1{"type":"atis-latch","atis":"","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b"}2{"type":"queue-operation","operation":"enqueue","timestamp":"2026-10-30T04:52:47.970Z","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","content":"Begin"}3{"type":"queue-operation","operation":"dequeue","timestamp":"2026-10-30T04:52:47.976Z","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b"}4{"parentUuid":null,"isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":"Begin"},"uuid":"ca65b50b-4860-4848-8310-85ed525ecddc","timestamp":"2026-10-30T04:52:47.980Z","permissionMode":"default","promptSource":"sdk","turnOrigin":"sdk","turnPosition":{"promptIndex":0,"turnIndex":1},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}5{"type":"api-request-shape","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","timestamp":"2026-10-30T04:52:47.994Z","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/RC0181\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":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"d43ab0e0b8ec9db790a6459cb2f4bc4ffce02825ca05063162023be60912ced9","message":{"role":"system","content":[],"output_config":{"effort":"medium"}}}7{"type":"api-request","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","id":"27fe825e-2e0c-442e-974f-dde8b3ae5275","timestamp":"2026-10-30T04:52:47.994Z","version":"2.1.314","querySource":"sdk","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","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":"bd03d7b5b55004217f6d04b9c3599261168f95b774be101ee14d86c3fd3acd03"}8{"parentUuid":"ca65b50b-4860-4848-8310-85ed525ecddc","isSidechain":false,"attachment":{"type":"session_context","context":{}},"type":"attachment","uuid":"d78b0cee-8d3e-44dc-a86a-a472e4316716","timestamp":"2026-10-30T04:52:47.985Z","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}9{"parentUuid":"d78b0cee-8d3e-44dc-a86a-a472e4316716","isSidechain":false,"attachment":{"type":"date","date":"2026-10-30"},"type":"attachment","uuid":"ac9bd693-f18f-4368-b728-fcfae48a8002","timestamp":"2026-10-30T04:52:47.985Z","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/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}10{"parentUuid":"ac9bd693-f18f-4368-b728-fcfae48a8002","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":"82ba7b28-777d-4162-bc23-422139d54a0a","timestamp":"2026-10-30T04:52:47.986Z","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/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b"}12{"parentUuid":"82ba7b28-777d-4162-bc23-422139d54a0a","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpfjsh1WbWaWR8gT9ye","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQSpAUKEAgTGAI4AUIIdGhpbmtpbmcSDHzv7uGi3Qw52b2DBhoMmpiltH6XGe2eMZzRIjD52JwRaSowYv+ESV0KR+FpiiATcEvXwv9d9RSWPk7U8ocxPUJ/6RnA63Bshn3r884qwQTPxHU1Fu/zsVjvR9HTFtetSy/c+J54j238b0hH5jBxXE+rL6V+rebyLLQcT10fNQoy/VLrCACmvDctHyiKJ32zi4iDK+vPwHzVxZ/NIwQk98TUSdABCQBJPArIREH1JLcmDrVU2nWA9xz/YzoV+9lP9DipNegrh/ZDotsc9OAXFGymeGdkzTPOASGvxSaPtw4mx073BcyQPJ68sRcwkA3Edknyj97ODIABncVgDBJCY2rp73EHGU53NAJqusu4gyxywN0R5xz/7Q0nojZxsZNM0FDaB/kqcADrQtWPujG6v5PdirYofHFaf1iKf/mbRQ2AnfRmrXzDlI+QbYBv+8dj1dKDhk578vGXvGu6zm39GnHJcWt+L2JENTgjr8PDrDJoteWt1rg7LsCBBgPT1uSIFOuPHbnmpyeuBfr11EqJf1VsDp1rnRKSZqQXtHMCqz8UXgDyrlhQtKXDPU+bj/IDP7Hp4Ue3m3PlycJ4dIZUt7Lluv+NhyNQ8XAcytEE8Vh5HyWGO6uiXyv+S/PiDvKyJaLF79OuRF2W7JwOSRNmwq27P5MPExdU2+NxkLAwwXdgpjfNeb+WM6kBHwliRW19qrx1rYPwZK6qtC5gkSKCVLUrJb4snuxtmk6wBqerGZnJ0CyMN//KPHcJTlHVsZc2vJiQoSZNATPKAbWF5JLwR3ntadMfFJUtVDSkJ8UaE+EmzSOaQXYpI8ZuOdwGzOqQAxd/nM2duOgb0Ogy0SdrjxhdwsEINOZmpr335zTTWNcXGAE="}],"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":131,"output_tokens_details":{"thinking_tokens":22},"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":393,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXpfjgXmSQPAxCTjiCtZ","requestRef":"27fe825e-2e0c-442e-974f-dde8b3ae5275","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"d4a7b557-15f5-4ba2-9e62-6ac3452077ce","timestamp":"2026-10-30T04:52:49.957Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"d4a7b557-15f5-4ba2-9e62-6ac3452077ce","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpfjsh1WbWaWR8gT9ye","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01VioKGHkwnBem8Who8BxdAZ","name":"Bash","input":{"command":"cat TASK.md; ls -R; ls out/state 2>/dev/null && cat out/state/*","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":131,"output_tokens_details":{"thinking_tokens":22},"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_011CgXpfjgXmSQPAxCTjiCtZ","requestRef":"27fe825e-2e0c-442e-974f-dde8b3ae5275","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"67e6475a-fcfb-476c-891d-fff7a1d8b60b","timestamp":"2026-10-30T04:52:50.676Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}14{"parentUuid":"67e6475a-fcfb-476c-891d-fff7a1d8b60b","isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 1\n# F5-conf-03 — Prove or refute: sums of normally distributed random variables\n\n## Scientific question\nTwo propositions about sums of normal random variables are given in `data/propositions.csv`. For each proposition, decide whether it is true (give a proof sketch) or false (give an explicit counterexample). For a false proposition, the counterexample must be made concrete: specify the joint construction of (X, Y), and produce a simulated sample from it that illustrates numerically that the marginals are normal while the sum is not (choose a construction whose departure from normality is clearly visible at the design sample size). The estimands are the truth values of propositions A and B and, for a false proposition, a verifiable counterexample.\n\n## Inputs\n- `data/propositions.csv` — columns `id`, `statement`: the two propositions (A and B) to assess.\n- `data/design.csv` — columns `parameter`, `value`, `description`: the random `seed` to use (`numpy.random.default_rng`) and the sample size `n` for the numerical illustration.\n\n## Information-availability rules\n- Use only the files under `data/`. The verdicts must rest on mathematical argument; the simulation is an illustration and a numerical check, not the proof.\n- Follow the design (seed, n) for the simulated sample.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F5-conf-03\" |\n| `statement_true` | boolean | — | verdict on proposition A |\n| `counterexample_provided` | boolean | — | true if a concrete counterexample to A is provided in `out/argument.md`, `out/analysis.py` and `out/counterexample.csv` |\n| `counterexample_values` | object | — | summary of the simulated counterexample sample: `construction` (string describing the joint law of (X, Y)), `n` (rows in `out/counterexample.csv`), `seed`, `mean_x`, `sd_x`, `mean_y`, `sd_y`, `mean_sum`, `sd_sum` (sample means and sample standard deviations, ddof = 1, of x, y and x + y), and `ks_sum_vs_normal` (Kolmogorov–Smirnov distance between the empirical distribution of x + y and the normal distribution with the sample mean and sample sd of x + y). If no counterexample is provided, an empty object. |\n| `statement_b_true` | boolean | — | verdict on proposition B (the baseline check) |\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 | — | {\"propositions.csv\": rows read, \"design.csv\": rows read} |\n| `n_analysed` | integer or null | — | sample size of the simulated counterexample sample |\n| `random_seed` | integer or null | — | seed used |\n\n- `out/counterexample.csv` — columns `x`, `y`: the simulated sample of size n from the counterexample construction (only if a counterexample is provided).\n- `out/argument.md` — the mathematical argument: the proof sketch for the true proposition(s) and the explicit counterexample (with the reasoning that its marginals are normal and its sum is not) for the false proposition(s).\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. State explicitly what the numerical illustration establishes and what it does not.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` and `out/counterexample.csv` from `data/` only, deterministically.\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}].\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.\nbundle.json\ndata\ngate_spec.json\nTASK.md\n\n./data:\ndesign.csv\npropositions.csv","is_error":true,"tool_use_id":"toolu_01VioKGHkwnBem8Who8BxdAZ"}]},"uuid":"b7d4faf6-91a5-4e81-b5e4-51ecdd8f308a","timestamp":"2026-10-30T04:52:50.792Z","toolUseResult":"Error: Exit code 1\n# F5-conf-03 — Prove or refute: sums of normally distributed random variables\n\n## Scientific question\nTwo propositions about sums of normal random variables are given in `data/propositions.csv`. For each proposition, decide whether it is true (give a proof sketch) or false (give an explicit counterexample). For a false proposition, the counterexample must be made concrete: specify the joint construction of (X, Y), and produce a simulated sample from it that illustrates numerically that the marginals are normal while the sum is not (choose a construction whose departure from normality is clearly visible at the design sample size). The estimands are the truth values of propositions A and B and, for a false proposition, a verifiable counterexample.\n\n## Inputs\n- `data/propositions.csv` — columns `id`, `statement`: the two propositions (A and B) to assess.\n- `data/design.csv` — columns `parameter`, `value`, `description`: the random `seed` to use (`numpy.random.default_rng`) and the sample size `n` for the numerical illustration.\n\n## Information-availability rules\n- Use only the files under `data/`. The verdicts must rest on mathematical argument; the simulation is an illustration and a numerical check, not the proof.\n- Follow the design (seed, n) for the simulated sample.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F5-conf-03\" |\n| `statement_true` | boolean | — | verdict on proposition A |\n| `counterexample_provided` | boolean | — | true if a concrete counterexample to A is provided in `out/argument.md`, `out/analysis.py` and `out/counterexample.csv` |\n| `counterexample_values` | object | — | summary of the simulated counterexample sample: `construction` (string describing the joint law of (X, Y)), `n` (rows in `out/counterexample.csv`), `seed`, `mean_x`, `sd_x`, `mean_y`, `sd_y`, `mean_sum`, `sd_sum` (sample means and sample standard deviations, ddof = 1, of x, y and x + y), and `ks_sum_vs_normal` (Kolmogorov–Smirnov distance between the empirical distribution of x + y and the normal distribution with the sample mean and sample sd of x + y). If no counterexample is provided, an empty object. |\n| `statement_b_true` | boolean | — | verdict on proposition B (the baseline check) |\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 | — | {\"propositions.csv\": rows read, \"design.csv\": rows read} |\n| `n_analysed` | integer or null | — | sample size of the simulated counterexample sample |\n| `random_seed` | integer or null | — | seed used |\n\n- `out/counterexample.csv` — columns `x`, `y`: the simulated sample of size n from the counterexample construction (only if a counterexample is provided).\n- `out/argument.md` — the mathematical argument: the proof sketch for the true proposition(s) and the explicit counterexample (with the reasoning that its marginals are normal and its sum is not) for the false proposition(s).\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. State explicitly what the numerical illustration establishes and what it does not.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` and `out/counterexample.csv` from `data/` only, deterministically.\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}].