spb/wp29_uqo

1{"type":"atis-latch","atis":"","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a"}2{"type":"queue-operation","operation":"enqueue","timestamp":"2026-10-30T04:52:42.488Z","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","content":"Begin"}3{"type":"queue-operation","operation":"dequeue","timestamp":"2026-10-30T04:52:42.494Z","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a"}4{"parentUuid":null,"isSidechain":false,"promptId":"85b06671-532b-4c9e-8e6f-8074c90eb744","type":"user","message":{"role":"user","content":"Begin"},"uuid":"b76a772f-3a1d-4398-bb16-1e7c332e7f3c","timestamp":"2026-10-30T04:52:42.499Z","permissionMode":"default","promptSource":"sdk","turnOrigin":"sdk","turnPosition":{"promptIndex":0,"turnIndex":1},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}5{"type":"api-request-shape","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","shapeHash":"eede6e4d945549fee9828dd471cd62f36fe68556045b0d15ba98001ddf689e37","timestamp":"2026-10-30T04:52:42.512Z","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/RC0183\nDate: 2026-10-30\n\nYou are a research assistant executing one bounded scientific task inside the current working directory, which is your workspace.\n\nEnvironment facts (identical for every task):\n- The task statement is the file `TASK.md` in the workspace. It is the complete and only authoritative description of what is required: the scientific question, the inputs under `data/`, the required output files and their exact keys, and the information-availability rules.\n- There is no network access. Use the Python interpreter `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels, matplotlib are installed). Standard shell tools are available. Do not try to install packages.\n- Write every deliverable under `./out/`. The required deliverables are listed in `TASK.md`; at minimum they always include `out/results.json`, `out/report.md`, and a replication entry point `out/analysis.py` that regenerates `out/results.json` from `data/` when run with `~/wp29/venv/bin/python out/analysis.py` from the workspace root.\n- You are working alone and unattended; nobody will answer questions. Make reasonable, documented decisions.\n\nIntegrity rules (identical for every task):\n- Never fabricate numbers, data, results, or references. Every number in `out/results.json` and `out/report.md` must be produced by code you ran on the provided inputs.\n- Respect the information-availability rules in `TASK.md` exactly (for example, never use information that would not have been available at the stated decision time).\n- If part of the task cannot be completed as specified, say so explicitly in `out/report.md`, explain why, and still write every required file (use `null` for values you could not legitimately produce). An honest statement of a limitation is always preferred to a fabricated or guessed value.\n- Do not modify anything under `data/`.\n- When you are done, end with a brief plain-text summary of what you produced and any limitations.\n\nComplete the task described in `TASK.md` by following this research protocol. The protocol adds no scientific information to the task; it organizes how you work and what evidence you leave behind.\n\nPHASES (execute in order; a phase is eligible only when its dependencies are satisfied):\n\nP0 Scope and contract (depends on: nothing)\n- Read `TASK.md` completely. In `out/state/contract.md`, restate in your own words: the scientific question; the quantity or quantities to be estimated (the estimands) and the assumptions under which they are meaningful; every required output file and key; the information-availability rules; what would make the task impossible or the result invalid.\n- Write the initial phase ledger `out/state/phases.json`: a JSON object mapping each phase id (P0 … P5) to {\"status\": \"pending\"|\"running\"|\"passed\"|\"failed\"|\"blocked\"|\"stale\"|\"skipped_optional\", \"checks\": [], \"notes\": \"\"}. Keep it current as you work. A phase may only be set to \"passed\" when the checks listed for it in this protocol have actually been executed and their outcome recorded in \"checks\".\n\nP1 Data audit and provenance (depends on: P0)\n- Inspect every input file: compute and record its SHA-256, row and column counts, schema, units, date ranges, missing values, duplicates and anomalies in `out/state/data_audit.md`.\n- Keep an exclusion ledger in `out/exclusions.csv` (columns: step, rule, n_before, n_after, n_removed, rationale) for every filtering step you apply, so that n_raw − total removed = n_analysed.\n- Identify any input that violates the information-availability rules and decide, in writing, how you will handle it.\n\nP2 Baseline (depends on: P1)\n- Before any elaborate method, compute the simplest valid baseline that answers the question (for example a naïve or unconditional estimate), with the same evaluation rule used later. Record it in `out/results.json` under the keys the task requires, or under `baseline_*` keys when the task does not name them.\n\nP3 Method and computation (depends on: P2)\n- Implement the analysis in `out/analysis.py` so that it reads only `data/`, writes `out/results.json` deterministically (fix every random seed you use and record it), and prints nothing that contradicts the written results. Any figure or table must be generated by this script.\n\nP4 Verification (depends on: P3)\n- Re-run `out/analysis.py` from a clean state and confirm it regenerates `out/results.json` with identical values. Record the check in `out/state/phases.json` under P4.\n- Check internal consistency: identities that must hold (for example counts that must add up, standard errors that must be positive, confidence intervals that must contain their estimates, date orderings that must respect the information rules), units, and magnitudes against the baseline. Record every check and its outcome in `out/state/checks.md`. A failed check must be fixed or honestly reported, never silently ignored.\n\nP5 Reporting (depends on: P4)\n- Write `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. Every quantitative statement must cite the key of `out/results.json` it comes from.\n- Write `out/claims.json`: a list of the central claims of your report, each as {\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}. Do not state a claim in the report that is not in this ledger.\n- Set the final statuses in `out/state/phases.json`.\n\nSTOPPING RULES\n- Stop and declare the task complete only when every phase P0–P5 is \"passed\" with recorded checks. If a phase is \"blocked\" (missing information, impossible requirement, violated availability rule), stop, set the status, explain in `out/report.md` (section Limitations and open issues) and still write every required file with `null` for values you could not legitimately produce.\n- Do not spend effort on extensions that the task does not require.\n\nRECOVERY RULES\n- Append a short dated entry to `out/state/log.md` after each phase transition and after any important decision, so that work can be resumed by reading `out/state/`.\n- If you discover that an upstream input or decision changed after a downstream phase passed, mark the downstream phases \"stale\" and redo them; do not reuse stale results.\n- If you are interrupted and later resumed, first read `out/state/` and continue from the last consistent state; never re-run expensive steps that already have recorded, unchanged outputs.\n\nEXECUTABLE GATES (additional, mandatory)\n- A read-only gate program is provided at `~/wp29/gates/pgar_gate.py`. Run it from the workspace root as `~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .` It checks the output contract of `TASK.md` (required files, keys, types, finite values, report sections, the claims ledger, the phase ledger, the exclusion ledger) and reproducibility (it re-runs `out/analysis.py` in a temporary copy and compares the regenerated `out/results.json` with yours). It never checks scientific correctness and it contains no reference answers.\n- You must run the gate at the end of P4 and again at the end of P5, and record each run's receipt (the gate writes `out/state/gate_receipts/<timestamp>.json`) in `out/state/phases.json`. You may not declare the task complete while the latest gate receipt reports `\"passed\": false`. Fix the reported problems and re-run the gate.\n- The controller will run the same gate after your session ends. If it fails, you will be resumed with the gate output and asked to fix the problems; each such cycle consumes your remaining budget.