HC1_se[1])\nH=np.linalg.inv(X.T@X)@X.T; r=y-X@(H@y); w=H[1]\nprint(np.sqrt((r**2).sum()/28*np.linalg.inv(X.T@X)[1,1]), np.sqrt(30/28*(r**2*w**2).sum()))\nEOF","description":"Update diagnostic, rerun, cross-check with 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match statsmodels. Now P4: clean rerun, consistency checks, gate."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1044,"cache_read_input_tokens":11449,"output_tokens":737,"output_tokens_details":{"thinking_tokens":50},"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":1044},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmq4VWnGSztY9XLfrgi","requestRef":"93f679c7-fc38-475a-b523-9017b656b8c7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"173e4cbb-3bd8-47ac-aad6-308070fc44cb","timestamp":"2026-10-30T04:15:36.064Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}47{"parentUuid":"173e4cbb-3bd8-47ac-aad6-308070fc44cb","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmq4mt3riv4LVb813Ci","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_012WQzQPSfcyaTKo74naFGN6","name":"Bash","input":{"command":"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 json; r=json.load(open('out/results.json'))\nc=[(\"SEs positive\", all(r[k]>0 for k in ['sd_beta_exact','sd_beta_mc','mean_se_conventional','mean_se_hc1'])),\n(\"coverages in [0,1]\", 0<=r['coverage_conventional']<=1 and 0<=r['coverage_hc1']<=1),\n(\"coverage*R integer\", abs(r['coverage_conventional']*2000-round(r['coverage_conventional']*2000))<1e-9),\n(\"sd_mc within 5% of exact (sampling sd of SD ~ exact/sqrt(2R)=1.6%)\", abs(r['sd_beta_mc']/r['sd_beta_exact']-1)<0.05),\n(\"mean betahat within 3 MCSE of 0.5\", abs(r['mean_beta_hat']-0.5)<3*r['sd_beta_exact']/2000**0.5),\n(\"mean_se_conv <= rms exact (Jensen)\", r['mean_se_conventional']<=r['rms_se_conventional_exact']*1.01),\n(\"undercover flag consistent\", r['conventional_ci_undercovers']==(r['coverage_conventional']<0.95-3*(0.95*0.05/2000)**0.5)),\n(\"R=2000,n=30\", r['n_replications']==2000 and r['n_obs_per_replication']==30)]\nfor k,v in c: print(v,k)\nEOF","description":"Reproducibility and consistency checks"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1044,"cache_read_input_tokens":11449,"output_tokens":737,"output_tokens_details":{"thinking_tokens":50},"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":1044},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXmq4VWnGSztY9XLfrgi","requestRef":"93f679c7-fc38-475a-b523-9017b656b8c7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"554c19e0-a1db-4cc2-8f71-b8b9aaf90b8c","timestamp":"2026-10-30T04:15:40.464Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}48{"parentUuid":"554c19e0-a1db-4cc2-8f71-b8b9aaf90b8c","isSidechain":false,"promptId":"6a467718-f2b4-4f12-aa3d-7bee6edb5c9d","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_012WQzQPSfcyaTKo74naFGN6","type":"tool_result","content":"IDENTICAL\nTrue SEs positive\nTrue coverages in [0,1]\nTrue coverage*R integer\nTrue sd_mc within 5% of exact (sampling sd of SD ~ exact/sqrt(2R)=1.6%)\nTrue mean betahat within 3 MCSE of 0.5\nTrue mean_se_conv <= rms exact (Jensen)\nTrue undercover flag consistent\nTrue R=2000,n=30","is_error":false}]},"uuid":"f8250155-5c0b-4ae4-8f81-55c3b4e355c4","timestamp":"2026-10-30T04:15:41.221Z","toolUseResult":{"stdout":"IDENTICAL\nTrue SEs positive\nTrue coverages in [0,1]\nTrue coverage*R integer\nTrue sd_mc within 5% of exact (sampling sd of SD ~ exact/sqrt(2R)=1.6%)\nTrue mean betahat within 3 MCSE of 0.5\nTrue mean_se_conv <= rms exact (Jensen)\nTrue undercover flag consistent\nTrue R=2000,n=30","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"554c19e0-a1db-4cc2-8f71-b8b9aaf90b8c","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}49{"type":"api-request-blob","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","hash":"ccdeeab20c6a27c59c69505faf1cc60a1094fa8e9b9f0f73bd24f064b107dade","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"SEs match statsmodels. Now P4: clean rerun, consistency checks, gate."