spb/wp29_uqo

1{"type":"atis-latch","atis":"","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}2{"type":"queue-operation","operation":"enqueue","timestamp":"2026-10-30T05:10:07.488Z","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","content":"Begin"}3{"type":"queue-operation","operation":"dequeue","timestamp":"2026-10-30T05:10:07.494Z","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}4{"parentUuid":null,"isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":"Begin"},"uuid":"ba615af8-0563-40d8-b9c5-9455b0b46632","timestamp":"2026-10-30T05:10:07.498Z","permissionMode":"default","promptSource":"sdk","turnOrigin":"sdk","turnPosition":{"promptIndex":0,"turnIndex":1},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}5{"type":"api-request-shape","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","timestamp":"2026-10-30T05:10:07.510Z","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/RC0242\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"}],"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":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"d43ab0e0b8ec9db790a6459cb2f4bc4ffce02825ca05063162023be60912ced9","message":{"role":"system","content":[],"output_config":{"effort":"medium"}}}7{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"b728ad34-a6a5-40b8-940d-5cd666d298ac","timestamp":"2026-10-30T05:10:07.510Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"62952b1ff8f57aee975e0ede9bdf6349cad49a34ff50369c200d6fb8055ffae7"}8{"parentUuid":"ba615af8-0563-40d8-b9c5-9455b0b46632","isSidechain":false,"attachment":{"type":"session_context","context":{}},"type":"attachment","uuid":"f6a4baa9-ae29-4e1c-a666-0294423f5d03","timestamp":"2026-10-30T05:10:07.503Z","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}9{"parentUuid":"f6a4baa9-ae29-4e1c-a666-0294423f5d03","isSidechain":false,"attachment":{"type":"date","date":"2026-10-30"},"type":"attachment","uuid":"b09b75c3-45c5-4397-beba-d725e1e18578","timestamp":"2026-10-30T05:10:07.503Z","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/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}10{"parentUuid":"b09b75c3-45c5-4397-beba-d725e1e18578","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":"2b0f1d28-3136-4cbe-9e4a-19ebec629593","timestamp":"2026-10-30T05:10:07.503Z","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/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}12{"parentUuid":"2b0f1d28-3136-4cbe-9e4a-19ebec629593","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXqzLAovEDiVXBenNuXD","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":2209,"cache_read_input_tokens":1504,"output_tokens":138,"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":2209},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":532,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXqzKuBivXzzZ9br77tK","requestRef":"b728ad34-a6a5-40b8-940d-5cd666d298ac","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"96765dc5-ce4a-4a65-85fe-83e351017407","timestamp":"2026-10-30T05:10:09.026Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"96765dc5-ce4a-4a65-85fe-83e351017407","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXqzLAovEDiVXBenNuXD","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01WrUtXYDhK155r4qNBcgk2S","name":"Bash","input":{"command":"cat TASK.md; ls -R | head -50; ls out/state 2>/dev/null && cat out/state/log.md","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":2209,"cache_read_input_tokens":1504,"output_tokens":138,"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":2209},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXqzKuBivXzzZ9br77tK","requestRef":"b728ad34-a6a5-40b8-940d-5cd666d298ac","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"35f9f0a4-55aa-486a-bbeb-8bc75edd239b","timestamp":"2026-10-30T05:10:09.533Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}14{"parentUuid":"35f9f0a4-55aa-486a-bbeb-8bc75edd239b","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 1\n# 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.\nbundle.json\ndata\ngate_spec.json\nTASK.md\n\n./data:\ndesign.csv","is_error":true,"tool_use_id":"toolu_01WrUtXYDhK155r4qNBcgk2S"}]},"uuid":"84f47a77-fab2-4091-9f7b-eabac66698cc","timestamp":"2026-10-30T05:10:09.620Z","toolUseResult":"Error: Exit code 1\n# 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.\nbundle.json\ndata\ngate_spec.json\nTASK.md\n\n./data:\ndesign.csv","sandboxed":false,"sourceToolAssistantUUID":"35f9f0a4-55aa-486a-bbeb-8bc75edd239b","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}15{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"ac9ee43da9ec09306d8755cd586039eff3be49eb5e8c4674fbdfe01f8f1f3388","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01WrUtXYDhK155r4qNBcgk2S","name":"Bash","input":{"command":"cat TASK.md; ls -R | head -50; ls out/state 2>/dev/null && cat out/state/log.md","description":"Read task and list workspace"}}]}}16{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"880b0953-6a5f-4046-bdb1-d38c7bb1c1b2","timestamp":"2026-10-30T05:10:09.625Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"b728ad34-a6a5-40b8-940d-5cd666d298ac","keep":2,"tail":["ac9ee43da9ec09306d8755cd586039eff3be49eb5e8c4674fbdfe01f8f1f3388","e0840160c1dcdeeb9bb054a86f3d67c798518c6a2546eea5f986675bac35c48e"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",3,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"96b63ac47ebf2177b83d7e992a7aefd126fabe7eceaf0bd4fa2ab45684f01b0e"}17{"parentUuid":"84f47a77-fab2-4091-9f7b-eabac66698cc","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXqzV75aTWtcoFYvTKgj","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_0157d1Kweoa6B15b3T6rHnDC","name":"Bash","input":{"command":"cat data/design.csv; shasum -a 256 data/design.csv; wc -l data/design.csv; cat gate_spec.json | head -50","description":"Inspect design file 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":1755,"cache_read_input_tokens":3713,"output_tokens":125,"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":1755},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXqzUqhXuxw4LvWbFuG8","requestRef":"880b0953-6a5f-4046-bdb1-d38c7bb1c1b2","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"81a697c2-df66-4487-a7b9-046a2aacc9f0","timestamp":"2026-10-30T05:10:11.105Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}18{"parentUuid":"81a697c2-df66-4487-a7b9-046a2aacc9f0","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_0157d1Kweoa6B15b3T6rHnDC","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)\n2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb  data/design.csv\n       8 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\": {","is_error":false}]},"uuid":"18a99c71-f73b-47ee-8e0f-e15eb8445368","timestamp":"2026-10-30T05:10:11.147Z","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)\n2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb  data/design.csv\n       8 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\": {","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"81a697c2-df66-4487-a7b9-046a2aacc9f0","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}19{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"bf4caefb4c3ff841b571b3feb00fcaac846a996f0d76fb0ef9d61530064f2e09","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_0157d1Kweoa6B15b3T6rHnDC","name":"Bash","input":{"command":"cat data/design.csv; shasum -a 256 data/design.csv; wc -l data/design.csv; cat gate_spec.json | head -50","description":"Inspect design file and gate spec"}}]}}20{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"ca459169-ac9b-4f9a-9499-60996ddf84e9","timestamp":"2026-10-30T05:10:11.150Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"880b0953-6a5f-4046-bdb1-d38c7bb1c1b2","keep":4,"tail":["bf4caefb4c3ff841b571b3feb00fcaac846a996f0d76fb0ef9d61530064f2e09","b2fbbc6116dabc1d41565f537cfbb478f5d48d02a4a7b91502d6910757ab32c9"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",5,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"b2aa4a6e30c29a33014a4ae17f1542264ddb2dbd49452ec8d4b78f577e2dcd32"}21{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"18a99c71-f73b-47ee-8e0f-e15eb8445368","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}22{"type":"atis-latch","atis":"","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}23{"parentUuid":"18a99c71-f73b-47ee-8e0f-e15eb8445368","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXqzbhhct7BaTFtAx4zi","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":784,"cache_read_input_tokens":5468,"output_tokens":1069,"output_tokens_details":{"thinking_tokens":103},"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":784},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":719,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXqzbP6a4apz4ozF891A","requestRef":"ca459169-ac9b-4f9a-9499-60996ddf84e9","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"bd3c1e34-d001-4fb3-a8ce-09658ba71f90","timestamp":"2026-10-30T05:10:12.953Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}24{"parentUuid":"bd3c1e34-d001-4fb3-a8ce-09658ba71f90","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXqzbhhct7BaTFtAx4zi","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Pmp87vXwpoFRAswbyb5QyP","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), OLS of y_t on (1, y_{t-1}) is biased in finite samples. Compare the Marriott–Pope/Kendall approximation -(1+3rho)/n with the Monte Carlo bias at the design (n, rho).\n\n**Estimands.** (i) bias_analytical = -(1+3rho)/n at design values (a first-order, O(1/n) asymptotic-expansion approximation; meaningful for stationary |rho|<1, Gaussian errors, intercept estimated). (ii) bias_mc = mean(rho_hat) - rho over R replications, with MC SE sd(rho_hat)/sqrt(R). Also discrepancy in SE units and baseline se_asymptotic = sqrt((1-rho^2)/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); out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py; out/claims.json; plus protocol files out/exclusions.csv, out/state/*.\n\n**Information rules.** Use only data/design.csv; follow design exactly (n=30, rho, sigma, intercept, stationary y_1, R, seed with numpy default_rng); c=0; fresh series per replication; OLS for t=2..n.\n\n**Invalidity.** Missing/contradictory design values; nonstationary rho (|rho|>=1) with \"stationary\" init; not using the seed; dropping replications without ledger.\nEOF\ncat > phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\"P2\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P3\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\"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":784,"cache_read_input_tokens":5468,"output_tokens":1069,"output_tokens_details":{"thinking_tokens":103},"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":784},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXqzbP6a4apz4ozF891A","requestRef":"ca459169-ac9b-4f9a-9499-60996ddf84e9","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"42b97cda-00b7-4d1c-b742-2b3b9b22f1e5","timestamp":"2026-10-30T05:10:20.268Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}25{"parentUuid":"42b97cda-00b7-4d1c-b742-2b3b9b22f1e5","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01Pmp87vXwpoFRAswbyb5QyP","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"cd3dd9bc-8f8e-4ad3-8b0a-c3fa0a411cfe","timestamp":"2026-10-30T05:10:20.298Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"42b97cda-00b7-4d1c-b742-2b3b9b22f1e5","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242/out/state","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}26{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"bc97353a5d6f69bef96cba961f9bb30bef9347b43c32ec2389620a9565138fba","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01Pmp87vXwpoFRAswbyb5QyP","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), OLS of y_t on (1, y_{t-1}) is biased in finite samples. Compare the Marriott–Pope/Kendall approximation -(1+3rho)/n with the Monte Carlo bias at the design (n, rho).\n\n**Estimands.** (i) bias_analytical = -(1+3rho)/n at design values (a first-order, O(1/n) asymptotic-expansion approximation; meaningful for stationary |rho|<1, Gaussian errors, intercept estimated). (ii) bias_mc = mean(rho_hat) - rho over R replications, with MC SE sd(rho_hat)/sqrt(R). Also discrepancy in SE units and baseline se_asymptotic = sqrt((1-rho^2)/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); out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py; out/claims.json; plus protocol files out/exclusions.csv, out/state/*.