\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.\nbundle.json\ndata\ngate_spec.json\nTASK.md\n\n./data:\ndesign.csv\npropositions.csv","sandboxed":false,"sourceToolAssistantUUID":"67e6475a-fcfb-476c-891d-fff7a1d8b60b","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}15{"type":"api-request-blob","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"69b176b3a870a7937e1838def25177d56dbe11fe1419f512c8a87b6e4f867f95","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01VioKGHkwnBem8Who8BxdAZ","name":"Bash","input":{"command":"cat TASK.md; ls -R; ls out/state 2>/dev/null && cat out/state/*","description":"Read task and list workspace"}}]}}16{"type":"api-request","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","id":"4f1082a6-ff6f-4d63-b902-62fb0742de11","timestamp":"2026-10-30T04:52:50.797Z","version":"2.1.314","querySource":"sdk","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","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":"27fe825e-2e0c-442e-974f-dde8b3ae5275","keep":2,"tail":["69b176b3a870a7937e1838def25177d56dbe11fe1419f512c8a87b6e4f867f95","8a4ff6c2cf07b817820f91a74805998cdb94be0fbb256a8d91c9c9f97f4cf397"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",3,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"30154d163bf98380883b8dcc3ba5312add780fbb277cc9f79f3b6696d831fc26"}17{"parentUuid":"b7d4faf6-91a5-4e81-b5e4-51ecdd8f308a","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpfud4uhaBo6WcS11wP","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01EmtP7rQ5GDRjfiFEukqDwQ","name":"Bash","input":{"command":"cat data/*.csv; cat bundle.json gate_spec.json | head -50; shasum -a 256 data/*","description":"Show data files and hashes"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1642,"cache_read_input_tokens":3713,"output_tokens":113,"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":1642},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXpfuLhZrnZPhzrzFELo","requestRef":"4f1082a6-ff6f-4d63-b902-62fb0742de11","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"0526849f-89dc-43f8-9b54-e677a06568a6","timestamp":"2026-10-30T04:52:54.553Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}18{"parentUuid":"0526849f-89dc-43f8-9b54-e677a06568a6","isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01EmtP7rQ5GDRjfiFEukqDwQ","type":"tool_result","content":"parameter,value,description\nseed,20261029,random seed for any simulation (numpy default_rng)\nn,100000,sample size for the numerical illustration (rows of out/counterexample.csv)\nid,statement\nA,\"If X and Y are each normally distributed random variables, then X + Y is normally distributed (a degenerate normal, i.e. a constant, counts as normal).\"\nB,\"If X and Y are independent and each normally distributed, then X + Y is normally distributed.\"\n{\n \"task_id\": \"F5-conf-03\",\n \"family\": \"F5\",\n \"split\": \"conf\",\n \"version\": \"1.0\",\n \"created_utc\": \"2026-10-30T03:42:22.079893+00:00\",\n \"files\": {\n \"TASK.md\": \"31fbaa2d88530fab7509ed52d12759f5b4fc91be27ba902545f08663f9c431d6\",\n \"gate_spec.json\": \"fe547a7a065d89426b9ef65fd59a96354191a660f0b1ce99e812e26e54b02c5d\",\n \"data/design.csv\": \"b9c14d67b34e811cafa44a01d8d03d44f7b31a9a01c882e8bc51ac563003a9df\",\n \"data/propositions.csv\": \"0e12befb7693999629fbe1a46d5243e78bd54681b05be6a8b81efe8d307db1f6\"\n }\n}{\n \"task_id\": \"F5-conf-03\",\n \"required_files\": [\n \"out/results.json\",\n \"out/report.md\",\n \"out/analysis.py\",\n \"out/claims.json\",\n \"out/argument.md\",\n \"out/counterexample.csv\"\n ],\n \"results_keys\": {\n \"task_id\": {\n \"type\": \"string\",\n \"nullable\": false\n },\n \"statement_true\": {\n \"type\": \"boolean\",\n \"nullable\": false\n },\n \"counterexample_provided\": {\n \"type\": \"boolean\",\n \"nullable\": false\n },\n \"counterexample_values\": {\n \"type\": \"object\",\n \"nullable\": false\n },\n \"statement_b_true\": {\n \"type\": \"boolean\",\n \"nullable\": false\n },\n \"feasibility\": {\n \"type\": \"string\",\n \"nullable\": false\n },\n \"feasibility_reason\": {\n \"type\": \"string\",\n \"nullable\": true\nb9c14d67b34e811cafa44a01d8d03d44f7b31a9a01c882e8bc51ac563003a9df data/design.csv\n0e12befb7693999629fbe1a46d5243e78bd54681b05be6a8b81efe8d307db1f6 data/propositions.csv","is_error":false}]},"uuid":"07f177d4-ea35-4a4a-b74c-aca96bfce1e8","timestamp":"2026-10-30T04:52:54.612Z","toolUseResult":{"stdout":"parameter,value,description\nseed,20261029,random seed for any simulation (numpy default_rng)\nn,100000,sample size for the numerical illustration (rows of out/counterexample.csv)\nid,statement\nA,\"If X and Y are each normally distributed random variables, then X + Y is normally distributed (a degenerate normal, i.e. a constant, counts as normal).\"\nB,\"If X and Y are independent and each normally distributed, then X + Y is normally distributed.\"\n{\n \"task_id\": \"F5-conf-03\",\n \"family\": \"F5\",\n \"split\": \"conf\",\n \"version\": \"1.0\",\n \"created_utc\": \"2026-10-30T03:42:22.079893+00:00\",\n \"files\": {\n \"TASK.md\": \"31fbaa2d88530fab7509ed52d12759f5b4fc91be27ba902545f08663f9c431d6\",\n \"gate_spec.json\": \"fe547a7a065d89426b9ef65fd59a96354191a660f0b1ce99e812e26e54b02c5d\",\n \"data/design.csv\": \"b9c14d67b34e811cafa44a01d8d03d44f7b31a9a01c882e8bc51ac563003a9df\",\n \"data/propositions.csv\": \"0e12befb7693999629fbe1a46d5243e78bd54681b05be6a8b81efe8d307db1f6\"\n }\n}{\n \"task_id\": \"F5-conf-03\",\n \"required_files\": [\n \"out/results.json\",\n \"out/report.md\",\n \"out/analysis.py\",\n \"out/claims.json\",\n \"out/argument.md\",\n \"out/counterexample.csv\"\n ],\n \"results_keys\": {\n \"task_id\": {\n \"type\": \"string\",\n \"nullable\": false\n },\n \"statement_true\": {\n \"type\": \"boolean\",\n \"nullable\": false\n },\n \"counterexample_provided\": {\n \"type\": \"boolean\",\n \"nullable\": false\n },\n \"counterexample_values\": {\n \"type\": \"object\",\n \"nullable\": false\n },\n \"statement_b_true\": {\n \"type\": \"boolean\",\n \"nullable\": false\n },\n \"feasibility\": {\n \"type\": \"string\",\n \"nullable\": false\n },\n \"feasibility_reason\": {\n \"type\": \"string\",\n \"nullable\": true\nb9c14d67b34e811cafa44a01d8d03d44f7b31a9a01c882e8bc51ac563003a9df data/design.csv\n0e12befb7693999629fbe1a46d5243e78bd54681b05be6a8b81efe8d307db1f6 data/propositions.csv","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"0526849f-89dc-43f8-9b54-e677a06568a6","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}19{"type":"api-request-blob","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"24fd7ce00fd7f1e63f6e038bc423737bc7d0b81ff7c6d82a3c9737e44b90674b","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01EmtP7rQ5GDRjfiFEukqDwQ","name":"Bash","input":{"command":"cat data/*.csv; cat bundle.json gate_spec.json | head -50; shasum -a 256 data/*","description":"Show data files and hashes"}}]}}20{"type":"api-request","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","id":"9cbb79e3-7a28-4dd5-969a-07db3079e882","timestamp":"2026-10-30T04:52:54.615Z","version":"2.1.314","querySource":"sdk","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","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":"4f1082a6-ff6f-4d63-b902-62fb0742de11","keep":4,"tail":["24fd7ce00fd7f1e63f6e038bc423737bc7d0b81ff7c6d82a3c9737e44b90674b","20e56e3e6503fd3bb130a46c9a91d8884ad7ddabfba3c919e751b245f580454a"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",5,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"46a8bb9f5fcbab7d114341d7609d1a38c72de58adea65d068cab20404624937e"}21{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"07f177d4-ea35-4a4a-b74c-aca96bfce1e8","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b"}22{"type":"atis-latch","atis":"","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b"}23{"parentUuid":"07f177d4-ea35-4a4a-b74c-aca96bfce1e8","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpgBrdUhzFZoeRmVtY5","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":988,"cache_read_input_tokens":5355,"output_tokens":1628,"output_tokens_details":{"thinking_tokens":322},"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":988},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":3115,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXpgBfiRPqXuvvGqm8mR","requestRef":"9cbb79e3-7a28-4dd5-969a-07db3079e882","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"8d268c43-9a9d-43a4-9a60-c7a0116beefa","timestamp":"2026-10-30T04:52:59.413Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181/out/state","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}24{"parentUuid":"8d268c43-9a9d-43a4-9a60-c7a0116beefa","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpgBrdUhzFZoeRmVtY5","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Njvc1SGMbvGBzVaHDYqf8A","name":"Bash","input":{"command":"mkdir -p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** Decide truth of two propositions on sums of normal r.v.s (data/propositions.csv):\n- A: X, Y each normal (marginally) => X+Y normal (constants count as degenerate normal).\n- B: X, Y independent and each normal => X+Y normal.\n**Estimands.** Truth values of A and B (by mathematical argument); for a false proposition, a concrete, verifiable counterexample: joint law of (X,Y), plus a simulated sample (seed, n from data/design.csv) showing normal marginals and non-normal sum.\n**Outputs.** out/results.json (task_id, statement_true, counterexample_provided, counterexample_values{construction,n,seed,mean_x,sd_x,mean_y,sd_y,mean_sum,sd_sum,ks_sum_vs_normal}, statement_b_true, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed); out/counterexample.csv (x,y); out/argument.md; out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py; out/claims.json; out/exclusions.csv.\n**Availability rules.** Only data/; verdicts from proof, simulation only illustrative; use design seed and n with numpy default_rng.\n**Invalidity.** Missing/inconsistent seed or n; a \"counterexample\" whose sum is actually normal (e.g. Y=-X gives a constant, which is explicitly allowed as normal, so it is NOT a counterexample); simulation treated as proof.\nEOF\ncat > log.md <<'EOF'\n- 2026-10-30 P0 passed: contract written.\nEOF\necho ok","description":"Write contract and log"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":988,"cache_read_input_tokens":5355,"output_tokens":1628,"output_tokens_details":{"thinking_tokens":322},"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":988},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXpgBfiRPqXuvvGqm8mR","requestRef":"9cbb79e3-7a28-4dd5-969a-07db3079e882","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"c40c85d2-843e-41f3-80b9-b31b30e9d214","timestamp":"2026-10-30T04:53:04.938Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181/out/state","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}25{"parentUuid":"c40c85d2-843e-41f3-80b9-b31b30e9d214","isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01Njvc1SGMbvGBzVaHDYqf8A","type":"tool_result","content":"ok","is_error":false}]},"uuid":"b3ebf73e-5229-4f03-87c8-b11f25321226","timestamp":"2026-10-30T04:53:04.984Z","toolUseResult":{"stdout":"ok","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"c40c85d2-843e-41f3-80b9-b31b30e9d214","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181/out/state","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}26{"parentUuid":"b3ebf73e-5229-4f03-87c8-b11f25321226","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpgBrdUhzFZoeRmVtY5","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01GE37ZvSnPdxGkGPvm4GrTP","name":"Bash","input":{"command":"cd out/state && cat > data_audit.md <<'EOF'\n# Data audit (P1)\n| file | sha256 | rows | cols | schema |\n|---|---|---|---|---|\n| data/propositions.csv | 0e12befb7693999629fbe1a46d5243e78bd54681b05be6a8b81efe8d307db1f6 | 2 | 2 | id (str), statement (str) |\n| data/design.csv | b9c14d67b34e811cafa44a01d8d03d44f7b31a9a01c882e8bc51ac563003a9df | 2 | 3 | parameter, value, description |\n\n- Hashes match bundle.json.