},{"type":"tool_use","id":"toolu_012WQzQPSfcyaTKo74naFGN6","name":"Bash","input":{"command":"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 json; r=json.load(open('out/results.json'))\nc=[(\"SEs positive\", all(r[k]>0 for k in ['sd_beta_exact','sd_beta_mc','mean_se_conventional','mean_se_hc1'])),\n(\"coverages in [0,1]\", 0<=r['coverage_conventional']<=1 and 0<=r['coverage_hc1']<=1),\n(\"coverage*R integer\", abs(r['coverage_conventional']*2000-round(r['coverage_conventional']*2000))<1e-9),\n(\"sd_mc within 5% of exact (sampling sd of SD ~ exact/sqrt(2R)=1.6%)\", abs(r['sd_beta_mc']/r['sd_beta_exact']-1)<0.05),\n(\"mean betahat within 3 MCSE of 0.5\", abs(r['mean_beta_hat']-0.5)<3*r['sd_beta_exact']/2000**0.5),\n(\"mean_se_conv <= rms exact (Jensen)\", r['mean_se_conventional']<=r['rms_se_conventional_exact']*1.01),\n(\"undercover flag consistent\", r['conventional_ci_undercovers']==(r['coverage_conventional']<0.95-3*(0.95*0.05/2000)**0.5)),\n(\"R=2000,n=30\", r['n_replications']==2000 and r['n_obs_per_replication']==30)]\nfor k,v in c: print(v,k)\nEOF","description":"Reproducibility and consistency checks"}}]}}50{"type":"api-request","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","id":"5e7cb5b6-f70a-4d5c-99dd-88622913a0ff","timestamp":"2026-10-30T04:15:41.225Z","version":"2.1.314","querySource":"sdk","shapeHash":"6bbd835952ff5e70d3a7334e92f6ecff4e25d57126d287d8df8169be9dafc906","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":"93f679c7-fc38-475a-b523-9017b656b8c7","keep":14,"tail":["ccdeeab20c6a27c59c69505faf1cc60a1094fa8e9b9f0f73bd24f064b107dade","4cb6bec305aeaeab6044f1337e18a9a6fb67ebc40a4142f0ae00a54ee4f11d2b"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",15,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"f1ec79b2cbe899f011bf02c1bbf5ea577c378d9f3310cb9e11bb84f2b83ba2a7"}51{"parentUuid":"f8250155-5c0b-4ae4-8f81-55c3b4e355c4","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmqZPaBcP14aiS5e6rw","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01UyBPFaLyHJGx8vEMCDd3M1","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n| check | outcome |\n|---|---|\n| Clean re-run (results.json deleted, script re-run) byte-identical to previous output | PASS |\n| se_conv and se_HC1 match statsmodels OLS bse / HC1_se on replication 1 (0.159330, 0.153937) | PASS |\n| All SE-type quantities positive | PASS |\n| Coverages in [0,1] and coverage×R integer | PASS |\n| sd_beta_mc (0.26965) within 5% of sd_beta_exact (0.26798); diff 0.6% < ~1.6% sampling sd | PASS |\n| mean β̂ (0.49620) within 3 MC SE of 0.5 (unbiasedness) | PASS |\n| mean_se_conventional (0.19026) ≤ exact sqrt(E[s²](X'X)⁻¹₁₁) (0.19318), Jensen | PASS |\n| conventional_ci_undercovers equals rule cov < 0.95 − 3·sqrt(.95·.05/2000) = 0.93538 | PASS |\n| R = 2000, n = 30, seed recorded | PASS |\n| Magnitude vs baseline: HC1 coverage (0.902) > conventional (0.844); mean se_conv well below sd exact, explaining undercoverage | consistent |\nEOF\ncat > out/state/log.md <<'EOF'\n# Log\n- 2026-10-30 P0 passed: contract written.\n- 2026-10-30 P1 passed: design.csv audited (hash matches bundle, no issues, no exclusions).\n- 2026-10-30 P2 passed: baseline = conventional-SE coverage (task's naive baseline), computed in analysis.py.\n- 2026-10-30 P3 passed: analysis.py vectorised MC, seed 20261030, numpy default_rng; replaced a loose diagnostic with exact rms_se_conventional_exact.\n- 2026-10-30 P4: clean rerun identical; checks in checks.md; running gate.\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . ; ls out/state/gate_receipts","description":"Record checks, log, run gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":880,"cache_read_input_tokens":12493,"output_tokens":835,"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":880},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXmqZ7D8fDG8n14mgXYe","requestRef":"5e7cb5b6-f70a-4d5c-99dd-88622913a0ff","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"1ba61c76-6105-43ee-81d0-a0e69a85078e","timestamp":"2026-10-30T04:15:48.891Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}52{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"1ba61c76-6105-43ee-81d0-a0e69a85078e","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c"}53{"type":"atis-latch","atis":"","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c"}54{"parentUuid":"1ba61c76-6105-43ee-81d0-a0e69a85078e","isSidechain":false,"promptId":"6a467718-f2b4-4f12-aa3d-7bee6edb5c9d","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01UyBPFaLyHJGx8vEMCDd3M1","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — FAILED (9 of 31 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 [ok] exclusion_ledger: 1 steps consistent\n [ok] positive:sd_beta_exact: 0.2679805928302833\n [ok] positive:sd_beta_mc: 0.2696473708309126\n [ok] positive:mean_se_conventional: 0.1902623101215266\n [ok] reproducibility: regenerated in 0.7s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0049/out/state/gate_receipts/20261030T041549.669220Z.json\n20261030T041549.669220Z.json","is_error":false}]},"uuid":"55b2fe5c-3431-407c-b70c-fb9651bff4ed","timestamp":"2026-10-30T04:15:49.680Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — FAILED (9 of 31 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 [ok] exclusion_ledger: 1 steps consistent\n [ok] positive:sd_beta_exact: 0.2679805928302833\n [ok] positive:sd_beta_mc: 0.2696473708309126\n [ok] positive:mean_se_conventional: 0.1902623101215266\n [ok] reproducibility: regenerated in 0.7s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0049/out/state/gate_receipts/20261030T041549.669220Z.json\n20261030T041549.669220Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"1ba61c76-6105-43ee-81d0-a0e69a85078e","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}55{"type":"api-request-blob","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","hash":"fe67507a66e0aac1fc7b8e40fb2ee7f912a6077ca8c51f355dca3ffcd56af25d","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01UyBPFaLyHJGx8vEMCDd3M1","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n| check | outcome |\n|---|---|\n| Clean re-run (results.json deleted, script re-run) byte-identical to previous output | PASS |\n| se_conv and se_HC1 match statsmodels OLS bse / HC1_se on replication 1 (0.159330, 0.153937) | PASS |\n| All SE-type quantities positive | PASS |\n| Coverages in [0,1] and coverage×R integer | PASS |\n| sd_beta_mc (0.26965) within 5% of sd_beta_exact (0.26798); diff 0.6% < ~1.6% sampling sd | PASS |\n| mean β̂ (0.49620) within 3 MC SE of 0.5 (unbiasedness) | PASS |\n| mean_se_conventional (0.19026) ≤ exact sqrt(E[s²](X'X)⁻¹₁₁) (0.19318), Jensen | PASS |\n| conventional_ci_undercovers equals rule cov < 0.95 − 3·sqrt(.95·.05/2000) = 0.93538 | PASS |\n| R = 2000, n = 30, seed recorded | PASS |\n| Magnitude vs baseline: HC1 coverage (0.902) > conventional (0.844); mean se_conv well below sd exact, explaining undercoverage | consistent |\nEOF\ncat > out/state/log.md <<'EOF'\n# Log\n- 2026-10-30 P0 passed: contract written.\n- 2026-10-30 P1 passed: design.csv audited (hash matches bundle, no issues, no exclusions).\n- 2026-10-30 P2 passed: baseline = conventional-SE coverage (task's naive baseline), computed in analysis.py.\n- 2026-10-30 P3 passed: analysis.py vectorised MC, seed 20261030, numpy default_rng; replaced a loose diagnostic with exact rms_se_conventional_exact.\n- 2026-10-30 P4: clean rerun identical; checks in checks.md; running gate.\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . ; ls out/state/gate_receipts","description":"Record checks, log, run gate"}}]}}56{"type":"api-request","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","id":"8b4077a1-a906-4e92-b48b-29bbb813bc1e","timestamp":"2026-10-30T04:15:49.683Z","version":"2.1.314","querySource":"sdk","shapeHash":"6bbd835952ff5e70d3a7334e92f6ecff4e25d57126d287d8df8169be9dafc906","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":"5e7cb5b6-f70a-4d5c-99dd-88622913a0ff","keep":16,"tail":["fe67507a66e0aac1fc7b8e40fb2ee7f912a6077ca8c51f355dca3ffcd56af25d","f6ad472c8b36e15502423729f5632f1c5669fe662daaad8214fadc382825be6e"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",17,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"c73e36316e4ffa250c07ae44c12e93c7b9495e16e44eec4e28be28d287415f69"}57{"parentUuid":"55b2fe5c-3431-407c-b70c-fb9651bff4ed","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmrBaBwMWu8tmkGiRhK","