spb/wp29_uqo

1{"type":"atis-latch","atis":"","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}2{"type":"queue-operation","operation":"enqueue","timestamp":"2026-10-30T05:13:20.994Z","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","content":"Begin"}3{"type":"queue-operation","operation":"dequeue","timestamp":"2026-10-30T05:13:21.000Z","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}4{"parentUuid":null,"isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":"Begin"},"uuid":"470d8d53-9b19-47c3-a5b6-fc1422153538","timestamp":"2026-10-30T05:13:21.005Z","permissionMode":"default","promptSource":"sdk","turnOrigin":"sdk","turnPosition":{"promptIndex":0,"turnIndex":1},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}5{"type":"api-request-shape","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","timestamp":"2026-10-30T05:13:21.022Z","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/RC0251\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\nSEPARATE REVIEW (additional)\n- After the gate passes, a separate reviewer session that has not seen your work in progress will examine `TASK.md` and everything under `out/` and may return a list of issues (file `out/review/review.json`). You will then be resumed once to address them: fix what is justified, explain in `out/report.md` (Limitations and open issues) what you disagree with, re-run the gate, and update `out/claims.json` and `out/state/phases.json`. The reviewer has no reference answers; its role is to challenge unsupported claims, violated information rules, unverified computations, and inconsistencies between your report and your results.\n"}],"tools":[{"name":"Bash","description":"execute shell commands","input_schema":{"$schema":"https://json-schema.org/draft/2020-12/schema","type":"object","properties":{"command":{"description":"The command to execute","type":"string"},"timeout":{"description":"Optional timeout in milliseconds (max 600000 for a foreground command)","type":"number"},"description":{"description":"Clear, concise description of what this command does in active voice. Never use words like \"complex\" or \"risk\" in the description - just describe what it does.\n\nSay what the command does in plain words: do not echo the command's text, its flags, or file paths - the user reads this description, often without seeing the command.\n\nFor simple commands (git, npm, standard CLI tools), keep it brief (5-10 words):\n- ls → \"List files in current directory\"\n- git status → \"Show working tree status\"\n- npm install → \"Install package dependencies\"\n\nFor commands that are harder to parse at a glance (piped commands, obscure flags, etc.), add enough context to clarify what it does:\n- find . -name \"*.tmp\" -exec rm {} \\; → \"Find and delete all .tmp files recursively\"\n- git reset --hard origin/main → \"Discard all local changes and match remote main\"\n- curl -s url | jq '.data[]' → \"Fetch JSON from URL and extract data array elements\"","type":"string"},"dangerouslyDisableSandbox":{"description":"Set this to true to dangerously override sandbox mode and run commands without sandboxing.","type":"boolean"}},"required":["command"],"additionalProperties":false}},{"name":"Edit","description":"modify file contents in place","input_schema":{"$schema":"https://json-schema.org/draft/2020-12/schema","type":"object","properties":{"file_path":{"description":"The absolute path to the file to modify","type":"string"},"old_string":{"description":"The text to replace","type":"string"},"new_string":{"description":"The text to replace it with (must be different from old_string)","type":"string"},"replace_all":{"description":"Replace all occurrences of old_string (default false)","default":false,"type":"boolean"}},"required":["file_path","old_string","new_string"],"additionalProperties":false}},{"name":"Read","description":"read files, images, PDFs, notebooks","input_schema":{"$schema":"https://json-schema.org/draft/2020-12/schema","type":"object","properties":{"file_path":{"description":"The absolute path to the file to read","type":"string"},"offset":{"description":"The line number to start reading from. Only provide if the file is too large to read at once","type":"integer","minimum":0,"maximum":9007199254740991},"limit":{"description":"The number of lines to read. Only provide if the file is too large to read at once.","type":"integer","exclusiveMinimum":0,"maximum":9007199254740991},"pages":{"description":"Page range for PDF files (e.g., \"1-5\", \"3\", \"10-20\"). Only applicable to PDF files. Maximum 20 pages per request.","type":"string"},"allow_large":{"description":"Set to true to read a text file, or a line range of one, that is over the usual size limits, up to what still fits in your context. Only use this when you genuinely need all of it or the user asked for the whole file; otherwise read it in parts with offset and limit, or search it.","type":"boolean"}},"required":["file_path"],"additionalProperties":false}}]}}6{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"d43ab0e0b8ec9db790a6459cb2f4bc4ffce02825ca05063162023be60912ced9","message":{"role":"system","content":[],"output_config":{"effort":"medium"}}}7{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"99898164-bb63-400c-a68c-c613dc8e29ae","timestamp":"2026-10-30T05:13:21.022Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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"}},"keep":0,"tail":["252097215a6af3e04abe3f3c5a1cce73f5f388825c554cef2907d381aaf4102e","d43ab0e0b8ec9db790a6459cb2f4bc4ffce02825ca05063162023be60912ced9"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",0,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"d0386289fe9a2af3823722888ffa0f00b89cbfead1e5c2f67ccb3b8af350ce49"}8{"parentUuid":"470d8d53-9b19-47c3-a5b6-fc1422153538","isSidechain":false,"attachment":{"type":"session_context","context":{}},"type":"attachment","uuid":"e475fec7-ec3f-4007-9a56-96480b8bdb21","timestamp":"2026-10-30T05:13:21.012Z","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}9{"parentUuid":"e475fec7-ec3f-4007-9a56-96480b8bdb21","isSidechain":false,"attachment":{"type":"date","date":"2026-10-30"},"type":"attachment","uuid":"bd2c3254-3a7d-468f-8228-315a1a25aff4","timestamp":"2026-10-30T05:13:21.012Z","rendered":[{"content":"<system-reminder>\nToday's date is 2026-10-30.\n</system-reminder>"}],"renderedRole":"system","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}10{"parentUuid":"bd2c3254-3a7d-468f-8228-315a1a25aff4","isSidechain":false,"attachment":{"type":"remote_session_change","url":null,"commit":"Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>","pr":"🤖 Generated with [Claude Code](https://claude.com/claude-code)","sendUserFileHint":false,"managedCommit":false,"managedPr":false},"type":"attachment","uuid":"137581a8-dd4b-48ea-8902-983abd04e8f4","timestamp":"2026-10-30T05:13:21.013Z","rendered":[{"content":"<system-reminder>\nAttribution for git commits and pull requests you create from here on (this replaces Claude Code's own earlier attribution guidance, such as a previous copy of this reminder; 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/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}12{"parentUuid":"137581a8-dd4b-48ea-8902-983abd04e8f4","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrEheXKGcHwmTnFdGxU","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":2811,"cache_read_input_tokens":1504,"output_tokens":129,"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":2811},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":367,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXrEhMfgJcFma4nDZLW6","requestRef":"99898164-bb63-400c-a68c-c613dc8e29ae","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6ba12554-0ae2-48f0-b75c-b53e34ef511c","timestamp":"2026-10-30T05:13:23.715Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"6ba12554-0ae2-48f0-b75c-b53e34ef511c","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrEheXKGcHwmTnFdGxU","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01A3dz5NJ45HAKU2BTddHCkh","name":"Bash","input":{"command":"cat TASK.md; ls -la; ls -R data out 2>/dev/null | head -50","description":"Read task and list workspace"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":4,"cache_creation_input_tokens":2811,"cache_read_input_tokens":1504,"output_tokens":129,"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":2811},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXrEhMfgJcFma4nDZLW6","requestRef":"99898164-bb63-400c-a68c-c613dc8e29ae","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"43878218-7227-41ab-8295-0be493ba9fe3","timestamp":"2026-10-30T05:13:24.309Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}14{"parentUuid":"43878218-7227-41ab-8295-0be493ba9fe3","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01A3dz5NJ45HAKU2BTddHCkh","type":"tool_result","content":"# F5-conf-02 — Finite-sample bias of the OLS estimator of an AR(1) coefficient\n\n## Scientific question\nIn the Gaussian AR(1) model y_t = c + ρ y_{t−1} + ε_t with ε_t ~ i.i.d. N(0, σ²), the OLS estimator ρ̂ of ρ (regression of y_t on a constant and y_{t−1}) is biased in finite samples. A classical analytical approximation (Marriott and Pope 1954; Kendall 1954) gives E[ρ̂] − ρ ≈ −(1 + 3ρ)/n for the regression with an estimated intercept. The estimands are (i) the value of this analytical bias approximation at the design values of (n, ρ), and (ii) the actual finite-sample bias E[ρ̂] − ρ at the same design, estimated by Monte Carlo with its Monte Carlo standard error. Compare the two and interpret the discrepancy with the correct scope for an approximation of this kind.\n\n## Inputs\n- `data/design.csv` — columns `parameter`, `value`, `description`: the simulation design (series length `n`, true coefficient `rho`, innovation standard deviation `sigma`, whether the regression includes an intercept, the initial condition, the number of replications `n_replications`, and the random `seed` to use with `numpy.random.default_rng`). Simulated data only; nothing is observed.\n\n## Information-availability rules\n- Use only `data/design.csv`. Follow the design exactly (n, ρ, σ, intercept, stationary initial condition, number of replications, seed). c = 0 in the data-generating process.\n- Each replication must simulate a fresh series of n observations and estimate ρ̂ by OLS of y_t on (1, y_{t−1}) for t = 2, …, n.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F5-conf-02\" |\n| `bias_analytical` | number | — | −(1 + 3ρ)/n at the design values |\n| `bias_mc` | number | — | Monte Carlo estimate of E[ρ̂] − ρ (mean of ρ̂ over replications minus ρ) |\n| `bias_mc_se` | number | — | Monte Carlo standard error of `bias_mc` (sd of ρ̂ across replications / √R) |\n| `rho_hat_mean` | number | — | mean of ρ̂ across replications |\n| `rho_hat_sd_mc` | number | — | standard deviation of ρ̂ across replications |\n| `discrepancy_se_units` | number | — | (bias_mc − bias_analytical) / bias_mc_se |\n| `se_asymptotic` | number | — | textbook asymptotic standard error √((1 − ρ²)/n) at the design values (the baseline quantity) |\n| `n_replications` | integer | — | number of Monte Carlo replications actually run |\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| `n_analysed` | integer or null | — | number of replications used in the main estimate |\n| `random_seed` | integer or null | — | seed used |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. The Method or Limitations section must state the nature of the analytical formula (what kind of approximation it is and in what sense it is accurate) and the scope of what the Monte Carlo evidence can and cannot establish.\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 (fixed seed).\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}]. Each claim's status must be justified by the listed results keys.\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 20 minutes of work; the Monte Carlo runs in seconds when vectorised.\ntotal 24\ndrwxr-xr-x    6 simon-pierreboucher  staff   192 oct.  29 23:42 .\ndrwxr-xr-x  142 simon-pierreboucher  staff  4544 oct.  30 01:13 ..