\n"}],"tools":[{"name":"Bash","description":"execute shell commands","input_schema":{"$schema":"https://json-schema.org/draft/2020-12/schema","type":"object","properties":{"command":{"description":"The command to execute","type":"string"},"timeout":{"description":"Optional timeout in milliseconds (max 600000 for a foreground command)","type":"number"},"description":{"description":"Clear, concise description of what this command does in active voice. 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the user's own instructions about these lines, such as a CLAUDE.md or memory rule, take precedence over this reminder, but do not add attribution lines this reminder leaves out):\n- End git commit messages with:\nCo-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>\n- End pull request descriptions with:\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n</system-reminder>"}],"renderedRole":"user","renderedBesideToolResult":true,"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a"}12{"parentUuid":"7c00bb27-a766-469e-ac1c-95000e93cbc8","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpfNzLAz1gq3fc1sdKJ","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":4,"cache_creation_input_tokens":2603,"cache_read_input_tokens":1504,"output_tokens":117,"output_tokens_details":{"thinking_tokens":15},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":2603},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":391,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXpfNhiPEm2oGdZtBjRR","requestRef":"b2f9bf0b-d8c5-4715-86b2-8128163435df","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"db78e92e-be51-45f7-9165-54f3c6164d93","timestamp":"2026-10-30T04:52:45.265Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"db78e92e-be51-45f7-9165-54f3c6164d93","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpfNzLAz1gq3fc1sdKJ","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01643zfUkQhjhNAzifUQoYp1","name":"Bash","input":{"command":"cat TASK.md; 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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). 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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). 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** Decide truth of two propositions about sums of normal r.v.s:\n- A: X, Y each normal (no joint assumption) => 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 a visibly non-normal sum.\n**Note.** The counterexample must yield a sum that is not normal *and not constant* (Y=-X is excluded since a constant counts as normal).\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); 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No availability-rule violations: inputs are statements and design parameters only.\n- No anomalies detected; no exclusions applied (the exclusion ledger records a no-op step).\nEOF\ncat > exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n1,keep all proposition rows (no filtering),2,2,0,both propositions must be assessed\nEOF\necho \"- 2026-10-30 P1: audited inputs (hashes match bundle), no issues, no exclusions. Counterexample choice: Y = S*X with S independent Rademacher sign; X+Y=(1+S)X has atom 1/2 at 0, nondegenerate.\" >> 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":1294,"cache_read_input_tokens":6120,"output_tokens":1643,"output_tokens_details":{"thinking_tokens":336},"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":1294},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXpfgM6yh5hR6BAJaJcY","requestRef":"10847219-cfeb-491f-a837-1f948b8301c5","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"1ee6d929-f55c-4439-8da1-1f94736bb4f1","timestamp":"2026-10-30T04:53:03.463Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183/out/state","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}27{"parentUuid":"1ee6d929-f55c-4439-8da1-1f94736bb4f1","isSidechain":false,"promptId":"85b06671-532b-4c9e-8e6f-8074c90eb744","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 1\n(eval):cd:1: no such file or directory: out\n(eval):18: no such file or directory: state/log.md","is_error":true,"tool_use_id":"toolu_01SrRzqetuKEnEyTQMCmh1v8"}]},"uuid":"1635c4ce-9f14-43e0-82ad-4677f400c705","timestamp":"2026-10-30T04:53:03.478Z","toolUseResult":"Error: Exit code 1\n(eval):cd:1: no such file or directory: out\n(eval):18: no such file or directory: state/log.md","sandboxed":false,"sourceToolAssistantUUID":"1ee6d929-f55c-4439-8da1-1f94736bb4f1","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183/out/state","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}28{"type":"api-request-blob","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","hash":"822380baf5a8104f288393a4ba2c59843742885aaf9da194144a02ee21780a1c","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01MpL37wZxUgAVePKDxAQRr2","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 about sums of normal r.v.s:\n- A: X, Y each normal (no joint assumption) => 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 a visibly non-normal sum.\n**Note.** The counterexample must yield a sum that is not normal *and not constant* (Y=-X is excluded since a constant counts as normal).\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 (6 sections); out/analysis.py; out/claims.json; plus state ledgers and out/exclusions.csv.\n**Information rules.** Only data/; verdicts rest on proofs, simulation is illustration only; use design seed and n with numpy default_rng.\n**Invalidity.** Missing/unparseable seed or n; a \"counterexample\" whose sum is constant or normal; using simulation as proof.\nEOF\ncat > log.md <<'EOF'\n# Log\n- 2026-10-30 P0: read TASK.md, wrote contract. P1 started.\nEOF","description":"Write contract and log"}},{"type":"tool_use","id":"toolu_01SrRzqetuKEnEyTQMCmh1v8","name":"Bash","input":{"command":"cd out && cat > 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 (str), value (int), description (str) |\n\n- Hashes match bundle.json.\n- propositions: ids A, B, unique; no missing values; no duplicates.\n- design: seed = 20261029, n = 100000 (both integers); no missing values or duplicates.\n- No dates/units (purely mathematical task). No availability-rule violations: inputs are statements and design parameters only.\n- No anomalies detected; no exclusions applied (the exclusion ledger records a no-op step).\nEOF\ncat > exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n1,keep all proposition rows (no filtering),2,2,0,both propositions must be assessed\nEOF\necho \"- 2026-10-30 P1: audited inputs (hashes match bundle), no issues, no exclusions. Counterexample choice: Y = S*X with S independent Rademacher sign; X+Y=(1+S)X has atom 1/2 at 0, nondegenerate.\" >> state/log.md","description":"Write data audit and exclusions"}}]}}29{"type":"api-request-blob","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","hash":"adf330406343c9ede624e24677dc4d0b06df34cabd7e8e11b4ee95d9f99c516a","message":{"role":"user","content":[{"tool_use_id":"toolu_01MpL37wZxUgAVePKDxAQRr2","type":"tool_result","content":"(Bash completed with no output)","is_error":false},{"type":"tool_result","content":"Exit code 1\n(eval):cd:1: no such file or directory: out\n(eval):18: no such file or directory: state/log.md","is_error":true,"tool_use_id":"toolu_01SrRzqetuKEnEyTQMCmh1v8"}]}}30{"type":"api-request","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","id":"cf88d41a-70fc-4903-b6fb-fc754836a3a5","timestamp":"2026-10-30T04:53:03.481Z","version":"2.1.314","querySource":"sdk","shapeHash":"eede6e4d945549fee9828dd471cd62f36fe68556045b0d15ba98001ddf689e37","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":"10847219-cfeb-491f-a837-1f948b8301c5","keep":6,"tail":["822380baf5a8104f288393a4ba2c59843742885aaf9da194144a02ee21780a1c","adf330406343c9ede624e24677dc4d0b06df34cabd7e8e11b4ee95d9f99c516a"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",1],"value":{"type":"ephemeral"}}],"requestDigest":"2c6afb5775c42cd390bb049a7dc756f4ecc0a7acda71a7849c82da711987d764"}31{"parentUuid":"1635c4ce-9f14-43e0-82ad-4677f400c705","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpgroRZpUxRnUqkBFFL","type":"message","role":"assistant","content":[{"type":"text","text":"The shell stayed in out/state; redo from workspace root."