\n\n**Information rules.** Use only data/design.csv; follow design exactly (n=30, rho, sigma, intercept, stationary y_1, R, seed with numpy default_rng); c=0; fresh series per replication; OLS for t=2..n.\n\n**Invalidity.** Missing/contradictory design values; nonstationary rho (|rho|>=1) with \"stationary\" init; not using the seed; dropping replications without ledger.\nEOF\ncat > phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\"P2\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P3\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\"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":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"875f847c-fcf4-444c-8e07-ba2175c8be1f","timestamp":"2026-10-30T05:10:20.301Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"ca459169-ac9b-4f9a-9499-60996ddf84e9","keep":6,"tail":["bc97353a5d6f69bef96cba961f9bb30bef9347b43c32ec2389620a9565138fba","bbb93fc41fcd1e229d728f467e2ad4294a4e7e3207475e54f4811f0bb4168e47"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"4074e26c5f745d416f683a77370475d0b44c4c19cfe03eff881606fb0c7d1e7a"}28{"parentUuid":"cd3dd9bc-8f8e-4ad3-8b0a-c3fa0a411cfe","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr1GmCjDTd4293TmSz5","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":1084,"cache_read_input_tokens":6252,"output_tokens":2334,"output_tokens_details":{"thinking_tokens":213},"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":1084},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1952,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXr1GaHxDgNeHh3f2iya","requestRef":"875f847c-fcf4-444c-8e07-ba2175c8be1f","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"03b6b062-012e-4649-9b56-12d22b32eb10","timestamp":"2026-10-30T05:10:23.526Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242/out/state","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}29{"parentUuid":"03b6b062-012e-4649-9b56-12d22b32eb10","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr1GmCjDTd4293TmSz5","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Kg3RRBQBBj3asg48h6oy2c","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-02: finite-sample bias of OLS rho_hat in a Gaussian AR(1) 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 deterministically.\"\"\"\nimport json, hashlib, os\nimport numpy as np\nimport pandas as pd\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDESIGN = os.path.join(ROOT, \"data\", \"design.csv\")\nOUT = os.path.join(ROOT, \"out\")\n\nd = pd.read_csv(DESIGN)\np = dict(zip(d[\"parameter\"].astype(str).str.strip(), d[\"value\"].astype(str).str.strip()))\nissues = []\nn = int(p[\"n\"]); rho = float(p[\"rho\"]); sigma = float(p[\"sigma\"])\nR = int(p[\"n_replications\"]); seed = int(p[\"seed\"])\nintercept = p[\"intercept\"].lower() == \"yes\"\ninit = p[\"initial_condition\"].lower()\nassert intercept, \"design requires intercept\"\nassert init == \"stationary\" and abs(rho) < 1, \"stationary init requires |rho|<1\"\nassert n >= 3 and R >= 2 and sigma > 0\n\n# ---- P2 baseline quantities (closed form) ----\nbias_analytical = -(1 + 3 * rho) / n\nse_asymptotic = float(np.sqrt((1 - rho ** 2) / n))\n# sensitivity: same formula with effective number of regression observations n-1\nbias_analytical_neff = -(1 + 3 * rho) / (n - 1)\n\n# ---- P3 Monte Carlo ----\n# Draw order: one (R, n) standard-normal matrix; column 0 scaled to the stationary\n# sd for y_1, columns 1..n-1 scaled by sigma as innovations e_2..e_n. c = 0.\nrng = np.random.default_rng(seed)\nz = rng.standard_normal((R, n))\ny = np.empty((R, n))\ny[:, 0] = z[:, 0] * sigma / np.sqrt(1 - rho ** 2)\neps = sigma * z[:, 1:]\nfor t in range(1, n):\n    y[:, t] = rho * y[:, t - 1] + eps[:, t - 1]\nx = y[:, :-1]; yy = y[:, 1:]          # t = 2..n  (n-1 pairs)\nxc = x - x.mean(axis=1, keepdims=True)\nyc = yy - yy.mean(axis=1, keepdims=True)\nrho_hat = (xc * yc).sum(axis=1) / (xc ** 2).sum(axis=1)\n\nfinite = np.isfinite(rho_hat)\nn_bad = int((~finite).sum())\nif n_bad:\n    issues.append({\"issue\": f\"{n_bad} non-finite rho_hat\", \"handling\": \"excluded; see exclusions.csv\"})\nrh = rho_hat[finite]\nRused = int(rh.size)\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 / np.sqrt(Rused)\ndisc = (bias_mc - bias_analytical) / bias_mc_se\ndisc_neff = (bias_mc - bias_analytical_neff) / bias_mc_se\nq = np.quantile(rh, [0.025, 0.5, 0.975])\n\npd.DataFrame([{\"step\": 1, \"rule\": \"drop replications with non-finite rho_hat\",\n               \"n_before\": R, \"n_after\": Rused, \"n_removed\": R - Rused,\n               \"rationale\": \"OLS undefined if regressor has zero variance\"}]\n             ).to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\n\nres = {\n    \"task_id\": \"F5-conf-02\",\n    \"bias_analytical\": float(bias_analytical),\n    \"bias_mc\": float(bias_mc),\n    \"bias_mc_se\": float(bias_mc_se),\n    \"rho_hat_mean\": rho_hat_mean,\n    \"rho_hat_sd_mc\": rho_hat_sd,\n    \"discrepancy_se_units\": float(disc),\n    \"se_asymptotic\": se_asymptotic,\n    \"n_replications\": R,\n    \"feasibility\": \"complete\",\n    \"feasibility_reason\": None,\n    \"data_issues\": issues,\n    \"n_input_rows\": {\"design.csv\": int(len(d))},\n    \"n_analysed\": Rused,\n    \"random_seed\": seed,\n    # supplementary keys\n    \"design_n\": n, \"design_rho\": rho, \"design_sigma\": sigma,\n    \"bias_mc_ci95\": [float(bias_mc - 1.96 * bias_mc_se), float(bias_mc + 1.96 * bias_mc_se)],\n    \"bias_analytical_neff\": float(bias_analytical_neff),\n    \"discrepancy_se_units_neff\": float(disc_neff),\n    \"bias_ratio_mc_to_analytical\": float(bias_mc / bias_analytical),\n    \"rho_hat_median\": float(q[1]),\n    \"rho_hat_q025\": float(q[0]), \"rho_hat_q975\": float(q[2]),\n    \"sd_ratio_mc_to_asymptotic\": float(rho_hat_sd / se_asymptotic),\n    \"share_rho_hat_below_rho\": float((rh < rho).mean()),\n    \"design_sha256\": hashlib.sha256(open(DESIGN, \"rb\").read()).hexdigest(),\n}\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n    json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run the 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":1084,"cache_read_input_tokens":6252,"output_tokens":2334,"output_tokens_details":{"thinking_tokens":213},"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":1084},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXr1GaHxDgNeHh3f2iya","requestRef":"875f847c-fcf4-444c-8e07-ba2175c8be1f","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"ae9e5933-ea0e-437e-b42f-8823817b7926","timestamp":"2026-10-30T05:10:38.436Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242/out/state","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}30{"parentUuid":"ae9e5933-ea0e-437e-b42f-8823817b7926","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 2\n(eval):1: no such file or directory: out/analysis.py\n/opt/homebrew/Cellar/python@3.14/3.14.4/Frameworks/Python.framework/Versions/3.14/Resources/Python.app/Contents/MacOS/Python: can't open file '/Users/simon-pierreboucher/wp29/runs/RC0242/out/state/out/analysis.py': [Errno 2] No such file or directory","is_error":true,"tool_use_id":"toolu_01Kg3RRBQBBj3asg48h6oy2c"}]},"uuid":"143ed0f3-c5f0-4e32-b265-f87a0586ed66","timestamp":"2026-10-30T05:10:38.479Z","toolUseResult":"Error: Exit code 2\n(eval):1: no such file or directory: out/analysis.py\n/opt/homebrew/Cellar/python@3.14/3.14.4/Frameworks/Python.framework/Versions/3.14/Resources/Python.app/Contents/MacOS/Python: can't open file '/Users/simon-pierreboucher/wp29/runs/RC0242/out/state/out/analysis.py': [Errno 2] No such file or directory","sandboxed":false,"sourceToolAssistantUUID":"ae9e5933-ea0e-437e-b42f-8823817b7926","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242/out/state","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}31{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"aeeaa30c6ad4d41b6c747aa749c887063f5312aedd8da42a7b84502f5b715268","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01Kg3RRBQBBj3asg48h6oy2c","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-02: finite-sample bias of OLS rho_hat in a Gaussian AR(1) 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 deterministically.\"\"\"\nimport json, hashlib, os\nimport numpy as np\nimport pandas as pd\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDESIGN = os.path.join(ROOT, \"data\", \"design.csv\")\nOUT = os.path.join(ROOT, \"out\")\n\nd = pd.read_csv(DESIGN)\np = dict(zip(d[\"parameter\"].astype(str).str.strip(), d[\"value\"].astype(str).str.strip()))\nissues = []\nn = int(p[\"n\"]); rho = float(p[\"rho\"]); sigma = float(p[\"sigma\"])\nR = int(p[\"n_replications\"]); seed = int(p[\"seed\"])\nintercept = p[\"intercept\"].lower() == \"yes\"\ninit = p[\"initial_condition\"].lower()\nassert intercept, \"design requires intercept\"\nassert init == \"stationary\" and abs(rho) < 1, \"stationary init requires |rho|<1\"\nassert n >= 3 and R >= 2 and sigma > 0\n\n# ---- P2 baseline quantities (closed form) ----\nbias_analytical = -(1 + 3 * rho) / n\nse_asymptotic = float(np.sqrt((1 - rho ** 2) / n))\n# sensitivity: same formula with effective number of regression observations n-1\nbias_analytical_neff = -(1 + 3 * rho) / (n - 1)\n\n# ---- P3 Monte Carlo ----\n# Draw order: one (R, n) standard-normal matrix; column 0 scaled to the stationary\n# sd for y_1, columns 1..n-1 scaled by sigma as innovations e_2..e_n. c = 0.\nrng = np.random.default_rng(seed)\nz = rng.standard_normal((R, n))\ny = np.empty((R, n))\ny[:, 0] = z[:, 0] * sigma / np.sqrt(1 - rho ** 2)\neps = sigma * z[:, 1:]\nfor t in range(1, n):\n    y[:, t] = rho * y[:, t - 1] + eps[:, t - 1]\nx = y[:, :-1]; yy = y[:, 1:]          # t = 2..n  (n-1 pairs)\nxc = x - x.mean(axis=1, keepdims=True)\nyc = yy - yy.mean(axis=1, keepdims=True)\nrho_hat = (xc * yc).sum(axis=1) / (xc ** 2).sum(axis=1)\n\nfinite = np.isfinite(rho_hat)\nn_bad = int((~finite).sum())\nif n_bad:\n    issues.append({\"issue\": f\"{n_bad} non-finite rho_hat\", \"handling\": \"excluded; see exclusions.csv\"})\nrh = rho_hat[finite]\nRused = int(rh.size)\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 / np.sqrt(Rused)\ndisc = (bias_mc - bias_analytical) / bias_mc_se\ndisc_neff = (bias_mc - bias_analytical_neff) / bias_mc_se\nq = np.quantile(rh, [0.025, 0.5, 0.975])\n\npd.DataFrame([{\"step\": 1, \"rule\": \"drop replications with non-finite rho_hat\",\n               \"n_before\": R, \"n_after\": Rused, \"n_removed\": R - Rused,\n               \"rationale\": \"OLS undefined if regressor has zero variance\"}]\n             ).to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\n\nres = {\n    \"task_id\": \"F5-conf-02\",\n    \"bias_analytical\": float(bias_analytical),\n    \"bias_mc\": float(bias_mc),\n    \"bias_mc_se\": float(bias_mc_se),\n    \"rho_hat_mean\": rho_hat_mean,\n    \"rho_hat_sd_mc\": rho_hat_sd,\n    \"discrepancy_se_units\": float(disc),\n    \"se_asymptotic\": se_asymptotic,\n    \"n_replications\": R,\n    \"feasibility\": \"complete\",\n    \"feasibility_reason\": None,\n    \"data_issues\": issues,\n    \"n_input_rows\": {\"design.csv\": int(len(d))},\n    \"n_analysed\": Rused,\n    \"random_seed\": seed,\n    # supplementary keys\n    \"design_n\": n, \"design_rho\": rho, \"design_sigma\": sigma,\n    \"bias_mc_ci95\": [float(bias_mc - 1.96 * bias_mc_se), float(bias_mc + 1.96 * bias_mc_se)],\n    \"bias_analytical_neff\": float(bias_analytical_neff),\n    \"discrepancy_se_units_neff\": float(disc_neff),\n    \"bias_ratio_mc_to_analytical\": float(bias_mc / bias_analytical),\n    \"rho_hat_median\": float(q[1]),\n    \"rho_hat_q025\": float(q[0]), \"rho_hat_q975\": float(q[2]),\n    \"sd_ratio_mc_to_asymptotic\": float(rho_hat_sd / se_asymptotic),\n    \"share_rho_hat_below_rho\": float((rh < rho).mean()),\n    \"design_sha256\": hashlib.sha256(open(DESIGN, \"rb\").read()).hexdigest(),\n}\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n    json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run the analysis script"}}]}}32{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"4967cb8f-9a11-4581-85b2-babbdd92068e","timestamp":"2026-10-30T05:10:38.482Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"875f847c-fcf4-444c-8e07-ba2175c8be1f","keep":8,"tail":["aeeaa30c6ad4d41b6c747aa749c887063f5312aedd8da42a7b84502f5b715268","f8e30a664d3a0ff18f58b20cfaf1d6cc758c4f6f0b20ad590b21fd9a3579167f"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",9,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"98e1bd36d79ca2063f41af7a1285ed20b675b093d3b876fbd871c188aa39fd8d"}33{"parentUuid":"143ed0f3-c5f0-4e32-b265-f87a0586ed66","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr2cXsBDgyBBEtFH2Xg","type":"message","role":"assistant","content":[{"type":"text","text":"Shell was still in out/state; rerunning from root."