\n- design: seed = 20261029, n = 100000 (integers, unitless). No missing values, no duplicates, no anomalies.\n- propositions: ids A, B unique; text complete. Note that A explicitly counts a constant as a (degenerate) normal, which rules out Y = -X as a counterexample.\n- No date fields; no information-availability violations. No exclusions (exclusions.csv records a no-op step).\nEOF\ncd .. && printf 'step,rule,n_before,n_after,n_removed,rationale\\n1,read propositions.csv (no filtering),2,2,0,all propositions assessed\\n2,read design.csv (no filtering),2,2,0,both design parameters used\\n3,simulate counterexample sample (no filtering),100000,100000,0,all simulated rows retained\\n' > exclusions.csv\necho \"- 2026-10-30 P1 passed: audit done, hashes match bundle, no issues.\" >> state/log.md","description":"Write data audit and exclusions"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":988,"cache_read_input_tokens":5355,"output_tokens":1628,"output_tokens_details":{"thinking_tokens":322},"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":988},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXpgBfiRPqXuvvGqm8mR","requestRef":"9cbb79e3-7a28-4dd5-969a-07db3079e882","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f151d618-791b-41f1-832c-66d9d577731b","timestamp":"2026-10-30T04:53:10.630Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181/out/state","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}27{"parentUuid":"f151d618-791b-41f1-832c-66d9d577731b","isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01GE37ZvSnPdxGkGPvm4GrTP","type":"tool_result","content":"(eval):cd:1: no such file or directory: out/state","is_error":false}]},"uuid":"f1100699-1472-464a-92b4-49b6efbce5ef","timestamp":"2026-10-30T04:53:10.669Z","toolUseResult":{"stdout":"(eval):cd:1: no such file or directory: out/state","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"f151d618-791b-41f1-832c-66d9d577731b","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181/out","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}28{"type":"api-request-blob","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"44f084b8449f9269eb0357b9319ef9314ba2eb514ed2f6d34f0aaa92508a4266","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01Njvc1SGMbvGBzVaHDYqf8A","name":"Bash","input":{"command":"mkdir -p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** Decide truth of two propositions on sums of normal r.v.s (data/propositions.csv):\n- A: X, Y each normal (marginally) => X+Y normal (constants count as degenerate normal).\n- B: X, Y independent and each normal => X+Y normal.\n**Estimands.** Truth values of A and B (by mathematical argument); for a false proposition, a concrete, verifiable counterexample: joint law of (X,Y), plus a simulated sample (seed, n from data/design.csv) showing normal marginals and non-normal sum.\n**Outputs.** out/results.json (task_id, statement_true, counterexample_provided, counterexample_values{construction,n,seed,mean_x,sd_x,mean_y,sd_y,mean_sum,sd_sum,ks_sum_vs_normal}, statement_b_true, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed); out/counterexample.csv (x,y); out/argument.md; out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py; out/claims.json; out/exclusions.csv.\n**Availability rules.** Only data/; verdicts from proof, simulation only illustrative; use design seed and n with numpy default_rng.\n**Invalidity.** Missing/inconsistent seed or n; a \"counterexample\" whose sum is actually normal (e.g. Y=-X gives a constant, which is explicitly allowed as normal, so it is NOT a counterexample); simulation treated as proof.\nEOF\ncat > log.md <<'EOF'\n- 2026-10-30 P0 passed: contract written.\nEOF\necho ok","description":"Write contract and log"}},{"type":"tool_use","id":"toolu_01GE37ZvSnPdxGkGPvm4GrTP","name":"Bash","input":{"command":"cd out/state && cat > data_audit.md <<'EOF'\n# Data audit (P1)\n| file | sha256 | rows | cols | schema |\n|---|---|---|---|---|\n| data/propositions.csv | 0e12befb7693999629fbe1a46d5243e78bd54681b05be6a8b81efe8d307db1f6 | 2 | 2 | id (str), statement (str) |\n| data/design.csv | b9c14d67b34e811cafa44a01d8d03d44f7b31a9a01c882e8bc51ac563003a9df | 2 | 3 | parameter, value, description |\n\n- Hashes match bundle.json.\n- design: seed = 20261029, n = 100000 (integers, unitless). No missing values, no duplicates, no anomalies.\n- propositions: ids A, B unique; text complete. Note that A explicitly counts a constant as a (degenerate) normal, which rules out Y = -X as a counterexample.\n- No date fields; no information-availability violations. No exclusions (exclusions.csv records a no-op step).\nEOF\ncd .. && printf 'step,rule,n_before,n_after,n_removed,rationale\\n1,read propositions.csv (no filtering),2,2,0,all propositions assessed\\n2,read design.csv (no filtering),2,2,0,both design parameters used\\n3,simulate counterexample sample (no filtering),100000,100000,0,all simulated rows retained\\n' > exclusions.csv\necho \"- 2026-10-30 P1 passed: audit done, hashes match bundle, no issues.\" >> state/log.md","description":"Write data audit and exclusions"}}]}}29{"type":"api-request-blob","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"9b406e4fcf70f8b696fec07ea80380da4a32615ef7d63145449138913c9ff31c","message":{"role":"user","content":[{"tool_use_id":"toolu_01Njvc1SGMbvGBzVaHDYqf8A","type":"tool_result","content":"ok","is_error":false},{"tool_use_id":"toolu_01GE37ZvSnPdxGkGPvm4GrTP","type":"tool_result","content":"(eval):cd:1: no such file or directory: out/state","is_error":false}]}}30{"type":"api-request","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","id":"e53a027f-850e-48aa-902b-7cbdf4e8d80e","timestamp":"2026-10-30T04:53:10.673Z","version":"2.1.314","querySource":"sdk","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","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":"9cbb79e3-7a28-4dd5-969a-07db3079e882","keep":6,"tail":["44f084b8449f9269eb0357b9319ef9314ba2eb514ed2f6d34f0aaa92508a4266","9b406e4fcf70f8b696fec07ea80380da4a32615ef7d63145449138913c9ff31c"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",1],"value":{"type":"ephemeral"}}],"requestDigest":"377278c3548652b06f0b12e42590c766bb2e92c82e60642066c8a35cd9ddb2fe"}31{"parentUuid":"f1100699-1472-464a-92b4-49b6efbce5ef","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXphNdJVDwFZN32YJ1S5","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQS9AYKEAgTGAI4AUIIdGhpbmtpbmcSDHsTeCOJWP0Cbte3jhoM8wEpaAVIiyhnGZMEIjDy8SXb6VHty2Fhrq2JnW1aSE9OpIytPDclWI74o0lQEw0SFMIE6rpYYZBxXLrXD2YqkQavblt5DTpW3siYf6Y+DtrhdnZNkx1E899xG1HQVAd5NSgbyYD2uUJ31RlauYCc+6DKB8Z/S5DIy04RlENTYBX2dBmthDrZRZMsfDzg6O7OzXqglcrbnodEjkKYVrfkNrFGafLMoWxKfcvWV39Umyhc6cMGyQTttLgS1EGnWYuqrwO5oRlCuTPGI2H2/KPp7uXU5tGo5/NPMxg032hOw0OtFEbckhTjUpNN4jHgzA8vHGKY29YkoP5WIBZ7fy9xR/bweUNoJwTqtPFvdCbqx6Q1nfx/5z060VLcjLwaI8C/zRom5j8LhHNDiJpnoh59Z2zNmqdXCcik6bIJQbVxAeyDHTAJJiuT4ugIa/0BgUtFGyXgKPZ4CfXrLor++XcPpJUa6FwRr2a9mcKVhZ1B8zAVYGzAkD03OHLOkejrDCBAlP2XhUw5gKgVY4EM4ac++3HSzDXMAtUS/isbz+Al7Z9+b7KYphzNaHv2f/NE4i04lPicVn9NNUmd6rNGYueGB0wYhQUQu4rUkHSgAWMp6w5HJkDyrvWN0GUNQa9w3iVIkevx73QUE3K0MxDTPObCZpb8q4W1K76xuSTsN+5V8Je/608DBJUI78vqijWkvF+GY7ulxJme6a89zx8kF1lzNArCAbsBuwM6OiNxoOtObzoGgK47oDNUS0B68t88vw+bdL8FffTkUbjao2FFaxYyQ9AZasXYBvNsDPzGCL6iIJ5qZvTbq3zNiFVGfSRvFhHt4Duxq9RE3wXbDAtGgiY48w156mzB7OsVKNv6EqAmHExuxfx+hgg3VnIEeA6FP/E2xvJ86xAkdg7dsuxowZvG4e/+xubG6T7AHHUVIpczyv4tJjB2n7jU6A2fLU99p+Fu4rcAVbef0mqKIhQ4lqsc/z1W1A8JtFLt+ptaPTacWrwnkeBcEOxEFlvBBnc+sF/mNycgrbP3/f+Oowr1ZSN51sqAx/TRvWrkV0r1z35yBk5ZgPGrxT3RX7VhuZRxObIvtkqV1tsFhlXOX7JdV/6WqOgC6ZQvuzX1EYoYZUjA80GwaRgB"}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1705,"cache_read_input_tokens":6343,"output_tokens":169,"output_tokens_details":{"thinking_tokens":59},"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":1705},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":590,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXphNQueveMpPhsf6YhB","requestRef":"e53a027f-850e-48aa-902b-7cbdf4e8d80e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f6bff804-a646-4dc4-9776-3e065fb32906","timestamp":"2026-10-30T04:53:12.763Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181/out","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}32{"parentUuid":"f6bff804-a646-4dc4-9776-3e065fb32906","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXphNdJVDwFZN32YJ1S5","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01XQLBWC5PLYpmcXMAVYtaPs","name":"Bash","input":{"command":"pwd; cd /Users/simon-pierreboucher/wp29/runs/RC0181; ls out out/state","description":"Check working directory"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1705,"cache_read_input_tokens":6343,"output_tokens":169,"output_tokens_details":{"thinking_tokens":59},"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":1705},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXphNQueveMpPhsf6YhB","requestRef":"e53a027f-850e-48aa-902b-7cbdf4e8d80e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"a6a17e0d-f564-4144-9ff7-b93074e793c4","timestamp":"2026-10-30T04:53:13.298Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181/out","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}33{"parentUuid":"a6a17e0d-f564-4144-9ff7-b93074e793c4","isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01XQLBWC5PLYpmcXMAVYtaPs","type":"tool_result","content":"/Users/simon-pierreboucher/wp29/runs/RC0181/out\nout:\nexclusions.csv\nstate\n\nout/state:\ncontract.md\nlog.md","is_error":false}]},"uuid":"ec083cae-7959-446b-9ecf-e79984497be9","timestamp":"2026-10-30T04:53:13.336Z","toolUseResult":{"stdout":"/Users/simon-pierreboucher/wp29/runs/RC0181/out\nout:\nexclusions.csv\nstate\n\nout/state:\ncontract.md\nlog.md","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"a6a17e0d-f564-4144-9ff7-b93074e793c4","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}34{"type":"api-request-blob","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"929af3ccae4641316aacf5fc71b41869a7cfc3e6e6f47b566d3fce9a652d1e21","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01XQLBWC5PLYpmcXMAVYtaPs","name":"Bash","input":{"command":"pwd; cd /Users/simon-pierreboucher/wp29/runs/RC0181; ls out out/state","description":"Check working