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1752,"cache_read_input_tokens":7414,"output_tokens":664,"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":1752},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXpgrWaDYCKXgwM5TfnV","requestRef":"cf88d41a-70fc-4903-b6fb-fc754836a3a5","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f4e66fc9-be4f-4c86-a46e-bc4749d195bf","timestamp":"2026-10-30T04:53:04.619Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183/out/state","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}32{"parentUuid":"f4e66fc9-be4f-4c86-a46e-bc4749d195bf","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpgroRZpUxRnUqkBFFL","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Pv2QSZzWg1X1dMSpfEGzrC","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0183/out && cat > 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 (str), value (int), description (str) |\n\n- Hashes match bundle.json.\n- propositions: ids A, B, unique; no missing values; no duplicates.\n- design: seed = 20261029, n = 100000 (both integers); no missing values or duplicates.\n- No dates/units (purely mathematical task). No availability-rule violations: inputs are statements and design parameters only.\n- No anomalies detected; no exclusions applied (the exclusion ledger records a no-op step).\nEOF\ncat > exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n1,keep all proposition rows (no filtering),2,2,0,both propositions must be assessed\nEOF\necho \"- 2026-10-30 P1: audited inputs (hashes match bundle), no issues, no exclusions. Counterexample choice: Y = S*X with S independent Rademacher sign; X+Y=(1+S)X has atom 1/2 at 0, nondegenerate.\" >> state/log.md; pwd","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":1752,"cache_read_input_tokens":7414,"output_tokens":664,"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":1752},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXpgrWaDYCKXgwM5TfnV","requestRef":"cf88d41a-70fc-4903-b6fb-fc754836a3a5","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"cb81e80e-cb92-4f97-93a8-302e93cf185c","timestamp":"2026-10-30T04:53:09.512Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183/out/state","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}33{"parentUuid":"cb81e80e-cb92-4f97-93a8-302e93cf185c","isSidechain":false,"promptId":"85b06671-532b-4c9e-8e6f-8074c90eb744","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01Pv2QSZzWg1X1dMSpfEGzrC","type":"tool_result","content":"/Users/simon-pierreboucher/wp29/runs/RC0183/out","is_error":false}]},"uuid":"bb9981eb-a522-4b83-8b81-58cb3174cd02","timestamp":"2026-10-30T04:53:09.530Z","toolUseResult":{"stdout":"/Users/simon-pierreboucher/wp29/runs/RC0183/out","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"cb81e80e-cb92-4f97-93a8-302e93cf185c","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183/out","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}34{"type":"api-request-blob","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","hash":"0d0d182c1a2c6be6c264879fb2966d6781dbc28792230ebb0f20213b6f5c76a3","message":{"role":"assistant","content":[{"type":"text","text":"The shell stayed in out/state; redo from workspace root."},{"type":"tool_use","id":"toolu_01Pv2QSZzWg1X1dMSpfEGzrC","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0183/out && cat > 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 (str), value (int), description (str) |\n\n- Hashes match bundle.json.\n- propositions: ids A, B, unique; no missing values; no duplicates.\n- design: seed = 20261029, n = 100000 (both integers); no missing values or duplicates.\n- No dates/units (purely mathematical task). No availability-rule violations: inputs are statements and design parameters only.\n- No anomalies detected; no exclusions applied (the exclusion ledger records a no-op step).\nEOF\ncat > exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n1,keep all proposition rows (no filtering),2,2,0,both propositions must be assessed\nEOF\necho \"- 2026-10-30 P1: audited inputs (hashes match bundle), no issues, no exclusions. Counterexample choice: Y = S*X with S independent Rademacher sign; X+Y=(1+S)X has atom 1/2 at 0, nondegenerate.\" >> state/log.md; pwd","description":"Write data audit and 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/Users/simon-pierreboucher/wp29/runs/RC0183 && cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-03: counterexample to 'sum of normals is normal' (proposition A),\nand baseline check for the independent case (proposition B).\n\nRun from workspace root:  ~/wp29/venv/bin/python out/analysis.py\nReads only data/; writes out/results.json and out/counterexample.csv deterministically.\n\"\"\"\nimport json\nimport os\n\nimport numpy as np\nimport pandas as pd\nfrom scipy import stats\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDATA = os.path.join(ROOT, \"data\")\nOUT = os.path.join(ROOT, \"out\")\n\nprops = pd.read_csv(os.path.join(DATA, \"propositions.csv\"))\ndesign = pd.read_csv(os.path.join(DATA, \"design.csv\"))\n\ndata_issues = []\nif sorted(props[\"id\"].tolist()) != [\"A\", \"B\"]:\n    data_issues.append({\"issue\": \"unexpected proposition ids\", \"handling\": \"reported\"})\ndmap = dict(zip(design[\"parameter\"], design[\"value\"]))\nseed = int(dmap[\"seed\"])\nn = int(dmap[\"n\"])\n\n# Single generator, fixed draw order: X, then S, then baseline independent Y.\nrng = np.random.default_rng(seed)\nx = rng.standard_normal(n)\ns = rng.choice(np.array([-1.0, 1.0]), size=n)  # Rademacher sign, independent of X\ny = s * x                                          # Y = S X ~ N(0,1) by symmetry\nz = x + y                                          # = (1+S) X : 0 w.p. 1/2, else 2X\n\ndef ks_vs_fitted_normal(v):\n    m, sd = float(np.mean(v)), float(np.std(v, ddof=1))\n    return float(stats.kstest(v, \"norm\", args=(m, sd)).statistic)\n\nks_sum = ks_vs_fitted_normal(z)\nks_x = ks_vs_fitted_normal(x)\nks_y = ks_vs_fitted_normal(y)\nfrac_sum_zero = float(np.mean(z == 0.0))\n\n# Baseline (proposition B): independent Y' ~ N(0,1), same evaluation rule.\ny_ind = rng.standard_normal(n)\nks_sum_indep = ks_vs_fitted_normal(x + y_ind)\n\npd.DataFrame({\"x\": x, \"y\": y}).to_csv(os.path.join(OUT, \"counterexample.csv\"),\n                                      index=False, float_format=\"%.17g\")\n# Re-read so that summary statistics describe exactly the written file.\ncx = pd.read_csv(os.path.join(OUT, \"counterexample.csv\"))\nxv, yv = cx[\"x\"].to_numpy(), cx[\"y\"].to_numpy()\nzv = xv + yv\n\ncv = {\n    \"construction\": (\"X ~ N(0,1); S independent of X with P(S=1)=P(S=-1)=1/2; Y = S*X. \"\n                     \"Then Y ~ N(0,1) by symmetry of N(0,1), and X+Y = (1+S)X equals 0 with \"\n                     \"probability 1/2 and 2X ~ N(0,4) otherwise (non-degenerate, not normal).\"),\n    \"n\": int(len(cx)),\n    \"seed\": seed,\n    \"mean_x\": float(np.mean(xv)), \"sd_x\": float(np.std(xv, ddof=1)),\n    \"mean_y\": float(np.mean(yv)), \"sd_y\": float(np.std(yv, ddof=1)),\n    \"mean_sum\": float(np.mean(zv)), \"sd_sum\": float(np.std(zv, ddof=1)),\n    \"ks_sum_vs_normal\": ks_vs_fitted_normal(zv),\n}\n\nresults = {\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\": data_issues,\n    \"n_input_rows\": {\"propositions.csv\": int(len(props)), \"design.csv\": int(len(design))},\n    \"n_analysed\": int(len(cx)),\n    \"random_seed\": seed,\n    # supplementary diagnostics\n    \"ks_x_vs_normal\": ks_vs_fitted_normal(xv),\n    \"ks_y_vs_normal\": ks_vs_fitted_normal(yv),\n    \"frac_sum_exactly_zero\": float(np.mean(zv == 0.0)),\n    \"ks_critical_value_alpha_0_01\": float(1.628 / np.sqrt(n)),\n    \"baseline_ks_sum_independent\": ks_sum_indep,\n}\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n    json.dump(results, f, indent=2)\nprint(json.dumps({k: results[k] for k in [\"statement_true\", \"statement_b_true\"]}))\nprint(\"ks_sum_vs_normal =\", cv[\"ks_sum_vs_normal\"], \"| baseline independent =\", ks_sum_indep)\nEOF\n~/wp29/venv/bin/python out/analysis.py && cat out/results.json && head -3 out/counterexample.csv && wc -l out/counterexample.csv","description":"Write and run analysis 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false, \"statement_b_true\": true}\nks_sum_vs_normal = 0.2508475723268392 | baseline independent = 0.0017646088927930625\n{\n  \"task_id\": \"F5-conf-03\",\n  \"statement_true\": false,\n  \"counterexample_provided\": true,\n  \"counterexample_values\": {\n    \"construction\": \"X ~ N(0,1); S independent of X with P(S=1)=P(S=-1)=1/2; Y = S*X. Then Y ~ N(0,1) by symmetry of N(0,1), and X+Y = (1+S)X equals 0 with probability 1/2 and 2X ~ N(0,4) otherwise (non-degenerate, not normal).