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":1548,"cache_read_input_tokens":13373,"output_tokens":2537,"output_tokens_details":{"thinking_tokens":43},"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":1548},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":829,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmrBJ4i1AwEGSzEtY5A","requestRef":"8b4077a1-a906-4e92-b48b-29bbb813bc1e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"61964cbb-3937-4cfd-9602-96231b3ecf9e","timestamp":"2026-10-30T04:15:51.739Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}58{"parentUuid":"61964cbb-3937-4cfd-9602-96231b3ecf9e","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmrBaBwMWu8tmkGiRhK","type":"message","role":"assistant","content":[{"type":"text","text":"The only failures at this point are the P5 deliverables, which don't exist yet; the reproducibility and key checks pass. Next I'll write the report, claims, and phase ledger."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1548,"cache_read_input_tokens":13373,"output_tokens":2537,"output_tokens_details":{"thinking_tokens":43},"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":1548},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmrBJ4i1AwEGSzEtY5A","requestRef":"8b4077a1-a906-4e92-b48b-29bbb813bc1e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"fca4787c-f241-4717-ba4b-ef76d79c0a18","timestamp":"2026-10-30T04:15:51.740Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}59{"parentUuid":"fca4787c-f241-4717-ba4b-ef76d79c0a18","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmrBaBwMWu8tmkGiRhK","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01NtVZiNB2eQHrCKxeZECkdN","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F2-conf-03 — Coverage of OLS slope confidence intervals in a small heteroskedastic sample\n\n## Question\nIn the fixed-design model y_i = 1 + 0.5 x_i + σ_i ε_i (n = 30, ε_i iid N(0,1); x_i and σ_i taken from `data/design.csv`), do nominal 95% intervals β̂ ± t₀.₉₇₅(28)·se reach 95% coverage? We compare the conventional OLS SE with the HC1 robust SE.\n\n## Data and exclusions\n`data/design.csv` has 30 rows (`n_input_rows`) and columns i, x, sigma. Its SHA-256 matches the bundle manifest. There are no missing values, duplicates, or invalid σ (all σ > 0), so `data_issues` = []. We removed nothing (`out/exclusions.csv`: 30 → 30). This is a feature of the design, not an error: σ_i grows with |x_i| (corr(x², σ²) ≈ 0.99, see `out/state/data_audit.md`). The error variance is therefore largest at the high-leverage points.\n\n## Method\n- Exact SD of β̂ (`sd_beta_exact`): β̂ = Σ w_i y_i with w = row 2 of (X'X)⁻¹X', so Var(β̂) = Σ w_i² σ_i². No simulation is involved.\n- Monte Carlo: R = 2000 replications (`n_replications`) of n = 30 (`n_obs_per_replication`). Only ε is redrawn, from numpy `default_rng` with seed 20261030 (`random_seed`). In each replication the script computes:\n - β̂;\n - se_conv = sqrt(s²·(X'X)⁻¹₂₂), with s² = RSS/(n−2);\n - se_HC1 = sqrt(n/(n−2)·Σ w_i² e_i²).\n- Both intervals use t₀.₉₇₅(28) = 2.0484 (`t_critical_28`). Coverage is the share of replications whose interval contains 0.5.\n- Decision rule: `conventional_ci_undercovers` is true iff coverage_conventional < 0.95 − 3·sqrt(0.95·0.05/2000) = 0.9354 (`undercoverage_threshold`).\n- The baseline is the naive conventional interval (`coverage_conventional`); the HC1 interval is the comparison.\n- SEs were cross-checked against statsmodels on one replication and agree to machine precision.\n\n## Results\n- Conventional interval: estimated coverage is **0.844** (`coverage_conventional`). That is far below 95% and below the 0.9354 threshold, so `conventional_ci_undercovers` = **true**. **The conventional interval does not attain its nominal coverage.**\n- HC1 interval: estimated coverage is **0.902** (`coverage_hc1`). It does much better than the conventional interval but is still below 95%.\n- Exact SD of β̂ is 0.2680 (`sd_beta_exact`). The Monte Carlo SD is 0.2696 (`sd_beta_mc`), which agrees.