\n-rw-r--r--    1 simon-pierreboucher  staff   420 oct.  29 23:42 bundle.json\ndrwxr-xr-x    3 simon-pierreboucher  staff    96 oct.  29 23:28 data\n-rw-r--r--    1 simon-pierreboucher  staff  1794 oct.  29 23:32 gate_spec.json\n-rw-r--r--    1 simon-pierreboucher  staff  4010 oct.  29 23:32 TASK.md\ndata:\ndesign.csv","is_error":false}]},"uuid":"834fd563-2ae7-4a01-b007-1db7a931111d","timestamp":"2026-10-30T05:13:24.363Z","toolUseResult":{"stdout":"# F5-conf-02 — Finite-sample bias of the OLS estimator of an AR(1) coefficient\n\n## Scientific question\nIn the Gaussian AR(1) model y_t = c + ρ y_{t−1} + ε_t with ε_t ~ i.i.d. N(0, σ²), the OLS estimator ρ̂ of ρ (regression of y_t on a constant and y_{t−1}) is biased in finite samples. A classical analytical approximation (Marriott and Pope 1954; Kendall 1954) gives E[ρ̂] − ρ ≈ −(1 + 3ρ)/n for the regression with an estimated intercept. The estimands are (i) the value of this analytical bias approximation at the design values of (n, ρ), and (ii) the actual finite-sample bias E[ρ̂] − ρ at the same design, estimated by Monte Carlo with its Monte Carlo standard error. Compare the two and interpret the discrepancy with the correct scope for an approximation of this kind.\n\n## Inputs\n- `data/design.csv` — columns `parameter`, `value`, `description`: the simulation design (series length `n`, true coefficient `rho`, innovation standard deviation `sigma`, whether the regression includes an intercept, the initial condition, the number of replications `n_replications`, and the random `seed` to use with `numpy.random.default_rng`). Simulated data only; nothing is observed.\n\n## Information-availability rules\n- Use only `data/design.csv`. Follow the design exactly (n, ρ, σ, intercept, stationary initial condition, number of replications, seed). c = 0 in the data-generating process.\n- Each replication must simulate a fresh series of n observations and estimate ρ̂ by OLS of y_t on (1, y_{t−1}) for t = 2, …, n.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F5-conf-02\" |\n| `bias_analytical` | number | — | −(1 + 3ρ)/n at the design values |\n| `bias_mc` | number | — | Monte Carlo estimate of E[ρ̂] − ρ (mean of ρ̂ over replications minus ρ) |\n| `bias_mc_se` | number | — | Monte Carlo standard error of `bias_mc` (sd of ρ̂ across replications / √R) |\n| `rho_hat_mean` | number | — | mean of ρ̂ across replications |\n| `rho_hat_sd_mc` | number | — | standard deviation of ρ̂ across replications |\n| `discrepancy_se_units` | number | — | (bias_mc − bias_analytical) / bias_mc_se |\n| `se_asymptotic` | number | — | textbook asymptotic standard error √((1 − ρ²)/n) at the design values (the baseline quantity) |\n| `n_replications` | integer | — | number of Monte Carlo replications actually run |\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| `n_analysed` | integer or null | — | number of replications used in the main estimate |\n| `random_seed` | integer or null | — | seed used |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. The Method or Limitations section must state the nature of the analytical formula (what kind of approximation it is and in what sense it is accurate) and the scope of what the Monte Carlo evidence can and cannot establish.\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 (fixed seed).\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}]. Each claim's status must be justified by the listed results keys.\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 20 minutes of work; the Monte Carlo runs in seconds when vectorised.\ntotal 24\ndrwxr-xr-x    6 simon-pierreboucher  staff   192 oct.  29 23:42 .\ndrwxr-xr-x  142 simon-pierreboucher  staff  4544 oct.  30 01:13 ..\n-rw-r--r--    1 simon-pierreboucher  staff   420 oct.  29 23:42 bundle.json\ndrwxr-xr-x    3 simon-pierreboucher  staff    96 oct.  29 23:28 data\n-rw-r--r--    1 simon-pierreboucher  staff  1794 oct.  29 23:32 gate_spec.json\n-rw-r--r--    1 simon-pierreboucher  staff  4010 oct.  29 23:32 TASK.md\ndata:\ndesign.csv","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"43878218-7227-41ab-8295-0be493ba9fe3","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}15{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"4327b61690eb2e929e105c0d486a090ae6c85061da47c74072e2634a4577aa5f","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01A3dz5NJ45HAKU2BTddHCkh","name":"Bash","input":{"command":"cat TASK.md; ls -la; ls -R data out 2>/dev/null | head -50","description":"Read task and list workspace"}}]}}16{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"8c8ff94a-455d-4214-991d-8be0de7ac615","timestamp":"2026-10-30T05:13:24.368Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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":"99898164-bb63-400c-a68c-c613dc8e29ae","keep":2,"tail":["4327b61690eb2e929e105c0d486a090ae6c85061da47c74072e2634a4577aa5f","cb90c21b694ae42153247b96eac84e1e81c0ef649a596baefdb4d30f594f0e7a"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",3,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"f8fca75169ee27f009706840363a11bc854605f0bfba8feb4648bf17a9118bcd"}17{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"834fd563-2ae7-4a01-b007-1db7a931111d","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}18{"type":"atis-latch","atis":"","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}19{"parentUuid":"834fd563-2ae7-4a01-b007-1db7a931111d","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrErYJrX4tkQYrtYoVJ","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01PbJFdJJ7eQtDitFjA8KaFV","name":"Bash","input":{"command":"cat data/design.csv; echo; shasum -a 256 data/design.csv; cat gate_spec.json bundle.json","description":"Show design, hash, and gate spec"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1963,"cache_read_input_tokens":4315,"output_tokens":119,"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":1963},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXrErHRgdn4NtNpQp26X","requestRef":"8c8ff94a-455d-4214-991d-8be0de7ac615","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"89808d6a-66d2-4855-8388-44f9831201ee","timestamp":"2026-10-30T05:13:26.050Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}20{"parentUuid":"89808d6a-66d2-4855-8388-44f9831201ee","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01PbJFdJJ7eQtDitFjA8KaFV","type":"tool_result","content":"parameter,value,description\nn,30,length of each simulated series (observations y_1..y_n)\nrho,0.8,autoregressive coefficient of the data-generating process\nsigma,1.0,standard deviation of the Gaussian innovations\nintercept,yes,the OLS regression of y_t on y_{t-1} includes a constant\ninitial_condition,stationary,\"y_1 is drawn from the stationary distribution N(0, sigma^2/(1-rho^2))\"\nn_replications,20000,number of Monte Carlo replications to run\nseed,20261029,random seed to use (numpy default_rng)\n\n2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb  data/design.csv\n{\n  \"task_id\": \"F5-conf-02\",\n  \"required_files\": [\n    \"out/results.json\",\n    \"out/report.md\",\n    \"out/analysis.py\",\n    \"out/claims.json\"\n  ],\n  \"results_keys\": {\n    \"task_id\": {\n      \"type\": \"string\",\n      \"nullable\": false\n    },\n    \"bias_analytical\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"bias_mc\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"bias_mc_se\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"rho_hat_mean\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"rho_hat_sd_mc\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"discrepancy_se_units\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"se_asymptotic\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"n_replications\": {\n      \"type\": \"integer\",\n      \"nullable\": false\n    },\n    \"feasibility\": {\n      \"type\": \"string\",\n      \"nullable\": false\n    },\n    \"feasibility_reason\": {\n      \"type\": \"string\",\n      \"nullable\": true\n    },\n    \"data_issues\": {\n      \"type\": \"array\",\n      \"nullable\": false\n    },\n    \"n_input_rows\": {\n      \"type\": \"object\",\n      \"nullable\": false\n    },\n    \"n_analysed\": {\n      \"type\": \"integer\",\n      \"nullable\": true\n    },\n    \"random_seed\": {\n      \"type\": \"integer\",\n      \"nullable\": true\n    }\n  },\n  \"report_sections\": [\n    \"Question\",\n    \"Data and exclusions\",\n    \"Method\",\n    \"Results\",\n    \"Uncertainty\",\n    \"Limitations and open issues\"\n  ],\n  \"family_checks\": [\n    \"claims_reference_existing_keys\",\n    \"phase_ledger_consistent\",\n    \"positive_se\"\n  ],\n  \"ci_pairs\": [],\n  \"positive_keys\": [\n    \"bias_mc_se\",\n    \"rho_hat_sd_mc\",\n    \"se_asymptotic\"\n  ],\n  \"chronology_pairs\": [],\n  \"analysis_timeout_s\": 300,\n  \"reproducibility_tolerance_rel\": 1e-06\n}{\n  \"task_id\": \"F5-conf-02\",\n  \"family\": \"F5\",\n  \"split\": \"conf\",\n  \"version\": \"1.0\",\n  \"created_utc\": \"2026-10-30T03:42:22.079893+00:00\",\n  \"files\": {\n    \"TASK.md\": \"2a389cdf509f84a0f7e0cf2780400eb5b6c1cd45ee0359a2d0708b803641d090\",\n    \"gate_spec.json\": \"1479a11a8587f31338a07b4532d5b9c2da1bba66c2486348acebf18090c30c6b\",\n    \"data/design.csv\": \"2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb\"\n  }\n}","is_error":false}]},"uuid":"390c2534-6184-4881-9284-469bcefcb3eb","timestamp":"2026-10-30T05:13:26.079Z","toolUseResult":{"stdout":"parameter,value,description\nn,30,length of each simulated series (observations y_1..y_n)\nrho,0.8,autoregressive coefficient of the data-generating process\nsigma,1.0,standard deviation of the Gaussian innovations\nintercept,yes,the OLS regression of y_t on y_{t-1} includes a constant\ninitial_condition,stationary,\"y_1 is drawn from the stationary distribution N(0, sigma^2/(1-rho^2))\"\nn_replications,20000,number of Monte Carlo replications to run\nseed,20261029,random seed to use (numpy default_rng)\n\n2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb  data/design.csv\n{\n  \"task_id\": \"F5-conf-02\",\n  \"required_files\": [\n    \"out/results.json\",\n    \"out/report.md\",\n    \"out/analysis.py\",\n    \"out/claims.json\"\n  ],\n  \"results_keys\": {\n    \"task_id\": {\n      \"type\": \"string\",\n      \"nullable\": false\n    },\n    \"bias_analytical\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"bias_mc\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"bias_mc_se\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"rho_hat_mean\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"rho_hat_sd_mc\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"discrepancy_se_units\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"se_asymptotic\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"n_replications\": {\n      \"type\": \"integer\",\n      \"nullable\": false\n    },\n    \"feasibility\": {\n      \"type\": \"string\",\n      \"nullable\": false\n    },\n    \"feasibility_reason\": {\n      \"type\": \"string\",\n      \"nullable\": true\n    },\n    \"data_issues\": {\n      \"type\": \"array\",\n      \"nullable\": false\n    },\n    \"n_input_rows\": {\n      \"type\": \"object\",\n      \"nullable\": false\n    },\n    \"n_analysed\": {\n      \"type\": \"integer\",\n      \"nullable\": true\n    },\n    \"random_seed\": {\n      \"type\": \"integer\",\n      \"nullable\": true\n    }\n  },\n  \"report_sections\": [\n    \"Question\",\n    \"Data and exclusions\",\n    \"Method\",\n    \"Results\",\n    \"Uncertainty\",\n    \"Limitations and open issues\"\n  ],\n  \"family_checks\": [\n    \"claims_reference_existing_keys\",\n    \"phase_ledger_consistent\",\n    \"positive_se\"\n  ],\n  \"ci_pairs\": [],\n  \"positive_keys\": [\n    \"bias_mc_se\",\n    \"rho_hat_sd_mc\",\n    \"se_asymptotic\"\n  ],\n  \"chronology_pairs\": [],\n  \"analysis_timeout_s\": 300,\n  \"reproducibility_tolerance_rel\": 1e-06\n}{\n  \"task_id\": \"F5-conf-02\",\n  \"family\": \"F5\",\n  \"split\": \"conf\",\n  \"version\": \"1.0\",\n  \"created_utc\": \"2026-10-30T03:42:22.079893+00:00\",\n  \"files\": {\n    \"TASK.md\": \"2a389cdf509f84a0f7e0cf2780400eb5b6c1cd45ee0359a2d0708b803641d090\",\n    \"gate_spec.json\": \"1479a11a8587f31338a07b4532d5b9c2da1bba66c2486348acebf18090c30c6b\",\n    \"data/design.csv\": \"2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb\"\n  }\n}","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"89808d6a-66d2-4855-8388-44f9831201ee","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}21{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"be1a548b75b7d88e6408f64c79cc796865489aee3d74793c68e07af4132b2e18","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01PbJFdJJ7eQtDitFjA8KaFV","name":"Bash","input":{"command":"cat data/design.csv; echo; shasum -a 256 data/design.csv; cat gate_spec.json bundle.json","description":"Show design, hash, and gate spec"}}]}}22{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"216cf4f7-7e20-497c-a675-700ec0f10ce7","timestamp":"2026-10-30T05:13:26.082Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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":"8c8ff94a-455d-4214-991d-8be0de7ac615","keep":4,"tail":["be1a548b75b7d88e6408f64c79cc796865489aee3d74793c68e07af4132b2e18","475f2c7837de47f323e77ade92f7c5d5c6d3e53f7973644a5fc984ab65f02f84"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",5,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"65500ab51a675025c49d86a220ca689b81a9b62bd4af3f59acdfe72795c4d0ca"}23{"parentUuid":"390c2534-6184-4881-9284-469bcefcb3eb","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrEytLdcuRcn1bZj4QL","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":1383,"cache_read_input_tokens":6278,"output_tokens":1139,"output_tokens_details":{"thinking_tokens":166},"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":1383},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1287,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXrEybEDTwy7ibra5mPH","requestRef":"216cf4f7-7e20-497c-a675-700ec0f10ce7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"b3682d84-5d0c-49f6-8fe5-6c74c87454a3","timestamp":"2026-10-30T05:13:28.777Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}24{"parentUuid":"b3682d84-5d0c-49f6-8fe5-6c74c87454a3","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrEytLdcuRcn1bZj4QL","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01VPBuzLC2oLgwdnP9z4thJg","name":"Bash","input":{"command":"mkdir -p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** In a Gaussian AR(1), y_t = c + rho*y_{t-1} + e_t (c=0 in DGP), how biased is the OLS estimate of rho (regression on constant and y_{t-1}) in finite samples, and how well does the Marriott-Pope/Kendall approximation -(1+3rho)/n describe it at the design (n, rho)?\n\n**Estimands.** (i) bias_analytical = -(1+3rho)/n evaluated at design values (deterministic). (ii) bias_mc = E[rho_hat] - rho estimated as the MC mean over R replications minus rho, with MC s.e. sd(rho_hat)/sqrt(R). Meaningful under: Gaussian iid innovations, |rho|<1, stationary start, OLS with intercept using t=2..n (n-1 effective obs). The analytical formula is a first-order (O(1/n)) asymptotic expansion of the bias; error is O(n^-2), so it need not match exactly at small n.\n\n**Outputs.** out/results.json keys: task_id, bias_analytical, bias_mc, bias_mc_se, rho_hat_mean, rho_hat_sd_mc, discrepancy_se_units, se_asymptotic, n_replications, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed. Plus out/report.md (6 sections), out/analysis.py, out/claims.json, state files, exclusions.csv.\n\n**Information rules.** Only data/design.csv; follow design exactly (n=30, rho=0.8, sigma=1, intercept, stationary y_1, R=20000, seed 20261029 via numpy default_rng). Fresh series each replication.\n\n**Invalidity.** Missing/inconsistent design params; non-stationary rho (|rho|>=1 makes stationary init impossible); not using the given seed; deviating from the regression spec.\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","description":"Write contract, phase ledger, log"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1383,"cache_read_input_tokens":6278,"output_tokens":1139,"output_tokens_details":{"thinking_tokens":166},"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":1383},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXrEybEDTwy7ibra5mPH","requestRef":"216cf4f7-7e20-497c-a675-700ec0f10ce7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"dff2fff5-4f96-412a-8574-86f3e4840ec9","timestamp":"2026-10-30T05:13:36.127Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}25{"parentUuid":"dff2fff5-4f96-412a-8574-86f3e4840ec9","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01VPBuzLC2oLgwdnP9z4thJg","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"d1b8aab4-91ae-47ac-b63b-b7937b7e1b63","timestamp":"2026-10-30T05:13:36.147Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"dff2fff5-4f96-412a-8574-86f3e4840ec9","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251/out/state","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}26{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"05d2353022a4884f19c905fa4798f76535fb8bcc1856ab5be9f9973bc7a6c947","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01VPBuzLC2oLgwdnP9z4thJg","name":"Bash","input":{"command":"mkdir -p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** In a Gaussian AR(1), y_t = c + rho*y_{t-1} + e_t (c=0 in DGP), how biased is the OLS estimate of rho (regression on constant and y_{t-1}) in finite samples, and how well does the Marriott-Pope/Kendall approximation -(1+3rho)/n describe it at the design (n, rho)?\n\n**Estimands.** (i) bias_analytical = -(1+3rho)/n evaluated at design values (deterministic). (ii) bias_mc = E[rho_hat] - rho estimated as the MC mean over R replications minus rho, with MC s.e. sd(rho_hat)/sqrt(R). Meaningful under: Gaussian iid innovations, |rho|<1, stationary start, OLS with intercept using t=2..n (n-1 effective obs). The analytical formula is a first-order (O(1/n)) asymptotic expansion of the bias; error is O(n^-2), so it need not match exactly at small n.\n\n**Outputs.** out/results.json keys: task_id, bias_analytical, bias_mc, bias_mc_se, rho_hat_mean, rho_hat_sd_mc, discrepancy_se_units, se_asymptotic, n_replications, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed. Plus out/report.md (6 sections), out/analysis.py, out/claims.json, state files, exclusions.csv.\n\n**Information rules.** Only data/design.csv; follow design exactly (n=30, rho=0.8, sigma=1, intercept, stationary y_1, R=20000, seed 20261029 via numpy default_rng). Fresh series each replication.\n\n**Invalidity.** Missing/inconsistent design params; non-stationary rho (|rho|>=1 makes stationary init impossible); not using the given seed; deviating from the regression spec.\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","description":"Write contract, phase ledger, log"}}]}}27{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"bbb6fbca-d020-44c6-acea-d3f6cc3bafa4","timestamp":"2026-10-30T05:13:36.150Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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":"216cf4f7-7e20-497c-a675-700ec0f10ce7","keep":6,"tail":["05d2353022a4884f19c905fa4798f76535fb8bcc1856ab5be9f9973bc7a6c947","8fd590a1459c4ed6e478c7d4d6a421ebb19345bf9dc207dc5ab3408cc074b3d6"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"aa49cdbf13a9c3b3ce72e9695a58c5e13774c455d09ffdedaa1a868b94ff17c6"}28{"parentUuid":"d1b8aab4-91ae-47ac-b63b-b7937b7e1b63","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrFivhBsCGRrypakPMS","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":1154,"cache_read_input_tokens":7661,"output_tokens":698,"output_tokens_details":{"thinking_tokens":174},"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":1154},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1579,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXrFieadnSUaNHJKPg1y","requestRef":"bbb6fbca-d020-44c6-acea-d3f6cc3bafa4","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"7583396a-0bbe-47fa-aa3c-6cb01b50d956","timestamp":"2026-10-30T05:13:39.153Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251/out/state","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}29{"parentUuid":"7583396a-0bbe-47fa-aa3c-6cb01b50d956","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrFivhBsCGRrypakPMS","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01J2bjJuKsSD7nfiVbu5jT1h","name":"Bash","input":{"command":"cd out/state && cat > data_audit.md <<'EOF'\n# Data audit (P1)\nFile: data/design.csv\n- SHA-256: 2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb (matches bundle.json)\n- 7 data rows x 3 columns (parameter, value, description); header present.\n- Parameters: n=30 (series length), rho=0.8, sigma=1.0, intercept=yes, initial_condition=stationary (y_1 ~ N(0, sigma^2/(1-rho^2))), n_replications=20000, seed=20261029.\n- Missing values: none. Duplicate parameter names: none. Units: dimensionless (sigma in units of y).\n- Date ranges: not applicable (simulated design, no dates).\n- Anomalies: none. |rho|<1 so the stationary initial condition is well defined.\n- Ambiguity noted: \"n\" in the formula -(1+3rho)/n is taken as the design series length n=30 (as TASK.md says \"at the design values\"); the regression uses n-1=29 observations. Sensitivity with 29 reported in report only as a remark.\n- Information availability: the only input is the design; no rule violations possible.\nEOF\necho \"- 2026-10-30 P1 passed: design audited, no issues.\" >> log.md","description":"Write data audit"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1154,"cache_read_input_tokens":7661,"output_tokens":698,"output_tokens_details":{"thinking_tokens":174},"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":1154},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXrFieadnSUaNHJKPg1y","requestRef":"bbb6fbca-d020-44c6-acea-d3f6cc3bafa4","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"4095d1f8-9c71-40ae-b3cb-d7dee3ecd91e","timestamp":"2026-10-30T05:13:43.744Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251/out/state","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}30{"parentUuid":"4095d1f8-9c71-40ae-b3cb-d7dee3ecd91e","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01J2bjJuKsSD7nfiVbu5jT1h","type":"tool_result","content":"(eval):cd:1: no such file or directory: out/state","is_error":false}]},"uuid":"217d7771-39b2-4f5c-95d3-fd3070166aae","timestamp":"2026-10-30T05:13:43.755Z","toolUseResult":{"stdout":"(eval):cd:1: no such file or directory: out/state","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"4095d1f8-9c71-40ae-b3cb-d7dee3ecd91e","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251/out/state","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}31{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"35193be151c158553db600f72571d6a380bb2e490435d72226ea28e88e425440","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01J2bjJuKsSD7nfiVbu5jT1h","name":"Bash","input":{"command":"cd out/state && cat > data_audit.md <<'EOF'\n# Data audit (P1)\nFile: data/design.csv\n- SHA-256: 2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb (matches bundle.json)\n- 7 data rows x 3 columns (parameter, value, description); header present.\n- Parameters: n=30 (series length), rho=0.8, sigma=1.0, intercept=yes, initial_condition=stationary (y_1 ~ N(0, sigma^2/(1-rho^2))), n_replications=20000, seed=20261029.\n- Missing values: none. Duplicate parameter names: none. Units: dimensionless (sigma in units of y).\n- Date ranges: not applicable (simulated design, no dates).\n- Anomalies: none. |rho|<1 so the stationary initial condition is well defined.\n- Ambiguity noted: \"n\" in the formula -(1+3rho)/n is taken as the design series length n=30 (as TASK.md says \"at the design values\"); the regression uses n-1=29 observations. Sensitivity with 29 reported in report only as a remark.\n- Information availability: the only input is the design; no rule violations possible.\nEOF\necho \"- 2026-10-30 P1 passed: design audited, no issues.