\",\n    \"n\": 100000,\n    \"seed\": 20261029,\n    \"mean_x\": -0.0033187423835634253,\n    \"sd_x\": 0.9982238690893596,\n    \"mean_y\": -0.0002490922243280974,\n    \"sd_y\": 0.9982293548745821,\n    \"mean_sum\": -0.003567834607891523,\n    \"sd_sum\": 1.4058866469982523,\n    \"ks_sum_vs_normal\": 0.2508475723268392\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\": 0.0020917798156042666,\n  \"ks_y_vs_normal\": 0.0019518220846299617,\n  \"frac_sum_exactly_zero\": 0.50047,\n  \"ks_critical_value_alpha_0_01\": 0.00514818803075412,\n  \"baseline_ks_sum_independent\": 0.0017646088927930625\n}x,y\n-1.2723895015320856,-1.2723895015320856\n1.6964018149914473,1.6964018149914473\n  100001 out/counterexample.csv","is_error":false}]},"uuid":"fc37e180-9dd2-477b-8fb2-64ec8977cb8b","timestamp":"2026-10-30T04:53:26.680Z","toolUseResult":{"stdout":"{\"statement_true\": false, \"statement_b_true\": true}\nks_sum_vs_normal = 0.2508475723268392 | baseline independent = 0.0017646088927930625\n{\n  \"task_id\": \"F5-conf-03\",\n  \"statement_true\": false,\n  \"counterexample_provided\": true,\n  \"counterexample_values\": {\n    \"construction\": \"X ~ N(0,1); S independent of X with P(S=1)=P(S=-1)=1/2; Y = S*X. Then Y ~ N(0,1) by symmetry of N(0,1), and X+Y = (1+S)X equals 0 with probability 1/2 and 2X ~ N(0,4) otherwise (non-degenerate, not normal).\",\n    \"n\": 100000,\n    \"seed\": 20261029,\n    \"mean_x\": -0.0033187423835634253,\n    \"sd_x\": 0.9982238690893596,\n    \"mean_y\": -0.0002490922243280974,\n    \"sd_y\": 0.9982293548745821,\n    \"mean_sum\": -0.003567834607891523,\n    \"sd_sum\": 1.4058866469982523,\n    \"ks_sum_vs_normal\": 0.2508475723268392\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\": 0.0020917798156042666,\n  \"ks_y_vs_normal\": 0.0019518220846299617,\n  \"frac_sum_exactly_zero\": 0.50047,\n  \"ks_critical_value_alpha_0_01\": 0.00514818803075412,\n  \"baseline_ks_sum_independent\": 0.0017646088927930625\n}x,y\n-1.2723895015320856,-1.2723895015320856\n1.6964018149914473,1.6964018149914473\n  100001 out/counterexample.csv","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"1dcf588f-dc55-4779-96cf-1992db1b0549","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}41{"type":"api-request-blob","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","hash":"05d7708e9e75002bfe6b80126e46a55729c7f4547aca71a8f2d4415dbf5d95e2","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_013VQyCmno3m27iQxDBQ3M3A","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0183 && cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-03: counterexample to 'sum of normals is normal' (proposition A),\nand baseline check for the independent case (proposition B).\n\nRun from workspace root:  ~/wp29/venv/bin/python out/analysis.py\nReads only data/; writes out/results.json and out/counterexample.csv deterministically.\n\"\"\"\nimport json\nimport os\n\nimport numpy as np\nimport pandas as pd\nfrom scipy import stats\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDATA = os.path.join(ROOT, \"data\")\nOUT = os.path.join(ROOT, \"out\")\n\nprops = pd.read_csv(os.path.join(DATA, \"propositions.csv\"))\ndesign = pd.read_csv(os.path.join(DATA, \"design.csv\"))\n\ndata_issues = []\nif sorted(props[\"id\"].tolist()) != [\"A\", \"B\"]:\n    data_issues.append({\"issue\": \"unexpected proposition ids\", \"handling\": \"reported\"})\ndmap = dict(zip(design[\"parameter\"], design[\"value\"]))\nseed = int(dmap[\"seed\"])\nn = int(dmap[\"n\"])\n\n# Single generator, fixed draw order: X, then S, then baseline independent Y.\nrng = np.random.default_rng(seed)\nx = rng.standard_normal(n)\ns = rng.choice(np.array([-1.0, 1.0]), size=n)  # Rademacher sign, independent of X\ny = s * x                                          # Y = S X ~ N(0,1) by symmetry\nz = x + y                                          # = (1+S) X : 0 w.p. 1/2, else 2X\n\ndef ks_vs_fitted_normal(v):\n    m, sd = float(np.mean(v)), float(np.std(v, ddof=1))\n    return float(stats.kstest(v, \"norm\", args=(m, sd)).statistic)\n\nks_sum = ks_vs_fitted_normal(z)\nks_x = ks_vs_fitted_normal(x)\nks_y = ks_vs_fitted_normal(y)\nfrac_sum_zero = float(np.mean(z == 0.0))\n\n# Baseline (proposition B): independent Y' ~ N(0,1), same evaluation rule.\ny_ind = rng.standard_normal(n)\nks_sum_indep = ks_vs_fitted_normal(x + y_ind)\n\npd.DataFrame({\"x\": x, \"y\": y}).to_csv(os.path.join(OUT, \"counterexample.csv\"),\n                                      index=False, float_format=\"%.17g\")\n# Re-read so that summary statistics describe exactly the written file.\ncx = pd.read_csv(os.path.join(OUT, \"counterexample.csv\"))\nxv, yv = cx[\"x\"].to_numpy(), cx[\"y\"].to_numpy()\nzv = xv + yv\n\ncv = {\n    \"construction\": (\"X ~ N(0,1); S independent of X with P(S=1)=P(S=-1)=1/2; Y = S*X. \"\n                     \"Then Y ~ N(0,1) by symmetry of N(0,1), and X+Y = (1+S)X equals 0 with \"\n                     \"probability 1/2 and 2X ~ N(0,4) otherwise (non-degenerate, not normal).\"),\n    \"n\": int(len(cx)),\n    \"seed\": seed,\n    \"mean_x\": float(np.mean(xv)), \"sd_x\": float(np.std(xv, ddof=1)),\n    \"mean_y\": float(np.mean(yv)), \"sd_y\": float(np.std(yv, ddof=1)),\n    \"mean_sum\": float(np.mean(zv)), \"sd_sum\": float(np.std(zv, ddof=1)),\n    \"ks_sum_vs_normal\": ks_vs_fitted_normal(zv),\n}\n\nresults = {\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\": data_issues,\n    \"n_input_rows\": {\"propositions.csv\": int(len(props)), \"design.csv\": int(len(design))},\n    \"n_analysed\": int(len(cx)),\n    \"random_seed\": seed,\n    # supplementary diagnostics\n    \"ks_x_vs_normal\": ks_vs_fitted_normal(xv),\n    \"ks_y_vs_normal\": ks_vs_fitted_normal(yv),\n    \"frac_sum_exactly_zero\": float(np.mean(zv == 0.0)),\n    \"ks_critical_value_alpha_0_01\": float(1.628 / np.sqrt(n)),\n    \"baseline_ks_sum_independent\": ks_sum_indep,\n}\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n    json.dump(results, f, indent=2)\nprint(json.dumps({k: results[k] for k in [\"statement_true\", \"statement_b_true\"]}))\nprint(\"ks_sum_vs_normal =\", cv[\"ks_sum_vs_normal\"], \"| baseline independent =\", ks_sum_indep)\nEOF\n~/wp29/venv/bin/python out/analysis.py && cat 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out/results.json /tmp/r1.json && shasum -a 256 out/counterexample.csv > /tmp/c1 && rm out/results.json out/counterexample.csv && ~/wp29/venv/bin/python out/analysis.py >/dev/null && cmp out/results.json /tmp/r1.json && echo RESULTS_IDENTICAL && shasum -a 256 -c /tmp/c1 && ~/wp29/venv/bin/python - <<'EOF'\nimport json,pandas as pd,numpy as np\nr=json.load(open('out/results.json'));c=r['counterexample_values']\nd=pd.read_csv('out/counterexample.csv')\nprint('rows',len(d)==c['n']==r['n_analysed']==100000)\nprint('seed',c['seed']==r['random_seed']==20261029)\nprint('sd>0',all(c[k]>0 for k in ['sd_x','sd_y','sd_sum']))\nprint('|y|==|x|',np.allclose(np.abs(d.x),np.abs(d.y)))\nprint('sd_sum near sqrt2',abs(c['sd_sum']-2**.5)<0.02)\nprint('ks_sum >> crit',c['ks_sum_vs_normal']>10*r['ks_critical_value_alpha_0_01'])\nprint('marginals/baseline below crit',max(r['ks_x_vs_normal'],r['ks_y_vs_normal'],r['baseline_ks_sum_independent'])<r['ks_critical_value_alpha_0_01'])\nprint('zero frac near .5',abs(r['frac_sum_exactly_zero']-.5)<0.01)\nEOF","description":"Reproducibility and consistency 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OK\nrows True\nseed True\nsd>0 True\n|y|==|x| True\nsd_sum near sqrt2 True\nks_sum >> crit True\nmarginals/baseline below crit True\nzero frac near .5 True","is_error":false}]},"uuid":"81212f8e-4500-4192-82bf-4bb63c7b3879","timestamp":"2026-10-30T04:53:35.202Z","toolUseResult":{"stdout":"RESULTS_IDENTICAL\nout/counterexample.csv: OK\nrows True\nseed True\nsd>0 True\n|y|==|x| True\nsd_sum near sqrt2 True\nks_sum >> crit True\nmarginals/baseline below crit True\nzero frac near .5 True","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"f7581a8e-e98e-485a-9de9-fdfa700d4d13","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}46{"type":"api-request-blob","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","hash":"1a2f2057a9b43d9e177de99456227c9ffb6d3c061b9fa521ac3c91335d0592c4","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01Tkgfgvp8eESBB8RgZCydHD","name":"Bash","input":{"command":"cp out/results.json /tmp/r1.json && shasum -a 256 out/counterexample.csv > /tmp/c1 && rm out/results.json out/counterexample.csv && ~/wp29/venv/bin/python out/analysis.py >/dev/null && cmp out/results.json /tmp/r1.json && echo RESULTS_IDENTICAL && shasum -a 256 -c /tmp/c1 && ~/wp29/venv/bin/python - <<'EOF'\nimport json,pandas as pd,numpy as np\nr=json.load(open('out/results.json'));c=r['counterexample_values']\nd=pd.read_csv('out/counterexample.csv')\nprint('rows',len(d)==c['n']==r['n_analysed']==100000)\nprint('seed',c['seed']==r['random_seed']==20261029)\nprint('sd>0',all(c[k]>0 for k in ['sd_x','sd_y','sd_sum']))\nprint('|y|==|x|',np.allclose(np.abs(d.x),np.abs(d.y)))\nprint('sd_sum near sqrt2',abs(c['sd_sum']-2**.5)<0.02)\nprint('ks_sum >> crit',c['ks_sum_vs_normal']>10*r['ks_critical_value_alpha_0_01'])\nprint('marginals/baseline below crit',max(r['ks_x_vs_normal'],r['ks_y_vs_normal'],r['baseline_ks_sum_independent'])<r['ks_critical_value_alpha_0_01'])\nprint('zero frac near .5',abs(r['frac_sum_exactly_zero']-.5)<0.01)\nEOF","description":"Reproducibility and consistency checks"}}]}}47{"type":"api-request","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","id":"4a4d2943-f09a-47ca-9588-e60016d53572","timestamp":"2026-10-30T04:53:35.205Z","version":"2.1.314","querySource":"sdk","shapeHash":"eede6e4d945549fee9828dd471cd62f36fe68556045b0d15ba98001ddf689e37","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":"9ac704cd-9bb7-42f0-99b4-97929f568c29","keep":12,"tail":["1a2f2057a9b43d9e177de99456227c9ffb6d3c061b9fa521ac3c91335d0592c4","f6ba7af6ea22d50bc5e1a409099586b287326550b589d2b38695184db04b6697"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",13,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"bf3de12e04047505c99176cc1075414ce1452e38ce8e21753f50c0359f268569"}48{"parentUuid":"81212f8e-4500-4192-82bf-4bb63c7b3879","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpjCNDozTQB2yc7uXbV","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":871,"cache_read_input_tokens":12601,"output_tokens":1282,"output_tokens_details":{"thinking_tokens":96},"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":871},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":538,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXpjC6MKMmg5oofDDsr4","requestRef":"4a4d2943-f09a-47ca-9588-e60016d53572","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6a5d3d7a-cf71-40ce-9c20-b48cc361f5a9","timestamp":"2026-10-30T04:53:37.140Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}49{"parentUuid":"6a5d3d7a-cf71-40ce-9c20-b48cc361f5a9","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpjCNDozTQB2yc7uXbV","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_0188ywnNopgg3j5bkJ5W1WcZ","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0183/out && cat > state/checks.md <<'EOF'\n# Verification checks (P4)\nAll executed 2026-10-30; all PASS.\n1. Clean re-run: deleted out/results.json and out/counterexample.csv, re-ran analysis.py; results.json byte-identical (cmp) and counterexample.csv SHA-256 identical. PASS\n2. Row counts: counterexample.csv rows = counterexample_values.n = n_analysed = 100000 = design n. PASS\n3. Seed: counterexample_values.seed = random_seed = 20261029 = design seed. PASS\n4. All sample SDs positive. PASS\n5. Construction identity |y| = |x| holds row-wise. PASS\n6. Magnitude: sd_sum = 1.4059 vs theoretical sqrt(2)=1.4142 (Var(X+Y)=E[(1+S)^2]E[X^2]=2). PASS (within 0.02)\n7. Theory check of KS: the law of X+Y has CDF 1/4 just below 0 and 3/4 at 0, while the fitted N(0,2) CDF is 1/2 at 0, so the population KS distance is 0.25; sample ks_sum_vs_normal = 0.2508. PASS\n8. ks_sum_vs_normal (0.251) > 10 x the nominal 1% KS critical value 1.628/sqrt(n)=0.0051; ks of x, y, and baseline independent sum (0.0021, 0.0020, 0.0018) are all below it. PASS (note: with estimated parameters the nominal critical value is conservative; does not affect conclusion)\n9. frac_sum_exactly_zero = 0.50047 ≈ 1/2. PASS\n10. n_input_rows matches audit (2, 2); exclusion ledger: 2 - 0 = 2. PASS\nEOF\ncat > state/phases.json <<'EOF'\n{\n \"P0\": {\"status\": \"passed\", \"checks\": [\"TASK.md read fully\", \"contract.md written\"], \"notes\": \"\"},\n \"P1\": {\"status\": \"passed\", \"checks\": [\"SHA-256 computed and matched bundle.json\", \"row/col counts, missing, duplicates checked\", \"exclusions.csv written (no-op step)\"], \"notes\": \"no data issues\"},\n \"P2\": {\"status\": \"passed\", \"checks\": [\"baseline_ks_sum_independent computed with same KS rule (0.0018)\"], \"notes\": \"baseline = independent case (prop B)\"},\n \"P3\": {\"status\": \"passed\", \"checks\": [\"analysis.py reads only data/, fixed seed 20261029, writes results.json and counterexample.csv\"], \"notes\": \"\"},\n \"P4\": {\"status\": \"running\", \"checks\": [\"clean re-run byte-identical: PASS\", \"10 consistency checks in checks.md: all PASS\"], \"notes\": \"\"},\n \"P5\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"}\n}\nEOF\necho \"- 2026-10-30 P2/P3 passed: analysis written and run; P4 checks all pass, running gate.\" >> state/log.md\ncd .. && ~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Record checks, phases, run gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":871,"cache_read_input_tokens":12601,"output_tokens":1282,"output_tokens_details":{"thinking_tokens":96},"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":871},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXpjC6MKMmg5oofDDsr4","requestRef":"4a4d2943-f09a-47ca-9588-e60016d53572","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"af22778f-8cf7-4aa0-aac1-ad6d30e25214","timestamp":"2026-10-30T04:53:46.745Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}50{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"af22778f-8cf7-4aa0-aac1-ad6d30e25214","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a"}51{"type":"atis-latch","atis":"","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a"}52{"parentUuid":"af22778f-8cf7-4aa0-aac1-ad6d30e25214","isSidechain":false,"promptId":"85b06671-532b-4c9e-8e6f-8074c90eb744","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 1\nPGAR GATE pgar_gate/1.0 — FAILED (11 of 27 checks failed)\n  [ok] file:out/results.json: present\n  [FAIL] file:out/report.md: missing or empty\n  [ok] file:out/analysis.py: present\n  [FAIL] file:out/claims.json: missing or empty\n  [FAIL] file:out/argument.md: missing or empty\n  [ok] file:out/counterexample.csv: present\n  [ok] results_json: parsed\n  [ok] key:task_id: ok\n  [ok] key:statement_true: ok\n  [ok] key:counterexample_provided: ok\n  [ok] key:counterexample_values: ok\n  [ok] key:statement_b_true: ok\n  [ok] key:feasibility: ok\n  [ok] key:feasibility_reason: ok\n  [ok] key:data_issues: ok\n  [ok] key:n_input_rows: ok\n  [ok] key:n_analysed: ok\n  [ok] key:random_seed: ok\n  [FAIL] section:Question: heading not found\n  [FAIL] section:Data and exclusions: heading not found\n  [FAIL] section:Method: heading not found\n  [FAIL] section:Results: heading not found\n  [FAIL] section:Uncertainty: heading not found\n  [FAIL] section:Limitations and open issues: heading not found\n  [FAIL] claims_json: out/claims.json missing\n  [FAIL] phase_ledger: phases not terminal: ['P4', 'P5']\n  [ok] reproducibility: regenerated in 0.8s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0183/out/state/gate_receipts/20261030T045347.602122Z.json","is_error":true,"tool_use_id":"toolu_0188ywnNopgg3j5bkJ5W1WcZ"}]},"uuid":"21dbe221-d36f-4251-a09d-681b31fa0173","timestamp":"2026-10-30T04:53:47.609Z","toolUseResult":"Error: Exit code 1\nPGAR GATE pgar_gate/1.0 — FAILED (11 of 27 checks failed)\n  [ok] file:out/results.json: present\n  [FAIL] file:out/report.md: missing or empty\n  [ok] file:out/analysis.py: present\n  [FAIL] file:out/claims.json: missing or empty\n  [FAIL] file:out/argument.md: missing or empty\n  [ok] file:out/counterexample.csv: present\n  [ok] results_json: parsed\n  [ok] key:task_id: ok\n  [ok] key:statement_true: ok\n  [ok] key:counterexample_provided: ok\n  [ok] key:counterexample_values: ok\n  [ok] key:statement_b_true: ok\n  [ok] key:feasibility: ok\n  [ok] key:feasibility_reason: ok\n  [ok] key:data_issues: ok\n  [ok] key:n_input_rows: ok\n  [ok] key:n_analysed: ok\n  [ok] key:random_seed: ok\n  [FAIL] section:Question: heading not found\n  [FAIL] section:Data and exclusions: heading not found\n  [FAIL] section:Method: heading not found\n  [FAIL] section:Results: heading not found\n  [FAIL] section:Uncertainty: heading not found\n  [FAIL] section:Limitations and open issues: heading not found\n  [FAIL] claims_json: out/claims.json missing\n  [FAIL] phase_ledger: phases not terminal: ['P4', 'P5']\n  [ok] reproducibility: regenerated in 0.8s; 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all PASS.