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2496,"cache_read_input_tokens":7336,"output_tokens":123,"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":2496},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXr2cEkpLXjzYwqvih5D","requestRef":"4967cb8f-9a11-4581-85b2-babbdd92068e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"4613f92d-29c0-46e0-b85a-00785a2fcc1c","timestamp":"2026-10-30T05:10:39.531Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242/out/state","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}34{"parentUuid":"4613f92d-29c0-46e0-b85a-00785a2fcc1c","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr2cXsBDgyBBEtFH2Xg","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01XDbTzMbFvBVW4ogP7931aD","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0242 && pwd","description":"Return to workspace root"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2496,"cache_read_input_tokens":7336,"output_tokens":123,"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":2496},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXr2cEkpLXjzYwqvih5D","requestRef":"4967cb8f-9a11-4581-85b2-babbdd92068e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"607454a6-6d3e-4c3c-a4d7-bca014213834","timestamp":"2026-10-30T05:10:40.116Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242/out/state","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}35{"parentUuid":"607454a6-6d3e-4c3c-a4d7-bca014213834","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01XDbTzMbFvBVW4ogP7931aD","type":"tool_result","content":"/Users/simon-pierreboucher/wp29/runs/RC0242","is_error":false}]},"uuid":"47944077-f6a6-4cba-ba10-0a726dbb95a8","timestamp":"2026-10-30T05:10:40.138Z","toolUseResult":{"stdout":"/Users/simon-pierreboucher/wp29/runs/RC0242","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"607454a6-6d3e-4c3c-a4d7-bca014213834","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}36{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"4797bff978ec23efd189bbc107f881e2f3330de5346c8af373418c5fdffe970d","message":{"role":"assistant","content":[{"type":"text","text":"Shell was still in out/state; rerunning from root."},{"type":"tool_use","id":"toolu_01XDbTzMbFvBVW4ogP7931aD","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0242 && pwd","description":"Return to workspace root"}}]}}37{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"664bcc42-f7d0-4519-bfb6-0c0d2469c7aa","timestamp":"2026-10-30T05:10:40.142Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"4967cb8f-9a11-4581-85b2-babbdd92068e","keep":10,"tail":["4797bff978ec23efd189bbc107f881e2f3330de5346c8af373418c5fdffe970d","19139c13a124f60c2eaa8d18dd2ad5866c26e892d37afab293643e9d5bc9cbe6"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",11,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"e82e6c6cdbe53c75a8ecdc6f6e2f7c000c276d63daf2c5242b076a145944aca8"}38{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"47944077-f6a6-4cba-ba10-0a726dbb95a8","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}39{"type":"atis-latch","atis":"","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}40{"parentUuid":"47944077-f6a6-4cba-ba10-0a726dbb95a8","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr2jhi82iFq9sGVTwRQ","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":153,"cache_read_input_tokens":9832,"output_tokens":2144,"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":153},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":338,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXr2jL98btLcuLXdyZsN","requestRef":"664bcc42-f7d0-4519-bfb6-0c0d2469c7aa","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"5a3035e5-8643-428b-832d-a75e3935548e","timestamp":"2026-10-30T05:10:41.356Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}41{"parentUuid":"5a3035e5-8643-428b-832d-a75e3935548e","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr2jhi82iFq9sGVTwRQ","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_018RfbT9Hn2N282BHyw9HGbQ","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-02: finite-sample bias of OLS rho_hat in a Gaussian AR(1) 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 deterministically.\"\"\"\nimport json, hashlib, os\nimport numpy as np\nimport pandas as pd\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDESIGN = os.path.join(ROOT, \"data\", \"design.csv\")\nOUT = os.path.join(ROOT, \"out\")\n\nd = pd.read_csv(DESIGN)\np = dict(zip(d[\"parameter\"].astype(str).str.strip(), d[\"value\"].astype(str).str.strip()))\nissues = []\nn = int(p[\"n\"]); rho = float(p[\"rho\"]); sigma = float(p[\"sigma\"])\nR = int(p[\"n_replications\"]); seed = int(p[\"seed\"])\nintercept = p[\"intercept\"].lower() == \"yes\"\ninit = p[\"initial_condition\"].lower()\nassert intercept, \"design requires intercept\"\nassert init == \"stationary\" and abs(rho) < 1, \"stationary init requires |rho|<1\"\nassert n >= 3 and R >= 2 and sigma > 0\n\n# ---- P2 baseline quantities (closed form) ----\nbias_analytical = -(1 + 3 * rho) / n\nse_asymptotic = float(np.sqrt((1 - rho ** 2) / n))\n# sensitivity: same formula with effective number of regression observations n-1\nbias_analytical_neff = -(1 + 3 * rho) / (n - 1)\n\n# ---- P3 Monte Carlo ----\n# Draw order: one (R, n) standard-normal matrix; column 0 scaled to the stationary\n# sd for y_1, columns 1..n-1 scaled by sigma as innovations e_2..e_n. c = 0.\nrng = np.random.default_rng(seed)\nz = rng.standard_normal((R, n))\ny = np.empty((R, n))\ny[:, 0] = z[:, 0] * sigma / np.sqrt(1 - rho ** 2)\neps = sigma * z[:, 1:]\nfor t in range(1, n):\n    y[:, t] = rho * y[:, t - 1] + eps[:, t - 1]\nx = y[:, :-1]; yy = y[:, 1:]          # t = 2..n  (n-1 pairs)\nxc = x - x.mean(axis=1, keepdims=True)\nyc = yy - yy.mean(axis=1, keepdims=True)\nrho_hat = (xc * yc).sum(axis=1) / (xc ** 2).sum(axis=1)\n\nfinite = np.isfinite(rho_hat)\nn_bad = int((~finite).sum())\nif n_bad:\n    issues.append({\"issue\": f\"{n_bad} non-finite rho_hat\", \"handling\": \"excluded; see exclusions.csv\"})\nrh = rho_hat[finite]\nRused = int(rh.size)\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 / np.sqrt(Rused)\ndisc = (bias_mc - bias_analytical) / bias_mc_se\ndisc_neff = (bias_mc - bias_analytical_neff) / bias_mc_se\nq = np.quantile(rh, [0.025, 0.5, 0.975])\n\npd.DataFrame([{\"step\": 1, \"rule\": \"drop replications with non-finite rho_hat\",\n               \"n_before\": R, \"n_after\": Rused, \"n_removed\": R - Rused,\n               \"rationale\": \"OLS undefined if regressor has zero variance\"}]\n             ).to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\n\nres = {\n    \"task_id\": \"F5-conf-02\",\n    \"bias_analytical\": float(bias_analytical),\n    \"bias_mc\": float(bias_mc),\n    \"bias_mc_se\": float(bias_mc_se),\n    \"rho_hat_mean\": rho_hat_mean,\n    \"rho_hat_sd_mc\": rho_hat_sd,\n    \"discrepancy_se_units\": float(disc),\n    \"se_asymptotic\": se_asymptotic,\n    \"n_replications\": R,\n    \"feasibility\": \"complete\",\n    \"feasibility_reason\": None,\n    \"data_issues\": issues,\n    \"n_input_rows\": {\"design.csv\": int(len(d))},\n    \"n_analysed\": Rused,\n    \"random_seed\": seed,\n    # supplementary keys\n    \"design_n\": n, \"design_rho\": rho, \"design_sigma\": sigma,\n    \"bias_mc_ci95\": [float(bias_mc - 1.96 * bias_mc_se), float(bias_mc + 1.96 * bias_mc_se)],\n    \"bias_analytical_neff\": float(bias_analytical_neff),\n    \"discrepancy_se_units_neff\": float(disc_neff),\n    \"bias_ratio_mc_to_analytical\": float(bias_mc / bias_analytical),\n    \"rho_hat_median\": float(q[1]),\n    \"rho_hat_q025\": float(q[0]), \"rho_hat_q975\": float(q[2]),\n    \"sd_ratio_mc_to_asymptotic\": float(rho_hat_sd / se_asymptotic),\n    \"share_rho_hat_below_rho\": float((rh < rho).mean()),\n    \"design_sha256\": hashlib.sha256(open(DESIGN, \"rb\").read()).hexdigest(),\n}\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n    json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run the 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":153,"cache_read_input_tokens":9832,"output_tokens":2144,"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":153},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXr2jL98btLcuLXdyZsN","requestRef":"664bcc42-f7d0-4519-bfb6-0c0d2469c7aa","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"525e4de1-7554-4aa1-8b04-f2e15352ddad","timestamp":"2026-10-30T05:10:54.273Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}42{"parentUuid":"525e4de1-7554-4aa1-8b04-f2e15352ddad","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_018RfbT9Hn2N282BHyw9HGbQ","type":"tool_result","content":"{\n  \"task_id\": \"F5-conf-02\",\n  \"bias_analytical\": -0.11333333333333334,\n  \"bias_mc\": -0.12234105846329002,\n  \"bias_mc_se\": 0.001045950949129853,\n  \"rho_hat_mean\": 0.67765894153671,\n  \"rho_hat_sd_mc\": 0.14791980178364494,\n  \"discrepancy_se_units\": -8.611995751282965,\n  \"se_asymptotic\": 0.1095445115010332,\n  \"n_replications\": 20000,\n  \"feasibility\": \"complete\",\n  \"feasibility_reason\": null,\n  \"data_issues\": [],\n  \"n_input_rows\": {\n    \"design.csv\": 7\n  },\n  \"n_analysed\": 20000,\n  \"random_seed\": 20261029,\n  \"design_n\": 30,\n  \"design_rho\": 0.8,\n  \"design_sigma\": 1.0,\n  \"bias_mc_ci95\": [\n    -0.12439112232358453,\n    -0.12029099460299551\n  ],\n  \"bias_analytical_neff\": -0.11724137931034484,\n  \"discrepancy_se_units_neff\": -4.875638917090426,\n  \"bias_ratio_mc_to_analytical\": 1.0794799276172649,\n  \"rho_hat_median\": 0.6989817190848994,\n  \"rho_hat_q025\": 0.33062299149836977,\n  \"rho_hat_q975\": 0.9018644910493487,\n  \"sd_ratio_mc_to_asymptotic\": 1.3503168689765876,\n  \"share_rho_hat_below_rho\": 0.78885,\n  \"design_sha256\": \"2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb\"\n}","is_error":false}]},"uuid":"98c2bbb6-7aaa-4b66-b9b9-1f4a4201a4e3","timestamp":"2026-10-30T05:10:54.554Z","toolUseResult":{"stdout":"{\n  \"task_id\": \"F5-conf-02\",\n  \"bias_analytical\": -0.11333333333333334,\n  \"bias_mc\": -0.12234105846329002,\n  \"bias_mc_se\": 0.001045950949129853,\n  \"rho_hat_mean\": 0.67765894153671,\n  \"rho_hat_sd_mc\": 0.14791980178364494,\n  \"discrepancy_se_units\": -8.611995751282965,\n  \"se_asymptotic\": 0.1095445115010332,\n  \"n_replications\": 20000,\n  \"feasibility\": \"complete\",\n  \"feasibility_reason\": null,\n  \"data_issues\": [],\n  \"n_input_rows\": {\n    \"design.csv\": 7\n  },\n  \"n_analysed\": 20000,\n  \"random_seed\": 20261029,\n  \"design_n\": 30,\n  \"design_rho\": 0.8,\n  \"design_sigma\": 1.0,\n  \"bias_mc_ci95\": [\n    -0.12439112232358453,\n    -0.12029099460299551\n  ],\n  \"bias_analytical_neff\": -0.11724137931034484,\n  \"discrepancy_se_units_neff\": -4.875638917090426,\n  \"bias_ratio_mc_to_analytical\": 1.0794799276172649,\n  \"rho_hat_median\": 0.6989817190848994,\n  \"rho_hat_q025\": 0.33062299149836977,\n  \"rho_hat_q975\": 0.9018644910493487,\n  \"sd_ratio_mc_to_asymptotic\": 1.3503168689765876,\n  \"share_rho_hat_below_rho\": 0.78885,\n  \"design_sha256\": \"2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb\"\n}","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"525e4de1-7554-4aa1-8b04-f2e15352ddad","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}43{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"b8b414835514e5c17fb3b59ca940bf489307684a3044d64fbb0ec1847ad3b430","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_018RfbT9Hn2N282BHyw9HGbQ","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-02: finite-sample bias of OLS rho_hat in a Gaussian AR(1) 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 deterministically.