directory"}}]}}35{"type":"api-request","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","id":"ee28116b-160b-43df-9e05-70e0ece429c7","timestamp":"2026-10-30T04:53:13.339Z","version":"2.1.314","querySource":"sdk","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","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":"e53a027f-850e-48aa-902b-7cbdf4e8d80e","keep":8,"tail":["929af3ccae4641316aacf5fc71b41869a7cfc3e6e6f47b566d3fce9a652d1e21","db5ae3c46eefffeab266f907b8a18e448268a30e0508aec2b2d3ce71e707c7b5"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",9,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"625cdcdeeef995229926abec75b2354cd4f04ddfbd6952ba46827124c13f48d3"}36{"parentUuid":"ec083cae-7959-446b-9ecf-e79984497be9","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpha1R8WeR84NZzNHgW","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQS8QcKEAgTGAI4AUIIdGhpbmtpbmcSDEZes5F96HR84NAxMxoMVKMNOeQg7fMwsUDCIjAtrzFEfGuB4VK1r0L1K//DmR5hWRJ2lJJlp4QkxXlHKY3LmXdP5LdDtjhfvqNlcGYqjge5yiL0R24XBuGwTjbrE0PQ6TL+4Na/lHRojlRt16V0YoovGB5IU+r2p1RGUDHWvjzWpr3CKTSo/zPSC0/KgY/OvJc2EeWV2FnDwyVa9GGyylVhgq3oog5PhEMCmHVP2eGOpkHIxGmaieJLnt3HZOrueTqgIc5KDeGUQPnvN2RY5zAkHhCYi6wzxPr8YZERQyr7+/N4QMZl/HLpe9QO9qsVUzWi+ROX6eNDzstM4heJt7oCacr8T9yyl6E9iRyvQu+7dgrP0ZiaEeDcJ3j0jw+fTCBZumwCfGT9JbCzMTNRYrm20ivs/vivgig3WInGSE0x9V/5ZUdQf6uKh0LN9QNTHrBlTJNhrjW9458r2ZeXjLw/V4FOxW8Y9C3CIscsqbF4wvI9tQmL0TpLUb+obdlvd8RVrXMXGpNDGgxjw88Bw7kJKrbIFh3rIPROASDhK6JysJCMCsanHDUpZiEtNpAeypQOEdaevvCKQxJ51pqgOiFEKI7T81nJ7dJgi2EwC1HZzNxXCVNpg/1+4leSHoUyFuQo+ggekj+uEND7EKC00doZCpnBMehmxYrXFR1oUTb+ji5JPg9NRcMlwMxV6fBp+lMXojGsNgKN+5LcOZnexGnQXWVT+JSBPAFe5HJOhs0M1jSpPZTqY/8gutw8oA1buP/6XYCoPeboAwZ5LRCpjzVNl2SnCQHiDeDOefWil9Ayt0NusGx8XjHRw5xOoXdusWE2jHllbigfAck7DbZZAivj3D9GfRDeuZb2tAJzecA5IKKs580sBGmuyceu1hxBWCp4oanBYyPGOOv2d0gg3jjagp/DpGRDRMJPhbORSZjFvb53Ok1VU5HhFMX0yZaJs+bEywcv/9YDAAfx5tB+/OoL3gR50u0HCYpTBQSrMPBT/CQFQi8OdXIbzfiUsgk5uo70qb45vlAmz0hTm4WF6GdLfvYGgibliZ1eRnQ4vl+OZ9PGPWqI+8CdHzlJf0gUJEqw3RjyiHsBXH88+gH4mh+bruHFl0vG/96R8/eZ0HwmLAg9LfhOMaFUKaTnG+/5qQheCOR7K8v31Hr6MPuIdA0FalXc+ckSQ29F+rz3tjizPSwz30yor5NOGFedPhcs0L+75ufT65WMHHkM7ej0l68e4oAZZgsSHwfRLWtOdMWLj7VGad/jR3vEGK540lmr+Jjz1d2KpTvP8fU+z7rk0pYlsgZroA5fM2jRTsmjGAE="}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":228,"cache_read_input_tokens":8048,"output_tokens":596,"output_tokens_details":{"thinking_tokens":116},"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":228},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1146,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXphZjnWxYCy9M2jp13F","requestRef":"ee28116b-160b-43df-9e05-70e0ece429c7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"0ddc2e55-a298-4408-b774-35612748599b","timestamp":"2026-10-30T04:53:16.239Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}37{"parentUuid":"0ddc2e55-a298-4408-b774-35612748599b","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpha1R8WeR84NZzNHgW","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_013f1xaYRTBNy3DQEW2Tjfcs","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n| file | sha256 | rows | cols | schema |\n|---|---|---|---|---|\n| data/propositions.csv | 0e12befb7693999629fbe1a46d5243e78bd54681b05be6a8b81efe8d307db1f6 | 2 | 2 | id (str), statement (str) |\n| data/design.csv | b9c14d67b34e811cafa44a01d8d03d44f7b31a9a01c882e8bc51ac563003a9df | 2 | 3 | parameter, value, description |\n\n- Hashes match bundle.json.\n- design: seed = 20261029, n = 100000 (integers, unitless). No missing values, no duplicates, no anomalies.\n- propositions: ids A, B unique; text complete. A explicitly counts a constant as a (degenerate) normal, which rules out Y = -X as a counterexample.\n- No date fields; no information-availability violations. No exclusions (exclusions.csv records no-op steps).\nEOF\ncat out/exclusions.csv out/state/log.md","description":"Rewrite data audit, verify files"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":228,"cache_read_input_tokens":8048,"output_tokens":596,"output_tokens_details":{"thinking_tokens":116},"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":228},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXphZjnWxYCy9M2jp13F","requestRef":"ee28116b-160b-43df-9e05-70e0ece429c7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"60d84a63-f511-4d51-ade1-c4a846203046","timestamp":"2026-10-30T04:53:20.163Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}38{"parentUuid":"60d84a63-f511-4d51-ade1-c4a846203046","isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_013f1xaYRTBNy3DQEW2Tjfcs","type":"tool_result","content":"step,rule,n_before,n_after,n_removed,rationale\n1,read propositions.csv (no filtering),2,2,0,all propositions assessed\n2,read design.csv (no filtering),2,2,0,both design parameters used\n3,simulate counterexample sample (no filtering),100000,100000,0,all simulated rows retained\n- 2026-10-30 P0 passed: contract written.\n- 2026-10-30 P1 passed: audit done, hashes match bundle, no issues.","is_error":false}]},"uuid":"a341ca37-4f9b-4336-8b17-bc0e922ab80f","timestamp":"2026-10-30T04:53:20.212Z","toolUseResult":{"stdout":"step,rule,n_before,n_after,n_removed,rationale\n1,read propositions.csv (no filtering),2,2,0,all propositions assessed\n2,read design.csv (no filtering),2,2,0,both design parameters used\n3,simulate counterexample sample (no filtering),100000,100000,0,all simulated rows retained\n- 2026-10-30 P0 passed: contract written.\n- 2026-10-30 P1 passed: audit done, hashes match bundle, no issues.","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"60d84a63-f511-4d51-ade1-c4a846203046","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}39{"type":"api-request-blob","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"9ee1003173f5b7526b44c56202548bf78958b05f01920b2da09427081d3f8a48","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_013f1xaYRTBNy3DQEW2Tjfcs","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n| file | sha256 | rows | cols | schema |\n|---|---|---|---|---|\n| data/propositions.csv | 0e12befb7693999629fbe1a46d5243e78bd54681b05be6a8b81efe8d307db1f6 | 2 | 2 | id (str), statement (str) |\n| data/design.csv | b9c14d67b34e811cafa44a01d8d03d44f7b31a9a01c882e8bc51ac563003a9df | 2 | 3 | parameter, value, description |\n\n- Hashes match bundle.json.\n- design: seed = 20261029, n = 100000 (integers, unitless). No missing values, no duplicates, no anomalies.\n- propositions: ids A, B unique; text complete. A explicitly counts a constant as a (degenerate) normal, which rules out Y = -X as a counterexample.\n- No date fields; no information-availability violations. No exclusions (exclusions.csv records no-op steps).\nEOF\ncat out/exclusions.csv out/state/log.md","description":"Rewrite data audit, verify files"}}]}}40{"type":"api-request","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","id":"070332f8-b0aa-4d88-92a0-9311dcd1059e","timestamp":"2026-10-30T04:53:20.215Z","version":"2.1.314","querySource":"sdk","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","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":"ee28116b-160b-43df-9e05-70e0ece429c7","keep":10,"tail":["9ee1003173f5b7526b44c56202548bf78958b05f01920b2da09427081d3f8a48","b62f245425e03f721eae80eae5b35835e273b1b82440bfb3ca1e4b54514f6ce5"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",11,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"cfa64b4bb2e6a7040a25b177f31ded1cd9daaf3901cd505144a4d77497b10a45"}41{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"a341ca37-4f9b-4336-8b17-bc0e922ab80f","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b"}42{"type":"atis-latch","atis":"","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b"}43{"parentUuid":"a341ca37-4f9b-4336-8b17-bc0e922ab80f","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpi5PVgS1EmgsxabAn3","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQShQkKEAgTGAI4AUIIdGhpbmtpbmcSDDB7W47ZyEdFIlaBsRoMS+HtlIkLCIKb/ZaDIjAMEGdTBjc5hhtX3y/72+loKc3R/Qv9A7zywybqTOBupgHesOPXYtlYKJsAlm7fJU0qogj0sAsB93OZlV4y/x5jVW1g1hjbIABRRxozZWMgVFPWBHqF1Ei+8HSYqyniupPEh9ZvgjWp03kgcPcwaiv0uaK2PP4oQCjc3BGj84phF5yWSON1oRyM4hmJExkXdl7xMsrPVJiaKoEdpavXLnO8kKGLefrwQbYy78/N05ZTWkpzEVdFuOhn/PfHCI2fnNk3EEyR8JUO78scZUlhLAQhY6HGOAPiXHs+n0sbKWQavKRmnuI9Amrd9FwMMO9K6ITNK2RS4vW45iMJCCB0rF/+e4tFd0WqYSgZ7tOgxnLwI2kxr/BMk2AitpV0D4BTx3CP1QPnMNf0JI5ltFNP/Z/hyfnA+ZlY/HKa1UJUxmP2/vZ3ODd8+idc4QPzMi/8qaRm0S1wfr5JFevX1A9iQXwi6xR+rNjgXcr6OiBG5DDNipKua3QhPAx/sdRy180vwZy8S984sV7tt1u5sUT1SfsfwYFJadKgB7as9FG7YG4qgY5POEl4pUKelfKGb/6KsA14poErJ+PfIzgbOKH6I+ZriIfEFwD9BOMtnmcAiSzfNLQGVdqKrQoXeZkUTq0bAWOuWATbdg/4tdKq0H8zFBOCxPTHeXJsKjSSlT+Sg/ZUnIT/RyYwPVujMa8TxW6XocEW9rl09Qx/Mibziik4rIl1svoE1d9SNKk4WfC8nE6hRUhHk9fCkdZkhYYeqV6FzUbzlhdkyZkWCQcGGefq4lkp/GwoSgyXDNaUSZJSaHtH10DE70LxPbCZvuvMocLtqCgcQ5BGcp0/yKnr8Ah4PhQJu7pwRTUQFOyz03L41kOKT8Ww0L3pXnyUEeacMk5UVlekvgCCREOqZ+5Sa6PwIDnmOq/1UxT40zbJ/i1XU0P24t2CIG6ROL7LzBfjODSXwDs0UUGTojLzCqwMIxUN7zFY5F8NCjGY1NVYgG0RnOi24CgAgiH6DH8GF5S1q2Zg02w2cjyeS5SeeGEDG/vBKl2SSKYmdNJU2tTUSr6c8P9v7LHSPJYOZmZ1UW10gAAQ7HvFJwzTgPvKmyWariE9Jq4gahqaXzzEbUKODD3ZmHuAAxu2/FfrQs8f6k64VrQmOYR/MMdVVThk/wSIkGqbmnNrLO4SihnG8Fi2NeyDvHaz3RRIBejJRPgPE1POVd7v4WdJCX2qrqhOe0dRwg4vXr8T2poR4vze25j1T5o+w/mNssQmzlf0ajejqCSWr0+5UB6SJ0/IAttGt1NYjNNFUpfT5SU3LGwpB9PHVLMppAcA1AIpXrRZp9IyGfxRfgqyJFliuIfgGIsF6omK3gxq3PaRItm4cYkiUpLz7JpoVFT1sOdBYM92aTriV1PJ5QPTHWJpEZ/KaKSZAfVxyx+D7DjfcrdNl6nKkaTCkEWbz3kPKLVa8J6MgTaG0124F2z4LN7qwvwMXRgB"}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":734,"cache_read_input_tokens":8276,"output_tokens":1850,"output_tokens_details":{"thinking_tokens":148},"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":734},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1433,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXpi5C69FeUHeeH9WA8a","requestRef":"070332f8-b0aa-4d88-92a0-9311dcd1059e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"b15553eb-f2ab-4f08-9509-99dd7f2574d5","timestamp":"2026-10-30T04:53:23.256Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}44{"parentUuid":"b15553eb-f2ab-4f08-9509-99dd7f2574d5","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpi5PVgS1EmgsxabAn3","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_011Zu9VRmCDgiH1gFXvWoVwH","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-03: counterexample to 'marginally normal X, Y => X+Y normal'.\nReads data/ only; writes out/results.json and out/counterexample.csv deterministically.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\n\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\nfrom scipy import stats\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nD, O = os.path.join(ROOT, \"data\"), os.path.join(ROOT, \"out\")\n\nprops = pd.read_csv(os.path.join(D, \"propositions.csv\"))\ndesign = pd.read_csv(os.path.join(D, \"design.csv\"))\nissues = []\nassert set(props[\"id\"]) == {\"A\", \"B\"}, \"unexpected proposition ids\"\npar = dict(zip(design[\"parameter\"], design[\"value\"]))\nseed, n = int(par[\"seed\"]), int(par[\"n\"])\nassert float(par[\"seed\"]) == seed and float(par[\"n\"]) == n and n > 0\n\nrng = np.random.default_rng(seed)\n# Counterexample construction: X ~ N(0,1), W ~ Rademacher (+/-1 w.p. 1/2) independent of X, Y = W*X.\n# Y ~ N(0,1) by symmetry of N(0,1); X+Y = (1+W)X equals 0 w.p. 1/2 and 2X otherwise -> atom at 0, not normal.\nx = rng.standard_normal(n)\nw = rng.choice(np.array([-1.0, 1.0]), size=n)\ny = w * x\ns = x + y\npd.DataFrame({\"x\": x, \"y\": y}).to_csv(os.path.join(O, \"counterexample.csv\"), index=False)\n\ndef ks_vs_fitted_normal(v):\n return float(stats.kstest(v, \"norm\", args=(v.mean(), v.std(ddof=1))).statistic)\n\n# Baseline / proposition-B check (same evaluation rule): independent X', Y' ~ N(0,1), drawn after the counterexample.\nxb, yb = rng.standard_normal(n), rng.standard_normal(n)\nsb = xb + yb\n\nr = lambda v: float(round(v, 10))\ncv = {\n \"construction\": \"X ~ N(0,1); W ~ Rademacher (P(W=1)=P(W=-1)=1/2) independent of X; Y = W*X. \"\n \"Then Y ~ N(0,1) but X+Y = (1+W)X is 0 with prob. 1/2 and 2X ~ N(0,4) otherwise (atom at 0).