\" >> log.md","description":"Write data audit"}}]}}32{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"62d0434f-e3d4-4eb2-85a9-816accb99ab9","timestamp":"2026-10-30T05:13:43.758Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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":"bbb6fbca-d020-44c6-acea-d3f6cc3bafa4","keep":8,"tail":["35193be151c158553db600f72571d6a380bb2e490435d72226ea28e88e425440","4a558070bfaf1125d3905700ef1362ec3335c67cb40a0c9059debe75ed18ad0c"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",9,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"a7184324a77727a5ee2c216b08cf2ac5e2777e57e15785cedae67f7d250a60df"}33{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"217d7771-39b2-4f5c-95d3-fd3070166aae","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}34{"type":"atis-latch","atis":"","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}35{"parentUuid":"217d7771-39b2-4f5c-95d3-fd3070166aae","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrGHTYNM6z56K97afPZ","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_0124duZfZNSg9C2fFhzTRNjz","name":"Bash","input":{"command":"pwd; ls out/state","description":"Check cwd"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":722,"cache_read_input_tokens":8815,"output_tokens":80,"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":722},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXrGHAv8vdYK7YuTqfL1","requestRef":"62d0434f-e3d4-4eb2-85a9-816accb99ab9","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f267ad2c-72b1-45cd-b980-1ef22e78a343","timestamp":"2026-10-30T05:13:45.216Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251/out/state","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}36{"parentUuid":"f267ad2c-72b1-45cd-b980-1ef22e78a343","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 1\n/Users/simon-pierreboucher/wp29/runs/RC0251/out/state\nls: out/state: No such file or directory","is_error":true,"tool_use_id":"toolu_0124duZfZNSg9C2fFhzTRNjz"}]},"uuid":"f4ed7efb-56b3-4eb2-9f32-f9cd038ecbfa","timestamp":"2026-10-30T05:13:45.230Z","toolUseResult":"Error: Exit code 1\n/Users/simon-pierreboucher/wp29/runs/RC0251/out/state\nls: out/state: No such file or directory","sandboxed":false,"sourceToolAssistantUUID":"f267ad2c-72b1-45cd-b980-1ef22e78a343","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251/out/state","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}37{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"d6718e641117be873a0e450185f624f25863e354099f506607fb0a66e1b8b485","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_0124duZfZNSg9C2fFhzTRNjz","name":"Bash","input":{"command":"pwd; ls out/state","description":"Check cwd"}}]}}38{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"e2c42b5d-3d11-475c-a938-885a8769c6a6","timestamp":"2026-10-30T05:13:45.233Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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":"62d0434f-e3d4-4eb2-85a9-816accb99ab9","keep":10,"tail":["d6718e641117be873a0e450185f624f25863e354099f506607fb0a66e1b8b485","de4fccdf16ace58984e67a0959cd917dadb4a02898d2ac578b8ea407a1c96f16"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",11,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"e45e2af13386654f14e262c18cc2e398fa5ded03a2db4d7d663a3b4fc16ef807"}39{"parentUuid":"f4ed7efb-56b3-4eb2-9f32-f9cd038ecbfa","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrGPn38jTCrvPsy4uKZ","type":"message","role":"assistant","content":[{"type":"text","text":"Shell persisted the cd; re-run in place."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":141,"cache_read_input_tokens":9537,"output_tokens":2453,"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":141},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXrGPVvhpU3grpCxDj74","requestRef":"e2c42b5d-3d11-475c-a938-885a8769c6a6","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"73b9ed0c-33b3-4817-90ae-4e48b7934252","timestamp":"2026-10-30T05:13:46.455Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}40{"parentUuid":"73b9ed0c-33b3-4817-90ae-4e48b7934252","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrGPn38jTCrvPsy4uKZ","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01NUSXQS1JYdAjFF13oFZ6SV","name":"Bash","input":{"command":"cat > data_audit.md <<'EOF'\n# Data audit (P1)\nFile: data/design.csv\n- SHA-256: 2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb (matches bundle.json)\n- 7 data rows x 3 columns (parameter, value, description); header present.\n- Parameters: n=30 (series length), rho=0.8, sigma=1.0, intercept=yes, initial_condition=stationary (y_1 ~ N(0, sigma^2/(1-rho^2))), n_replications=20000, seed=20261029.\n- Missing values: none. Duplicate parameter names: none. Units: dimensionless (sigma in units of y).\n- Date ranges: not applicable (simulated design, no dates).\n- Anomalies: none. |rho|<1 so the stationary initial condition is well defined.\n- Ambiguity noted: \"n\" in the formula -(1+3rho)/n is taken as the design series length n=30 (as TASK.md says \"at the design values\"); the regression uses n-1=29 observations. Sensitivity with 29 is mentioned in the report as a remark only.\n- Information availability: the only input is the design; no rule violations possible.\n- Exclusions: none expected; out/exclusions.csv records a check that drops non-finite rho_hat replications (expected 0 removed).\nEOF\necho \"- 2026-10-30 P1 passed: design audited, no issues.\" >> log.md; cd /Users/simon-pierreboucher/wp29/runs/RC0251","description":"Write data audit"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":141,"cache_read_input_tokens":9537,"output_tokens":2453,"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":141},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXrGPVvhpU3grpCxDj74","requestRef":"e2c42b5d-3d11-475c-a938-885a8769c6a6","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"fbc55b59-39ff-4bda-b08c-71a7256e2a32","timestamp":"2026-10-30T05:13:50.605Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}41{"parentUuid":"fbc55b59-39ff-4bda-b08c-71a7256e2a32","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01NUSXQS1JYdAjFF13oFZ6SV","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"c60b90a6-247c-4028-8ce4-009ff790c028","timestamp":"2026-10-30T05:13:50.624Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"fbc55b59-39ff-4bda-b08c-71a7256e2a32","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}42{"parentUuid":"c60b90a6-247c-4028-8ce4-009ff790c028","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrGPn38jTCrvPsy4uKZ","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_0159N8vRnzBqn3z7H8VREuqB","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-02: Finite-sample bias of OLS AR(1) coefficient (with intercept).\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nReads only data/design.csv; writes out/results.json and out/exclusions.csv.\n\"\"\"\nimport json, math, csv\nfrom pathlib import Path\nimport numpy as np\nimport pandas as pd\n\nROOT = Path(__file__).resolve().parent.parent\nd = pd.read_csv(ROOT / \"data\" / \"design.csv\")\np = dict(zip(d[\"parameter\"], d[\"value\"]))\nn = int(p[\"n\"]); rho = float(p[\"rho\"]); sigma = float(p[\"sigma\"])\nR = int(p[\"n_replications\"]); seed = int(p[\"seed\"])\nassert str(p[\"intercept\"]).strip().lower() == \"yes\"\nassert str(p[\"initial_condition\"]).strip().lower() == \"stationary\"\nassert abs(rho) < 1\n\n# --- Baseline / analytical quantities ---\nbias_analytical = -(1 + 3 * rho) / n\nse_asymptotic = math.sqrt((1 - rho ** 2) / n)\n\n# --- Monte Carlo (vectorised over replications), c = 0 ---\nrng = np.random.default_rng(seed)\n# Draw order: first y_1 for all R replications, then the (R, n-1) innovation matrix.\ny = np.empty((R, n))\ny[:, 0] = rng.normal(0.0, sigma / math.sqrt(1 - rho ** 2), size=R)\neps = rng.normal(0.0, sigma, size=(R, n - 1))\nfor t in range(1, n):\n    y[:, t] = rho * y[:, t - 1] + eps[:, t - 1]\n\n# OLS of y_t on (1, y_{t-1}), t = 2..n: slope = cov(x,z)/var(x) with demeaning\nx = y[:, :-1]; z = y[:, 1:]\nxc = x - x.mean(axis=1, keepdims=True)\nzc = z - z.mean(axis=1, keepdims=True)\nrho_hat = (xc * zc).sum(axis=1) / (xc ** 2).sum(axis=1)\n\n# Spot check against explicit least squares for the first replication\nX0 = np.column_stack([np.ones(n - 1), x[0]])\nb0 = np.linalg.lstsq(X0, z[0], rcond=None)[0]\nassert abs(b0[1] - rho_hat[0]) < 1e-10\n\n# Exclusion ledger: non-finite estimates (none expected)\nfinite = np.isfinite(rho_hat)\nrh = rho_hat[finite]\nwith open(ROOT / \"out\" / \"exclusions.csv\", \"w\", newline=\"\") as f:\n    w = csv.writer(f)\n    w.writerow([\"step\", \"rule\", \"n_before\", \"n_after\", \"n_removed\", \"rationale\"])\n    w.writerow([1, \"drop replications with non-finite rho_hat\", R, int(finite.sum()),\n                int(R - finite.sum()), \"OLS slope undefined if regressor has zero variance (probability zero)\"])\n\nrho_hat_mean = float(rh.mean())\nrho_hat_sd = float(rh.std(ddof=1))\nbias_mc = rho_hat_mean - rho\nbias_mc_se = rho_hat_sd / math.sqrt(rh.size)\ndisc = (bias_mc - bias_analytical) / bias_mc_se\n\nres = {\n    \"task_id\": \"F5-conf-02\",\n    \"bias_analytical\": bias_analytical,\n    \"bias_mc\": bias_mc,\n    \"bias_mc_se\": bias_mc_se,\n    \"rho_hat_mean\": rho_hat_mean,\n    \"rho_hat_sd_mc\": rho_hat_sd,\n    \"discrepancy_se_units\": disc,\n    \"se_asymptotic\": se_asymptotic,\n    \"n_replications\": R,\n    \"feasibility\": \"complete\",\n    \"feasibility_reason\": None,\n    \"data_issues\": [],\n    \"n_input_rows\": {\"design.csv\": int(len(d))},\n    \"n_analysed\": int(rh.size),\n    \"random_seed\": seed,\n    # supplementary (not required) descriptive quantities\n    \"supp_bias_analytical_n_minus_1\": -(1 + 3 * rho) / (n - 1),\n    \"supp_rho_hat_median\": float(np.median(rh)),\n    \"supp_ratio_bias_mc_to_analytical\": bias_mc / bias_analytical,\n    \"supp_ratio_sd_mc_to_se_asymptotic\": rho_hat_sd / se_asymptotic,\n}\nwith open(ROOT / \"out\" / \"results.json\", \"w\") as f:\n    json.dump(res, f, indent=2)\nfor k, v in res.items():\n    print(f\"{k}: {v}\")\nEOF\n~/wp29/venv/bin/python out/analysis.py && cat out/exclusions.csv","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":141,"cache_read_input_tokens":9537,"output_tokens":2453,"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":141},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXrGPVvhpU3grpCxDj74","requestRef":"e2c42b5d-3d11-475c-a938-885a8769c6a6","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"a4314e55-ea6e-4e24-91d8-fdc2a8a82b4d","timestamp":"2026-10-30T05:14:03.154Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}43{"parentUuid":"a4314e55-ea6e-4e24-91d8-fdc2a8a82b4d","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_0159N8vRnzBqn3z7H8VREuqB","type":"tool_result","content":"task_id: F5-conf-02\nbias_analytical: -0.11333333333333334\nbias_mc: -0.1237101032106388\nbias_mc_se: 0.001052971374380562\nrho_hat_mean: 0.6762898967893612\nrho_hat_sd_mc: 0.14891263984396286\ndiscrepancy_se_units: -9.854750214278015\nse_asymptotic: 0.1095445115010332\nn_replications: 20000\nfeasibility: complete\nfeasibility_reason: None\ndata_issues: []\nn_input_rows: {'design.csv': 7}\nn_analysed: 20000\nrandom_seed: 20261029\nsupp_bias_analytical_n_minus_1: -0.11724137931034484\nsupp_rho_hat_median: 0.6987087985454113\nsupp_ratio_bias_mc_to_analytical: 1.0915597342115186\nsupp_ratio_sd_mc_to_se_asymptotic: 1.3593801990030177\nstep,rule,n_before,n_after,n_removed,rationale\r\n1,drop replications with non-finite rho_hat,20000,20000,0,OLS slope undefined if regressor has zero variance (probability zero)","is_error":false}]},"uuid":"c757b20e-71be-451a-a20e-80013ac3f173","timestamp":"2026-10-30T05:14:03.377Z","toolUseResult":{"stdout":"task_id: F5-conf-02\nbias_analytical: -0.11333333333333334\nbias_mc: -0.1237101032106388\nbias_mc_se: 0.001052971374380562\nrho_hat_mean: 0.6762898967893612\nrho_hat_sd_mc: 0.14891263984396286\ndiscrepancy_se_units: -9.854750214278015\nse_asymptotic: 0.1095445115010332\nn_replications: 20000\nfeasibility: complete\nfeasibility_reason: None\ndata_issues: []\nn_input_rows: {'design.csv': 7}\nn_analysed: 20000\nrandom_seed: 20261029\nsupp_bias_analytical_n_minus_1: -0.11724137931034484\nsupp_rho_hat_median: 0.6987087985454113\nsupp_ratio_bias_mc_to_analytical: 1.0915597342115186\nsupp_ratio_sd_mc_to_se_asymptotic: 1.3593801990030177\nstep,rule,n_before,n_after,n_removed,rationale\r\n1,drop replications with non-finite rho_hat,20000,20000,0,OLS slope undefined if regressor has zero variance (probability zero)","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"a4314e55-ea6e-4e24-91d8-fdc2a8a82b4d","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}44{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"93591b43b886152c370dcbe497427cb005896ef6644fbd65e0cc88d6e340133d","message":{"role":"assistant","content":[{"type":"text","text":"Shell persisted the cd; re-run in place."