\n- The mean of se_conv is only 0.1903 (`mean_se_conventional`), about 71% of the true SD. As an exact check, sqrt(E[s²]·(X'X)⁻¹₂₂) = 0.1932 (`rms_se_conventional_exact`). The conventional SE ignores that the large error variances sit at high-leverage x, so it is biased downward, and this explains the undercoverage.\n- The mean of se_HC1 is 0.2408 (`mean_se_hc1`). It is closer to the true SD but still biased downward in n = 30, which matches HC1's known small-sample bias.\n- Mean β̂ is 0.4962 (`mean_beta_hat`), consistent with OLS being unbiased.\n\n## Uncertainty\nBinomial Monte Carlo standard errors at R = 2000:\n- coverage_conventional: 0.0081 (`mcse_coverage_conventional`);\n- coverage_hc1: 0.0067 (`mcse_coverage_hc1`);\n- at the nominal level 0.95: 0.0049 (`mcse_at_nominal_095`).\n\nThe conventional shortfall (0.95 − 0.844 = 0.106) is about 22 nominal-level MC SEs, so the conclusion is not sensitive to Monte Carlo noise. The HC1 shortfall (0.048) is also many MC SEs, so HC1 undercoverage is likewise distinguishable from noise. sd_beta_mc differs from the exact value by 0.6%, within the expected sampling error of an SD estimated from 2000 draws (≈1.6%).\n\n## Limitations and open issues\n- The results apply only to this single fixed design with normal errors. They do not carry over to other designs, error distributions, or sample sizes.\n- The coverage estimates depend on the seed within their MC SEs. The yes/no conclusion does not, given its margin.\n- The script does not compute exact coverage probabilities (e.g., by numerical integration). Coverage was estimated by Monte Carlo as the task specified.\n- The task did not ask for small-sample refinements such as HC2/HC3 or degrees-of-freedom corrections, and none were evaluated.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The conventional nominal 95% interval does not attain its nominal coverage: estimated coverage 0.844, more than three MC standard errors below 0.95.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"mcse_at_nominal_095\",\"undercoverage_threshold\"],\"status\":\"supported\",\"caveat\":\"Specific to this fixed design, normal errors, R=2000 and seed 20261030.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval covers better (0.902) than the conventional interval but still falls short of 95%.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\",\"coverage_conventional\"],\"status\":\"supported\",\"caveat\":\"MC SE about 0.0067; HC1 known to be downward biased in small samples.\"},\n {\"id\":\"C3\",\"text\":\"The exact SD of the OLS slope is 0.2680, matched by the Monte Carlo SD 0.2696.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\"],\"status\":\"supported\",\"caveat\":\"Exact value is analytic; MC value has ~1.6% sampling error.\"},\n {\"id\":\"C4\",\"text\":\"The conventional SE is biased downward (mean 0.1903 vs true SD 0.2680), which explains the undercoverage.\",\"results_keys\":[\"mean_se_conventional\",\"sd_beta_exact\",\"rms_se_conventional_exact\"],\"status\":\"supported\",\"caveat\":\"Mechanism attributed to heteroskedasticity concentrated at high-leverage x.\"}\n]\nEOF\necho ok","description":"Write report and claims"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1548,"cache_read_input_tokens":13373,"output_tokens":2537,"output_tokens_details":{"thinking_tokens":43},"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":1548},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXmrBJ4i1AwEGSzEtY5A","requestRef":"8b4077a1-a906-4e92-b48b-29bbb813bc1e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"25c26507-523b-4b02-b349-bd6c9119e3a0","timestamp":"2026-10-30T04:16:10.866Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}60{"parentUuid":"25c26507-523b-4b02-b349-bd6c9119e3a0","isSidechain":false,"promptId":"6a467718-f2b4-4f12-aa3d-7bee6edb5c9d","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01NtVZiNB2eQHrCKxeZECkdN","type":"tool_result","content":"ok","is_error":false}]},"uuid":"4886ad50-8606-44b1-abc8-44f2551fc99f","timestamp":"2026-10-30T04:16:10.917Z","toolUseResult":{"stdout":"ok","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"25c26507-523b-4b02-b349-bd6c9119e3a0","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}61{"type":"api-request-blob","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","hash":"4e6e8b