\",\n \"n\": int(len(x)), \"seed\": seed,\n \"mean_x\": r(x.mean()), \"sd_x\": r(x.std(ddof=1)),\n \"mean_y\": r(y.mean()), \"sd_y\": r(y.std(ddof=1)),\n \"mean_sum\": r(s.mean()), \"sd_sum\": r(s.std(ddof=1)),\n \"ks_sum_vs_normal\": r(ks_vs_fitted_normal(s)),\n}\nres = {\n \"task_id\": \"F5-conf-03\",\n \"statement_true\": False,\n \"counterexample_provided\": True,\n \"counterexample_values\": cv,\n \"statement_b_true\": True,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": None,\n \"data_issues\": issues,\n \"n_input_rows\": {\"propositions.csv\": int(len(props)), \"design.csv\": int(len(design))},\n \"n_analysed\": int(len(x)),\n \"random_seed\": seed,\n # supplementary diagnostics\n \"ks_x_vs_normal\": r(ks_vs_fitted_normal(x)),\n \"ks_y_vs_normal\": r(ks_vs_fitted_normal(y)),\n \"frac_sum_exactly_zero\": r(np.mean(s == 0.0)),\n \"frac_w_equal_1\": r(np.mean(w == 1.0)),\n \"corr_xy\": r(np.corrcoef(x, y)[0, 1]),\n \"ks_critical_value_5pct_approx\": r(1.358 / np.sqrt(n)),\n \"baseline_independent_mean_sum\": r(sb.mean()),\n \"baseline_independent_sd_sum\": r(sb.std(ddof=1)),\n \"baseline_independent_ks_sum_vs_normal\": r(ks_vs_fitted_normal(sb)),\n}\nwith open(os.path.join(O, \"results.json\"), \"w\") as f:\n json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis script"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":734,"cache_read_input_tokens":8276,"output_tokens":1850,"output_tokens_details":{"thinking_tokens":148},"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":734},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXpi5C69FeUHeeH9WA8a","requestRef":"070332f8-b0aa-4d88-92a0-9311dcd1059e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6e106297-b26b-4ae7-a06d-76e912188e41","timestamp":"2026-10-30T04:53:35.186Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}45{"parentUuid":"6e106297-b26b-4ae7-a06d-76e912188e41","isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_011Zu9VRmCDgiH1gFXvWoVwH","type":"tool_result","content":"{\n \"task_id\": \"F5-conf-03\",\n \"statement_true\": false,\n \"counterexample_provided\": true,\n \"counterexample_values\": {\n \"construction\": \"X ~ N(0,1); W ~ Rademacher (P(W=1)=P(W=-1)=1/2) independent of X; Y = W*X. Then Y ~ N(0,1) but X+Y = (1+W)X is 0 with prob. 1/2 and 2X ~ N(0,4) otherwise (atom at 0).\",\n \"n\": 100000,\n \"seed\": 20261029,\n \"mean_x\": -0.0033187424,\n \"sd_x\": 0.9982238691,\n \"mean_y\": -0.0002490922,\n \"sd_y\": 0.9982293549,\n \"mean_sum\": -0.0035678346,\n \"sd_sum\": 1.405886647,\n \"ks_sum_vs_normal\": 0.2508475723\n },\n \"statement_b_true\": true,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [],\n \"n_input_rows\": {\n \"propositions.csv\": 2,\n \"design.csv\": 2\n },\n \"n_analysed\": 100000,\n \"random_seed\": 20261029,\n \"ks_x_vs_normal\": 0.0020917798,\n \"ks_y_vs_normal\": 0.0019518221,\n \"frac_sum_exactly_zero\": 0.50047,\n \"frac_w_equal_1\": 0.49953,\n \"corr_xy\": -0.0082268898,\n \"ks_critical_value_5pct_approx\": 0.0042943731,\n \"baseline_independent_mean_sum\": -0.0154521314,\n \"baseline_independent_sd_sum\": 1.4124003044,\n \"baseline_independent_ks_sum_vs_normal\": 0.0020272536\n}","is_error":false}]},"uuid":"1b3b700f-e0b2-4839-bef8-aa7db0b16ec0","timestamp":"2026-10-30T04:53:36.049Z","toolUseResult":{"stdout":"{\n \"task_id\": \"F5-conf-03\",\n \"statement_true\": false,\n \"counterexample_provided\": true,\n \"counterexample_values\": {\n \"construction\": \"X ~ N(0,1); W ~ Rademacher (P(W=1)=P(W=-1)=1/2) independent of X; Y = W*X. Then Y ~ N(0,1) but X+Y = (1+W)X is 0 with prob. 1/2 and 2X ~ N(0,4) otherwise (atom at 0).\",\n \"n\": 100000,\n \"seed\": 20261029,\n \"mean_x\": -0.0033187424,\n \"sd_x\": 0.9982238691,\n \"mean_y\": -0.0002490922,\n \"sd_y\": 0.9982293549,\n \"mean_sum\": -0.0035678346,\n \"sd_sum\": 1.405886647,\n \"ks_sum_vs_normal\": 0.2508475723\n },\n \"statement_b_true\": true,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [],\n \"n_input_rows\": {\n \"propositions.csv\": 2,\n \"design.csv\": 2\n },\n \"n_analysed\": 100000,\n \"random_seed\": 20261029,\n \"ks_x_vs_normal\": 0.0020917798,\n \"ks_y_vs_normal\": 0.0019518221,\n \"frac_sum_exactly_zero\": 0.50047,\n \"frac_w_equal_1\": 0.49953,\n \"corr_xy\": -0.0082268898,\n \"ks_critical_value_5pct_approx\": 0.0042943731,\n \"baseline_independent_mean_sum\": -0.0154521314,\n \"baseline_independent_sd_sum\": 1.4124003044,\n \"baseline_independent_ks_sum_vs_normal\": 0.0020272536\n}","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"6e106297-b26b-4ae7-a06d-76e912188e41","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}46{"type":"api-request-blob","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"fe38ea7088c04db0505909b57e552037f9d43e6c2d77607a22165f468df68030","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_011Zu9VRmCDgiH1gFXvWoVwH","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-03: counterexample to 'marginally normal X, Y => X+Y normal'.\nReads data/ only; writes out/results.json and out/counterexample.csv deterministically.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\n\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\nfrom scipy import stats\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nD, O = os.path.join(ROOT, \"data\"), os.path.join(ROOT, \"out\")\n\nprops = pd.read_csv(os.path.join(D, \"propositions.csv\"))\ndesign = pd.read_csv(os.path.join(D, \"design.csv\"))\nissues = []\nassert set(props[\"id\"]) == {\"A\", \"B\"}, \"unexpected proposition ids\"\npar = dict(zip(design[\"parameter\"], design[\"value\"]))\nseed, n = int(par[\"seed\"]), int(par[\"n\"])\nassert float(par[\"seed\"]) == seed and float(par[\"n\"]) == n and n > 0\n\nrng = np.random.default_rng(seed)\n# Counterexample construction: X ~ N(0,1), W ~ Rademacher (+/-1 w.p. 1/2) independent of X, Y = W*X.\n# Y ~ N(0,1) by symmetry of N(0,1); X+Y = (1+W)X equals 0 w.p. 1/2 and 2X otherwise -> atom at 0, not normal.\nx = rng.standard_normal(n)\nw = rng.choice(np.array([-1.0, 1.0]), size=n)\ny = w * x\ns = x + y\npd.DataFrame({\"x\": x, \"y\": y}).to_csv(os.path.join(O, \"counterexample.csv\"), index=False)\n\ndef ks_vs_fitted_normal(v):\n return float(stats.kstest(v, \"norm\", args=(v.mean(), v.std(ddof=1))).statistic)\n\n# Baseline / proposition-B check (same evaluation rule): independent X', Y' ~ N(0,1), drawn after the counterexample.\nxb, yb = rng.standard_normal(n), rng.standard_normal(n)\nsb = xb + yb\n\nr = lambda v: float(round(v, 10))\ncv = {\n \"construction\": \"X ~ N(0,1); W ~ Rademacher (P(W=1)=P(W=-1)=1/2) independent of X; Y = W*X. \"\n \"Then Y ~ N(0,1) but X+Y = (1+W)X is 0 with prob. 1/2 and 2X ~ N(0,4) otherwise (atom at 0).\",\n \"n\": int(len(x)), \"seed\": seed,\n \"mean_x\": r(x.mean()), \"sd_x\": r(x.std(ddof=1)),\n \"mean_y\": r(y.mean()), \"sd_y\": r(y.std(ddof=1)),\n \"mean_sum\": r(s.mean()), \"sd_sum\": r(s.std(ddof=1)),\n \"ks_sum_vs_normal\": r(ks_vs_fitted_normal(s)),\n}\nres = {\n \"task_id\": \"F5-conf-03\",\n \"statement_true\": False,\n \"counterexample_provided\": True,\n \"counterexample_values\": cv,\n \"statement_b_true\": True,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": None,\n \"data_issues\": issues,\n \"n_input_rows\": {\"propositions.csv\": int(len(props)), \"design.csv\": int(len(design))},\n \"n_analysed\": int(len(x)),\n \"random_seed\": seed,\n # supplementary diagnostics\n \"ks_x_vs_normal\": r(ks_vs_fitted_normal(x)),\n \"ks_y_vs_normal\": r(ks_vs_fitted_normal(y)),\n \"frac_sum_exactly_zero\": r(np.mean(s == 0.0)),\n \"frac_w_equal_1\": r(np.mean(w == 1.0)),\n \"corr_xy\": r(np.corrcoef(x, y)[0, 1]),\n \"ks_critical_value_5pct_approx\": r(1.358 / np.sqrt(n)),\n \"baseline_independent_mean_sum\": r(sb.mean()),\n \"baseline_independent_sd_sum\": r(sb.std(ddof=1)),\n \"baseline_independent_ks_sum_vs_normal\": r(ks_vs_fitted_normal(sb)),\n}\nwith open(os.path.join(O, \"results.json\"), \"w\") as f:\n json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis script"}}]}}47{"type":"api-request","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","id":"6136d166-3fcd-4a99-ac34-6082ef4542f6","timestamp":"2026-10-30T04:53:36.052Z","version":"2.1.314","querySource":"sdk","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","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":"070332f8-b0aa-4d88-92a0-9311dcd1059e","keep":12,"tail":["fe38ea7088c04db0505909b57e552037f9d43e6c2d77607a22165f468df68030","4aeb7f20dba47af649e18a33853df3e7aedb88cc1ec5bf2611a07b4a3247cf39"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",13,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"e0b4e4d72c45f6169dc92d5a2b270fdc4e196197d6afaefdabc68cbf9f4c3504"}48{"parentUuid":"1b3b700f-e0b2-4839-bef8-aa7db0b16ec0","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpjFD8GodDyE7uaj92T","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":2486,"cache_read_input_tokens":9010,"output_tokens":628,"output_tokens_details":{"thinking_tokens":94},"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":2486},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":987,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXpjEum1AzF7ncFkJcMs","requestRef":"6136d166-3fcd-4a99-ac34-6082ef4542f6","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"24b860e8-e96c-4617-8426-4750d1cd24a9","timestamp":"2026-10-30T04:53:38.538Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}49{"parentUuid":"24b860e8-e96c-4617-8426-4750d1cd24a9","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpjFD8GodDyE7uaj92T","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01CMpqd9FWnYb3v6WyJ8pb5J","name":"Bash","input":{"command":"shasum -a 256 out/results.json out/counterexample.csv > /tmp/h1; rm out/results.json out/counterexample.csv; ~/wp29/venv/bin/python out/analysis.py >/dev/null; shasum -a 256 out/results.json out/counterexample.csv | diff - /tmp/h1 && echo IDENTICAL\n~/wp29/venv/bin/python - <<'EOF'\nimport json,pandas as pd,numpy as np\nr=json.load(open('out/results.json'));c=pd.read_csv('out/counterexample.csv');cv=r['counterexample_values']\nprint('rows',len(c)==cv['n']==r['n_analysed']==100000, list(c.columns))\nprint('|y|==|x|',np.allclose(np.abs(c.y),np.abs(c.x)))\ns=c.x+c.y;print('sum identity', abs(s.mean()-cv['mean_sum'])<1e-9, abs(s.std()-cv['sd_sum'])<1e-9)\nprint('sd_sum vs sqrt(2)', cv['sd_sum'], np.sqrt(2))\nprint('nonzero sums = 2x', np.allclose(s[s!=0], 2*c.x[s!=0]))\nprint('seed', r['random_seed']==cv['seed']==20261029)\nEOF","description":"Rerun for reproducibility and consistency checks"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2486,"cache_read_input_tokens":9010,"output_tokens":628,"output_tokens_details":{"thinking_tokens":94},"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":2486},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXpjEum1AzF7ncFkJcMs","requestRef":"6136d166-3fcd-4a99-ac34-6082ef4542f6","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6387803d-a6c0-4aeb-88cc-daa692c45785","timestamp":"2026-10-30T04:53:42.097Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}50{"parentUuid":"6387803d-a6c0-4aeb-88cc-daa692c45785","isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01CMpqd9FWnYb3v6WyJ8pb5J","type":"tool_result","content":"IDENTICAL\nrows True ['x', 'y']\n|y|==|x| True\nsum identity True True\nsd_sum vs sqrt(2) 1.405886647 1.4142135623730951\nnonzero sums = 2x True\nseed True","is_error":false}]},"uuid":"75e4f2b1-d05b-4064-b7fd-7edae1c84c1a","timestamp":"2026-10-30T04:53:43.249Z","toolUseResult":{"stdout":"IDENTICAL\nrows True ['x', 'y']\n|y|==|x| True\nsum identity True True\nsd_sum vs sqrt(2) 1.405886647 1.4142135623730951\nnonzero sums = 2x True\nseed True","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"6387803d-a6c0-4aeb-88cc-daa692c45785","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}51{"type":"api-request-blob","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"9040fc794a49654da7653c93c66b44d768decd3360c9a3e07a727d5b5bfc053d","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01CMpqd9FWnYb3v6WyJ8pb5J","name":"Bash","input":{"command":"shasum -a 256 out/results.json out/counterexample.csv > /tmp/h1; rm out/results.json out/counterexample.csv; ~/wp29/venv/bin/python out/analysis.py >/dev/null; shasum -a 256 out/results.json out/counterexample.csv | diff - /tmp/h1 && echo IDENTICAL\n~/wp29/venv/bin/python - <<'EOF'\nimport json,pandas as pd,numpy as np\nr=json.load(open('out/results.json'));c=pd.read_csv('out/counterexample.csv');cv=r['counterexample_values']\nprint('rows',len(c)==cv['n']==r['n_analysed']==100000, list(c.columns))\nprint('|y|==|x|',np.allclose(np.abs(c.y),np.abs(c.x)))\ns=c.x+c.y;print('sum identity', abs(s.mean()-cv['mean_sum'])<1e-9, abs(s.std()-cv['sd_sum'])<1e-9)\nprint('sd_sum vs sqrt(2)', cv['sd_sum'], np.sqrt(2))\nprint('nonzero sums = 2x', np.allclose(s[s!