\"\"\"\nimport json, hashlib, os\nimport numpy as np\nimport pandas as pd\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDESIGN = os.path.join(ROOT, \"data\", \"design.csv\")\nOUT = os.path.join(ROOT, \"out\")\n\nd = pd.read_csv(DESIGN)\np = dict(zip(d[\"parameter\"].astype(str).str.strip(), d[\"value\"].astype(str).str.strip()))\nissues = []\nn = int(p[\"n\"]); rho = float(p[\"rho\"]); sigma = float(p[\"sigma\"])\nR = int(p[\"n_replications\"]); seed = int(p[\"seed\"])\nintercept = p[\"intercept\"].lower() == \"yes\"\ninit = p[\"initial_condition\"].lower()\nassert intercept, \"design requires intercept\"\nassert init == \"stationary\" and abs(rho) < 1, \"stationary init requires |rho|<1\"\nassert n >= 3 and R >= 2 and sigma > 0\n\n# ---- P2 baseline quantities (closed form) ----\nbias_analytical = -(1 + 3 * rho) / n\nse_asymptotic = float(np.sqrt((1 - rho ** 2) / n))\n# sensitivity: same formula with effective number of regression observations n-1\nbias_analytical_neff = -(1 + 3 * rho) / (n - 1)\n\n# ---- P3 Monte Carlo ----\n# Draw order: one (R, n) standard-normal matrix; column 0 scaled to the stationary\n# sd for y_1, columns 1..n-1 scaled by sigma as innovations e_2..e_n. c = 0.\nrng = np.random.default_rng(seed)\nz = rng.standard_normal((R, n))\ny = np.empty((R, n))\ny[:, 0] = z[:, 0] * sigma / np.sqrt(1 - rho ** 2)\neps = sigma * z[:, 1:]\nfor t in range(1, n):\n    y[:, t] = rho * y[:, t - 1] + eps[:, t - 1]\nx = y[:, :-1]; yy = y[:, 1:]          # t = 2..n  (n-1 pairs)\nxc = x - x.mean(axis=1, keepdims=True)\nyc = yy - yy.mean(axis=1, keepdims=True)\nrho_hat = (xc * yc).sum(axis=1) / (xc ** 2).sum(axis=1)\n\nfinite = np.isfinite(rho_hat)\nn_bad = int((~finite).sum())\nif n_bad:\n    issues.append({\"issue\": f\"{n_bad} non-finite rho_hat\", \"handling\": \"excluded; see exclusions.csv\"})\nrh = rho_hat[finite]\nRused = int(rh.size)\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 / np.sqrt(Rused)\ndisc = (bias_mc - bias_analytical) / bias_mc_se\ndisc_neff = (bias_mc - bias_analytical_neff) / bias_mc_se\nq = np.quantile(rh, [0.025, 0.5, 0.975])\n\npd.DataFrame([{\"step\": 1, \"rule\": \"drop replications with non-finite rho_hat\",\n               \"n_before\": R, \"n_after\": Rused, \"n_removed\": R - Rused,\n               \"rationale\": \"OLS undefined if regressor has zero variance\"}]\n             ).to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\n\nres = {\n    \"task_id\": \"F5-conf-02\",\n    \"bias_analytical\": float(bias_analytical),\n    \"bias_mc\": float(bias_mc),\n    \"bias_mc_se\": float(bias_mc_se),\n    \"rho_hat_mean\": rho_hat_mean,\n    \"rho_hat_sd_mc\": rho_hat_sd,\n    \"discrepancy_se_units\": float(disc),\n    \"se_asymptotic\": se_asymptotic,\n    \"n_replications\": R,\n    \"feasibility\": \"complete\",\n    \"feasibility_reason\": None,\n    \"data_issues\": issues,\n    \"n_input_rows\": {\"design.csv\": int(len(d))},\n    \"n_analysed\": Rused,\n    \"random_seed\": seed,\n    # supplementary keys\n    \"design_n\": n, \"design_rho\": rho, \"design_sigma\": sigma,\n    \"bias_mc_ci95\": [float(bias_mc - 1.96 * bias_mc_se), float(bias_mc + 1.96 * bias_mc_se)],\n    \"bias_analytical_neff\": float(bias_analytical_neff),\n    \"discrepancy_se_units_neff\": float(disc_neff),\n    \"bias_ratio_mc_to_analytical\": float(bias_mc / bias_analytical),\n    \"rho_hat_median\": float(q[1]),\n    \"rho_hat_q025\": float(q[0]), \"rho_hat_q975\": float(q[2]),\n    \"sd_ratio_mc_to_asymptotic\": float(rho_hat_sd / se_asymptotic),\n    \"share_rho_hat_below_rho\": float((rh < rho).mean()),\n    \"design_sha256\": hashlib.sha256(open(DESIGN, \"rb\").read()).hexdigest(),\n}\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n    json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run the analysis script"}}]}}44{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"ee0013eb-f689-4b52-b57f-86cab763335f","timestamp":"2026-10-30T05:10:54.557Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"664bcc42-f7d0-4519-bfb6-0c0d2469c7aa","keep":12,"tail":["b8b414835514e5c17fb3b59ca940bf489307684a3044d64fbb0ec1847ad3b430","3bfdd16c0c137463d8de3df1b5aedf7d114b83dcf68a4978ba77fb96fe42660a"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",13,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"4c72ab6c7247112f4a267fc30a3ea6aa5a0aadac328244e6d25093821b0bd785"}45{"parentUuid":"98c2bbb6-7aaa-4b66-b9b9-1f4a4201a4e3","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr3oEaNtFdDHP8Ezjns","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":2739,"cache_read_input_tokens":9985,"output_tokens":829,"output_tokens_details":{"thinking_tokens":150},"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":2739},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1088,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXr3nxDAXPF2sMKPLR6r","requestRef":"ee0013eb-f689-4b52-b57f-86cab763335f","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"c6ddf149-9f55-4c82-a150-a7e911ec2cad","timestamp":"2026-10-30T05:10:56.698Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}46{"parentUuid":"c6ddf149-9f55-4c82-a150-a7e911ec2cad","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr3oEaNtFdDHP8Ezjns","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01GCUXE7nP9t6J6UKyufVgcD","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\n~/wp29/venv/bin/python - <<'EOF'\nimport json,numpy as np,statsmodels.api as sm\nr=json.load(open('out/results.json'))\n# independent re-sim for first 3 reps with statsmodels OLS\nn,rho,R,seed=30,0.8,20000,20261029\nz=np.random.default_rng(seed).standard_normal((R,n))\nfor i in range(3):\n    y=np.empty(n);y[0]=z[i,0]/np.sqrt(1-rho**2)\n    for t in range(1,n): y[t]=rho*y[t-1]+z[i,t]\n    print(sm.OLS(y[1:],sm.add_constant(y[:-1])).fit().params[1])\nprint(\"se>0\",r['bias_mc_se']>0,\"ci contains\",r['bias_mc_ci95'][0]<r['bias_mc']<r['bias_mc_ci95'][1])\nprint(\"mean-rho==bias\",abs(r['rho_hat_mean']-0.8-r['bias_mc'])<1e-15)\nprint(\"se==sd/sqrtR\",abs(r['rho_hat_sd_mc']/np.sqrt(20000)-r['bias_mc_se'])<1e-15)\nprint(\"disc recompute\",(r['bias_mc']-r['bias_analytical'])/r['bias_mc_se'])\nprint(\"analytical\",-(1+2.4)/30, \"se_asy\",np.sqrt(0.36/30))\nEOF\ncat out/exclusions.csv","description":"Verify reproducibility and consistency"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2739,"cache_read_input_tokens":9985,"output_tokens":829,"output_tokens_details":{"thinking_tokens":150},"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":2739},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXr3nxDAXPF2sMKPLR6r","requestRef":"ee0013eb-f689-4b52-b57f-86cab763335f","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"8ea6d685-ed4f-4dc6-93d6-532900531d2d","timestamp":"2026-10-30T05:11:01.633Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}47{"parentUuid":"8ea6d685-ed4f-4dc6-93d6-532900531d2d","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01GCUXE7nP9t6J6UKyufVgcD","type":"tool_result","content":"IDENTICAL\n0.5925175276187395\n0.8045542977567159\n0.8453133267086479\nse>0 True ci contains True\nmean-rho==bias True\nse==sd/sqrtR True\ndisc recompute -8.611995751282965\nanalytical -0.11333333333333333 se_asy 0.10954451150103323\nstep,rule,n_before,n_after,n_removed,rationale\n1,drop replications with non-finite rho_hat,20000,20000,0,OLS undefined if regressor has zero variance","is_error":false}]},"uuid":"351caf09-0348-4fac-9c24-69251b8111b5","timestamp":"2026-10-30T05:11:02.838Z","toolUseResult":{"stdout":"IDENTICAL\n0.5925175276187395\n0.8045542977567159\n0.8453133267086479\nse>0 True ci contains True\nmean-rho==bias True\nse==sd/sqrtR True\ndisc recompute -8.611995751282965\nanalytical -0.11333333333333333 se_asy 0.10954451150103323\nstep,rule,n_before,n_after,n_removed,rationale\n1,drop replications with non-finite rho_hat,20000,20000,0,OLS undefined if regressor has zero variance","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"8ea6d685-ed4f-4dc6-93d6-532900531d2d","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}48{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"24b66e7ede902bd00625d563675b57e776d1d69a8bb4f05c53020d3aee56f1d1","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01GCUXE7nP9t6J6UKyufVgcD","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\n~/wp29/venv/bin/python - <<'EOF'\nimport json,numpy as np,statsmodels.api as sm\nr=json.load(open('out/results.json'))\n# independent re-sim for first 3 reps with statsmodels OLS\nn,rho,R,seed=30,0.8,20000,20261029\nz=np.random.default_rng(seed).standard_normal((R,n))\nfor i in range(3):\n    y=np.empty(n);y[0]=z[i,0]/np.sqrt(1-rho**2)\n    for t in range(1,n): y[t]=rho*y[t-1]+z[i,t]\n    print(sm.OLS(y[1:],sm.add_constant(y[:-1])).fit().params[1])\nprint(\"se>0\",r['bias_mc_se']>0,\"ci contains\",r['bias_mc_ci95'][0]<r['bias_mc']<r['bias_mc_ci95'][1])\nprint(\"mean-rho==bias\",abs(r['rho_hat_mean']-0.8-r['bias_mc'])<1e-15)\nprint(\"se==sd/sqrtR\",abs(r['rho_hat_sd_mc']/np.sqrt(20000)-r['bias_mc_se'])<1e-15)\nprint(\"disc recompute\",(r['bias_mc']-r['bias_analytical'])/r['bias_mc_se'])\nprint(\"analytical\",-(1+2.4)/30, \"se_asy\",np.sqrt(0.36/30))\nEOF\ncat out/exclusions.csv","description":"Verify reproducibility and consistency"}}]}}49{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"1dcfabcb-0f43-4de4-a6e3-e6deb112bb91","timestamp":"2026-10-30T05:11:02.841Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"ee0013eb-f689-4b52-b57f-86cab763335f","keep":14,"tail":["24b66e7ede902bd00625d563675b57e776d1d69a8bb4f05c53020d3aee56f1d1","ce4b69aad6c4b15420158fdf1d36017e10e934291a4f5935f948c245d1088fb7"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",15,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"3efb6eb31cdc0505c73e047a7e61accb9318c00d3f5c052bbc79d849b4ff3a12"}50{"parentUuid":"351caf09-0348-4fac-9c24-69251b8111b5","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr4QhXKkCL8nY7SQ8us","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01ASijkDTtnxCDSJCsKgpTAJ","name":"Bash","input":{"command":"~/wp29/venv/bin/python - <<'EOF'\nimport json,numpy as np\nn,rho,R,seed=30,0.8,20000,20261029\nz=np.random.default_rng(seed).standard_normal((R,n))\ny=np.empty((R,n));y[:,0]=z[:,0]/np.sqrt(1-rho**2)\nfor t in range(1,n): y[:,t]=rho*y[:,t-1]+z[:,t]\nimport statsmodels.api as sm\nprint([round(sm.OLS(y[i,1:],sm.add_constant(y[i,:-1])).fit().params[1],12) for i in range(3)])\nEOF","description":"Cross-check first 3 rho_hat vs script internals"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1005,"cache_read_input_tokens":12724,"output_tokens":307,"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":1005},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXr4QRQ2jMhbgxsL8mnQ","requestRef":"1dcfabcb-0f43-4de4-a6e3-e6deb112bb91","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"599e9583-5677-4b3f-aba7-27759a3dd90e","timestamp":"2026-10-30T05:11:05.604Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}51{"parentUuid":"599e9583-5677-4b3f-aba7-27759a3dd90e","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01ASijkDTtnxCDSJCsKgpTAJ","type":"tool_result","content":"[np.float64(0.592517527619), np.float64(0.804554297757), np.float64(0.845313326709)]","is_error":false}]},"uuid":"d2a02475-9728-49c4-85d9-c3fc8748b928","timestamp":"2026-10-30T05:11:06.520Z","toolUseResult":{"stdout":"[np.float64(0.592517527619), np.float64(0.804554297757), np.float64(0.845313326709)]","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"599e9583-5677-4b3f-aba7-27759a3dd90e","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}52{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"4946b1f04fb771a2f8a102318bccfa5cf534b05b5fc15c08481833141aa2dca7","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01ASijkDTtnxCDSJCsKgpTAJ","name":"Bash","input":{"command":"~/wp29/venv/bin/python - <<'EOF'\nimport json,numpy as np\nn,rho,R,seed=30,0.8,20000,20261029\nz=np.random.default_rng(seed).standard_normal((R,n))\ny=np.empty((R,n));y[:,0]=z[:,0]/np.sqrt(1-rho**2)\nfor t in range(1,n): y[:,t]=rho*y[:,t-1]+z[:,t]\nimport statsmodels.api as sm\nprint([round(sm.OLS(y[i,1:],sm.add_constant(y[i,:-1])).fit().params[1],12) for i in range(3)])\nEOF","description":"Cross-check first 3 rho_hat vs script