595b4ee7a63b6859d98ad16ba510a328e2fa775119cf47d0e12adf2678","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQSgAcKEAgTGAI4AUIIdGhpbmtpbmcSDEZP1FBkj/W+QNg5KhoMHErnYC8Hxkxgg/MOIjBMDz0cAIjxzRvXUJqVokIYG2efyzoYswudds9GB+0SoTaQtZs8sejBGYYJ6o/a3AUqnQaq2+WP3xd9MzG8x0EdH/mnw8HO9RJYvxTfvvnl9dJ5I0kv6uNvs1V4sSvOB8allsQmMM7WBe6v8YnI9UU6BZOpj7Wd4lBJA0YAYVC1xd5BdtbFvxv4cZ1Jt5G9OOr3yHeRX8XtMs5cpUvrFpbG0kFZ+xh4zOMtX/h0+UMEXl1SGXh6TbR5CvoNcv9GlS+rtXGGAinadm9msb7wE9mfR8dbOYqtyIdu5anWIQTCzHNam50iaw3GYG898G2BSzDV/ZO3CWSIjUut5SheleagijrrqAt3aldnvewisXiQ2St2kcImjpFFDbK7Iu4bsDcZ1Vw9/Go7xVRVzvXEu83u5xJFaefx0PkeytqE5lP1ngkzKm2YnYY2Rd67n2PLpDYR+kHqxAPgAwkqr4ncxbksNn/TkPiNB+tLFqd37zuWtsCV52g+YEZe9U/SrqaH3P+XYEe8coa/FPdKA8XLVDCsBlR2w6Lp9FZI8PDrZKV793bGb/5kpLNpDItHjgPfkxFJrtR1UCfmgkijTxMOZybnRGbLLaU2mnxk3j29hz4o87d1fQhcTmchVdOCkH1sc7UKeIKAihyjL/eBii2LEFdHxIcq43My/WyYyzp9tUl+bm3YJCRuFvd0V1ShboKzxR+Byi/ai79/S7tOE/mhi9GTErzR2hE8gRnxNA8gbxWl9ih2/fwvBw6ZTKM6r7Pq+hsKFVPgW7SrHxanzYzDIS020LSZUz+g8R26dKfj549MMnsMAuAdJThFCbINhLBvNAxEd+9CSpUfo8LTqvvMXcnbPgz+1snwveucwnaCUWO5czXGShPB58wG4WE8iifRE8RWXAkzPg3844o4DWWfL65Phc4XRDOaNvKS4J57Pv1+8nG5i1eaUfLS7l/8WFwGFTMuJkEi+nrPBaW/j//n+8x1g77J8ZISIqbX2wydIbx9XzhkGHtcllWkkN78SI7xLrdINpuLY4b9IokMdAzOEd+xOD2T/meIrEarHD5Q1u6cYCysfwxcfjNfBP8aK7xMo66BTzbr+6gWaByr0rZtxXBzAmbWE1owziBOKgVh0sVaWBgB"},{"type":"text","text":"The only failures at this point are the P5 deliverables, which don't exist yet; the reproducibility and key checks pass. Next I'll write the report, claims, and phase ledger."},{"type":"tool_use","id":"toolu_01NtVZiNB2eQHrCKxeZECkdN","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F2-conf-03 — Coverage of OLS slope confidence intervals in a small heteroskedastic sample\n\n## Question\nIn the fixed-design model y_i = 1 + 0.5 x_i + σ_i ε_i (n = 30, ε_i iid N(0,1); x_i and σ_i taken from `data/design.csv`), do nominal 95% intervals β̂ ± t₀.₉₇₅(28)·se reach 95% coverage? We compare the conventional OLS SE with the HC1 robust SE.\n\n## Data and exclusions\n`data/design.csv` has 30 rows (`n_input_rows`) and columns i, x, sigma. Its SHA-256 matches the bundle manifest. There are no missing values, duplicates, or invalid σ (all σ > 0), so `data_issues` = []. We removed nothing (`out/exclusions.csv`: 30 → 30). This is a feature of the design, not an error: σ_i grows with |x_i| (corr(x², σ²) ≈ 0.99, see `out/state/data_audit.md`). The error variance is therefore largest at the high-leverage points.\n\n## Method\n- Exact SD of β̂ (`sd_beta_exact`): β̂ = Σ w_i y_i with w = row 2 of (X'X)⁻¹X', so Var(β̂) = Σ w_i² σ_i². No simulation is involved.\n- Monte Carlo: R = 2000 replications (`n_replications`) of n = 30 (`n_obs_per_replication`). Only ε is redrawn, from numpy `default_rng` with seed 20261030 (`random_seed`). In each replication the script computes:\n - β̂;\n - se_conv = sqrt(s²·(X'X)⁻¹₂₂), with s² = RSS/(n−2);\n - se_HC1 = sqrt(n/(n−2)·Σ w_i² e_i²).\n- Both intervals use t₀.₉₇₅(28) = 2.0484 (`t_critical_28`). Coverage is the share of replications whose interval contains 0.5.\n- Decision rule: `conventional_ci_undercovers` is true iff coverage_conventional < 0.95 − 3·sqrt(0.95·0.05/2000) = 0.9354 (`undercoverage_threshold`).\n- The baseline is the naive conventional interval (`coverage_conventional`); the HC1 interval is the comparison.\n- SEs were cross-checked against statsmodels on one replication and agree to machine precision.\n\n## Results\n- Conventional interval: estimated coverage is **0.844** (`coverage_conventional`). That is far below 95% and below the 0.9354 threshold, so `conventional_ci_undercovers` = **true**. **The conventional interval does not attain its nominal coverage.**\n- HC1 interval: estimated coverage is **0.902** (`coverage_hc1`). It does much better than the conventional interval but is still below 95%.\n- Exact SD of β̂ is 0.2680 (`sd_beta_exact`). The Monte Carlo SD is 0.2696 (`sd_beta_mc`), which agrees.\n- The mean of se_conv is only 0.1903 (`mean_se_conventional`), about 71% of the true SD. As an exact check, sqrt(E[s²]·(X'X)⁻¹₂₂) = 0.1932 (`rms_se_conventional_exact`). The conventional SE ignores that the large error variances sit at high-leverage x, so it is biased downward, and this explains the undercoverage.