},{"type":"tool_use","id":"toolu_01NUSXQS1JYdAjFF13oFZ6SV","name":"Bash","input":{"command":"cat > data_audit.md <<'EOF'\n# Data audit (P1)\nFile: data/design.csv\n- SHA-256: 2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb (matches bundle.json)\n- 7 data rows x 3 columns (parameter, value, description); header present.\n- Parameters: n=30 (series length), rho=0.8, sigma=1.0, intercept=yes, initial_condition=stationary (y_1 ~ N(0, sigma^2/(1-rho^2))), n_replications=20000, seed=20261029.\n- Missing values: none. Duplicate parameter names: none. Units: dimensionless (sigma in units of y).\n- Date ranges: not applicable (simulated design, no dates).\n- Anomalies: none. |rho|<1 so the stationary initial condition is well defined.\n- Ambiguity noted: \"n\" in the formula -(1+3rho)/n is taken as the design series length n=30 (as TASK.md says \"at the design values\"); the regression uses n-1=29 observations. Sensitivity with 29 is mentioned in the report as a remark only.\n- Information availability: the only input is the design; no rule violations possible.\n- Exclusions: none expected; out/exclusions.csv records a check that drops non-finite rho_hat replications (expected 0 removed).\nEOF\necho \"- 2026-10-30 P1 passed: design audited, no issues.\" >> log.md; cd /Users/simon-pierreboucher/wp29/runs/RC0251","description":"Write data audit"}},{"type":"tool_use","id":"toolu_0159N8vRnzBqn3z7H8VREuqB","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-02: Finite-sample bias of OLS AR(1) coefficient (with intercept).\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nReads only data/design.csv; writes out/results.json and out/exclusions.csv.\n\"\"\"\nimport json, math, csv\nfrom pathlib import Path\nimport numpy as np\nimport pandas as pd\n\nROOT = Path(__file__).resolve().parent.parent\nd = pd.read_csv(ROOT / \"data\" / \"design.csv\")\np = dict(zip(d[\"parameter\"], d[\"value\"]))\nn = int(p[\"n\"]); rho = float(p[\"rho\"]); sigma = float(p[\"sigma\"])\nR = int(p[\"n_replications\"]); seed = int(p[\"seed\"])\nassert str(p[\"intercept\"]).strip().lower() == \"yes\"\nassert str(p[\"initial_condition\"]).strip().lower() == \"stationary\"\nassert abs(rho) < 1\n\n# --- Baseline / analytical quantities ---\nbias_analytical = -(1 + 3 * rho) / n\nse_asymptotic = math.sqrt((1 - rho ** 2) / n)\n\n# --- Monte Carlo (vectorised over replications), c = 0 ---\nrng = np.random.default_rng(seed)\n# Draw order: first y_1 for all R replications, then the (R, n-1) innovation matrix.\ny = np.empty((R, n))\ny[:, 0] = rng.normal(0.0, sigma / math.sqrt(1 - rho ** 2), size=R)\neps = rng.normal(0.0, sigma, size=(R, n - 1))\nfor t in range(1, n):\n    y[:, t] = rho * y[:, t - 1] + eps[:, t - 1]\n\n# OLS of y_t on (1, y_{t-1}), t = 2..n: slope = cov(x,z)/var(x) with demeaning\nx = y[:, :-1]; z = y[:, 1:]\nxc = x - x.mean(axis=1, keepdims=True)\nzc = z - z.mean(axis=1, keepdims=True)\nrho_hat = (xc * zc).sum(axis=1) / (xc ** 2).sum(axis=1)\n\n# Spot check against explicit least squares for the first replication\nX0 = np.column_stack([np.ones(n - 1), x[0]])\nb0 = np.linalg.lstsq(X0, z[0], rcond=None)[0]\nassert abs(b0[1] - rho_hat[0]) < 1e-10\n\n# Exclusion ledger: non-finite estimates (none expected)\nfinite = np.isfinite(rho_hat)\nrh = rho_hat[finite]\nwith open(ROOT / \"out\" / \"exclusions.csv\", \"w\", newline=\"\") as f:\n    w = csv.writer(f)\n    w.writerow([\"step\", \"rule\", \"n_before\", \"n_after\", \"n_removed\", \"rationale\"])\n    w.writerow([1, \"drop replications with non-finite rho_hat\", R, int(finite.sum()),\n                int(R - finite.sum()), \"OLS slope undefined if regressor has zero variance (probability zero)\"])\n\nrho_hat_mean = float(rh.mean())\nrho_hat_sd = float(rh.std(ddof=1))\nbias_mc = rho_hat_mean - rho\nbias_mc_se = rho_hat_sd / math.sqrt(rh.size)\ndisc = (bias_mc - bias_analytical) / bias_mc_se\n\nres = {\n    \"task_id\": \"F5-conf-02\",\n    \"bias_analytical\": bias_analytical,\n    \"bias_mc\": bias_mc,\n    \"bias_mc_se\": bias_mc_se,\n    \"rho_hat_mean\": rho_hat_mean,\n    \"rho_hat_sd_mc\": rho_hat_sd,\n    \"discrepancy_se_units\": disc,\n    \"se_asymptotic\": se_asymptotic,\n    \"n_replications\": R,\n    \"feasibility\": \"complete\",\n    \"feasibility_reason\": None,\n    \"data_issues\": [],\n    \"n_input_rows\": {\"design.csv\": int(len(d))},\n    \"n_analysed\": int(rh.size),\n    \"random_seed\": seed,\n    # supplementary (not required) descriptive quantities\n    \"supp_bias_analytical_n_minus_1\": -(1 + 3 * rho) / (n - 1),\n    \"supp_rho_hat_median\": float(np.median(rh)),\n    \"supp_ratio_bias_mc_to_analytical\": bias_mc / bias_analytical,\n    \"supp_ratio_sd_mc_to_se_asymptotic\": rho_hat_sd / se_asymptotic,\n}\nwith open(ROOT / \"out\" / \"results.json\", \"w\") as f:\n    json.dump(res, f, indent=2)\nfor k, v in res.items():\n    print(f\"{k}: {v}\")\nEOF\n~/wp29/venv/bin/python out/analysis.py && cat out/exclusions.csv","description":"Write and run analysis script"}}]}}45{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"9da76867c58474fd84774487834c10177914224d117d1584c8daa1016bf76206","message":{"role":"user","content":[{"tool_use_id":"toolu_01NUSXQS1JYdAjFF13oFZ6SV","type":"tool_result","content":"(Bash completed with no output)","is_error":false},{"tool_use_id":"toolu_0159N8vRnzBqn3z7H8VREuqB","type":"tool_result","content":"task_id: F5-conf-02\nbias_analytical: -0.11333333333333334\nbias_mc: -0.1237101032106388\nbias_mc_se: 0.001052971374380562\nrho_hat_mean: 0.6762898967893612\nrho_hat_sd_mc: 0.14891263984396286\ndiscrepancy_se_units: -9.854750214278015\nse_asymptotic: 0.1095445115010332\nn_replications: 20000\nfeasibility: complete\nfeasibility_reason: None\ndata_issues: []\nn_input_rows: {'design.csv': 7}\nn_analysed: 20000\nrandom_seed: 20261029\nsupp_bias_analytical_n_minus_1: -0.11724137931034484\nsupp_rho_hat_median: 0.6987087985454113\nsupp_ratio_bias_mc_to_analytical: 1.0915597342115186\nsupp_ratio_sd_mc_to_se_asymptotic: 1.3593801990030177\nstep,rule,n_before,n_after,n_removed,rationale\r\n1,drop replications with non-finite rho_hat,20000,20000,0,OLS slope undefined if regressor has zero variance (probability zero)","is_error":false}]}}46{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"9a05b5f6-56e4-4456-b304-75cc5a9dc423","timestamp":"2026-10-30T05:14:03.380Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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":"e2c42b5d-3d11-475c-a938-885a8769c6a6","keep":12,"tail":["93591b43b886152c370dcbe497427cb005896ef6644fbd65e0cc88d6e340133d","9da76867c58474fd84774487834c10177914224d117d1584c8daa1016bf76206"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",13,"content",1],"value":{"type":"ephemeral"}}],"requestDigest":"6db20d2a443a10357f5b370690a22c3dab4f25f5c1e2951b48eff534e8914a0f"}47{"parentUuid":"c757b20e-71be-451a-a20e-80013ac3f173","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrHjKa3aS5wsYfnPkKN","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":2851,"cache_read_input_tokens":9678,"output_tokens":671,"output_tokens_details":{"thinking_tokens":142},"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":2851},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1019,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXrHj3wxymR7Qso45G7q","requestRef":"9a05b5f6-56e4-4456-b304-75cc5a9dc423","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"4969d2e3-8968-4eed-be47-4afe4b266096","timestamp":"2026-10-30T05:14:07.116Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}48{"parentUuid":"4969d2e3-8968-4eed-be47-4afe4b266096","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrHjKa3aS5wsYfnPkKN","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01WKVUJFzRcC69ehySmWwq2s","name":"Bash","input":{"command":"cp out/results.json /tmp/r1.json; rm out/results.json out/exclusions.csv; ~/wp29/venv/bin/python out/analysis.py >/dev/null; cmp /tmp/r1.json out/results.json && echo IDENTICAL; ~/wp29/venv/bin/python -c \"\nimport json;r=json.load(open('out/results.json'))\nprint('se>0',r['bias_mc_se']>0,r['rho_hat_sd_mc']>0,r['se_asymptotic']>0)\nprint('mean-rho==bias',abs(r['rho_hat_mean']-0.8-r['bias_mc'])<1e-12)\nprint('se=sd/sqrtR',abs(r['rho_hat_sd_mc']/20000**.5-r['bias_mc_se'])<1e-12)\nprint('disc',(r['bias_mc']-r['bias_analytical'])/r['bias_mc_se'])\nprint('analytical',-(1+3*.8)/30)\nprint('95% MC CI',r['bias_mc']-1.96*r['bias_mc_se'],r['bias_mc']+1.96*r['bias_mc_se'])\nprint('disc vs n-1 formula',(r['bias_mc']-r['supp_bias_analytical_n_minus_1'])/r['bias_mc_se'])\n\"","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":2851,"cache_read_input_tokens":9678,"output_tokens":671,"output_tokens_details":{"thinking_tokens":142},"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":2851},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXrHj3wxymR7Qso45G7q","requestRef":"9a05b5f6-56e4-4456-b304-75cc5a9dc423","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"4b5e6608-9160-4274-91cb-f13870120d95","timestamp":"2026-10-30T05:14:10.678Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}49{"parentUuid":"4b5e6608-9160-4274-91cb-f13870120d95","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01WKVUJFzRcC69ehySmWwq2s","type":"tool_result","content":"IDENTICAL\nse>0 True True True\nmean-rho==bias True\nse=sd/sqrtR True\ndisc -9.854750214278015\nanalytical -0.11333333333333334\n95% MC CI -0.1257739271044247 -0.1216462793168529\ndisc vs n-1 formula -6.143304611770056","is_error":false}]},"uuid":"abd8e25d-5b13-48ff-8612-f3dde27d5550","timestamp":"2026-10-30T05:14:10.946Z","toolUseResult":{"stdout":"IDENTICAL\nse>0 True True True\nmean-rho==bias True\nse=sd/sqrtR True\ndisc -9.854750214278015\nanalytical -0.11333333333333334\n95% MC CI -0.1257739271044247 -0.1216462793168529\ndisc vs n-1 formula -6.143304611770056","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"4b5e6608-9160-4274-91cb-f13870120d95","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}50{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"fb1a3f6163890bb868041ea138391c4391bfdf70bc89002721b71026e6ef654e","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01WKVUJFzRcC69ehySmWwq2s","name":"Bash","input":{"command":"cp out/results.json /tmp/r1.json; rm out/results.json out/exclusions.csv; ~/wp29/venv/bin/python out/analysis.py >/dev/null; cmp /tmp/r1.json out/results.json && echo IDENTICAL; ~/wp29/venv/bin/python -c \"\nimport json;r=json.load(open('out/results.json'))\nprint('se>0',r['bias_mc_se']>0,r['rho_hat_sd_mc']>0,r['se_asymptotic']>0)\nprint('mean-rho==bias',abs(r['rho_hat_mean']-0.8-r['bias_mc'])<1e-12)\nprint('se=sd/sqrtR',abs(r['rho_hat_sd_mc']/20000**.5-r['bias_mc_se'])<1e-12)\nprint('disc',(r['bias_mc']-r['bias_analytical'])/r['bias_mc_se'])\nprint('analytical',-(1+3*.8)/30)\nprint('95% MC CI',r['bias_mc']-1.96*r['bias_mc_se'],r['bias_mc']+1.96*r['bias_mc_se'])\nprint('disc vs n-1 formula',(r['bias_mc']-r['supp_bias_analytical_n_minus_1'])/r['bias_mc_se'])\n\"","description":"Reproducibility and consistency