=0], 2*c.x[s!=0]))\nprint('seed', r['random_seed']==cv['seed']==20261029)\nEOF","description":"Rerun for reproducibility and consistency checks"}}]}}52{"type":"api-request","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","id":"7f388f8c-ab42-4ff2-a910-29866b623941","timestamp":"2026-10-30T04:53:43.252Z","version":"2.1.314","querySource":"sdk","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","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":"6136d166-3fcd-4a99-ac34-6082ef4542f6","keep":14,"tail":["9040fc794a49654da7653c93c66b44d768decd3360c9a3e07a727d5b5bfc053d","98f52b6ac8535755ec2ac7cb12c442804402103d4720e7dd70a030bb29fe3626"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",15,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"89f94bd59a91f57d1c090894254cad89838ce96fbe0ff3e8f61200f661d93e1d"}53{"parentUuid":"75e4f2b1-d05b-4064-b7fd-7edae1c84c1a","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpjmwZdJKB2hWh9Tey9","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQS6wkKEAgTGAI4AUIIdGhpbmtpbmcSDG9O9o9Ope/pfspeaBoMlCRswCCQJK9VPjWcIjDWUbDmZHGOLc/KtDTrhUuV2RdV1F2rGxTTPepFmZz10hAjhGAwZqETCLD9y6pQfj8qiAnweVQG3nZk1jVFe+0YSy5EBc2Vo1wSK0cujVYfMGj0e5gzMgNiO0JXsSY6rccZ1xR1RsVPHjlu/zPfuYrn+7NyvkD2geFRp/n1MmEVFxxxJOOv10M1+CxLUdf/y8NzbIrqWYDy5GIZ0K+4CHNCoYRk2cRoHEKcj3fexGjsamDnSkHgQWYXryuNPpJCq7N9MlijcKekW15VyfXALL4FDC2JrOgXATRwD+wYFjKBlDJrp6l6ghJHj16V0FypbsT2kvUYXUpf5q1FGiVHe9Iu6kDPm3W3liIeN837dE5RVu1mCEBun2/ea3anmfIQQzcsoMNJ6vCLI0a/Ny7rT/phDM3BB/9gUoKbjGtJBpEldUz5aNQBGCCajtRv5gVjbS5jDLSHyI03gHivUfYh01fjHEeJfPlROL6E/ZextXSPoGZvpWQjosIsO5D4jTvuT1RFJ010jrmC79c+OxHCPkJLmAE/5NhdpCO8KZvkRCCTCaPz1mbHiG8eoJIcpLviC7frDCO3uIasK3jBdW2nsHZwvGz2pHpgyQyPBPc5OuhchW7KjJjRQoDBpLvaDubRMPj4hSmr2Y8lL0q17Zi4c8SOHe6Hmb0wTeq9VUg/feWm/u3Ija07rkUvXUiICMCcDnm4FFYsAjbVUM4zz0qAH+MK/JCnZ1gfz/Y+y5Vk46nmzmXGE62KCO22Q71SrkWEuisS2Btijctysi6pmwlSoBTl6ud/GEQBPN9XLt/njsmbcmOFxOhZOJIuKQCKar39NmfzIX67/a2bv3PhF2mORXoGuBxsh6xi3GBPd/tSdskdN/2HTOpLuManDK3n35sN1LEL4H3BHmFm6q2wFGRjKpWX20HA5qby4JWt2gX3NTNzrdGpAWySsnXvQfZbvcP4ULR66PcRQC/lbh4/JoMPdG/p0XV4mhF+BJKyLLo8ayJ1NMSndAihZT2wLvRSSj40QlcJWkwXjAEhI/ta7BFOJ2dmWqgpUOJVa964LYgNToYjJ9R0PqN8K/QMl/3zJGKjfC8UhFEcRaoH6abhjZ+4YK/MDS8IR3I6/u1ZT2lbASg0VBkoOPPJNIYOpnru4kcSa//Xz4xZCvVXZi+ANg9f7SJmVmyZmt73NgZasKgXrNPW+PJXNFLqsBJ6IdnTydpyydEDdrwboHFnoHUGt0WxVsDeDoerIc23mt25E6tzmjiPDH7nIZnLIrlChRuMWACrhk5xTmY64IkRfxIJjzWtxw9jEqFM8eeM876GJB7r5PMXhUiHa6Y0EA/RC4E8L4le6FKaJsfeUcrSI/UA2P32dvpHVPpdb2wGDn0sd9bieq94uJ9HpHmt6m5Jwi5U1/AJwLiM4CSKJdPJ6Uh8MTO+im+V+q0ooX+R0wn8qMAKDd5Hhg8/S8cqnkjOqq4Dc1pPps+DeVrDRnFHjYka6wOgBXZ4xh8ZvjiJpt45NaN0vmfc/0rHeTBui45tVYTQ4gB2uYbvC9ZHKlwYO5SY5shPZmjKzEvd6BAJ0TEXr9YN/H1M04+cdC+Yg2BzJDVGyCuFLTLctjuHYLkoaqw/lhgB"}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":714,"cache_read_input_tokens":11496,"output_tokens":2336,"output_tokens_details":{"thinking_tokens":273},"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":714},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1966,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXpjmcxqWg2eqXmyWBcp","requestRef":"7f388f8c-ab42-4ff2-a910-29866b623941","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"5ff54dce-c1f8-491d-bf96-7b430a9e12e9","timestamp":"2026-10-30T04:53:48.415Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}54{"parentUuid":"5ff54dce-c1f8-491d-bf96-7b430a9e12e9","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpjmwZdJKB2hWh9Tey9","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01HHF7xnyahK5Rk8aP6RhjgN","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Clean re-run: deleted out/results.json and out/counterexample.csv, re-ran analysis.py; SHA-256 of both files identical to the first run. PASS\n2. counterexample.csv has columns x,y and 100000 rows = counterexample_values.n = n_analysed = design n. PASS\n3. random_seed = counterexample_values.seed = 20261029 (design). PASS\n4. Construction identity |y| = |x| for every row (Y = ±X). PASS\n5. mean_sum / sd_sum recomputed from CSV match results.json (|diff| < 1e-9). PASS\n6. Nonzero sums equal 2x exactly; frac_sum_exactly_zero = 0.50047 ≈ 1/2 = P(W=-1); consistent with frac_w_equal_1 = 0.49953 (sum = 1). PASS\n7. Magnitudes: sd_x, sd_y ≈ 1; sd_sum = 1.406 ≈ sqrt(2) (theory: Var(X+Y)=E[(1+W)^2]E[X^2]=2). corr_xy ≈ 0 (theory: 0). PASS\n8. Theoretical KS distance between law of X+Y (0.5·δ0 + 0.5·N(0,4)) and N(0,2): 0.25, attained at 0 (CDF jumps 0.25→0.75 vs Φ(0)=0.5; difference decreases away from 0). Observed ks_sum_vs_normal = 0.2508. PASS\n9. Baseline (independent normals, prop. B): KS = 0.0020, two orders of magnitude below 0.2508; marginal KS for x, y ≈ 0.002, same order as baseline → marginals look normal, sum does not. PASS\n10. Note: ks_critical_value_5pct_approx = 1.358/sqrt(n) is the known-parameter KS critical value; with estimated parameters (Lilliefors) the correct value is smaller (~0.0028), so it is conservative for rejection. Reported as approximate only. NOTED\nEOF\ncat > out/argument.md <<'EOF'\n# Mathematical argument\n\n## Proposition B (TRUE): X, Y independent, X ~ N(μ1, σ1²), Y ~ N(μ2, σ2²) ⇒ X + Y ~ N(μ1+μ2, σ1²+σ2²).\n*Proof sketch.* The characteristic function of N(μ, σ²) is φ(t) = exp(iμt − σ²t²/2) (σ = 0 allowed: constant). By independence,\nφ_{X+Y}(t) = E[e^{itX}] E[e^{itY}] = exp(i(μ1+μ2)t − (σ1²+σ2²)t²/2),\nwhich is the characteristic function of N(μ1+μ2, σ1²+σ2²). By the uniqueness theorem for characteristic functions, X+Y has that law. ∎\n(More generally, the conclusion holds whenever (X, Y) is jointly Gaussian, since X+Y is a linear functional of a Gaussian vector.)\n\n## Proposition A (FALSE): marginal normality of X and Y does not imply normality of X + Y.\nNote that Y = −X is **not** a counterexample: X+Y ≡ 0 is a degenerate normal, which the proposition explicitly allows.\n\n**Counterexample.** Let X ~ N(0,1) and let W be independent of X with P(W = 1) = P(W = −1) = 1/2. Define Y = W·X.\n\n*Y is N(0,1).* For any Borel set B, P(Y ∈ B) = ½P(X ∈ B) + ½P(−X ∈ B) = P(X ∈ B), because −X ~ X by symmetry of N(0,1). So X and Y are both standard normal. (They are uncorrelated, E[XY] = E[W]E[X²] = 0, but not independent, since |Y| = |X|, and (X, Y) is not jointly Gaussian.)\n\n*X + Y is not normal.* X + Y = (1+W)X, which equals 0 when W = −1 and 2X when W = 1. Hence\nP(X + Y = 0) ≥ P(W = −1) = 1/2,\nindeed the law of X+Y is the mixture ½·δ₀ + ½·N(0,4). A normal distribution is either continuous (σ > 0, every point has probability 0) or a point mass (σ = 0, P(X+Y = c) = 1 for some c). X+Y has an atom of mass exactly 1/2 at 0 (P(2X = 0) = 0), so it is neither: X+Y is not normal, not even degenerately. Equivalently, E[X+Y] = 0 and Var(X+Y) = 2, yet P(X+Y = 0) = 1/2, impossible for N(0,2). ∎\n\nThe KS distance between the law of X+Y and N(0, 2) (matching mean and variance) is exactly 1/4: at 0 the CDF of X+Y jumps from 1/4 to 3/4 while Φ(0) = 1/2, and the gap shrinks away from 0.\n\n## Numerical illustration\n`out/analysis.py` draws n = 100000 pairs from this construction with `numpy.random.default_rng(20261029)` (design.csv) and writes them to `out/counterexample.csv`. See `out/results.json` → `counterexample_values` and `out/report.md`. The simulation illustrates, but does not prove, the claims above.\nEOF\necho \"- 2026-10-30 P2 passed: baseline (independent normals, KS of sum) computed in analysis.py. P3 passed: analysis.py written, seed 20261029. P4 passed: reproducibility + 10 consistency checks (state/checks.md).\" >> out/state/log.md","description":"Write checks and argument"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":714,"cache_read_input_tokens":11496,"output_tokens":2336,"output_tokens_details":{"thinking_tokens":273},"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":714},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXpjmcxqWg2eqXmyWBcp","requestRef":"7f388f8c-ab42-4ff2-a910-29866b623941","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"12d5444b-addf-4613-9637-5b4615b4dd1b","timestamp":"2026-10-30T04:54:05.942Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}55{"parentUuid":"12d5444b-addf-4613-9637-5b4615b4dd1b","isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01HHF7xnyahK5Rk8aP6RhjgN","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"d373a1c7-7240-420b-a4b0-9ab23e4b2fa1","timestamp":"2026-10-30T04:54:05.995Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"12d5444b-addf-4613-9637-5b4615b4dd1b","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}56{"type":"api-request-blob","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"37112ba4e3639fcc05da2e212e95e1b70ec2fd08dbcab1252fef291f4a3da847","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01HHF7xnyahK5Rk8aP6RhjgN","name":"Bash","input":{"command":"cat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Clean re-run: deleted out/results.json and out/counterexample.csv, re-ran analysis.py; SHA-256 of both files identical to the first run. PASS\n2. counterexample.csv has columns x,y and 100000 rows = counterexample_values.n = n_analysed = design n. PASS\n3. random_seed = counterexample_values.seed = 20261029 (design). PASS\n4. Construction identity |y| = |x| for every row (Y = ±X). PASS\n5. mean_sum / sd_sum recomputed from CSV match results.json (|diff| < 1e-9). PASS\n6. Nonzero sums equal 2x exactly; frac_sum_exactly_zero = 0.50047 ≈ 1/2 = P(W=-1); consistent with frac_w_equal_1 = 0.49953 (sum = 1). PASS\n7. Magnitudes: sd_x, sd_y ≈ 1; sd_sum = 1.406 ≈ sqrt(2) (theory: Var(X+Y)=E[(1+W)^2]E[X^2]=2). corr_xy ≈ 0 (theory: 0). PASS\n8. Theoretical KS distance between law of X+Y (0.5·δ0 + 0.5·N(0,4)) and N(0,2): 0.25, attained at 0 (CDF jumps 0.25→0.75 vs Φ(0)=0.5; difference decreases away from 0). Observed ks_sum_vs_normal = 0.2508. PASS\n9. Baseline (independent normals, prop. B): KS = 0.0020, two orders of magnitude below 0.2508; marginal KS for x, y ≈ 0.002, same order as baseline → marginals look normal, sum does not. PASS\n10. Note: ks_critical_value_5pct_approx = 1.358/sqrt(n) is the known-parameter KS critical value; with estimated parameters (Lilliefors) the correct value is smaller (~0.0028), so it is conservative for rejection. Reported as approximate only. NOTED\nEOF\ncat > out/argument.md <<'EOF'\n# Mathematical argument\n\n## Proposition B (TRUE): X, Y independent, X ~ N(μ1, σ1²), Y ~ N(μ2, σ2²) ⇒ X + Y ~ N(μ1+μ2, σ1²+σ2²).\n*Proof sketch.* The characteristic function of N(μ, σ²) is φ(t) = exp(iμt − σ²t²/2) (σ = 0 allowed: constant). By independence,\nφ_{X+Y}(t) = E[e^{itX}] E[e^{itY}] = exp(i(μ1+μ2)t − (σ1²+σ2²)t²/2),\nwhich is the characteristic function of N(μ1+μ2, σ1²+σ2²). By the uniqueness theorem for characteristic functions, X+Y has that law. ∎\n(More generally, the conclusion holds whenever (X, Y) is jointly Gaussian, since X+Y is a linear functional of a Gaussian vector.)\n\n## Proposition A (FALSE): marginal normality of X and Y does not imply normality of X + Y.\nNote that Y = −X is **not** a counterexample: X+Y ≡ 0 is a degenerate normal, which the proposition explicitly allows.