\n1. Clean re-run: deleted out/results.json and out/counterexample.csv, re-ran analysis.py; results.json byte-identical (cmp) and counterexample.csv SHA-256 identical. PASS\n2. Row counts: counterexample.csv rows = counterexample_values.n = n_analysed = 100000 = design n. PASS\n3. Seed: counterexample_values.seed = random_seed = 20261029 = design seed. PASS\n4. All sample SDs positive. PASS\n5. Construction identity |y| = |x| holds row-wise. PASS\n6. Magnitude: sd_sum = 1.4059 vs theoretical sqrt(2)=1.4142 (Var(X+Y)=E[(1+S)^2]E[X^2]=2). PASS (within 0.02)\n7. Theory check of KS: the law of X+Y has CDF 1/4 just below 0 and 3/4 at 0, while the fitted N(0,2) CDF is 1/2 at 0, so the population KS distance is 0.25; sample ks_sum_vs_normal = 0.2508. PASS\n8. ks_sum_vs_normal (0.251) > 10 x the nominal 1% KS critical value 1.628/sqrt(n)=0.0051; ks of x, y, and baseline independent sum (0.0021, 0.0020, 0.0018) are all below it. PASS (note: with estimated parameters the nominal critical value is conservative; does not affect conclusion)\n9. frac_sum_exactly_zero = 0.50047 ≈ 1/2. PASS\n10. n_input_rows matches audit (2, 2); exclusion ledger: 2 - 0 = 2. PASS\nEOF\ncat > state/phases.json <<'EOF'\n{\n \"P0\": {\"status\": \"passed\", \"checks\": [\"TASK.md read fully\", \"contract.md written\"], \"notes\": \"\"},\n \"P1\": {\"status\": \"passed\", \"checks\": [\"SHA-256 computed and matched bundle.json\", \"row/col counts, missing, duplicates checked\", \"exclusions.csv written (no-op step)\"], \"notes\": \"no data issues\"},\n \"P2\": {\"status\": \"passed\", \"checks\": [\"baseline_ks_sum_independent computed with same KS rule (0.0018)\"], \"notes\": \"baseline = independent case (prop B)\"},\n \"P3\": {\"status\": \"passed\", \"checks\": [\"analysis.py reads only data/, fixed seed 20261029, writes results.json and counterexample.csv\"], \"notes\": \"\"},\n \"P4\": {\"status\": \"running\", \"checks\": [\"clean re-run byte-identical: PASS\", \"10 consistency checks in checks.md: all PASS\"], \"notes\": \"\"},\n \"P5\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"}\n}\nEOF\necho \"- 2026-10-30 P2/P3 passed: analysis written and run; P4 checks all pass, running gate.\" >> state/log.md\ncd .. && ~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Record checks, phases, run gate"}}]}}54{"type":"api-request","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","id":"61a08034-807d-4f96-b8e7-46c5be3cacf7","timestamp":"2026-10-30T04:53:47.613Z","version":"2.1.314","querySource":"sdk","shapeHash":"eede6e4d945549fee9828dd471cd62f36fe68556045b0d15ba98001ddf689e37","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":"4a4d2943-f09a-47ca-9588-e60016d53572","keep":14,"tail":["b53197e0d64e963cb98ba31a531129c65761d602a5e3be0d73f1a07f68800638","cb3e1b9ef275969dafe73c138cc38653c64664f050cf5c19edb0436d3c191a1f"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",15,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"e89a1f1fe86693b0ee517636adcdece57b7eb595934c5498273811645ffdfccc"}55{"parentUuid":"21dbe221-d36f-4251-a09d-681b31fa0173","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpk7SL4CLtQP5KsCuL8","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":1896,"cache_read_input_tokens":13472,"output_tokens":3783,"output_tokens_details":{"thinking_tokens":58},"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":1896},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":734,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXpk79xrT63GY47Mg3p9","requestRef":"61a08034-807d-4f96-b8e7-46c5be3cacf7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"14bd12bb-c82a-4368-89eb-2b9a3a6c5202","timestamp":"2026-10-30T04:53:49.592Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}56{"parentUuid":"14bd12bb-c82a-4368-89eb-2b9a3a6c5202","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpk7SL4CLtQP5KsCuL8","type":"message","role":"assistant","content":[{"type":"text","text":"The P4-relevant checks pass (reproducibility, keys). The remaining failures are P5 deliverables. Writing those now."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1896,"cache_read_input_tokens":13472,"output_tokens":3783,"output_tokens_details":{"thinking_tokens":58},"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":1896},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXpk79xrT63GY47Mg3p9","requestRef":"61a08034-807d-4f96-b8e7-46c5be3cacf7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"12fb9980-6f73-401b-a1e1-8cfc4bc1563b","timestamp":"2026-10-30T04:53:49.593Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}57{"parentUuid":"12fb9980-6f73-401b-a1e1-8cfc4bc1563b","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXpk7SL4CLtQP5KsCuL8","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01AMV7CJZNK7ybhyi3j8ZK3E","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0183/out && cat > argument.md <<'EOF'\n# Mathematical argument\n\nNotation: N(μ, σ²) with σ² ≥ 0; σ² = 0 is the degenerate (constant) normal. φ_W(t) = E[e^{itW}] is the characteristic function.\n\n## Proposition B — TRUE\n*If X and Y are independent and each normal, X + Y is normal.*\n\n**Proof sketch.** Let X ~ N(μ₁, σ₁²), Y ~ N(μ₂, σ₂²). Then φ_X(t) = exp(iμ₁t − σ₁²t²/2), φ_Y(t) = exp(iμ₂t − σ₂²t²/2). By independence, φ_{X+Y}(t) = φ_X(t) φ_Y(t) = exp(i(μ₁+μ₂)t − (σ₁²+σ₂²)t²/2), which is the characteristic function of N(μ₁+μ₂, σ₁²+σ₂²). By the uniqueness theorem for characteristic functions, X + Y ~ N(μ₁+μ₂, σ₁²+σ₂²) (degenerate if both variances are 0). ∎\n\n## Proposition A — FALSE\n*If X and Y are each normal (no assumption on their joint law), X + Y is normal (constants count).*\n\nMarginal normality does not pin down the joint law, so it does not pin down the law of the sum.\n\n**Counterexample.** Let X ~ N(0,1) and let S be independent of X with P(S = 1) = P(S = −1) = 1/2. Define Y = S·X.\n\n1. *Y is N(0,1).* For any Borel set B, P(Y ∈ B) = ½P(X ∈ B) + ½P(−X ∈ B) = P(X ∈ B), because −X has the same law as X (N(0,1) is symmetric). So X and Y are both standard normal.\n2. *X + Y is not normal.* X + Y = (1 + S)X, which is 0 when S = −1 and 2X when S = 1. Hence P(X + Y = 0) ≥ P(S = −1) = 1/2 (in fact exactly 1/2, because P(X=0)=0).\n   - A non-degenerate normal distribution has no atoms, so it gives probability 0 to {0}; X + Y has an atom of mass 1/2, so it is not non-degenerate normal.\n   - A degenerate normal is a point mass (probability 1 on one point). But P(X + Y = 0) = 1/2 < 1 and, on {S = 1}, X + Y = 2X has a continuous N(0,4) law, so X + Y is not constant.\n   Therefore the law of X + Y, the mixture ½δ₀ + ½N(0,4), is not normal in either sense. ∎\n\n(Also note Cov(X, Y) = E[S]E[X²] = 0: X and Y are uncorrelated yet dependent, so the counterexample also shows \"uncorrelated normal marginals\" is not enough; joint normality or independence is what is needed.)\n\nRemark on the obvious candidate Y = −X: it gives X + Y ≡ 0, which is a degenerate normal and therefore *not* a counterexample under the statement's convention; this is why the random-sign construction is used.\n\n**Numerical illustration** (not part of the proof): `out/analysis.py` draws n = 100000 pairs with seed 20261029 (design.csv) and writes them to `out/counterexample.csv`. Population value of the KS distance between the law of X + Y and the fitted N(0, 2): the true CDF jumps from 1/4 to 3/4 at 0 whereas the N(0,2) CDF equals 1/2 there, so the distance is 1/4. The sample value is reported as `counterexample_values.ks_sum_vs_normal` in results.json.\nEOF\ncat > report.md <<'EOF'\n# Report — F5-conf-03: sums of normally distributed random variables\n\n## Question\nTwo propositions (data/propositions.csv): **A** — if X and Y are each normal, X + Y is normal (a constant counts as normal); **B** — if X and Y are independent and each normal, X + Y is normal. For each we decide true/false by mathematical argument (full argument in `out/argument.md`), and for a false proposition we give a concrete counterexample with a simulated sample.\n\n## Data and exclusions\nInputs: `data/propositions.csv` (2 rows) and `data/design.csv` (2 rows: seed 20261029, n 100000) (`n_input_rows`, `random_seed`). SHA-256 hashes match the bundle manifest (out/state/data_audit.md). No missing values, duplicates or anomalies (`data_issues` = []). No rows excluded (out/exclusions.csv: 2 − 0 = 2).\n\n## Method\n- B: characteristic-function proof (product of normal CFs is a normal CF; uniqueness theorem).