checks"}}]}}51{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"c2c23229-791e-45c4-a847-c6cd67896363","timestamp":"2026-10-30T05:14:10.949Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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":"9a05b5f6-56e4-4456-b304-75cc5a9dc423","keep":14,"tail":["fb1a3f6163890bb868041ea138391c4391bfdf70bc89002721b71026e6ef654e","f9f80124f687d6cdd6cb6e25504884b95401272c6ca399e7b1c77886dfb93f42"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",15,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"3b7fc24580530ecc8eaad3284cdee599af1dedb6a61d4041de2145a6161cf0e3"}52{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"abd8e25d-5b13-48ff-8612-f3dde27d5550","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}53{"type":"atis-latch","atis":"","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}54{"parentUuid":"abd8e25d-5b13-48ff-8612-f3dde27d5550","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrJHiiGgr9NDZXtGFX5","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQSkgcKEAgTGAI4AUIIdGhpbmtpbmcSDPoSTSs6M/eZBCxjVhoMb9rgCzuzQYZyE0TwIjDkRATaLddWNRaWuZcOrTttUiYRcAi7eYCm0VOCNH4rwcnziUj/IXtkPJPY3D/ARacqrwbmjmb7gGBGZZDSDyCx8i+M0ZeeSyjeQkFboC1BPtwqztOPOh/Wy0K0A64+475TLlrol0vVoz6MOCNr9OLfZKj3QSXturEwYnCc/4ITtUo7gmYFiLw6L3GkmdawwpwsMjuvyBGvV9Atxa1QLEUzGwahBvk99C7WJeLGDYUg6Eq8n7VpgIJF5V7KRMif8jEx6WWEavn2+Cbq5gAc9iCuvEBnbMJNPS3AeuM9JYI/Hb1mroWliSuNhQQOuJUeQkTUkM7b3xYKkAY47Ps9YiSxNRvAbjf6p/HD+zU+xUhyNLY8FZRb6npkJ/gzDNYh5afPwRPKRNJqwVq83zTUwX5ls5EC8uC5WMOTsKGEd3JPjGdiNPWVE6dmNU0Mm3gBQFbPYaL2a27+4W8dvs2QItaQieSgMGI8pl/0xkRtNYQ+IcGhWLulLMMDDaxNIvg5Cy2c88ITdLfkflf3MC13Ux0tNEhjrtSsIosRz/GOi2F+bZp5YysLIys/Ife/q+F+Pn7xRTagRyqkFosmx+5KWp7F/vyiM3FIV7mzrUxVarNtFjxGq/OSssXQkcniWGxn4FPh4T4lvcPYFp7kCu8fBbdDVNGqF+EDxR+AiT4rszEa9xclJGw9WOENGX1SmNyCfe+mDkHSBgmayBwZlcjJ2CjmHfl7su3jhDpJGoDUJucMPoD17u/+OXTrA4nVnDfqybpHnSrUjd0+xxx9p9f3n1pdFMQLVBRxMjMslAt6sbQhH3u/xROFbA7fQrs2a6epnmu7LPH36yYqstQ/odLW+otf82PbpeqKeyWF3Oxy4m2zVlqFddri09Njfw8SPCqNe4QYNS2ZKqdqWKGjwVRjNkDpVo8OdI51dzMegn75PXO3vMeJeG76vGPsx27mOiHtnkvQ5MWgodgr8fRr9gDVifAV2J/YiKB7ounTGgOv4MWFCRJ5y3AeLxd5czeZrR2SHh2/Sm5+QC8WcV97TDafk/VcsvLg/qrIwDWJnJEHDqEUfwvGb5zf6m/JgUudoOHZRna6ElSESqysvOA7MQqSHgsyumI2GKiKSNX3wA7TmZOWTms/Ek9jHastLOhaU0pY1N+vFxgB"}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":782,"cache_read_input_tokens":12529,"output_tokens":689,"output_tokens_details":{"thinking_tokens":56},"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":782},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":416,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXrJHRrQWbHcam1n59Lm","requestRef":"c2c23229-791e-45c4-a847-c6cd67896363","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"04bc29fe-82b6-458c-9b05-749e8208b804","timestamp":"2026-10-30T05:14:12.758Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}55{"parentUuid":"04bc29fe-82b6-458c-9b05-749e8208b804","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrJHiiGgr9NDZXtGFX5","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_0131jMF9aBZFwaBSCchiSvXy","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n| check | outcome |\n|---|---|\n| Clean re-run of out/analysis.py (results.json and exclusions.csv deleted first) reproduces results.json byte-identically | PASS (cmp identical) |\n| OLS slope via demeaned formula equals np.linalg.lstsq with intercept (replication 1, tol 1e-10) | PASS (assert in script) |\n| bias_mc == rho_hat_mean - rho | PASS (|diff|<1e-12) |\n| bias_mc_se == rho_hat_sd_mc / sqrt(R) | PASS |\n| bias_mc_se, rho_hat_sd_mc, se_asymptotic > 0 | PASS |\n| bias_analytical == -(1+3*0.8)/30 = -0.11333 | PASS |\n| discrepancy_se_units recomputed = -9.855 | PASS |\n| Exclusion ledger: 20000 raw - 0 removed = 20000 = n_analysed | PASS |\n| Magnitude vs baseline: bias_mc (-0.1237) same sign/order as bias_analytical (-0.1133); rho_hat_sd_mc (0.149) vs se_asymptotic (0.110) plausible (small-n inflation) | PASS |\n| Design followed: n=30, rho=0.8, sigma=1, c=0, intercept, stationary y_1, R=20000, seed=20261029 | PASS |\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . ; ls out/state/gate_receipts","description":"Write checks, 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":782,"cache_read_input_tokens":12529,"output_tokens":689,"output_tokens_details":{"thinking_tokens":56},"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":782},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXrJHRrQWbHcam1n59Lm","requestRef":"c2c23229-791e-45c4-a847-c6cd67896363","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"de3e6af5-b528-4c8c-903f-57b255f712ff","timestamp":"2026-10-30T05:14:17.252Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}56{"parentUuid":"de3e6af5-b528-4c8c-903f-57b255f712ff","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_0131jMF9aBZFwaBSCchiSvXy","type":"tool_result","content":"PGAR 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:bias_analytical: ok\n  [ok] key:bias_mc: ok\n  [ok] key:bias_mc_se: ok\n  [ok] key:rho_hat_mean: ok\n  [ok] key:rho_hat_sd_mc: ok\n  [ok] key:discrepancy_se_units: ok\n  [ok] key:se_asymptotic: ok\n  [ok] key:n_replications: 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:n_analysed: 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: ['P1', 'P2', 'P3', 'P4', 'P5']\n  [ok] positive:bias_mc_se: 0.001052971374380562\n  [ok] positive:rho_hat_sd_mc: 0.14891263984396286\n  [ok] positive:se_asymptotic: 0.1095445115010332\n  [ok] reproducibility: regenerated in 0.2s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0251/out/state/gate_receipts/20261030T051417.533751Z.json\n20261030T051417.533751Z.json","is_error":false}]},"uuid":"31b09d7c-7fca-472a-a754-733e57e730ef","timestamp":"2026-10-30T05:14:17.543Z","toolUseResult":{"stdout":"PGAR 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:bias_analytical: ok\n  [ok] key:bias_mc: ok\n  [ok] key:bias_mc_se: ok\n  [ok] key:rho_hat_mean: ok\n  [ok] key:rho_hat_sd_mc: ok\n  [ok] key:discrepancy_se_units: ok\n  [ok] key:se_asymptotic: ok\n  [ok] key:n_replications: 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:n_analysed: 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: ['P1', 'P2', 'P3', 'P4', 'P5']\n  [ok] positive:bias_mc_se: 0.001052971374380562\n  [ok] positive:rho_hat_sd_mc: 0.14891263984396286\n  [ok] positive:se_asymptotic: 0.1095445115010332\n  [ok] reproducibility: regenerated in 0.2s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0251/out/state/gate_receipts/20261030T051417.533751Z.json\n20261030T051417.533751Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"de3e6af5-b528-4c8c-903f-57b255f712ff","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}57{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"9a8def956c601f982310b777b2d79c30b795e8514e8d882b881d3035e38e6261","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_0131jMF9aBZFwaBSCchiSvXy","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n| check | outcome |\n|---|---|\n| Clean re-run of out/analysis.py (results.json and exclusions.csv deleted first) reproduces results.json byte-identically | PASS (cmp identical) |\n| OLS slope via demeaned formula equals np.linalg.lstsq with intercept (replication 1, tol 1e-10) | PASS (assert in script) |\n| bias_mc == rho_hat_mean - rho | PASS (|diff|<1e-12) |\n| bias_mc_se == rho_hat_sd_mc / sqrt(R) | PASS |\n| bias_mc_se, rho_hat_sd_mc, se_asymptotic > 0 | PASS |\n| bias_analytical == -(1+3*0.8)/30 = -0.11333 | PASS |\n| discrepancy_se_units recomputed = -9.855 | PASS |\n| Exclusion ledger: 20000 raw - 0 removed = 20000 = n_analysed | PASS |\n| Magnitude vs baseline: bias_mc (-0.1237) same sign/order as bias_analytical (-0.1133); rho_hat_sd_mc (0.149) vs se_asymptotic (0.110) plausible (small-n inflation) | PASS |\n| Design followed: n=30, rho=0.8, sigma=1, c=0, intercept, stationary y_1, R=20000, seed=20261029 | PASS |\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . ; ls out/state/gate_receipts","description":"Write checks, run gate"}}]}}58{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"584c86e9-8d98-4a84-813d-641b7e2c8ff3","timestamp":"2026-10-30T05:14:17.546Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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":"c2c23229-791e-45c4-a847-c6cd67896363","keep":16,"tail":["9a8def956c601f982310b777b2d79c30b795e8514e8d882b881d3035e38e6261","bff8d9ad51185c1a2afebba28c1bc3501722f9615ff535c832e60fa4e6bff0d3"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",17,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"429994cd03d3b11609da80d3d979fbe363453aedf7a44bc4729672e18cf9f4e8"}59{"parentUuid":"31b09d7c-7fca-472a-a754-733e57e730ef","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrJmxqLae3hefKevgX2","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQS6gYKEAgTGAI4AUIIdGhpbmtpbmcSDH2AZ8nlxz2ucqetMBoMhmqN6KtU+gp1j0EdIjC6AjXqfihKvsk+nw82H6XEmDHXrPK9btpaV5/cH1Cb0OJY7Z/JSyIMj0zalSxyNyQqhwZnVMKC5wJG+UUIBtdxqeG+MzpuJSqyxJaHWrFG/wDbXUZvqJJyuYuCd156IdRvxcDGiyOqBDT8OVB9UyjGvmcZ10Z6GfHV20M5WcHk4sVh6iNHi4sv1HNk9DsUA79lHyFSGIZ6TdQ2BGBt7+ySBbRGiTHdm5QQ2xt3tzQkwN18RMKElFjt2XN0K0Rji5+equbkH9PUmEYXwdqCBklWF5xUtLNtULz8QdtUrx+sDzsC6BojzeYkYbIlhRXrLlzOz0KxnpeypZLdv8exXM9coKD/uVvvDRKPmzXa0cMMeXVWONubfAfwuUKjl13T92lKDvBfHobLAkSQvXYtKI2CCORwMB8qaCZO/Ni4kq8y7GUZOGVUtpyD24kjGV2hHlMcZXcDP/qQIfdMrdxoyF0qPqwGzXVzGHLbESdavVJxEOuvDiqmF/JRrM0ERPiN9lmeVz8fhy+slNDvBmlHJzJ/yc65YZUcrmNV1RKROiQpwZpIy3I3flvzeBBbskf37H+t+D0r6gB36/ZhpeInf0IWs63EAvwIfrU9pUyJVRUKOH8Kk/aUKvS3G4rlHbXyczwPyt7+LwzHr0QEIuzC+bDcBQA9tu6nKC1GluPmKEpjYtqHmDWmyCEg9OXAmt9E0p9aWYatkzCQ6vgQbf/0aGo+Jdsup50wfcWjJ1EQLIjPl4zweGpQrUumummq6BDwLC889bNJtkATPbUDSKSJqHra5yJtUusdWmdwmxCm1uh6zci5C8aynnJfTSw3BU+tzkfORkbZGlAXU9mVDUlzAAVj45b8nF0hUOhSgD4ZkVDcDZf0IHiO4lDnYvHphB/iqTu/3+PjtP+RJTV7UBk6F0wOz8PWKz8gD9kDq6lH1BhI2c0RsPXg1lkSWugfiHzvGI2agXhFiF8UL3Tv3g1TJUJW8I5d7qci3dG1n3aE9kfEc23Ycjtazyl2lBjsS8zf8wdni5vEofmmQPw/RdUOYtsHtldAsk6lvZNy1WGqcf6U80m9PLqAlj2TSwSE45B5POrZIcgisHUg5fwNGAE="}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1438,"cache_read_input_tokens":13311,"output_tokens":3498,"output_tokens_details":{"thinking_tokens":35},"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":1438},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":557,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXrJmdFJwrfoWZLUS3Ym","requestRef":"584c86e9-8d98-4a84-813d-641b7e2c8ff3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"1bedd031-ae63-481a-8183-bb63e115b244","timestamp":"2026-10-30T05:14:19.489Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}60{"parentUuid":"1bedd031-ae63-481a-8183-bb63e115b244","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrJmxqLae3hefKevgX2","type":"message","role":"assistant","content":[{"type":"text","text":"P4 gate failures are only for P5 deliverables not yet written (expected). Writing report and claims."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1438,"cache_read_input_tokens":13311,"output_tokens":3498,"output_tokens_details":{"thinking_tokens":35},"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":1438},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXrJmdFJwrfoWZLUS3Ym","requestRef":"584c86e9-8d98-4a84-813d-641b7e2c8ff3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"64f65724-71ff-4b68-b8ee-4d1cfacb90d1","timestamp":"2026-10-30T05:14:19.490Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}61{"parentUuid":"64f65724-71ff-4b68-b8ee-4d1cfacb90d1","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrJmxqLae3hefKevgX2","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01VhWew6oE1sSxNKT16pPHvJ","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-conf-02 — Finite-sample bias of the OLS AR(1) coefficient\n\n## Question\nIn the Gaussian AR(1) y_t = c + ρ y_{t−1} + ε_t (c = 0, σ = 1), how large is the finite-sample bias of the OLS estimator ρ̂ from a regression of y_t on (1, y_{t−1}), and how well does the Marriott–Pope/Kendall approximation −(1+3ρ)/n describe it at the design n = 30, ρ = 0.8?\n\n## Data and exclusions\nThe only input is `data/design.csv` (7 rows, `n_input_rows`; SHA-256 recorded in `out/state/data_audit.md`): n = 30, ρ = 0.8, σ = 1, intercept included, stationary start, R = 20000 replications, seed 20261029 (`random_seed`). No data issues were found (`data_issues` = []). The one filtering rule, dropping replications with a non-finite ρ̂, removed 0 replications (`out/exclusions.csv`). That leaves `n_analysed` = 20000 = `n_replications`.\n\n## Method\n- **Analytical baseline.** `bias_analytical` = −(1+3ρ)/n with n = 30 (the design series length), which gives −0.11333. The textbook asymptotic standard error is `se_asymptotic` = √((1−ρ²)/n) = 0.1095.\n- **Monte Carlo.** We used `numpy.random.default_rng(20261029)`. The draws come in a fixed order: first y_1 ~ N(0, σ²/(1−ρ²)) for all R series, then an R×(n−1) matrix of N(0, σ²) innovations. Each series is built by recursion with c = 0. For each series, ρ̂ is the OLS slope of y_t on (1, y_{t−1}) for t = 2,…,30 (29 observations). It is computed from demeaned cross-products, and the result was checked against `numpy.linalg.lstsq` on one replication. Then `bias_mc` = mean(ρ̂) − ρ and `bias_mc_se` = sd(ρ̂)/√R.