\n- The mean of se_HC1 is 0.2408 (`mean_se_hc1`). It is closer to the true SD but still biased downward in n = 30, which matches HC1's known small-sample bias.\n- Mean β̂ is 0.4962 (`mean_beta_hat`), consistent with OLS being unbiased.\n\n## Uncertainty\nBinomial Monte Carlo standard errors at R = 2000:\n- coverage_conventional: 0.0081 (`mcse_coverage_conventional`);\n- coverage_hc1: 0.0067 (`mcse_coverage_hc1`);\n- at the nominal level 0.95: 0.0049 (`mcse_at_nominal_095`).\n\nThe conventional shortfall (0.95 − 0.844 = 0.106) is about 22 nominal-level MC SEs, so the conclusion is not sensitive to Monte Carlo noise. The HC1 shortfall (0.048) is also many MC SEs, so HC1 undercoverage is likewise distinguishable from noise. sd_beta_mc differs from the exact value by 0.6%, within the expected sampling error of an SD estimated from 2000 draws (≈1.6%).\n\n## Limitations and open issues\n- The results apply only to this single fixed design with normal errors. They do not carry over to other designs, error distributions, or sample sizes.\n- The coverage estimates depend on the seed within their MC SEs. The yes/no conclusion does not, given its margin.\n- The script does not compute exact coverage probabilities (e.g., by numerical integration). Coverage was estimated by Monte Carlo as the task specified.\n- The task did not ask for small-sample refinements such as HC2/HC3 or degrees-of-freedom corrections, and none were evaluated.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The conventional nominal 95% interval does not attain its nominal coverage: estimated coverage 0.844, more than three MC standard errors below 0.95.\",\"results_keys\":[\"coverage_conventional\",\"conventional_ci_undercovers\",\"mcse_at_nominal_095\",\"undercoverage_threshold\"],\"status\":\"supported\",\"caveat\":\"Specific to this fixed design, normal errors, R=2000 and seed 20261030.\"},\n {\"id\":\"C2\",\"text\":\"The HC1 interval covers better (0.902) than the conventional interval but still falls short of 95%.\",\"results_keys\":[\"coverage_hc1\",\"mcse_coverage_hc1\",\"coverage_conventional\"],\"status\":\"supported\",\"caveat\":\"MC SE about 0.0067; HC1 known to be downward biased in small samples.\"},\n {\"id\":\"C3\",\"text\":\"The exact SD of the OLS slope is 0.2680, matched by the Monte Carlo SD 0.2696.\",\"results_keys\":[\"sd_beta_exact\",\"sd_beta_mc\"],\"status\":\"supported\",\"caveat\":\"Exact value is analytic; MC value has ~1.6% sampling error.\"},\n {\"id\":\"C4\",\"text\":\"The conventional SE is biased downward (mean 0.1903 vs true SD 0.2680), which explains the undercoverage.\",\"results_keys\":[\"mean_se_conventional\",\"sd_beta_exact\",\"rms_se_conventional_exact\"],\"status\":\"supported\",\"caveat\":\"Mechanism attributed to heteroskedasticity concentrated at high-leverage x.\"}\n]\nEOF\necho ok","description":"Write report and claims"}}]}}62{"type":"api-request","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","id":"cf741a94-42b3-41a2-a456-4614bf4b3eb2","timestamp":"2026-10-30T04:16:10.920Z","version":"2.1.314","querySource":"sdk","shapeHash":"6bbd835952ff5e70d3a7334e92f6ecff4e25d57126d287d8df8169be9dafc906","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":"8b4077a1-a906-4e92-b48b-29bbb813bc1e","keep":18,"tail":["4e6e8b595b4ee7a63b6859d98ad16ba510a328e2fa775119cf47d0e12adf2678","f473c433b8839a17d34dfbc3fca9694d666b06668c51b802fb428770d11427ad"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",19,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"84596789512b62f49b698b10eaf34b92d9e32c114c499028a4e88148396ee9f9"}63{"parentUuid":"4886ad50-8606-44b1-abc8-44f2551fc99f","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmskNSCC9dqfC5DJuAQ","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01YKjSnoE6cXAhaGd1drLiia","name":"Bash","input":{"command":"cat > out/state/phases.json <<'EOF'\n{\n \"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully; contract.md written with estimands, outputs, rules, invalidity conditions\"],\"notes\":\"\"},\n \"P1\":{\"status\":\"passed\",\"checks\":[\"SHA-256 computed and matches bundle.json\",\"30x3 schema, 0 missing, 0 duplicates, sigma>0\",\"exclusions.csv sums 30-0=30\"],\"notes\":\"No availability violations.