\n- A: counterexample X ~ N(0,1), S an independent fair random sign, Y = S·X (`counterexample_values.construction`). Y ~ N(0,1) by symmetry; X + Y = (1+S)X equals 0 with probability 1/2 and is N(0,4) otherwise, a law with an atom that is not a point mass, so it is neither a non-degenerate nor a degenerate normal. Y = −X was rejected because its sum is the constant 0, which the statement counts as normal.\n- Numerical illustration: `out/analysis.py` draws X then S from `numpy.random.default_rng(20261029)`, n = 100000, writes `out/counterexample.csv`, and computes sample means/SDs (ddof = 1) and the one-sample Kolmogorov–Smirnov distance between each variable and a normal with its own sample mean and SD. Baseline with the same KS rule: X plus a further independent N(0,1) draw (the setting of proposition B).\n\n## Results\n- Proposition A is **false** (`statement_true` = false); a concrete counterexample is provided (`counterexample_provided` = true).\n- Proposition B is **true** (`statement_b_true` = true).\n- Simulated counterexample (n = 100000, `n_analysed`): mean_x = −0.0033, sd_x = 0.9982; mean_y = −0.0002, sd_y = 0.9982 (`counterexample_values.mean_x`, `.sd_x`, `.mean_y`, `.sd_y`), as expected for N(0,1) marginals. Marginal KS distances are 0.0021 and 0.0020 (`ks_x_vs_normal`, `ks_y_vs_normal`).\n- Sum: mean_sum = −0.0036, sd_sum = 1.4059 (`counterexample_values.mean_sum`, `.sd_sum`; theory: 0 and √2 ≈ 1.414). The fraction of exactly-zero sums is 0.50047 (`frac_sum_exactly_zero`; theory 1/2). The KS distance of the sum from its fitted normal is 0.2508 (`counterexample_values.ks_sum_vs_normal`; population value 0.25).\n- Baseline: for an independent sum the same KS distance is 0.0018 (`baseline_ks_sum_independent`), which matches B.\n- For scale, the nominal 1% KS critical value 1.628/√n is 0.0051 (`ks_critical_value_alpha_0_01`). The sum's KS distance is about 50 times that value. The marginal and baseline distances fall below it.\n\n## Uncertainty\nThe verdicts come from proofs and carry no sampling uncertainty. The numbers in the simulation do: sample means and SDs differ from their theoretical values by roughly 1/√n ≈ 0.003. The nominal KS critical value treats the normal's parameters as known. Here they are estimated (a Lilliefors setting), so the nominal value is conservative. That does not change any conclusion, because 0.25 vs 0.005 is far outside any plausible critical value. All results come from one seed. The run is deterministic and reproduces exactly (out/state/checks.md).\n\n## Limitations and open issues\n- **What the illustration establishes:** for this seed and n, the sample from the stated construction looks like it has N(0,1) marginals. Its sum has an atom at 0 of about half the mass and sits far from any normal fit. The simulation agrees with the theory: SD ≈ √2, zero-fraction ≈ 1/2, KS ≈ 1/4.\n- **What it does not establish:** a finite sample cannot prove that the marginals are exactly normal, and it cannot prove that A or B is true or false. Both verdicts rest only on the arguments in `out/argument.md`. A small marginal KS distance only shows consistency with normality.\n- No open issues. The task is complete (`feasibility` = \"complete\").\nEOF\ncat > claims.json <<'EOF'\n[\n {\"id\": \"C1\", \"text\": \"Proposition A is false: X ~ N(0,1), Y = S X with S an independent fair sign gives normal marginals but X+Y = (1+S)X, a mixture of a point mass at 0 (prob 1/2) and N(0,4), which is neither normal nor constant.\", \"results_keys\": [\"statement_true\", \"counterexample_provided\", \"counterexample_values\"], \"status\": \"supported\", \"caveat\": \"Supported by mathematical proof in argument.md; simulation is illustrative only.\"},\n {\"id\": \"C2\", \"text\": \"Proposition B is true: the sum of independent normals is normal with summed means and variances (characteristic-function proof).\", \"results_keys\": [\"statement_b_true\", \"baseline_ks_sum_independent\"], \"status\": \"supported\", \"caveat\": \"Simulation baseline is illustrative only.\"},\n {\"id\": \"C3\", \"text\": \"In the simulated sample (seed 20261029, n=100000) the marginals agree with N(0,1) (sample SDs ~0.998, KS ~0.002) while the sum has about half its mass exactly at 0 and KS distance ~0.251 from its fitted normal, matching the population value 0.25.\", \"results_keys\": [\"counterexample_values\", \"ks_x_vs_normal\", \"ks_y_vs_normal\", \"frac_sum_exactly_zero\", \"ks_critical_value_alpha_0_01\", \"n_analysed\", \"random_seed\"], \"status\": \"supported\", \"caveat\": \"Single seed; nominal KS critical value ignores parameter estimation (conservative).\"}\n]\nEOF\necho \"- 2026-10-30 P4 passed (gate run 1: reproducibility OK, failures only missing P5 files). P5: wrote argument, report, claims.\" >> state/log.md","description":"Write argument, report, claims"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1896,"cache_read_input_tokens":13472,"output_tokens":3783,"output_tokens_details":{"thinking_tokens":58},"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":1896},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXpk79xrT63GY47Mg3p9","requestRef":"61a08034-807d-4f96-b8e7-46c5be3cacf7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"011ce25b-21fa-4760-b69c-e31d826a5669","timestamp":"2026-10-30T04:54:20.331Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}58{"parentUuid":"011ce25b-21fa-4760-b69c-e31d826a5669","isSidechain":false,"promptId":"85b06671-532b-4c9e-8e6f-8074c90eb744","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01AMV7CJZNK7ybhyi3j8ZK3E","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"f070a7f1-068c-40f6-9e33-6115f38c5ce2","timestamp":"2026-10-30T04:54:20.349Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"011ce25b-21fa-4760-b69c-e31d826a5669","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183/out","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}59{"type":"api-request-blob","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","hash":"372c9e93044bf025bacc18e373c9170a3bdb4ed84b2f4fd3fced934b2b26accf","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"The P4-relevant checks pass (reproducibility, keys). The remaining failures are P5 deliverables. Writing those now."},{"type":"tool_use","id":"toolu_01AMV7CJZNK7ybhyi3j8ZK3E","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0183/out && cat > argument.md <<'EOF'\n# Mathematical argument\n\nNotation: N(μ, σ²) with σ² ≥ 0; σ² = 0 is the degenerate (constant) normal. φ_W(t) = E[e^{itW}] is the characteristic function.\n\n## Proposition B — TRUE\n*If X and Y are independent and each normal, X + Y is normal.*\n\n**Proof sketch.** Let X ~ N(μ₁, σ₁²), Y ~ N(μ₂, σ₂²). Then φ_X(t) = exp(iμ₁t − σ₁²t²/2), φ_Y(t) = exp(iμ₂t − σ₂²t²/2). By independence, φ_{X+Y}(t) = φ_X(t) φ_Y(t) = exp(i(μ₁+μ₂)t − (σ₁²+σ₂²)t²/2), which is the characteristic function of N(μ₁+μ₂, σ₁²+σ₂²). By the uniqueness theorem for characteristic functions, X + Y ~ N(μ₁+μ₂, σ₁²+σ₂²) (degenerate if both variances are 0). ∎\n\n## Proposition A — FALSE\n*If X and Y are each normal (no assumption on their joint law), X + Y is normal (constants count).*\n\nMarginal normality does not pin down the joint law, so it does not pin down the law of the sum.\n\n**Counterexample.** Let X ~ N(0,1) and let S be independent of X with P(S = 1) = P(S = −1) = 1/2. Define Y = S·X.\n\n1. *Y is N(0,1).* For any Borel set B, P(Y ∈ B) = ½P(X ∈ B) + ½P(−X ∈ B) = P(X ∈ B), because −X has the same law as X (N(0,1) is symmetric). So X and Y are both standard normal.\n2. *X + Y is not normal.* X + Y = (1 + S)X, which is 0 when S = −1 and 2X when S = 1. Hence P(X + Y = 0) ≥ P(S = −1) = 1/2 (in fact exactly 1/2, because P(X=0)=0).\n   - A non-degenerate normal distribution has no atoms, so it gives probability 0 to {0}; X + Y has an atom of mass 1/2, so it is not non-degenerate normal.\n   - A degenerate normal is a point mass (probability 1 on one point). But P(X + Y = 0) = 1/2 < 1 and, on {S = 1}, X + Y = 2X has a continuous N(0,4) law, so X + Y is not constant.\n   Therefore the law of X + Y, the mixture ½δ₀ + ½N(0,4), is not normal in either sense. ∎\n\n(Also note Cov(X, Y) = E[S]E[X²] = 0: X and Y are uncorrelated yet dependent, so the counterexample also shows \"uncorrelated normal marginals\" is not enough; joint normality or independence is what is needed.)\n\nRemark on the obvious candidate Y = −X: it gives X + Y ≡ 0, which is a degenerate normal and therefore *not* a counterexample under the statement's convention; this is why the random-sign construction is used.