internals"}}]}}53{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"e7492a87-e2a4-4de0-bce1-653dad473bd0","timestamp":"2026-10-30T05:11:06.525Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"1dcfabcb-0f43-4de4-a6e3-e6deb112bb91","keep":16,"tail":["4946b1f04fb771a2f8a102318bccfa5cf534b05b5fc15c08481833141aa2dca7","533d7ab2869112acfa544a9fc865daa3d07fdc993627e6c839cf75b37e35e89b"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",17,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"21599b23be62e6c97c6d02c4aaec61809f020e24f38ae7892e45a2dcf1ad03d5"}54{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"d2a02475-9728-49c4-85d9-c3fc8748b928","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}55{"type":"atis-latch","atis":"","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}56{"parentUuid":"d2a02475-9728-49c4-85d9-c3fc8748b928","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr4gQaScYmtyZhHxaSk","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":350,"cache_read_input_tokens":13729,"output_tokens":231,"output_tokens_details":{"thinking_tokens":67},"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":350},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":558,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXr4g8y4MTn2gpJEmTV4","requestRef":"e7492a87-e2a4-4de0-bce1-653dad473bd0","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"93ad4204-210c-4ad3-bdf3-815c3871efdc","timestamp":"2026-10-30T05:11:08.238Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}57{"parentUuid":"93ad4204-210c-4ad3-bdf3-815c3871efdc","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr4gQaScYmtyZhHxaSk","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01C8KcQAYjYaxro4ZaScQY1w","name":"Bash","input":{"command":"~/wp29/venv/bin/python -c \"\nimport runpy,io,contextlib\nwith contextlib.redirect_stdout(io.StringIO()): g=runpy.run_path('out/analysis.py')\nprint(g['rho_hat'][:3])\"","description":"Print script's first three rho_hat values"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":350,"cache_read_input_tokens":13729,"output_tokens":231,"output_tokens_details":{"thinking_tokens":67},"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":350},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXr4g8y4MTn2gpJEmTV4","requestRef":"e7492a87-e2a4-4de0-bce1-653dad473bd0","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"188da6d5-dc9e-4051-af87-f88b2da09881","timestamp":"2026-10-30T05:11:09.053Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}58{"parentUuid":"188da6d5-dc9e-4051-af87-f88b2da09881","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01C8KcQAYjYaxro4ZaScQY1w","type":"tool_result","content":"[0.59251753 0.8045543  0.84531333]","is_error":false}]},"uuid":"afc5dba3-e4ce-4bd0-bf57-fec2a9240b51","timestamp":"2026-10-30T05:11:09.330Z","toolUseResult":{"stdout":"[0.59251753 0.8045543  0.84531333]","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"188da6d5-dc9e-4051-af87-f88b2da09881","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}59{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"a61ad4b6084e0ead827fa7615f89ced7237eebede7244a9d1e4b1cff13e9a0f1","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01C8KcQAYjYaxro4ZaScQY1w","name":"Bash","input":{"command":"~/wp29/venv/bin/python -c \"\nimport runpy,io,contextlib\nwith contextlib.redirect_stdout(io.StringIO()): g=runpy.run_path('out/analysis.py')\nprint(g['rho_hat'][:3])\"","description":"Print script's first three rho_hat values"}}]}}60{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"3d88d271-041e-4545-8a16-e29dfc2f3a14","timestamp":"2026-10-30T05:11:09.333Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"e7492a87-e2a4-4de0-bce1-653dad473bd0","keep":18,"tail":["a61ad4b6084e0ead827fa7615f89ced7237eebede7244a9d1e4b1cff13e9a0f1","71e20503f6c939978cde7f22c539395437531fec0b058edd25c2cef80b47cb7c"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",19,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"83d34d2d860f540363552bf888dc7767d47cd4c02366dfab2bdb8f00b79622a3"}61{"parentUuid":"afc5dba3-e4ce-4bd0-bf57-fec2a9240b51","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr4tPuAMCYhJNjqCh9N","type":"message","role":"assistant","content":[{"type":"text","text":"Matches statsmodels. Now the state files, report, and claims."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":255,"cache_read_input_tokens":14079,"output_tokens":1575,"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":255},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXr4t8XZ2mWDPKpYPvoK","requestRef":"3d88d271-041e-4545-8a16-e29dfc2f3a14","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f73a7429-de4b-44bc-baf4-d408c0d19dc9","timestamp":"2026-10-30T05:11:10.285Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}62{"parentUuid":"f73a7429-de4b-44bc-baf4-d408c0d19dc9","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr4tPuAMCYhJNjqCh9N","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01NKiqNdnm44oiRpsdUmNvox","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n- File: data/design.csv — SHA-256 2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb\n- 7 data rows (+header), 3 columns: parameter (str), value (str/numeric), description (str).\n- Values: n=30, 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- No missing values, no duplicate parameters, no dates (simulation design only). Units: dimensionless.\n- Consistency: |rho|<1 so the stationary initial condition is well defined; sigma>0; n>=3.\n- Information-availability: only input is design.csv; no violations. c=0 per TASK.md.\n- Note (not a data defect): n=30 is the series length, so the regression uses n-1=29 pairs. The analytical formula is evaluated with n=30 as the task specifies (\"at the design values\"); the n-1 version is reported as a sensitivity key (bias_analytical_neff).\n- Exclusions: one rule (drop non-finite rho_hat), removed 0 of 20000 (out/exclusions.csv).\nEOF\ncat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Clean re-run: deleted out/results.json and out/exclusions.csv, re-ran analysis.py; byte-identical results.json (cmp) — PASS.\n2. Independent OLS check: statsmodels OLS of y_t on (1, y_{t-1}) for replications 1-3 reproduces the script's rho_hat (0.59252, 0.80455, 0.84531) — PASS.\n3. rho_hat_mean - rho == bias_mc (to 1e-15) — PASS.\n4. bias_mc_se == rho_hat_sd_mc/sqrt(20000) and > 0 — PASS.\n5. bias_mc_ci95 contains bias_mc — PASS.\n6. discrepancy_se_units recomputed = -8.612 — PASS.\n7. bias_analytical = -(1+3*0.8)/30 = -0.11333; se_asymptotic = sqrt(0.36/30) = 0.10954 — PASS.\n8. Counts: n_replications 20000 - 0 removed = n_analysed 20000 — PASS.\n9. Magnitude sanity: bias_mc (-0.122) same sign and order as analytical (-0.113); |bias| ~ 1.1 x se_asymptotic, plausible for n=30, rho=0.8 — PASS.\nEOF\ncat > out/state/phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"passed\",\"checks\":[\"sha256 recorded\",\"schema/rows/missing/duplicates checked\",\"availability rules: no violations\",\"exclusions.csv: 20000-0=20000\"],\"notes\":\"see data_audit.md\"},\n\"P2\":{\"status\":\"passed\",\"checks\":[\"bias_analytical and se_asymptotic computed in closed form and verified by hand (checks.md #7)\"],\"notes\":\"\"},\n\"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py implemented, seed 20261029 via default_rng, vectorised MC run\"],\"notes\":\"\"},\n\"P4\":{\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical\",\"statsmodels cross-check\",\"identities/CI/SE/count checks all pass (checks.md)\"],\"notes\":\"\"},\n\"P5\":{\"status\":\"passed\",\"checks\":[\"report.md with required sections, numbers cite results keys\",\"claims.json written and consistent with report\"],\"notes\":\"\"}}\nEOF\ncat >> out/state/log.md <<'EOF'\n- 2026-10-30 P1 passed: design audited, no issues; decision: analytical formula uses n=30, n-1 reported as sensitivity.\n- 2026-10-30 P2/P3 passed: analysis.py written and run (seed 20261029).\n- 2026-10-30 P4 passed: reproducibility and consistency checks recorded in checks.md.\n- 2026-10-30 P5 passed: report.md and claims.json written.\nEOF","description":"Write audit, checks, phases, log"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":255,"cache_read_input_tokens":14079,"output_tokens":1575,"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":255},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXr4t8XZ2mWDPKpYPvoK","requestRef":"3d88d271-041e-4545-8a16-e29dfc2f3a14","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"42e7a7c0-526f-4e06-bc7a-6dee84f7afda","timestamp":"2026-10-30T05:11:22.675Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}63{"parentUuid":"42e7a7c0-526f-4e06-bc7a-6dee84f7afda","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01NKiqNdnm44oiRpsdUmNvox","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"6bb1be19-ca0e-438a-8156-e5020f2bb1e9","timestamp":"2026-10-30T05:11:22.716Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"42e7a7c0-526f-4e06-bc7a-6dee84f7afda","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}64{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"11d5356ada83a0c407eefd32d2e96f0c747d311a9ed823475d02b5e4c7d0bacc","message":{"role":"assistant","content":[{"type":"text","text":"Matches statsmodels. Now the state files, report, and claims."},{"type":"tool_use","id":"toolu_01NKiqNdnm44oiRpsdUmNvox","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n- File: data/design.csv — SHA-256 2f459c539378cbe54d830c18af466f2fa4230ce48a609aa6464f8334a0d36ecb\n- 7 data rows (+header), 3 columns: parameter (str), value (str/numeric), description (str).\n- Values: n=30, 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- No missing values, no duplicate parameters, no dates (simulation design only). Units: dimensionless.\n- Consistency: |rho|<1 so the stationary initial condition is well defined; sigma>0; n>=3.\n- Information-availability: only input is design.csv; no violations. c=0 per TASK.md.\n- Note (not a data defect): n=30 is the series length, so the regression uses n-1=29 pairs. The analytical formula is evaluated with n=30 as the task specifies (\"at the design values\"); the n-1 version is reported as a sensitivity key (bias_analytical_neff).\n- Exclusions: one rule (drop non-finite rho_hat), removed 0 of 20000 (out/exclusions.csv).\nEOF\ncat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Clean re-run: deleted out/results.json and out/exclusions.csv, re-ran analysis.py; byte-identical results.json (cmp) — PASS.\n2. Independent OLS check: statsmodels OLS of y_t on (1, y_{t-1}) for replications 1-3 reproduces the script's rho_hat (0.59252, 0.80455, 0.84531) — PASS.\n3. rho_hat_mean - rho == bias_mc (to 1e-15) — PASS.\n4. bias_mc_se == rho_hat_sd_mc/sqrt(20000) and > 0 — PASS.\n5. bias_mc_ci95 contains bias_mc — PASS.\n6. discrepancy_se_units recomputed = -8.612 — PASS.\n7. bias_analytical = -(1+3*0.8)/30 = -0.11333; se_asymptotic = sqrt(0.36/30) = 0.10954 — PASS.\n8. Counts: n_replications 20000 - 0 removed = n_analysed 20000 — PASS.\n9. Magnitude sanity: bias_mc (-0.122) same sign and order as analytical (-0.113); |bias| ~ 1.1 x se_asymptotic, plausible for n=30, rho=0.8 — PASS.\nEOF\ncat > out/state/phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"passed\",\"checks\":[\"sha256 recorded\",\"schema/rows/missing/duplicates checked\",\"availability rules: no violations\",\"exclusions.csv: 20000-0=20000\"],\"notes\":\"see data_audit.md\"},\n\"P2\":{\"status\":\"passed\",\"checks\":[\"bias_analytical and se_asymptotic computed in closed form and verified by hand (checks.md #7)\"],\"notes\":\"\"},\n\"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py implemented, seed 20261029 via default_rng, vectorised MC run\"],\"notes\":\"\"},\n\"P4\":{\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical\",\"statsmodels cross-check\",\"identities/CI/SE/count checks all pass (checks.md)\"],\"notes\":\"\"},\n\"P5\":{\"status\":\"passed\",\"checks\":[\"report.md with required sections, numbers cite results keys\",\"claims.json written and consistent with report\"],\"notes\":\"\"}}\nEOF\ncat >> out/state/log.md <<'EOF'\n- 2026-10-30 P1 passed: design audited, no issues; decision: analytical formula uses n=30, n-1 reported as sensitivity.\n- 2026-10-30 P2/P3 passed: analysis.py written and run (seed 20261029).\n- 2026-10-30 P4 passed: reproducibility and consistency checks recorded in checks.md.\n- 2026-10-30 P5 passed: report.md and claims.json written.