\n- **Nature of the analytical formula.** −(1+3ρ)/n is the leading term of an asymptotic expansion of E[ρ̂] − ρ in powers of 1/n: bias = −(1+3ρ)/n + O(n⁻²). It is accurate in the sense that the approximation error shrinks faster than 1/n as n → ∞. It is not an exact formula, and it is not guaranteed to be accurate at any particular small n. The neglected higher-order terms are expected to matter more when n is small and when ρ is close to 1.\n\n## Results\n- Mean of ρ̂: `rho_hat_mean` = 0.6763. Monte Carlo bias: `bias_mc` = −0.1237.\n- Analytical approximation: `bias_analytical` = −0.1133. The Monte Carlo bias is about 9% larger in magnitude (`supp_ratio_bias_mc_to_analytical` = 1.092).\n- Standardised difference: `discrepancy_se_units` = −9.85 Monte Carlo standard errors. The formula therefore under-states the magnitude of the true bias at this design, and the gap is far too large to be Monte Carlo noise.\n- Is the gap just a matter of using n − 1 = 29 (the effective regression sample) in place of n = 30? No. That version of the formula gives −0.1172 (`supp_bias_analytical_n_minus_1`), which still leaves a gap of about −6.1 standard errors (computed in the P4 checks).\n- Size of the bias relative to sampling spread: the bias is roughly the same size as the asymptotic s.e. (`se_asymptotic` = 0.1095). The Monte Carlo sd of ρ̂ is `rho_hat_sd_mc` = 0.1489, about 1.36 times the asymptotic s.e. (`supp_ratio_sd_mc_to_se_asymptotic`). The distribution of ρ̂ is skewed to the left: its median is 0.699 (`supp_rho_hat_median`), above its mean.\n\n## Uncertainty\nThe Monte Carlo standard error of the bias is `bias_mc_se` = 0.00105. A normal-approximation 95% interval for the true bias is therefore about [−0.1258, −0.1216]. This interval does not contain −0.1133 (`bias_analytical`). With R = 20000 independent replications, the central limit theorem justifies the normal approximation for the mean even though ρ̂ is skewed. `bias_analytical` and `se_asymptotic` are deterministic and have no Monte Carlo error. The results are exactly reproducible given the seed. A different seed would move `bias_mc` by roughly ±1 `bias_mc_se`.\n\n## Limitations and open issues\n- **Scope of the Monte Carlo evidence.** The simulation measures the exact finite-sample bias, up to Monte Carlo error, at a single design point: n = 30, ρ = 0.8, Gaussian errors, stationary start, intercept estimated. It shows that at this point the first-order formula is off by about 0.010, roughly 9% of the bias. It does **not** show that the formula is \"wrong\" in its intended asymptotic sense, because a gap at fixed n is consistent with an O(n⁻²) remainder. A single n cannot verify or refute a rate statement. The results also do not carry over to other n, other ρ (especially values near 1), non-Gaussian or heteroskedastic errors, non-stationary starts, or regressions without an intercept, where the leading term is −2ρ/n instead.\n- **Ambiguity in n.** The formula was evaluated at n = 30 as instructed (\"at the design values\"). The n − 1 variant is reported only as a supplementary check, and it does not change the conclusion.\n- **Supplementary keys.** Keys prefixed `supp_` are descriptive extras computed by `out/analysis.py`. They are not required by the task.\n- No part of the task was infeasible (`feasibility` = \"complete\").\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"At n=30, rho=0.8 the Monte Carlo estimate of the OLS bias of rho_hat (with intercept) is about -0.124 (mean rho_hat about 0.676), with MC standard error about 0.001.\",\"results_keys\":[\"bias_mc\",\"rho_hat_mean\",\"bias_mc_se\"],\"status\":\"supported\",\"caveat\":\"Single design point; R=20000, seed 20261029.\"},\n {\"id\":\"C2\",\"text\":\"The Marriott-Pope/Kendall approximation -(1+3rho)/n gives -0.1133, which under-states the magnitude of the true bias by about 9%; the gap is about -9.9 MC standard errors and so is not Monte Carlo noise.\",\"results_keys\":[\"bias_analytical\",\"bias_mc\",\"discrepancy_se_units\",\"supp_ratio_bias_mc_to_analytical\"],\"status\":\"supported\",\"caveat\":\"The discrepancy is consistent with the O(n^-2) remainder of a first-order asymptotic expansion; it does not refute the formula's asymptotic validity.\"},\n {\"id\":\"C3\",\"text\":\"Using n-1=29 in the formula does not close the gap (about -6.1 MC standard errors remain).\",\"results_keys\":[\"supp_bias_analytical_n_minus_1\",\"bias_mc\",\"bias_mc_se\"],\"status\":\"supported\",\"caveat\":\"The standardized gap for the n-1 variant is computed from these keys (recorded in checks); it is not a separate results key.\"},\n {\"id\":\"C4\",\"text\":\"The finite-sample sd of rho_hat (0.149) exceeds the asymptotic s.e. sqrt((1-rho^2)/n)=0.110 by a factor of about 1.36, and the bias is about the same size as the asymptotic s.e.\",\"results_keys\":[\"rho_hat_sd_mc\",\"se_asymptotic\",\"supp_ratio_sd_mc_to_se_asymptotic\",\"bias_mc\"],\"status\":\"supported\",\"caveat\":\"Descriptive, at this single design.\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P1']={\"status\":\"passed\",\"checks\":[\"SHA-256 computed and matches bundle.json\",\"7 rows x 3 cols, no missing/duplicates\",\"exclusions.csv ledger: 20000-0=20000\"],\"notes\":\"no data issues\"}\np['P2']={\"status\":\"passed\",\"checks\":[\"bias_analytical=-0.11333 and se_asymptotic=0.10954 computed as baseline\"],\"notes\":\"\"}\np['P3']={\"status\":\"passed\",\"checks\":[\"analysis.py runs, fixed seed 20261029 from design\",\"OLS slope verified vs lstsq\"],\"notes\":\"\"}\np['P4']={\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical\",\"identities in out/state/checks.md all PASS\",\"gate run 20261030T051417.533751Z: only P5-deliverable failures (report/claims/ledger not yet written), reproducibility ok\"],\"notes\":\"gate_receipts: 20261030T051417.533751Z.json\"}\np['P5']={\"status\":\"passed\",\"checks\":[\"report.md with 6 sections citing keys\",\"claims.json written\",\"final gate run (see notes)\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P2-P4 passed (baseline, MC, verification; gate#1 failures only for missing P5 files). P5 report+claims written.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v '\\[ok\\]'","description":"Write report, claims, phases; 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":1438,"cache_read_input_tokens":13311,"output_tokens":3498,"output_tokens_details":{"thinking_tokens":35},"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":1438},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXrJmdFJwrfoWZLUS3Ym","requestRef":"584c86e9-8d98-4a84-813d-641b7e2c8ff3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"0a0c15b3-3082-4066-93d1-ed703783398b","timestamp":"2026-10-30T05:14:47.632Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}62{"parentUuid":"0a0c15b3-3082-4066-93d1-ed703783398b","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01VhWew6oE1sSxNKT16pPHvJ","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 32 checks failed)\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0251/out/state/gate_receipts/20261030T051447.946386Z.json","is_error":false}]},"uuid":"03b39169-2083-43fd-9f28-f703c53fb5c9","timestamp":"2026-10-30T05:14:47.954Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 32 checks failed)\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0251/out/state/gate_receipts/20261030T051447.946386Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"0a0c15b3-3082-4066-93d1-ed703783398b","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}63{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"828a0dc74cb42ae3017a1ef4821e24bf38f7e0dd325aad9272a28259436814de","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"P4 gate failures are only for P5 deliverables not yet written (expected). Writing report and claims."},{"type":"tool_use","id":"toolu_01VhWew6oE1sSxNKT16pPHvJ","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-conf-02 — Finite-sample bias of the OLS AR(1) coefficient\n\n## Question\nIn the Gaussian AR(1) y_t = c + ρ y_{t−1} + ε_t (c = 0, σ = 1), how large is the finite-sample bias of the OLS estimator ρ̂ from a regression of y_t on (1, y_{t−1}), and how well does the Marriott–Pope/Kendall approximation −(1+3ρ)/n describe it at the design n = 30, ρ = 0.8?\n\n## Data and exclusions\nThe only input is `data/design.csv` (7 rows, `n_input_rows`; SHA-256 recorded in `out/state/data_audit.md`): n = 30, ρ = 0.8, σ = 1, intercept included, stationary start, R = 20000 replications, seed 20261029 (`random_seed`). No data issues were found (`data_issues` = []). The one filtering rule, dropping replications with a non-finite ρ̂, removed 0 replications (`out/exclusions.csv`). That leaves `n_analysed` = 20000 = `n_replications`.\n\n## Method\n- **Analytical baseline.** `bias_analytical` = −(1+3ρ)/n with n = 30 (the design series length), which gives −0.11333. The textbook asymptotic standard error is `se_asymptotic` = √((1−ρ²)/n) = 0.1095.\n- **Monte Carlo.** We used `numpy.random.default_rng(20261029)`. The draws come in a fixed order: first y_1 ~ N(0, σ²/(1−ρ²)) for all R series, then an R×(n−1) matrix of N(0, σ²) innovations. Each series is built by recursion with c = 0. For each series, ρ̂ is the OLS slope of y_t on (1, y_{t−1}) for t = 2,…,30 (29 observations). It is computed from demeaned cross-products, and the result was checked against `numpy.linalg.lstsq` on one replication. Then `bias_mc` = mean(ρ̂) − ρ and `bias_mc_se` = sd(ρ̂)/√R.\n- **Nature of the analytical formula.** −(1+3ρ)/n is the leading term of an asymptotic expansion of E[ρ̂] − ρ in powers of 1/n: bias = −(1+3ρ)/n + O(n⁻²). It is accurate in the sense that the approximation error shrinks faster than 1/n as n → ∞. It is not an exact formula, and it is not guaranteed to be accurate at any particular small n. The neglected higher-order terms are expected to matter more when n is small and when ρ is close to 1.\n\n## Results\n- Mean of ρ̂: `rho_hat_mean` = 0.6763. Monte Carlo bias: `bias_mc` = −0.1237.\n- Analytical approximation: `bias_analytical` = −0.1133. The Monte Carlo bias is about 9% larger in magnitude (`supp_ratio_bias_mc_to_analytical` = 1.092).\n- Standardised difference: `discrepancy_se_units` = −9.85 Monte Carlo standard errors. The formula therefore under-states the magnitude of the true bias at this design, and the gap is far too large to be Monte Carlo noise.\n- Is the gap just a matter of using n − 1 = 29 (the effective regression sample) in place of n = 30? No. That version of the formula gives −0.1172 (`supp_bias_analytical_n_minus_1`), which still leaves a gap of about −6.1 standard errors (computed in the P4 checks).\n- Size of the bias relative to sampling spread: the bias is roughly the same size as the asymptotic s.e. (`se_asymptotic` = 0.1095). The Monte Carlo sd of ρ̂ is `rho_hat_sd_mc` = 0.1489, about 1.36 times the asymptotic s.e. (`supp_ratio_sd_mc_to_se_asymptotic`). The distribution of ρ̂ is skewed to the left: its median is 0.699 (`supp_rho_hat_median`), above its mean.\n\n## Uncertainty\nThe Monte Carlo standard error of the bias is `bias_mc_se` = 0.00105. A normal-approximation 95% interval for the true bias is therefore about [−0.1258, −0.1216]. This interval does not contain −0.1133 (`bias_analytical`). With R = 20000 independent replications, the central limit theorem justifies the normal approximation for the mean even though ρ̂ is skewed. `bias_analytical` and `se_asymptotic` are deterministic and have no Monte Carlo error. The results are exactly reproducible given the seed. A different seed would move `bias_mc` by roughly ±1 `bias_mc_se`.\n\n## Limitations and open issues\n- **Scope of the Monte Carlo evidence.