\"},\n \"P2\":{\"status\":\"passed\",\"checks\":[\"Baseline coverage_conventional computed with same coverage rule as HC1\"],\"notes\":\"Baseline is the task-defined naive conventional interval.\"},\n \"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py reads only data/, fixed seed 20261030, writes results.json\",\"SEs cross-checked vs statsmodels\"],\"notes\":\"\"},\n \"P4\":{\"status\":\"passed\",\"checks\":[\"Clean rerun byte-identical\",\"Consistency checks all PASS (out/state/checks.md)\",\"Gate run 20261030T041549.669220Z: contract/repro checks ok; failures only for not-yet-written P5 files (report, claims)\"],\"notes\":\"gate receipt: out/state/gate_receipts/20261030T041549.669220Z.json\"},\n \"P5\":{\"status\":\"running\",\"checks\":[\"report.md with 6 sections written\",\"claims.json with 4 claims written\"],\"notes\":\"\"}\n}\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v '\\[ok\\]'","description":"Update phases and run final gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2544,"cache_read_input_tokens":14921,"output_tokens":617,"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":2544},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXmsk5Zy1bjGje7pBSU9","requestRef":"cf741a94-42b3-41a2-a456-4614bf4b3eb2","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"251fbd1e-2280-4842-b068-fb805f3c3bbb","timestamp":"2026-10-30T04:16:16.990Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}64{"parentUuid":"251fbd1e-2280-4842-b068-fb805f3c3bbb","isSidechain":false,"promptId":"6a467718-f2b4-4f12-aa3d-7bee6edb5c9d","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01YKjSnoE6cXAhaGd1drLiia","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — FAILED (1 of 32 checks failed)\n [FAIL] phase_ledger: phases not terminal: ['P5']\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0049/out/state/gate_receipts/20261030T041617.730923Z.json","is_error":false}]},"uuid":"16d6714b-aa92-41b0-a3b4-538a3c6eaa03","timestamp":"2026-10-30T04:16:17.738Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — FAILED (1 of 32 checks failed)\n [FAIL] phase_ledger: phases not terminal: ['P5']\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0049/out/state/gate_receipts/20261030T041617.730923Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"251fbd1e-2280-4842-b068-fb805f3c3bbb","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0049","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","version":"2.1.314","gitBranch":"HEAD"}65{"type":"api-request-blob","sessionId":"a1dcd699-3220-46af-b0ba-94dfc94bdf7c","hash":"d3f2f4ef180ecb852de3bb0f27821e29daf84c7f500c3eeb6bfe30cbfdeefa1d","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01YKjSnoE6cXAhaGd1drLiia","name":"Bash","input":{"command":"cat > out/state/phases.json <<'EOF'\n{\n \"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully; contract.md written with estimands, outputs, rules, invalidity 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\"P5\":{\"status\":\"running\",\"checks\":[\"report.md with 6 sections written\",\"claims.json with 4 claims written\"],\"notes\":\"\"}\n}\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v '\\[ok\\]'","description":"Update phases and run final 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It covers the true β = 0.5 only 84.4% of the time, far below the 93.5% cut-off for \"below 95% by more than three Monte Carlo standard errors\". The final gate run passes all 32 checks, and re-running `out/analysis.py` from scratch gives identical results.\n\n| Quantity | Value |\n|---|---|\n| Coverage, conventional interval | 0.844 (Monte Carlo SE 0.0081) |\n| Coverage, HC1 robust interval | 0.902 (Monte Carlo SE 0.0067) |\n| Exact SD of β̂ (analytical) | 0.2680 |\n| SD of β̂ across the simulations | 0.2696 |\n| Average conventional SE | 0.1903 |\n| Conventional interval undercovers? | yes |\n\n- **Why it undercovers:** the conventional standard error averages only about 71% of the true SD of β̂. 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