\nEOF","description":"Write audit, checks, phases, log"}}]}}65{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"c1bfc293-69bc-4a88-bc01-f3c7679e0f2a","timestamp":"2026-10-30T05:11:22.720Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"3d88d271-041e-4545-8a16-e29dfc2f3a14","keep":20,"tail":["11d5356ada83a0c407eefd32d2e96f0c747d311a9ed823475d02b5e4c7d0bacc","c1e148f4581bf3defac314797308a013a03631179ee4b713eff389b9aa15bc2f"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",21,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"5fd388732f65407c903178ddc2a7e96cf2b03e289414a239b46641a8ebf7a019"}66{"parentUuid":"6bb1be19-ca0e-438a-8156-e5020f2bb1e9","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr5sdHumSU6r14x8RCB","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01L67HyPipaUppcPgZA8Yd3M","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-conf-02 — Finite-sample bias of OLS ρ̂ in a Gaussian AR(1)\n\n## Question\nIn the Gaussian AR(1) y_t = c + ρ y_{t−1} + ε_t, ε_t ~ N(0, σ²), OLS of y_t on (1, y_{t−1}) is biased downward in small samples. We compare the Marriott–Pope/Kendall approximation E[ρ̂] − ρ ≈ −(1+3ρ)/n with a Monte Carlo estimate of the actual bias at the design n = 30, ρ = 0.8 (`design_n`, `design_rho`).\n\n## Data and exclusions\nThe only input is `data/design.csv` (7 rows, `n_input_rows`; SHA-256 in `design_sha256`): n = 30, ρ = 0.8, σ = 1 (`design_sigma`), intercept included, stationary initial condition, R = 20000 replications (`n_replications`), seed 20261029 (`random_seed`). No data problems were found (`data_issues` is empty). One exclusion rule (drop replications with a non-finite ρ̂) removed 0 replications, so `n_analysed` = 20000 (`out/exclusions.csv`).\n\n## Method\n- **Analytical approximation** (`bias_analytical`): −(1+3ρ)/n with n = 30, the series length given in the design. This formula is the leading term of an asymptotic expansion of E[ρ̂] in powers of 1/n, derived for a stationary Gaussian AR(1) with an estimated mean/intercept. Its error is O(n⁻²), so it is accurate *as n → ∞* (relative error shrinks like 1/n). It is not an exact finite-sample result and gives no guarantee at any fixed n, especially when ρ is near 1, where higher-order terms are larger. Because the regression actually uses n − 1 = 29 pairs, and both n and n − 1 are consistent with the same first-order expansion, I also report the formula evaluated at n − 1 as a sensitivity check (`bias_analytical_neff`).\n- **Monte Carlo** (`bias_mc`): for each of R = 20000 replications, y_1 ~ N(0, σ²/(1−ρ²)), then y_t = 0.8 y_{t−1} + ε_t for t = 2…30 (c = 0). ρ̂ is the OLS slope of y_t on (1, y_{t−1}) for t = 2…30. One (R × n) standard-normal matrix is drawn from `numpy.random.default_rng(20261029)`. bias_mc = mean(ρ̂) − ρ; its MC standard error is sd(ρ̂)/√R (`bias_mc_se`). Baseline reference: the textbook asymptotic SE √((1−ρ²)/n) (`se_asymptotic`).\n- Checks: a statsmodels OLS fit reproduces the first replications exactly, and a clean re-run gives byte-identical output (`out/state/checks.md`).\n\n## Results\n| quantity | value | key |\n|---|---|---|\n| Analytical bias −(1+3ρ)/n | −0.1133 | `bias_analytical` |\n| MC bias | −0.1223 | `bias_mc` |\n| MC SE of bias | 0.00105 | `bias_mc_se` |\n| mean ρ̂ | 0.6777 | `rho_hat_mean` |\n| median ρ̂ | 0.6990 | `rho_hat_median` |\n| sd ρ̂ across replications | 0.1479 | `rho_hat_sd_mc` |\n| asymptotic SE √((1−ρ²)/n) | 0.1095 | `se_asymptotic` |\n| (bias_mc − bias_analytical)/SE | −8.61 | `discrepancy_se_units` |\n| MC bias / analytical bias | 1.079 | `bias_ratio_mc_to_analytical` |\n| analytical bias using n−1 = 29 | −0.1172 | `bias_analytical_neff` |\n| discrepancy vs n−1 version (SE units) | −4.88 | `discrepancy_se_units_neff` |\n\nInterpretation:\n- **Size and direction of the bias.** The OLS estimator is clearly biased downward. On average ρ̂ is about 0.68 rather than 0.8, a bias of −0.122 (`bias_mc`). That is larger than the asymptotic SE itself (`se_asymptotic` = 0.110). About 79% of the ρ̂ values fall below the true ρ (`share_rho_hat_below_rho`).\n- **How well the approximation does.** It gets the sign and most of the size right: the actual bias is about 8% larger than predicted (`bias_mc_ratio_mc_to_analytical` = 1.079).\n- **The gap is real, not simulation noise.** The difference is −8.6 MC standard errors (`discrepancy_se_units`). Even with n − 1 in the formula, the gap is still −4.9 SE (`discrepancy_se_units_neff`).\n- **Why the gap is expected.** A first-order O(1/n) approximation should leave a remainder of order 1/n². With n = 30 and ρ = 0.8, a remainder of about −0.009 is consistent with that. The gap is statistically significant but small in substantive terms. It does not show that the formula is \"wrong\"; it is the expected size of the higher-order terms.\n- **Spread of ρ̂.** The sampling sd of ρ̂ is 1.35 times the asymptotic SE (`sd_ratio_mc_to_asymptotic`). The distribution is left-skewed: its 2.5%–97.5% range is 0.331 to 0.902 (`rho_hat_q025`, `rho_hat_q975`). So first-order asymptotics also understate the dispersion at this design.\n\n## Uncertainty\nThe MC standard error of the bias is 0.00105 (`bias_mc_se`), giving a 95% interval for the true finite-sample bias of [−0.1244, −0.1203] (`bias_mc_ci95`). This interval excludes the analytical value −0.1133 (`bias_analytical`) and also its n−1 version −0.1172 (`bias_analytical_neff`). The analytical quantities are deterministic and have no sampling uncertainty. The results are exact for the fixed seed; a different seed would move `bias_mc` by roughly ±0.002 (2 × `bias_mc_se`).\n\n## Limitations and open issues\n- **What the analytical formula is.** −(1+3ρ)/n is a first-order asymptotic (large-n) approximation to the mean bias, with an O(n⁻²) remainder. It is accurate in the sense that its relative error vanishes as n grows. It carries no exact finite-sample guarantee, and its accuracy gets worse as ρ → 1 and as n gets smaller.\n- **What the Monte Carlo can establish.** It estimates the bias at exactly one design point: n = 30, ρ = 0.8, Gaussian errors, stationary start, intercept included, c = 0. It cannot establish:\n  - the approximation's accuracy at other (n, ρ) values;\n  - behaviour with non-Gaussian errors or non-stationary starting values;\n  - the general size of the higher-order terms.\n\n  Making such claims would need a grid of designs or analytical higher-order expansions, which this task did not require.\n- **Ambiguity in \"n\".** Whether n in the formula means the series length (30) or the number of regression pairs (29) is a matter of convention. I used 30 as the task specifies, and both versions are reported. Neither version falls within the MC confidence interval.\n- **Mean bias only.** The bias is a statement about the mean. Because the ρ̂ distribution is skewed, the median bias (`rho_hat_median` − 0.8 ≈ −0.10) differs from the mean bias.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"At n=30, rho=0.8 the OLS estimator of rho is downward biased; the Monte Carlo bias is about -0.122 with MC SE about 0.001.\",\"results_keys\":[\"bias_mc\",\"bias_mc_se\",\"rho_hat_mean\",\"bias_mc_ci95\"],\"status\":\"supported\",\"caveat\":\"Single design point; fixed seed.\"},\n {\"id\":\"C2\",\"text\":\"The Marriott-Pope/Kendall approximation -(1+3rho)/n = -0.113 captures the sign and roughly 93% of the magnitude of the bias (MC bias is ~8% larger).\",\"results_keys\":[\"bias_analytical\",\"bias_mc\",\"bias_ratio_mc_to_analytical\"],\"status\":\"supported\",\"caveat\":\"Evaluated with n = series length 30; with n-1=29 the formula gives -0.117.\"},\n {\"id\":\"C3\",\"text\":\"The discrepancy between MC and analytical bias is statistically significant (-8.6 MC SEs; -4.9 with n-1), consistent with an O(1/n^2) remainder of a first-order approximation rather than a failure of it.\",\"results_keys\":[\"discrepancy_se_units\",\"discrepancy_se_units_neff\",\"bias_mc_se\"],\"status\":\"supported\",\"caveat\":\"Attribution to higher-order terms is interpretive; the MC does not estimate those terms separately.\"},\n {\"id\":\"C4\",\"text\":\"The finite-sample bias exceeds the textbook asymptotic SE, and the MC sd of rho_hat is about 1.35 times the asymptotic SE.\",\"results_keys\":[\"bias_mc\",\"se_asymptotic\",\"rho_hat_sd_mc\",\"sd_ratio_mc_to_asymptotic\"],\"status\":\"supported\",\"caveat\":\"Specific to this design.\"},\n {\"id\":\"C5\",\"text\":\"The MC evidence does not establish the accuracy of the approximation at other (n, rho), error distributions or initial conditions.\",\"results_keys\":[\"design_n\",\"design_rho\"],\"status\":\"not_evaluated\",\"caveat\":\"Scope statement; only one design point was simulated.\"}\n]\nEOF\n~/wp29/venv/bin/python -c \"import json;json.load(open('out/claims.json'));print('ok')\"; ls out out/state","description":"Write report and claims"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1590,"cache_read_input_tokens":14334,"output_tokens":3528,"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":1590},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXr5sLgvrv49gQbos2p9","requestRef":"c1bfc293-69bc-4a88-bc01-f3c7679e0f2a","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6998780a-9fb3-412c-8737-9913d08ec8b4","timestamp":"2026-10-30T05:11:51.738Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}67{"parentUuid":"6998780a-9fb3-412c-8737-9913d08ec8b4","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01L67HyPipaUppcPgZA8Yd3M","type":"tool_result","content":"ok\nout:\nanalysis.py\nclaims.json\nexclusions.csv\nreport.md\nresults.json\nstate\n\nout/state:\nchecks.md\ncontract.md\ndata_audit.md\nlog.md\nphases.json","is_error":false}]},"uuid":"e523d17b-dab4-42dc-8dcf-c332ce7beb21","timestamp":"2026-10-30T05:11:51.798Z","toolUseResult":{"stdout":"ok\nout:\nanalysis.py\nclaims.json\nexclusions.csv\nreport.md\nresults.json\nstate\n\nout/state:\nchecks.md\ncontract.md\ndata_audit.md\nlog.md\nphases.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"6998780a-9fb3-412c-8737-9913d08ec8b4","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}68{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"0d320fbea3da14d59566d17b10bc030ffe8969666657209efd2e4f36fa80c105","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01L67HyPipaUppcPgZA8Yd3M","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-conf-02 — Finite-sample bias of OLS ρ̂ in a Gaussian AR(1)\n\n## Question\nIn the Gaussian AR(1) y_t = c + ρ y_{t−1} + ε_t, ε_t ~ N(0, σ²), OLS of y_t on (1, y_{t−1}) is biased downward in small samples. We compare the Marriott–Pope/Kendall approximation E[ρ̂] − ρ ≈ −(1+3ρ)/n with a Monte Carlo estimate of the actual bias at the design n = 30, ρ = 0.8 (`design_n`, `design_rho`).\n\n## Data and exclusions\nThe only input is `data/design.csv` (7 rows, `n_input_rows`; SHA-256 in `design_sha256`): n = 30, ρ = 0.8, σ = 1 (`design_sigma`), intercept included, stationary initial condition, R = 20000 replications (`n_replications`), seed 20261029 (`random_seed`). No data problems were found (`data_issues` is empty). One exclusion rule (drop replications with a non-finite ρ̂) removed 0 replications, so `n_analysed` = 20000 (`out/exclusions.csv`).\n\n## Method\n- **Analytical approximation** (`bias_analytical`): −(1+3ρ)/n with n = 30, the series length given in the design. This formula is the leading term of an asymptotic expansion of E[ρ̂] in powers of 1/n, derived for a stationary Gaussian AR(1) with an estimated mean/intercept. Its error is O(n⁻²), so it is accurate *as n → ∞* (relative error shrinks like 1/n). It is not an exact finite-sample result and gives no guarantee at any fixed n, especially when ρ is near 1, where higher-order terms are larger. Because the regression actually uses n − 1 = 29 pairs, and both n and n − 1 are consistent with the same first-order expansion, I also report the formula evaluated at n − 1 as a sensitivity check (`bias_analytical_neff`).\n- **Monte Carlo** (`bias_mc`): for each of R = 20000 replications, y_1 ~ N(0, σ²/(1−ρ²)), then y_t = 0.8 y_{t−1} + ε_t for t = 2…30 (c = 0). ρ̂ is the OLS slope of y_t on (1, y_{t−1}) for t = 2…30. One (R × n) standard-normal matrix is drawn from `numpy.random.default_rng(20261029)`. bias_mc = mean(ρ̂) − ρ; its MC standard error is sd(ρ̂)/√R (`bias_mc_se`). Baseline reference: the textbook asymptotic SE √((1−ρ²)/n) (`se_asymptotic`).\n- Checks: a statsmodels OLS fit reproduces the first replications exactly, and a clean re-run gives byte-identical output (`out/state/checks.md`).