** The simulation measures the exact finite-sample bias, up to Monte Carlo error, at a single design point: n = 30, ρ = 0.8, Gaussian errors, stationary start, intercept estimated. It shows that at this point the first-order formula is off by about 0.010, roughly 9% of the bias. It does **not** show that the formula is \"wrong\" in its intended asymptotic sense, because a gap at fixed n is consistent with an O(n⁻²) remainder. A single n cannot verify or refute a rate statement. The results also do not carry over to other n, other ρ (especially values near 1), non-Gaussian or heteroskedastic errors, non-stationary starts, or regressions without an intercept, where the leading term is −2ρ/n instead.\n- **Ambiguity in n.** The formula was evaluated at n = 30 as instructed (\"at the design values\"). The n − 1 variant is reported only as a supplementary check, and it does not change the conclusion.\n- **Supplementary keys.** Keys prefixed `supp_` are descriptive extras computed by `out/analysis.py`. They are not required by the task.\n- No part of the task was infeasible (`feasibility` = \"complete\").\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"At n=30, rho=0.8 the Monte Carlo estimate of the OLS bias of rho_hat (with intercept) is about -0.124 (mean rho_hat about 0.676), with MC standard error about 0.001.\",\"results_keys\":[\"bias_mc\",\"rho_hat_mean\",\"bias_mc_se\"],\"status\":\"supported\",\"caveat\":\"Single design point; R=20000, seed 20261029.\"},\n {\"id\":\"C2\",\"text\":\"The Marriott-Pope/Kendall approximation -(1+3rho)/n gives -0.1133, which under-states the magnitude of the true bias by about 9%; the gap is about -9.9 MC standard errors and so is not Monte Carlo noise.\",\"results_keys\":[\"bias_analytical\",\"bias_mc\",\"discrepancy_se_units\",\"supp_ratio_bias_mc_to_analytical\"],\"status\":\"supported\",\"caveat\":\"The discrepancy is consistent with the O(n^-2) remainder of a first-order asymptotic expansion; it does not refute the formula's asymptotic validity.\"},\n {\"id\":\"C3\",\"text\":\"Using n-1=29 in the formula does not close the gap (about -6.1 MC standard errors remain).\",\"results_keys\":[\"supp_bias_analytical_n_minus_1\",\"bias_mc\",\"bias_mc_se\"],\"status\":\"supported\",\"caveat\":\"The standardized gap for the n-1 variant is computed from these keys (recorded in checks); it is not a separate results key.\"},\n {\"id\":\"C4\",\"text\":\"The finite-sample sd of rho_hat (0.149) exceeds the asymptotic s.e. sqrt((1-rho^2)/n)=0.110 by a factor of about 1.36, and the bias is about the same size as the asymptotic s.e.\",\"results_keys\":[\"rho_hat_sd_mc\",\"se_asymptotic\",\"supp_ratio_sd_mc_to_se_asymptotic\",\"bias_mc\"],\"status\":\"supported\",\"caveat\":\"Descriptive, at this single design.\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P1']={\"status\":\"passed\",\"checks\":[\"SHA-256 computed and matches bundle.json\",\"7 rows x 3 cols, no missing/duplicates\",\"exclusions.csv ledger: 20000-0=20000\"],\"notes\":\"no data issues\"}\np['P2']={\"status\":\"passed\",\"checks\":[\"bias_analytical=-0.11333 and se_asymptotic=0.10954 computed as baseline\"],\"notes\":\"\"}\np['P3']={\"status\":\"passed\",\"checks\":[\"analysis.py runs, fixed seed 20261029 from design\",\"OLS slope verified vs lstsq\"],\"notes\":\"\"}\np['P4']={\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical\",\"identities in out/state/checks.md all PASS\",\"gate run 20261030T051417.533751Z: only P5-deliverable failures (report/claims/ledger not yet written), reproducibility ok\"],\"notes\":\"gate_receipts: 20261030T051417.533751Z.json\"}\np['P5']={\"status\":\"passed\",\"checks\":[\"report.md with 6 sections citing keys\",\"claims.json written\",\"final gate run (see notes)\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P2-P4 passed (baseline, MC, verification; gate#1 failures only for missing P5 files). P5 report+claims written.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v '\\[ok\\]'","description":"Write report, claims, phases; run gate"}}]}}64{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"84f67952-9c70-4800-95f2-f9c3a8a88caf","timestamp":"2026-10-30T05:14:47.958Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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":"584c86e9-8d98-4a84-813d-641b7e2c8ff3","keep":18,"tail":["828a0dc74cb42ae3017a1ef4821e24bf38f7e0dd325aad9272a28259436814de","d176b205b2d2390d8e73e60469ad94f024d4bdad741e741c21ead8ac869de26c"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",19,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"3fc7dd3cb0aa95cb56c7a925e57fc561152c028ce72700253865633db9a8429c"}65{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"03b39169-2083-43fd-9f28-f703c53fb5c9","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}66{"type":"atis-latch","atis":"","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}67{"parentUuid":"03b39169-2083-43fd-9f28-f703c53fb5c9","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrM1v2yGqbsnuVQDjoy","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01XRUv7JY488U1QhFHenvrmR","name":"Bash","input":{"command":"~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P5']['checks'][-1]=\"final gate run 20261030T051447.946386Z: PASSED 0/32 failed\"\np['P5']['notes']=\"gate_receipts: 20261030T051447.946386Z.json (passed)\"\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P5 passed; final gate PASSED (20261030T051447.946386Z).\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | head -1","description":"Record final gate receipt and reconfirm"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":3593,"cache_read_input_tokens":14749,"output_tokens":321,"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":3593},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXrM1euwaPyUq59Wz516","requestRef":"84f67952-9c70-4800-95f2-f9c3a8a88caf","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"fbc69bf4-88ca-4752-91ad-932891d4a05d","timestamp":"2026-10-30T05:14:51.480Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}68{"parentUuid":"fbc69bf4-88ca-4752-91ad-932891d4a05d","isSidechain":false,"promptId":"e51cbe8f-794b-43ff-b61e-32fbdee3b072","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01XRUv7JY488U1QhFHenvrmR","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 32 checks failed)","is_error":false}]},"uuid":"efeb45e9-1b38-4cf1-89dd-eabbe1bc0738","timestamp":"2026-10-30T05:14:51.791Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 32 checks failed)","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"fbc69bf4-88ca-4752-91ad-932891d4a05d","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}69{"type":"api-request-blob","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","hash":"21ad89f5a7f6490cc0bf03e135d6a09ce1436ec7cc12286f9569344c29419486","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01XRUv7JY488U1QhFHenvrmR","name":"Bash","input":{"command":"~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P5']['checks'][-1]=\"final gate run 20261030T051447.946386Z: PASSED 0/32 failed\"\np['P5']['notes']=\"gate_receipts: 20261030T051447.946386Z.json (passed)\"\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P5 passed; final gate PASSED (20261030T051447.946386Z).\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | head -1","description":"Record final gate receipt and reconfirm"}}]}}70{"type":"api-request","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","id":"d2a8dde2-abde-4d6a-960c-44d47aef12a1","timestamp":"2026-10-30T05:14:51.795Z","version":"2.1.314","querySource":"sdk","shapeHash":"669b89ccc3d1c271bcba114abb2f1889b772dfe5c4ded12f57ce489aeac11ea0","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":"84f67952-9c70-4800-95f2-f9c3a8a88caf","keep":20,"tail":["21ad89f5a7f6490cc0bf03e135d6a09ce1436ec7cc12286f9569344c29419486","a46ae02a2ae23598b9579610a6ee4005d2540c2450c46476c3ceda6404b0c912"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",21,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"d75cb131628d4dab26cedc6bcb68bc190c0d14fc967709ee86892110c8845244"}71{"parentUuid":"efeb45e9-1b38-4cf1-89dd-eabbe1bc0738","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrMJK23KiiuvXUUJebD","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":361,"cache_read_input_tokens":18342,"output_tokens":843,"output_tokens_details":{"thinking_tokens":21},"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":361},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":6443,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXrMJ4PdECSomuybghUx","requestRef":"d2a8dde2-abde-4d6a-960c-44d47aef12a1","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"b8905085-d710-420e-beba-269178332a85","timestamp":"2026-10-30T05:15:00.819Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}72{"parentUuid":"b8905085-d710-420e-beba-269178332a85","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXrMJK23KiiuvXUUJebD","type":"message","role":"assistant","content":[{"type":"text","text":"I ran the simulation and the comparison exactly as `design.csv` specifies. At n = 30 and ρ = 0.8, the textbook bias formula understates the true bias by about 9%, and the gap is far too large to be simulation noise. The final gate check passes (0 of 32 failures), and a clean re-run of `out/analysis.py` reproduces `out/results.json` byte for byte.\n\n**Results** (20,000 simulated series, seed 20261029, none excluded):\n\n| Quantity | Value |\n|---|---|\n| Formula bias, −(1+3ρ)/n | −0.1133 |\n| Simulated bias | −0.1237 |\n| Simulation standard error of that bias | 0.00105 |\n| Approximate 95% interval for the true bias | [−0.1258, −0.1216] |\n| Mean of the estimates | 0.6763 |\n| Gap between the two biases | −9.85 standard errors |\n| Spread (sd) of the estimates | 0.149 |\n| Textbook asymptotic standard error | 0.110 |\n\n- **Not just an n vs n−1 issue:** the regression itself uses 29 observations. Using 29 instead of 30 in the formula gives −0.1172, which still leaves a gap of about −6.1 standard errors.\n- **How to read the gap:** the formula is only the first term of a large-sample approximation, so it is accurate in the sense that its error shrinks faster than 1/n as n grows. A gap at a single small n fits that and does not show the formula is wrong; it just doesn't hold up well here.\n- **What this covers:** the simulation measures the exact bias at this one design only. It says nothing about other n, ρ near 1, non-Gaussian errors, or a regression without an intercept.\n\n**Choices and limitations:**\n- I evaluated the formula at n = 30 because the task says \"at the design values\"; the n−1 version is reported only as a side check.\n- I added four extra keys prefixed `supp_` to `results.json` (the n−1 formula value, the median estimate and two ratios). The task doesn't require them.\n- The −6.1 figure for the n−1 version is not stored as its own key; it was computed during verification and is recorded in `out/state/log.md`.\n- The task was fully feasible, so nothing is reported as `null`.\n\nEverything is in `out/`. Open `report.md` first; the other required files are `results.json`, `analysis.py` and `claims.json`. The state files and gate receipts are under `out/state/`."}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":361,"cache_read_input_tokens":18342,"output_tokens":843,"output_tokens_details":{"thinking_tokens":21},"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":361},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXrMJ4PdECSomuybghUx","requestRef":"d2a8dde2-abde-4d6a-960c-44d47aef12a1","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"805b8561-6e9e-48b3-8ddb-4d043ff54c46","timestamp":"2026-10-30T05:15:01.437Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0251","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","version":"2.1.314","gitBranch":"HEAD"}73{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"805b8561-6e9e-48b3-8ddb-4d043ff54c46","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758"}74{"type":"cost-state","sessionId":"00d1dc27-606a-46f1-aa6b-f4d65fd60758","totalCostUSD":0.3202348,"totalAPIDuration":98929,"totalAPIDurationWithoutRetries":98924,"totalToolDuration":1489,"totalLinesAdded":0,"totalLinesRemoved":0,"totalDuration":100596,"startTime":1793337200850,"modelUsage":{"claude-opus-5-5":{"inputTokens":24,"outputTokens":10640,"thinkingTokens":617,"cacheReadInputTokens":106719,"cacheCreationInputTokens":17199,"cacheCreationEphemeral5mInputTokens":17199,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.3202348}},"hasUnknownModelCost":false}75