\n\n**Counterexample.** Let X ~ N(0,1) and let W be independent of X with P(W = 1) = P(W = −1) = 1/2. Define Y = W·X.\n\n*Y is N(0,1).* For any Borel set B, P(Y ∈ B) = ½P(X ∈ B) + ½P(−X ∈ B) = P(X ∈ B), because −X ~ X by symmetry of N(0,1). So X and Y are both standard normal. (They are uncorrelated, E[XY] = E[W]E[X²] = 0, but not independent, since |Y| = |X|, and (X, Y) is not jointly Gaussian.)\n\n*X + Y is not normal.* X + Y = (1+W)X, which equals 0 when W = −1 and 2X when W = 1. Hence\nP(X + Y = 0) ≥ P(W = −1) = 1/2,\nindeed the law of X+Y is the mixture ½·δ₀ + ½·N(0,4). A normal distribution is either continuous (σ > 0, every point has probability 0) or a point mass (σ = 0, P(X+Y = c) = 1 for some c). X+Y has an atom of mass exactly 1/2 at 0 (P(2X = 0) = 0), so it is neither: X+Y is not normal, not even degenerately. Equivalently, E[X+Y] = 0 and Var(X+Y) = 2, yet P(X+Y = 0) = 1/2, impossible for N(0,2). ∎\n\nThe KS distance between the law of X+Y and N(0, 2) (matching mean and variance) is exactly 1/4: at 0 the CDF of X+Y jumps from 1/4 to 3/4 while Φ(0) = 1/2, and the gap shrinks away from 0.\n\n## Numerical illustration\n`out/analysis.py` draws n = 100000 pairs from this construction with `numpy.random.default_rng(20261029)` (design.csv) and writes them to `out/counterexample.csv`. See `out/results.json` → `counterexample_values` and `out/report.md`. The simulation illustrates, but does not prove, the claims above.\nEOF\necho \"- 2026-10-30 P2 passed: baseline (independent normals, KS of sum) computed in analysis.py. P3 passed: analysis.py written, seed 20261029. P4 passed: reproducibility + 10 consistency checks (state/checks.md).\" >> out/state/log.md","description":"Write checks and argument"}}]}}57{"type":"api-request","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","id":"94e23a2b-064d-4b68-851e-7133c21a1acd","timestamp":"2026-10-30T04:54:05.998Z","version":"2.1.314","querySource":"sdk","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","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":"7f388f8c-ab42-4ff2-a910-29866b623941","keep":16,"tail":["37112ba4e3639fcc05da2e212e95e1b70ec2fd08dbcab1252fef291f4a3da847","058caf2061d0f8a788b227003880d3f35db13947c0564f8538e53d1f0c504cc8"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",17,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"28ab66412ea4ba748948884dbf930dcf49921a3584aca0d83bd5230997224f12"}58{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"d373a1c7-7240-420b-a4b0-9ab23e4b2fa1","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b"}59{"type":"atis-latch","atis":"","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b"}60{"parentUuid":"d373a1c7-7240-420b-a4b0-9ab23e4b2fa1","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpmT35hRgiGU1jjbvrn","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01EyFGj2A9wkMU161gH31jnU","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# Report — F5-conf-03: sums of normally distributed random variables\n\n## Question\nAre the following true? **A:** if X and Y are each normally distributed, X + Y is normal (constants count as degenerate normals). **B:** if X and Y are independent and each normal, X + Y is normal. Verdicts rest on the proofs in `out/argument.md`; the simulation is only an illustration.\n\n## Data and exclusions\n`data/propositions.csv` (2 rows) and `data/design.csv` (2 rows) were read in full (`n_input_rows`). SHA-256 hashes match `bundle.json`. No data issues were found (`data_issues` = []), and nothing was excluded (`out/exclusions.csv`). The design fixes seed = 20261029 (`random_seed`) and n = 100000 (`n_analysed`).\n\n## Method\n- **B:** proved with characteristic functions plus independence (`out/argument.md`).\n- **A:** refuted with an explicit counterexample. X ~ N(0,1), W = ±1 with probability 1/2 each, independent of X, and Y = W·X. Then Y ~ N(0,1) by symmetry, but X+Y = (1+W)X has law ½δ₀ + ½N(0,4). That law has an atom of mass 1/2 at 0, so it is not normal, not even a degenerate normal. Y = −X was deliberately not used: its sum is a constant, which the proposition counts as normal.\n- **Numerical illustration:** `out/analysis.py` simulates n pairs with `numpy.random.default_rng(seed)` and writes them to `out/counterexample.csv`. It computes sample means and SDs (ddof = 1). It also computes the KS distance of each variable from a normal with the same sample mean and SD.\n- **Baseline:** with the same rule, the script computes the KS distance of the sum of two *independent* N(0,1) samples drawn from the same generator after the counterexample sample. This is the prop. B case.\n\n## Results\n- Verdict A: **false** (`statement_true` = false). A counterexample is given (`counterexample_provided` = true; construction in `counterexample_values.construction`).\n- Verdict B: **true** (`statement_b_true` = true).\n- Marginals: mean_x = −0.0033, sd_x = 0.9982, mean_y = −0.0002 and sd_y = 0.9982 (`counterexample_values.*`). Their KS distances from a fitted normal are 0.0021 (`ks_x_vs_normal`) and 0.0020 (`ks_y_vs_normal`). These are the same size as the baseline for a truly normal sum, 0.0020 (`baseline_independent_ks_sum_vs_normal`).\n- Sum: mean_sum = −0.0036 and sd_sum = 1.4059, close to √2 (`counterexample_values.mean_sum`, `.sd_sum`). However, its KS distance from N(mean_sum, sd_sum²) is **0.2508** (`counterexample_values.ks_sum_vs_normal`). That is about 120 times the baseline and close to the exact theoretical value of 1/4. The cause is that 50.05% of the simulated sums are exactly 0 (`frac_sum_exactly_zero`), which a continuous normal would give with probability 0.\n- The sample correlation of x and y is −0.0082 (`corr_xy`). So x and y are uncorrelated but dependent (|y| = |x|), and (X, Y) is not jointly Gaussian.\n- Feasibility: `feasibility` = \"complete\".\n\n## Uncertainty\nThe verdicts are mathematical and carry no sampling uncertainty. The simulated statistics do vary with the sample. For comparison, an approximate 5% KS critical value is 0.0043 (`ks_critical_value_5pct_approx`). This uses the known-parameter formula 1.358/√n, which is conservative when the parameters are estimated. The marginal KS values fall below it, and the sum's KS value exceeds it by a factor of about 58. The atom fraction 0.50047 is within about 0.3 binomial SDs of 1/2 (SD = √(0.25/n) ≈ 0.0016).\n\n## Limitations and open issues\n- **What the simulation shows and what it does not.** At this seed and n, the sample's marginals are numerically indistinguishable from normal while its sum clearly is not. That is consistent with the proof. A finite sample cannot prove that a distribution is or is not normal; the verdicts rest only on `out/argument.md`.\n- The KS statistics are descriptive. No formal Lilliefors-corrected p-values were computed, and none are needed for the verdict.\n- No other open issues.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"Proposition A is false: marginal normality of X and Y does not imply normality of X+Y.\",\"results_keys\":[\"statement_true\"],\"status\":\"supported\",\"caveat\":\"Supported by the mathematical counterexample in argument.md; the simulation is illustrative only.\"},\n {\"id\":\"C2\",\"text\":\"Counterexample: X ~ N(0,1), W Rademacher independent of X, Y = W*X; Y ~ N(0,1) but X+Y = 0.5*delta_0 + 0.5*N(0,4) is not normal (atom of mass 1/2 at 0).\",\"results_keys\":[\"counterexample_provided\",\"counterexample_values\"],\"status\":\"supported\",\"caveat\":\"Y = -X is not a valid counterexample because constants count as degenerate normals.\"},\n {\"id\":\"C3\",\"text\":\"Proposition B is true: the sum of independent normals is normal with summed means and variances.\",\"results_keys\":[\"statement_b_true\",\"baseline_independent_ks_sum_vs_normal\"],\"status\":\"supported\",\"caveat\":\"Proof via characteristic functions; the baseline simulation only illustrates it.\"},\n {\"id\":\"C4\",\"text\":\"In the simulated sample (seed 20261029, n=100000) the marginals look normal (KS about 0.002, the same as the independent baseline) while the sum departs clearly (KS 0.2508, about 1/4 as theory predicts; about 50% of the sums are exactly zero).\",\"results_keys\":[\"counterexample_values\",\"ks_x_vs_normal\",\"ks_y_vs_normal\",\"baseline_independent_ks_sum_vs_normal\",\"frac_sum_exactly_zero\",\"n_analysed\",\"random_seed\"],\"status\":\"supported\",\"caveat\":\"Finite-sample illustration; not a proof. The KS critical value used is approximate (known-parameter formula).\"},\n {\"id\":\"C5\",\"text\":\"X and Y in the counterexample are uncorrelated but dependent, so (X,Y) is not jointly Gaussian.\",\"results_keys\":[\"corr_xy\"],\"status\":\"supported\",\"caveat\":\"Zero correlation is exact in theory; the sample value is -0.0082.\"}\n]\nEOF\ncat > out/state/phases.json <<'EOF'\n{\n \"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read in full\",\"contract.md written with estimands, outputs, rules, invalidity conditions\"],\"notes\":\"\"},\n \"P1\":{\"status\":\"passed\",\"checks\":[\"SHA-256 of both inputs computed and matched bundle.json\",\"schema/rows/missing/duplicates inspected\",\"exclusions.csv written (0 removed; 100000 analysed)\"],\"notes\":\"No availability violations.\"},\n \"P2\":{\"status\":\"passed\",\"checks\":[\"baseline: KS of sum of independent normals = 0.0020 under same rule (baseline_* keys)\"],\"notes\":\"\"},\n \"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py reads data/ only, seed 20261029 from design, writes results.json and counterexample.csv\"],\"notes\":\"\"},\n \"P4\":{\"status\":\"passed\",\"checks\":[\"clean re-run produced byte-identical results.json and counterexample.csv\",\"10 consistency checks in state/checks.md all pass\"],\"notes\":\"\"},\n \"P5\":{\"status\":\"passed\",\"checks\":[\"report.md with required sections citing results keys\",\"claims.json written; all report claims in ledger\",\"argument.md written\"],\"notes\":\"\"}\n}\nEOF\necho \"- 2026-10-30 P5 passed: report, claims, argument written. Task complete.\" >> out/state/log.md\n~/wp29/venv/bin/python -c \"import json;json.load(open('out/claims.json'));json.load(open('out/state/phases.json'));print('ok')\"; ls out","description":"Write report, claims, phase ledger"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2351,"cache_read_input_tokens":12210,"output_tokens":2937,"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":2351},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXpmSrRCgpTGJRLbsKDA","requestRef":"94e23a2b-064d-4b68-851e-7133c21a1acd","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"284ed009-f0ba-4d3a-ab11-436c9050f925","timestamp":"2026-10-30T04:54:31.447Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}61{"parentUuid":"284ed009-f0ba-4d3a-ab11-436c9050f925","isSidechain":false,"promptId":"a98c6146-473d-47ef-a39f-00f4dbc804af","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01EyFGj2A9wkMU161gH31jnU","type":"tool_result","content":"ok\nanalysis.py\nargument.md\nclaims.json\ncounterexample.csv\nexclusions.csv\nreport.md\nresults.json\nstate","is_error":false}]},"uuid":"3336c17b-4f74-45df-b591-6769e0f524c5","timestamp":"2026-10-30T04:54:31.517Z","toolUseResult":{"stdout":"ok\nanalysis.py\nargument.md\nclaims.json\ncounterexample.csv\nexclusions.csv\nreport.md\nresults.json\nstate","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"284ed009-f0ba-4d3a-ab11-436c9050f925","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}62{"type":"api-request-blob","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","hash":"92bdd728dcdf08a61f28324afee2940c740e32af3f266e907c56de97e1157418","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01EyFGj2A9wkMU161gH31jnU","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# Report — F5-conf-03: sums of normally distributed random variables\n\n## Question\nAre the following true? **A:** if X and Y are each normally distributed, X + Y is normal (constants count as degenerate normals). **B:** if X and Y are independent and each normal, X + Y is normal. Verdicts rest on the proofs in `out/argument.md`; the simulation is only an illustration.