\n\n## Results\n| quantity | value | key |\n|---|---|---|\n| Analytical bias −(1+3ρ)/n | −0.1133 | `bias_analytical` |\n| MC bias | −0.1223 | `bias_mc` |\n| MC SE of bias | 0.00105 | `bias_mc_se` |\n| mean ρ̂ | 0.6777 | `rho_hat_mean` |\n| median ρ̂ | 0.6990 | `rho_hat_median` |\n| sd ρ̂ across replications | 0.1479 | `rho_hat_sd_mc` |\n| asymptotic SE √((1−ρ²)/n) | 0.1095 | `se_asymptotic` |\n| (bias_mc − bias_analytical)/SE | −8.61 | `discrepancy_se_units` |\n| MC bias / analytical bias | 1.079 | `bias_ratio_mc_to_analytical` |\n| analytical bias using n−1 = 29 | −0.1172 | `bias_analytical_neff` |\n| discrepancy vs n−1 version (SE units) | −4.88 | `discrepancy_se_units_neff` |\n\nInterpretation:\n- **Size and direction of the bias.** The OLS estimator is clearly biased downward. On average ρ̂ is about 0.68 rather than 0.8, a bias of −0.122 (`bias_mc`). That is larger than the asymptotic SE itself (`se_asymptotic` = 0.110). About 79% of the ρ̂ values fall below the true ρ (`share_rho_hat_below_rho`).\n- **How well the approximation does.** It gets the sign and most of the size right: the actual bias is about 8% larger than predicted (`bias_mc_ratio_mc_to_analytical` = 1.079).\n- **The gap is real, not simulation noise.** The difference is −8.6 MC standard errors (`discrepancy_se_units`). Even with n − 1 in the formula, the gap is still −4.9 SE (`discrepancy_se_units_neff`).\n- **Why the gap is expected.** A first-order O(1/n) approximation should leave a remainder of order 1/n². With n = 30 and ρ = 0.8, a remainder of about −0.009 is consistent with that. The gap is statistically significant but small in substantive terms. It does not show that the formula is \"wrong\"; it is the expected size of the higher-order terms.\n- **Spread of ρ̂.** The sampling sd of ρ̂ is 1.35 times the asymptotic SE (`sd_ratio_mc_to_asymptotic`). The distribution is left-skewed: its 2.5%–97.5% range is 0.331 to 0.902 (`rho_hat_q025`, `rho_hat_q975`). So first-order asymptotics also understate the dispersion at this design.\n\n## Uncertainty\nThe MC standard error of the bias is 0.00105 (`bias_mc_se`), giving a 95% interval for the true finite-sample bias of [−0.1244, −0.1203] (`bias_mc_ci95`). This interval excludes the analytical value −0.1133 (`bias_analytical`) and also its n−1 version −0.1172 (`bias_analytical_neff`). The analytical quantities are deterministic and have no sampling uncertainty. The results are exact for the fixed seed; a different seed would move `bias_mc` by roughly ±0.002 (2 × `bias_mc_se`).\n\n## Limitations and open issues\n- **What the analytical formula is.** −(1+3ρ)/n is a first-order asymptotic (large-n) approximation to the mean bias, with an O(n⁻²) remainder. It is accurate in the sense that its relative error vanishes as n grows. It carries no exact finite-sample guarantee, and its accuracy gets worse as ρ → 1 and as n gets smaller.\n- **What the Monte Carlo can establish.** It estimates the bias at exactly one design point: n = 30, ρ = 0.8, Gaussian errors, stationary start, intercept included, c = 0. It cannot establish:\n  - the approximation's accuracy at other (n, ρ) values;\n  - behaviour with non-Gaussian errors or non-stationary starting values;\n  - the general size of the higher-order terms.\n\n  Making such claims would need a grid of designs or analytical higher-order expansions, which this task did not require.\n- **Ambiguity in \"n\".** Whether n in the formula means the series length (30) or the number of regression pairs (29) is a matter of convention. I used 30 as the task specifies, and both versions are reported. Neither version falls within the MC confidence interval.\n- **Mean bias only.** The bias is a statement about the mean. Because the ρ̂ distribution is skewed, the median bias (`rho_hat_median` − 0.8 ≈ −0.10) differs from the mean bias.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"At n=30, rho=0.8 the OLS estimator of rho is downward biased; the Monte Carlo bias is about -0.122 with MC SE about 0.001.\",\"results_keys\":[\"bias_mc\",\"bias_mc_se\",\"rho_hat_mean\",\"bias_mc_ci95\"],\"status\":\"supported\",\"caveat\":\"Single design point; fixed seed.\"},\n {\"id\":\"C2\",\"text\":\"The Marriott-Pope/Kendall approximation -(1+3rho)/n = -0.113 captures the sign and roughly 93% of the magnitude of the bias (MC bias is ~8% larger).\",\"results_keys\":[\"bias_analytical\",\"bias_mc\",\"bias_ratio_mc_to_analytical\"],\"status\":\"supported\",\"caveat\":\"Evaluated with n = series length 30; with n-1=29 the formula gives -0.117.\"},\n {\"id\":\"C3\",\"text\":\"The discrepancy between MC and analytical bias is statistically significant (-8.6 MC SEs; -4.9 with n-1), consistent with an O(1/n^2) remainder of a first-order approximation rather than a failure of it.\",\"results_keys\":[\"discrepancy_se_units\",\"discrepancy_se_units_neff\",\"bias_mc_se\"],\"status\":\"supported\",\"caveat\":\"Attribution to higher-order terms is interpretive; the MC does not estimate those terms separately.\"},\n {\"id\":\"C4\",\"text\":\"The finite-sample bias exceeds the textbook asymptotic SE, and the MC sd of rho_hat is about 1.35 times the asymptotic SE.\",\"results_keys\":[\"bias_mc\",\"se_asymptotic\",\"rho_hat_sd_mc\",\"sd_ratio_mc_to_asymptotic\"],\"status\":\"supported\",\"caveat\":\"Specific to this design.\"},\n {\"id\":\"C5\",\"text\":\"The MC evidence does not establish the accuracy of the approximation at other (n, rho), error distributions or initial conditions.\",\"results_keys\":[\"design_n\",\"design_rho\"],\"status\":\"not_evaluated\",\"caveat\":\"Scope statement; only one design point was simulated.\"}\n]\nEOF\n~/wp29/venv/bin/python -c \"import json;json.load(open('out/claims.json'));print('ok')\"; ls out out/state","description":"Write report and claims"}}]}}69{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"df516eb7-8476-417a-a7a2-f21c05d27f6b","timestamp":"2026-10-30T05:11:51.802Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"c1bfc293-69bc-4a88-bc01-f3c7679e0f2a","keep":22,"tail":["0d320fbea3da14d59566d17b10bc030ffe8969666657209efd2e4f36fa80c105","7ce52889ca0ba4027eb8b0c2574b483bf79fc626b4f6d56b42dbc0f841d40b3e"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",23,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"4b508732111ea842dc03a832c470b7a313158105d7bf45240e57257730c0f877"}70{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"e523d17b-dab4-42dc-8dcf-c332ce7beb21","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}71{"type":"atis-latch","atis":"","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}72{"type":"tools-used","tools":["Bash","Edit"],"sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}73{"parentUuid":"e523d17b-dab4-42dc-8dcf-c332ce7beb21","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr81xAUmiCCrSoJyDr8","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":3598,"cache_read_input_tokens":15924,"output_tokens":216,"output_tokens_details":{"thinking_tokens":55},"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":3598},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":438,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXr81gHnkVp4usM38JZV","requestRef":"df516eb7-8476-417a-a7a2-f21c05d27f6b","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f3f738f4-6e64-4eab-8f6b-6fa0bfce36e2","timestamp":"2026-10-30T05:11:53.299Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}74{"parentUuid":"f3f738f4-6e64-4eab-8f6b-6fa0bfce36e2","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr81xAUmiCCrSoJyDr8","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01TTLFL1V3R3T3uYECuuoYna","name":"Edit","input":{"replace_all":false,"file_path":"/Users/simon-pierreboucher/wp29/runs/RC0242/out/report.md","old_string":"`bias_mc_ratio_mc_to_analytical`","new_string":"`bias_ratio_mc_to_analytical`"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":3598,"cache_read_input_tokens":15924,"output_tokens":216,"output_tokens_details":{"thinking_tokens":55},"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":3598},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXr81gHnkVp4usM38JZV","requestRef":"df516eb7-8476-417a-a7a2-f21c05d27f6b","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"a575ef7b-b39c-4fcb-a871-529b0df4b629","timestamp":"2026-10-30T05:11:54.056Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}75{"parentUuid":"a575ef7b-b39c-4fcb-a871-529b0df4b629","isSidechain":false,"promptId":"b9094fd4-39ac-49a4-89d7-67ac863db877","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01TTLFL1V3R3T3uYECuuoYna","type":"tool_result","content":"The file /Users/simon-pierreboucher/wp29/runs/RC0242/out/report.md has been updated successfully."}]},"uuid":"b9038123-9b62-4bdf-987c-36cf9687a470","timestamp":"2026-10-30T05:11:54.066Z","toolUseResult":{"filePath":"/Users/simon-pierreboucher/wp29/runs/RC0242/out/report.md","oldString":"`bias_mc_ratio_mc_to_analytical`","newString":"`bias_ratio_mc_to_analytical`","originalFile":"# F5-conf-02 — Finite-sample bias of OLS ρ̂ in a Gaussian AR(1)\n\n## Question\nIn the Gaussian AR(1) y_t = c + ρ y_{t−1} + ε_t, ε_t ~ N(0, σ²), OLS of y_t on (1, y_{t−1}) is biased downward in small samples. We compare the Marriott–Pope/Kendall approximation E[ρ̂] − ρ ≈ −(1+3ρ)/n with a Monte Carlo estimate of the actual bias at the design n = 30, ρ = 0.8 (`design_n`, `design_rho`).\n\n## Data and exclusions\nThe only input is `data/design.csv` (7 rows, `n_input_rows`; SHA-256 in `design_sha256`): n = 30, ρ = 0.8, σ = 1 (`design_sigma`), intercept included, stationary initial condition, R = 20000 replications (`n_replications`), seed 20261029 (`random_seed`). No data problems were found (`data_issues` is empty). One exclusion rule (drop replications with a non-finite ρ̂) removed 0 replications, so `n_analysed` = 20000 (`out/exclusions.csv`).\n\n## Method\n- **Analytical approximation** (`bias_analytical`): −(1+3ρ)/n with n = 30, the series length given in the design. This formula is the leading term of an asymptotic expansion of E[ρ̂] in powers of 1/n, derived for a stationary Gaussian AR(1) with an estimated mean/intercept. Its error is O(n⁻²), so it is accurate *as n → ∞* (relative error shrinks like 1/n). It is not an exact finite-sample result and gives no guarantee at any fixed n, especially when ρ is near 1, where higher-order terms are larger. Because the regression actually uses n − 1 = 29 pairs, and both n and n − 1 are consistent with the same first-order expansion, I also report the formula evaluated at n − 1 as a sensitivity check (`bias_analytical_neff`).\n- **Monte Carlo** (`bias_mc`): for each of R = 20000 replications, y_1 ~ N(0, σ²/(1−ρ²)), then y_t = 0.8 y_{t−1} + ε_t for t = 2…30 (c = 0). ρ̂ is the OLS slope of y_t on (1, y_{t−1}) for t = 2…30. One (R × n) standard-normal matrix is drawn from `numpy.random.default_rng(20261029)`. bias_mc = mean(ρ̂) − ρ; its MC standard error is sd(ρ̂)/√R (`bias_mc_se`). Baseline reference: the textbook asymptotic SE √((1−ρ²)/n) (`se_asymptotic`).\n- Checks: a statsmodels OLS fit reproduces the first replications exactly, and a clean re-run gives byte-identical output (`out/state/checks.md`).\n\n## Results\n| quantity | value | key |\n|---|---|---|\n| Analytical bias −(1+3ρ)/n | −0.1133 | `bias_analytical` |\n| MC bias | −0.1223 | `bias_mc` |\n| MC SE of bias | 0.00105 | `bias_mc_se` |\n| mean ρ̂ | 0.6777 | `rho_hat_mean` |\n| median ρ̂ | 0.6990 | `rho_hat_median` |\n| sd ρ̂ across replications | 0.1479 | `rho_hat_sd_mc` |\n| asymptotic SE √((1−ρ²)/n) | 0.1095 | `se_asymptotic` |\n| (bias_mc − bias_analytical)/SE | −8.61 | `discrepancy_se_units` |\n| MC bias / analytical bias | 1.079 | `bias_ratio_mc_to_analytical` |\n| analytical bias using n−1 = 29 | −0.1172 | `bias_analytical_neff` |\n| discrepancy vs n−1 version (SE units) | −4.88 | `discrepancy_se_units_neff` |\n\nInterpretation:\n- **Size and direction of the bias.** The OLS estimator is clearly biased downward. On average ρ̂ is about 0.68 rather than 0.8, a bias of −0.122 (`bias_mc`). That is larger than the asymptotic SE itself (`se_asymptotic` = 0.110). About 79% of the ρ̂ values fall below the true ρ (`share_rho_hat_below_rho`).\n- **How well the approximation does.** It gets the sign and most of the size right: the actual bias is about 8% larger than predicted (`bias_mc_ratio_mc_to_analytical` = 1.079).\n- **The gap is real, not simulation noise.** The difference is −8.6 MC standard errors (`discrepancy_se_units`). Even with n − 1 in the formula, the gap is still −4.9 SE (`discrepancy_se_units_neff`).\n- **Why the gap is expected.** A first-order O(1/n) approximation should leave a remainder of order 1/n². With n = 30 and ρ = 0.8, a remainder of about −0.009 is consistent with that. The gap is statistically significant but small in substantive terms. It does not show that the formula is \"wrong\"; it is the expected size of the higher-order terms.\n- **Spread of ρ̂.** The sampling sd of ρ̂ is 1.35 times the asymptotic SE (`sd_ratio_mc_to_asymptotic`). The distribution is left-skewed: its 2.5%–97.5% range is 0.331 to 0.902 (`rho_hat_q025`, `rho_hat_q975`). So first-order asymptotics also understate the dispersion at this design.\n\n## Uncertainty\nThe MC standard error of the bias is 0.00105 (`bias_mc_se`), giving a 95% interval for the true finite-sample bias of [−0.1244, −0.1203] (`bias_mc_ci95`). This interval excludes the analytical value −0.1133 (`bias_analytical`) and also its n−1 version −0.1172 (`bias_analytical_neff`). The analytical quantities are deterministic and have no sampling uncertainty. The results are exact for the fixed seed; a different seed would move `bias_mc` by roughly ±0.002 (2 × `bias_mc_se`).\n\n## Limitations and open issues\n- **What the analytical formula is.** −(1+3ρ)/n is a first-order asymptotic (large-n) approximation to the mean bias, with an O(n⁻²) remainder. It is accurate in the sense that its relative error vanishes as n grows. It carries no exact finite-sample guarantee, and its accuracy gets worse as ρ → 1 and as n gets smaller.\n- **What the Monte Carlo can establish.** It estimates the bias at exactly one design point: n = 30, ρ = 0.8, Gaussian errors, stationary start, intercept included, c = 0. It cannot establish:\n  - the approximation's accuracy at other (n, ρ) values;\n  - behaviour with non-Gaussian errors or non-stationary starting values;\n  - the general size of the higher-order terms.\n\n  Making such claims would need a grid of designs or analytical higher-order expansions, which this task did not require.\n- **Ambiguity in \"n\".** Whether n in the formula means the series length (30) or the number of regression pairs (29) is a matter of convention. I used 30 as the task specifies, and both versions are reported. Neither version falls within the MC confidence interval.\n- **Mean bias only.** The bias is a statement about the mean. Because the ρ̂ distribution is skewed, the median bias (`rho_hat_median` − 0.8 ≈ −0.10) differs from the mean bias.\n","structuredPatch":[{"oldStart":28,"oldLines":7,"newStart":28,"newLines":7,"lines":[" "," Interpretation:"," - **Size and direction of the bias.** The OLS estimator is clearly biased downward. On average ρ̂ is about 0.68 rather than 0.8, a bias of −0.122 (`bias_mc`). That is larger than the asymptotic SE itself (`se_asymptotic` = 0.110). About 79% of the ρ̂ values fall below the true ρ (`share_rho_hat_below_rho`).","-- **How well the approximation does.** It gets the sign and most of the size right: the actual bias is about 8% larger than predicted (`bias_mc_ratio_mc_to_analytical` = 1.079).","+- **How well the approximation does.** It gets the sign and most of the size right: the actual bias is about 8% larger than predicted (`bias_ratio_mc_to_analytical` = 1.079)."," - **The gap is real, not simulation noise.** The difference is −8.6 MC standard errors (`discrepancy_se_units`). Even with n − 1 in the formula, the gap is still −4.9 SE (`discrepancy_se_units_neff`)."," - **Why the gap is expected.** A first-order O(1/n) approximation should leave a remainder of order 1/n². With n = 30 and ρ = 0.8, a remainder of about −0.009 is consistent with that. The gap is statistically significant but small in substantive terms. It does not show that the formula is \"wrong\"; it is the expected size of the higher-order terms."," - **Spread of ρ̂.** The sampling sd of ρ̂ is 1.35 times the asymptotic SE (`sd_ratio_mc_to_asymptotic`). The distribution is left-skewed: its 2.5%–97.5% range is 0.331 to 0.902 (`rho_hat_q025`, `rho_hat_q975`). So first-order asymptotics also understate the dispersion at this design."]}],"userModified":false,"replaceAll":false,"contentNotInModelContext":true},"sourceToolAssistantUUID":"a575ef7b-b39c-4fcb-a871-529b0df4b629","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}76{"type":"api-request-blob","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","hash":"92ef9d1609d0aee101f4307170262f931dc5443ad5815f7ffb5dee9dbe2b92b4","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQSkAcKEAgTGAI4AUIIdGhpbmtpbmcSDDRXGzONdK5DG2QBzBoMZ15DewifUQIaJ/eOIjBUxgU3mQK251ka+wUYjvblP7598S0gNDCT2CyNMBkviInq9I6uGZ6K6Fm53pBmrmMqrQZM7ugqalBlA88oe9jWxp+hlP0BJpRl/bQ27Qi2jUkXXqOPVzUNx/vzH4bfaKrM3TgLXD1cEfks6X1Jp7NTpk0HmtlBCzm+qzbJR4bHq6Cg9MwdMZskNz8j+tF44ZVsqu7i2viSQQZ4Nl+oKwN/aTv6H3XOoOy3M/Q4nh1Y0whfWKocrmWYZEM3d5QnJFmwGq08k46d7/MG7mrV0KbvWQnNJehgziXrgvC5xcYJTkBqWtnV6TM44msK3kc4muqyTW1Cyxe8s0LQMifMN9lxLGNU3M60IROEwREx40DuXUMFHTXCuilz4P4cZl94/fJZRw50urIizLaJFQi26NXuYmnQNFYyM/lrleYgqfwMo7q32Ekmmq+DOVZ7BcAS9h0cTiFcUcMaL+icEx7I5bRMS5Upj1TG8r2Vv9elmRp7enjiR4Mu8dSZWTiybM9H31QxqkNyR58bX5s0EmMvTSp3EODleK0dO4HI6mFIY7mnCB64W4Ei4XynA8ksMw0QPyWjJZNTwcVSavqLzouAWf66SyhvLCHI9MSbfeIKS1181eNpKZ9pQCkp7y7YGr7V9K6iOLSYhM1uITMcTTJJTRsmeCZ/9vigQ6Mfs/2qGnXWpAMRZUE7/iYqaJhj2Numb/Uq1WYS48sPa/NT6w8mHQt+aNrShxU1J1G9QEAP9nNM3ikywJ4ipYa7i1oONsgB2HRdKaL7PQ4V/U0KWnhqBL1dfTAVFEzGkt2qJzZFbf3cje5OUlLFOImZF21cVXBizSEWzJLUGRZ3S1lGIaA09u41dZsoDd7eSH1vEy4SwZk39WUgaRT+ZwgSCqgiK+H94NO5yifLIzn8R0Xf7J+x9JHVhMAOqEZthItuMnqknwvHpap4MmvtrtiPVWhMp3M6TwD0swscU25ROs7m/tn7KtQa0cuGKDKCViqid3NkMmN8Uqspe1TJeGPdsfs5fHpRhlw6VRc5nzN5z7exWKNi+zMzISDP3yBC6nl6aDvGF/6wucD/vMB4z8jqIhV40Y4NW654+q+HX1J4Y3Q6ibhi5z5DmZIj937aHTJTOa8h+su54HVhh5XBPgbPW3Z+s+9PESkYAQ=="},{"type":"tool_use","id":"toolu_01TTLFL1V3R3T3uYECuuoYna","name":"Edit","input":{"replace_all":false,"file_path":"/Users/simon-pierreboucher/wp29/runs/RC0242/out/report.md","old_string":"`bias_mc_ratio_mc_to_analytical`","new_string":"`bias_ratio_mc_to_analytical`"}}]}}77{"type":"api-request","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","id":"72f90425-edad-4105-88b0-463078880160","timestamp":"2026-10-30T05:11:54.069Z","version":"2.1.314","querySource":"sdk","shapeHash":"b17acbadd5ddddfa07657e0246e2d83ff535761396f92210a9c7ece69f1a31ab","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":"df516eb7-8476-417a-a7a2-f21c05d27f6b","keep":24,"tail":["92ef9d1609d0aee101f4307170262f931dc5443ad5815f7ffb5dee9dbe2b92b4","cfa3ff67a15baad2d1c8578f3b857f8491c5a129af14f498e5cb406ad1f9bfee"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",25,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"88f9b86b21863fcfa2a842673fbe53da005b4f6d259f0f72021521a9dfb50721"}78{"parentUuid":"b9038123-9b62-4bdf-987c-36cf9687a470","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr8BgYoNafNtK2esGin","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQS2wYKEAgTGAI4AUIIdGhpbmtpbmcSDIhiZWBitVxvEOOdahoMRjFxZzpT78fl9Op8IjAHG6vVyOws4n+e2W8Uo5zMHegFUi3MDT0qF+w3jjJ21Cxu6VcBCn+Zb++BZoeV8X8q+AV1T5fBTYSgIiLPeOJuGYYuI5mVvGx2CXFiiOBtcKNIgwYrFt/Ns03nXco7rxPegCPfcl93CcKmKR5t5fUxAwn3AjjBcbDYsx4MN/Q1i+KMxbsc/wlCMm3Gew6XW0DbY7eL8lOGMpbcEAoL72PBzfdDLWFDfcFHoR4awrT7Paijb90bpQCeufAeNADFKuvluQBw1YFVspz+9O6SFJN/2QRE6X+ZbqaugixOKT4Im/933t1HOGIIofkPstkXpYAOcy0eE28S7JiLiWcyljxI/csayHXDO3lw4i/cjZRg300wuTzEF+MwY7ytJAfbVhRLVIVrImNCkvAubmLiKKCkM2RzePmWiAyhSEUIUJZRU/9GMIyAJUrAkhfycSlU0MkZYZgYEGztNKw3cwxWATgXFq9btcuRmXBXACmjBiEmb20KjSa7BEeYc/qJEAgpmnwmrAtMsgqLQlrpjMbjapyQXktGj+P2KnagBIOmXlseCfef8dr8QuNVC9jSoV0G4DjdID4q4Xl9mmY1ATGT8Ba3o4FoFA/KUw0gXhRxeLMLKMbodAeSWgttNAqDOcydkLhrJ3XoJUMZpLujcSazCqkq7bpphVXSS6xKTQF74EFL6KTEM+tZXIkE/POx2zNmOdKCPcm7VAVqrtHFOils41b+6ljBOWkT96qeLu9Z4TjoCzSphMXxSwzPylZGhZiAuDYQ+SLGdmTuTLDPv564hQD2D6oISk1+uFIEVIMApBhEJdg+DaAjaKKynuqR/rVOPCl0I/Xfo2gRgAGs32BD2GpSceAgrjj//NBugUoRCqqfClfI0yJcrsHNKrZZfGW1S9GItbuwzQBP0udpk8wuX1HOqUej3pCOmWD/xqRtgO+8Ncjy5q5ejKiaiCt5Jq6EdiqKhxary7m70EC8Kg65B3P33sSVn7nQpE/tPrQhb8pTv2pGXQflo2EsQN5LM7RZZvW8ZorqqVbAZMAjQGllP2//uvDavgBaxi+sTrXhNFiS1L86SIOBLEhiz4j9GAE="}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":286,"cache_read_input_tokens":19522,"output_tokens":893,"output_tokens_details":{"thinking_tokens":41},"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":286},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":6874,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXr8BPgrh41Jh33o58uX","requestRef":"72f90425-edad-4105-88b0-463078880160","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"aaba2ec6-679f-4213-ac66-dff484dd6552","timestamp":"2026-10-30T05:12:02.103Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}79{"parentUuid":"aaba2ec6-679f-4213-ac66-dff484dd6552","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXr8BgYoNafNtK2esGin","type":"message","role":"assistant","content":[{"type":"text","text":"I ran the simulation: the OLS estimate of ρ is clearly biased downward, and the textbook approximation gets about 93% of that bias right. The remaining gap is real, not simulation noise. All required files are written and every protocol phase (P0–P5) is marked passed with its checks recorded.\n\n**Design:** series length 30, true ρ = 0.8, 20,000 simulated series, seed 20261029. No replications were dropped.\n\n| Quantity | Value |\n|---|---|\n| Approximation −(1+3ρ)/n | −0.1133 |\n| Simulated bias | −0.1223 |\n| Simulation standard error (SE) of that bias | 0.00105 |\n| 95% interval for the true bias | −0.1244 to −0.1203 |\n| Average estimate of ρ | 0.678 |\n| Spread (sd) of the estimates | 0.148 |\n| Textbook large-sample SE √((1−ρ²)/n) | 0.110 |\n\n- **The gap:** the actual bias is about 8% larger than the approximation predicts, which is −8.6 simulation SEs away. The approximation is a large-sample formula whose error shrinks like 1/n², and a leftover of about −0.009 at n = 30 is the expected size for that. So the gap is statistically significant but small in practice; it doesn't show the formula is wrong.\n- **Size relative to sampling error:** the bias is larger than the textbook SE itself. The estimates are also 1.35 times more spread out than that SE suggests, and skewed to the left.\n- **What \"n\" means:** the formula doesn't say whether n is the series length (30) or the number of regression pairs (29). I used 30 as the task specifies; with 29 the formula gives −0.117, still 4.9 SEs from the simulated bias and outside the interval.\n\n**Checks:** a clean re-run reproduced `results.json` byte for byte. An independent statsmodels regression on the first three simulated series gave the same estimates. The arithmetic identities (bias = mean − ρ, SE = sd/√R, interval contains the estimate, counts add up) all hold.\n\n**Limitation:** this is one design point (n = 30, ρ = 0.8, normal errors, stationary start). It says nothing about how accurate the approximation is at other sample sizes or values of ρ, which the report states explicitly.\n\nFiles are in `out/`:\n- `results.json`\n- `report.md`\n- `analysis.py`\n- `claims.json`\n- `exclusions.csv`\n- `state/` (contract, data audit, checks, phase ledger, log)"}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":286,"cache_read_input_tokens":19522,"output_tokens":893,"output_tokens_details":{"thinking_tokens":41},"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":286},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXr8BPgrh41Jh33o58uX","requestRef":"72f90425-edad-4105-88b0-463078880160","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"8a271b06-2f15-454b-a865-aca1c9065652","timestamp":"2026-10-30T05:12:02.888Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0242","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","version":"2.1.314","gitBranch":"HEAD"}80{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"8a271b06-2f15-454b-a865-aca1c9065652","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa"}81{"type":"cost-state","sessionId":"04b82eb8-a19e-4c40-b544-bb7c254295aa","totalCostUSD":0.3887524,"totalAPIDuration":112440,"totalAPIDurationWithoutRetries":112433,"totalToolDuration":2919,"totalLinesAdded":1,"totalLinesRemoved":1,"totalDuration":115551,"startTime":1793337007346,"modelUsage":{"claude-opus-5-5":{"inputTokens":28,"outputTokens":13512,"thinkingTokens":675,"cacheReadInputTokens":134402,"cacheCreationInputTokens":18304,"cacheCreationEphemeral5mInputTokens":18304,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.3887524}},"hasUnknownModelCost":false}82