\n\n## Data and exclusions\n`data/propositions.csv` (2 rows) and `data/design.csv` (2 rows) were read in full (`n_input_rows`). SHA-256 hashes match `bundle.json`. No data issues were found (`data_issues` = []), and nothing was excluded (`out/exclusions.csv`). The design fixes seed = 20261029 (`random_seed`) and n = 100000 (`n_analysed`).\n\n## Method\n- **B:** proved with characteristic functions plus independence (`out/argument.md`).\n- **A:** refuted with an explicit counterexample. X ~ N(0,1), W = ±1 with probability 1/2 each, independent of X, and Y = W·X. Then Y ~ N(0,1) by symmetry, but X+Y = (1+W)X has law ½δ₀ + ½N(0,4). That law has an atom of mass 1/2 at 0, so it is not normal, not even a degenerate normal. Y = −X was deliberately not used: its sum is a constant, which the proposition counts as normal.\n- **Numerical illustration:** `out/analysis.py` simulates n pairs with `numpy.random.default_rng(seed)` and writes them to `out/counterexample.csv`. It computes sample means and SDs (ddof = 1). It also computes the KS distance of each variable from a normal with the same sample mean and SD.\n- **Baseline:** with the same rule, the script computes the KS distance of the sum of two *independent* N(0,1) samples drawn from the same generator after the counterexample sample. This is the prop. B case.\n\n## Results\n- Verdict A: **false** (`statement_true` = false). A counterexample is given (`counterexample_provided` = true; construction in `counterexample_values.construction`).\n- Verdict B: **true** (`statement_b_true` = true).\n- Marginals: mean_x = −0.0033, sd_x = 0.9982, mean_y = −0.0002 and sd_y = 0.9982 (`counterexample_values.*`). Their KS distances from a fitted normal are 0.0021 (`ks_x_vs_normal`) and 0.0020 (`ks_y_vs_normal`). These are the same size as the baseline for a truly normal sum, 0.0020 (`baseline_independent_ks_sum_vs_normal`).\n- Sum: mean_sum = −0.0036 and sd_sum = 1.4059, close to √2 (`counterexample_values.mean_sum`, `.sd_sum`). However, its KS distance from N(mean_sum, sd_sum²) is **0.2508** (`counterexample_values.ks_sum_vs_normal`). That is about 120 times the baseline and close to the exact theoretical value of 1/4. The cause is that 50.05% of the simulated sums are exactly 0 (`frac_sum_exactly_zero`), which a continuous normal would give with probability 0.\n- The sample correlation of x and y is −0.0082 (`corr_xy`). So x and y are uncorrelated but dependent (|y| = |x|), and (X, Y) is not jointly Gaussian.\n- Feasibility: `feasibility` = \"complete\".\n\n## Uncertainty\nThe verdicts are mathematical and carry no sampling uncertainty. The simulated statistics do vary with the sample. For comparison, an approximate 5% KS critical value is 0.0043 (`ks_critical_value_5pct_approx`). This uses the known-parameter formula 1.358/√n, which is conservative when the parameters are estimated. The marginal KS values fall below it, and the sum's KS value exceeds it by a factor of about 58. The atom fraction 0.50047 is within about 0.3 binomial SDs of 1/2 (SD = √(0.25/n) ≈ 0.0016).\n\n## Limitations and open issues\n- **What the simulation shows and what it does not.** At this seed and n, the sample's marginals are numerically indistinguishable from normal while its sum clearly is not. That is consistent with the proof. A finite sample cannot prove that a distribution is or is not normal; the verdicts rest only on `out/argument.md`.\n- The KS statistics are descriptive. No formal Lilliefors-corrected p-values were computed, and none are needed for the verdict.\n- No other open issues.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"Proposition A is false: marginal normality of X and Y does not imply normality of X+Y.\",\"results_keys\":[\"statement_true\"],\"status\":\"supported\",\"caveat\":\"Supported by the mathematical counterexample in argument.md; the simulation is illustrative only.\"},\n {\"id\":\"C2\",\"text\":\"Counterexample: X ~ N(0,1), W Rademacher independent of X, Y = W*X; Y ~ N(0,1) but X+Y = 0.5*delta_0 + 0.5*N(0,4) is not normal (atom of mass 1/2 at 0).\",\"results_keys\":[\"counterexample_provided\",\"counterexample_values\"],\"status\":\"supported\",\"caveat\":\"Y = -X is not a valid counterexample because constants count as degenerate normals.\"},\n {\"id\":\"C3\",\"text\":\"Proposition B is true: the sum of independent normals is normal with summed means and variances.\",\"results_keys\":[\"statement_b_true\",\"baseline_independent_ks_sum_vs_normal\"],\"status\":\"supported\",\"caveat\":\"Proof via characteristic functions; the baseline simulation only illustrates it.\"},\n {\"id\":\"C4\",\"text\":\"In the simulated sample (seed 20261029, n=100000) the marginals look normal (KS about 0.002, the same as the independent baseline) while the sum departs clearly (KS 0.2508, about 1/4 as theory predicts; about 50% of the sums are exactly zero).\",\"results_keys\":[\"counterexample_values\",\"ks_x_vs_normal\",\"ks_y_vs_normal\",\"baseline_independent_ks_sum_vs_normal\",\"frac_sum_exactly_zero\",\"n_analysed\",\"random_seed\"],\"status\":\"supported\",\"caveat\":\"Finite-sample illustration; not a proof. The KS critical value used is approximate (known-parameter formula).\"},\n {\"id\":\"C5\",\"text\":\"X and Y in the counterexample are uncorrelated but dependent, so (X,Y) is not jointly Gaussian.\",\"results_keys\":[\"corr_xy\"],\"status\":\"supported\",\"caveat\":\"Zero correlation is exact in theory; the sample value is -0.0082.\"}\n]\nEOF\ncat > out/state/phases.json <<'EOF'\n{\n \"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read in full\",\"contract.md written with estimands, outputs, rules, invalidity conditions\"],\"notes\":\"\"},\n \"P1\":{\"status\":\"passed\",\"checks\":[\"SHA-256 of both inputs computed and matched bundle.json\",\"schema/rows/missing/duplicates inspected\",\"exclusions.csv written (0 removed; 100000 analysed)\"],\"notes\":\"No availability violations.\"},\n \"P2\":{\"status\":\"passed\",\"checks\":[\"baseline: KS of sum of independent normals = 0.0020 under same rule (baseline_* keys)\"],\"notes\":\"\"},\n \"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py reads data/ only, seed 20261029 from design, writes results.json and counterexample.csv\"],\"notes\":\"\"},\n \"P4\":{\"status\":\"passed\",\"checks\":[\"clean re-run produced byte-identical results.json and counterexample.csv\",\"10 consistency checks in state/checks.md all pass\"],\"notes\":\"\"},\n \"P5\":{\"status\":\"passed\",\"checks\":[\"report.md with required sections citing results keys\",\"claims.json written; all report claims in ledger\",\"argument.md written\"],\"notes\":\"\"}\n}\nEOF\necho \"- 2026-10-30 P5 passed: report, claims, argument written. Task complete.\" >> out/state/log.md\n~/wp29/venv/bin/python -c \"import json;json.load(open('out/claims.json'));json.load(open('out/state/phases.json'));print('ok')\"; ls out","description":"Write report, claims, phase ledger"}}]}}63{"type":"api-request","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","id":"bb23cab5-2a49-4b30-8b45-f615bc5f5929","timestamp":"2026-10-30T04:54:31.520Z","version":"2.1.314","querySource":"sdk","shapeHash":"47b7636614dba2f4e82948232db5055e82959bf76553cac3661cf89390142763","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":"94e23a2b-064d-4b68-851e-7133c21a1acd","keep":18,"tail":["92bdd728dcdf08a61f28324afee2940c740e32af3f266e907c56de97e1157418","2ff9b6108deb375094106991164c77c7abc30258e27a7df32d0db43638b6bcc8"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",19,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"f3fd3f7d13b40703f70983f91fc1fc69c443ecc3d02f728fff81195363984a81"}64{"parentUuid":"3336c17b-4f74-45df-b591-6769e0f524c5","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpoLGLkrzpeBjXKCJP3","type":"message","role":"assistant","content":[{"type":"text","text":"Proposition A is **false** and proposition B is **true**. Everything required is written under `out/`, and re-running `out/analysis.py` from a clean state gave byte-identical `results.json` and `counterexample.csv`.\n\n**Proposition A** (if X and Y are each normal, then X + Y is normal):\n- **Counterexample:** take X ~ N(0,1) and an independent random sign W (+1 or −1, each with probability ½), and set Y = W·X. Y is standard normal because the normal distribution is symmetric.\n- **Why the sum is not normal:** X + Y is 0 whenever W = −1, and 2X otherwise. So it equals exactly 0 with probability ½ and is spread out as N(0,4) the rest of the time. A normal is either continuous or a single constant, so this law is neither.\n- **Why not Y = −X:** that pair would make the sum a constant, which the proposition explicitly counts as normal, so it is not a counterexample.\n\n**Proposition B** (independent normals sum to a normal) is proved using characteristic functions. The proofs and the counterexample are in `out/argument.md`.\n\n**Simulation** (seed 20261029, n = 100,000, from `design.csv`):\n- **Marginals look normal:** x and y each have SD ≈ 0.998. Their Kolmogorov–Smirnov (KS) distances from a fitted normal are about 0.002. That matches the baseline of two independent normals added together (KS 0.0020).\n- **The sum clearly does not:** its KS distance from a fitted normal is 0.2508, close to the theoretical value of exactly ¼. 50.05% of the simulated sums are exactly zero.\n\n**Limitations:**\n- The simulation only illustrates the result; the verdicts rest on the proofs.\n- The KS statistics are descriptive. The 5% critical value quoted for comparison (0.0043) is an approximation that is conservative here.\n\nNo data issues were found and nothing was excluded. I also wrote `report.md`, `claims.json`, `exclusions.csv` and the `out/state/` records, and all phases P0–P5 are marked passed with their checks recorded."}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2986,"cache_read_input_tokens":14561,"output_tokens":713,"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":2986},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXpoKzTm6Wr6gjcRTJwS","requestRef":"bb23cab5-2a49-4b30-8b45-f615bc5f5929","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"8ffddf47-e5f6-46b9-82e9-0c999287c713","timestamp":"2026-10-30T04:54:39.744Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0181","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","version":"2.1.314","gitBranch":"HEAD"}65{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"8ffddf47-e5f6-46b9-82e9-0c999287c713","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b"}66{"type":"cost-state","sessionId":"c1807878-d3f1-4230-a5fe-80e295a9ca1b","totalCostUSD":0.3184262,"totalAPIDuration":109378,"totalAPIDurationWithoutRetries":109371,"totalToolDuration":2408,"totalLinesAdded":0,"totalLinesRemoved":0,"totalDuration":111916,"startTime":1793335967835,"modelUsage":{"claude-opus-5-5":{"inputTokens":22,"outputTokens":11101,"thinkingTokens":1034,"cacheReadInputTokens":80516,"cacheCreationInputTokens":16043,"cacheCreationEphemeral5mInputTokens":16043,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.3184262}},"hasUnknownModelCost":false}67