\n\n**Numerical illustration** (not part of the proof): `out/analysis.py` draws n = 100000 pairs with seed 20261029 (design.csv) and writes them to `out/counterexample.csv`. Population value of the KS distance between the law of X + Y and the fitted N(0, 2): the true CDF jumps from 1/4 to 3/4 at 0 whereas the N(0,2) CDF equals 1/2 there, so the distance is 1/4. The sample value is reported as `counterexample_values.ks_sum_vs_normal` in results.json.\nEOF\ncat > report.md <<'EOF'\n# Report — F5-conf-03: sums of normally distributed random variables\n\n## Question\nTwo propositions (data/propositions.csv): **A** — if X and Y are each normal, X + Y is normal (a constant counts as normal); **B** — if X and Y are independent and each normal, X + Y is normal. For each we decide true/false by mathematical argument (full argument in `out/argument.md`), and for a false proposition we give a concrete counterexample with a simulated sample.\n\n## Data and exclusions\nInputs: `data/propositions.csv` (2 rows) and `data/design.csv` (2 rows: seed 20261029, n 100000) (`n_input_rows`, `random_seed`). SHA-256 hashes match the bundle manifest (out/state/data_audit.md). No missing values, duplicates or anomalies (`data_issues` = []). No rows excluded (out/exclusions.csv: 2 − 0 = 2).\n\n## Method\n- B: characteristic-function proof (product of normal CFs is a normal CF; uniqueness theorem).\n- A: counterexample X ~ N(0,1), S an independent fair random sign, Y = S·X (`counterexample_values.construction`). Y ~ N(0,1) by symmetry; X + Y = (1+S)X equals 0 with probability 1/2 and is N(0,4) otherwise, a law with an atom that is not a point mass, so it is neither a non-degenerate nor a degenerate normal. Y = −X was rejected because its sum is the constant 0, which the statement counts as normal.\n- Numerical illustration: `out/analysis.py` draws X then S from `numpy.random.default_rng(20261029)`, n = 100000, writes `out/counterexample.csv`, and computes sample means/SDs (ddof = 1) and the one-sample Kolmogorov–Smirnov distance between each variable and a normal with its own sample mean and SD. Baseline with the same KS rule: X plus a further independent N(0,1) draw (the setting of proposition B).\n\n## Results\n- Proposition A is **false** (`statement_true` = false); a concrete counterexample is provided (`counterexample_provided` = true).\n- Proposition B is **true** (`statement_b_true` = true).\n- Simulated counterexample (n = 100000, `n_analysed`): mean_x = −0.0033, sd_x = 0.9982; mean_y = −0.0002, sd_y = 0.9982 (`counterexample_values.mean_x`, `.sd_x`, `.mean_y`, `.sd_y`), as expected for N(0,1) marginals. Marginal KS distances are 0.0021 and 0.0020 (`ks_x_vs_normal`, `ks_y_vs_normal`).\n- Sum: mean_sum = −0.0036, sd_sum = 1.4059 (`counterexample_values.mean_sum`, `.sd_sum`; theory: 0 and √2 ≈ 1.414). The fraction of exactly-zero sums is 0.50047 (`frac_sum_exactly_zero`; theory 1/2). The KS distance of the sum from its fitted normal is 0.2508 (`counterexample_values.ks_sum_vs_normal`; population value 0.25).\n- Baseline: for an independent sum the same KS distance is 0.0018 (`baseline_ks_sum_independent`), which matches B.\n- For scale, the nominal 1% KS critical value 1.628/√n is 0.0051 (`ks_critical_value_alpha_0_01`). The sum's KS distance is about 50 times that value. The marginal and baseline distances fall below it.\n\n## Uncertainty\nThe verdicts come from proofs and carry no sampling uncertainty. The numbers in the simulation do: sample means and SDs differ from their theoretical values by roughly 1/√n ≈ 0.003. The nominal KS critical value treats the normal's parameters as known. Here they are estimated (a Lilliefors setting), so the nominal value is conservative. That does not change any conclusion, because 0.25 vs 0.005 is far outside any plausible critical value. All results come from one seed. The run is deterministic and reproduces exactly (out/state/checks.md).\n\n## Limitations and open issues\n- **What the illustration establishes:** for this seed and n, the sample from the stated construction looks like it has N(0,1) marginals. Its sum has an atom at 0 of about half the mass and sits far from any normal fit. The simulation agrees with the theory: SD ≈ √2, zero-fraction ≈ 1/2, KS ≈ 1/4.\n- **What it does not establish:** a finite sample cannot prove that the marginals are exactly normal, and it cannot prove that A or B is true or false. Both verdicts rest only on the arguments in `out/argument.md`. A small marginal KS distance only shows consistency with normality.\n- No open issues. The task is complete (`feasibility` = \"complete\").\nEOF\ncat > claims.json <<'EOF'\n[\n {\"id\": \"C1\", \"text\": \"Proposition A is false: X ~ N(0,1), Y = S X with S an independent fair sign gives normal marginals but X+Y = (1+S)X, a mixture of a point mass at 0 (prob 1/2) and N(0,4), which is neither normal nor constant.\", \"results_keys\": [\"statement_true\", \"counterexample_provided\", \"counterexample_values\"], \"status\": \"supported\", \"caveat\": \"Supported by mathematical proof in argument.md; simulation is illustrative only.\"},\n {\"id\": \"C2\", \"text\": \"Proposition B is true: the sum of independent normals is normal with summed means and variances (characteristic-function proof).\", \"results_keys\": [\"statement_b_true\", \"baseline_ks_sum_independent\"], \"status\": \"supported\", \"caveat\": \"Simulation baseline is illustrative only.\"},\n {\"id\": \"C3\", \"text\": \"In the simulated sample (seed 20261029, n=100000) the marginals agree with N(0,1) (sample SDs ~0.998, KS ~0.002) while the sum has about half its mass exactly at 0 and KS distance ~0.251 from its fitted normal, matching the population value 0.25.\", \"results_keys\": [\"counterexample_values\", \"ks_x_vs_normal\", \"ks_y_vs_normal\", \"frac_sum_exactly_zero\", \"ks_critical_value_alpha_0_01\", \"n_analysed\", \"random_seed\"], \"status\": \"supported\", \"caveat\": \"Single seed; nominal KS critical value ignores parameter estimation (conservative).\"}\n]\nEOF\necho \"- 2026-10-30 P4 passed (gate run 1: reproducibility OK, failures only missing P5 files). 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Both verdicts come from proofs in `out/argument.md`, not from the simulation. The final gate run passed all 27 checks, and re-running `out/analysis.py` from scratch produces identical results.\n\n- **A is false.** \"If X and Y are each normal, then X + Y is normal.\"\n  - **Counterexample:** take X standard normal, flip an independent fair coin to get a sign S of +1 or −1, and set Y = S·X.\n  - **Why the marginals are normal:** the standard normal is symmetric, so Y is standard normal too.\n  - **Why the sum is not normal:** X + Y = (1+S)X is exactly 0 half the time and has a normal spread with variance 4 the other half. A normal distribution can't put probability 1/2 on a single point, and the sum isn't a constant either.\n  - **Why not Y = −X:** the obvious choice gives a sum that is always 0, which the statement counts as normal. So it isn't a counterexample here.\n- **B is true.** \"If X and Y are independent and each normal, then X + Y is normal.\" Proved with characteristic functions: multiplying two normal characteristic functions gives another normal one.\n\n**Simulation** (seed 20261029, 100,000 pairs, saved to `out/counterexample.csv`):\n\n| Quantity | Simulated | Theory |\n|---|---|---|\n| SD of x and of y | 0.998 each | 1 |\n| Distance of x and y from a fitted normal (Kolmogorov–Smirnov) | about 0.002 | 0 |\n| SD of x + y | 1.406 | √2 ≈ 1.414 |\n| Share of sums exactly 0 | 0.50047 | 1/2 |\n| Distance of x + y from a fitted normal | 0.2508 | 0.25 |\n| Distance for an independent sum (B case, for comparison) | 0.0018 | 0 |\n\nFor scale, the usual 1% threshold for that distance at this sample size is 0.0051, so the sum misses it by about 50 times. That threshold is somewhat conservative here because the normal's mean and SD are estimated from the data, but the gap is far too large for that to matter.\n\n**What the simulation does and doesn't show:** it matches the theory, but a finite sample can't prove the marginals are exactly normal or decide either proposition. It also uses a single seed. The report says this explicitly.\n\nOne slip: I once ran the gate from the wrong folder, which left a stray failure receipt in `out/out/`. I deleted it, logged it in `out/state/log.md`, and re-ran the gate from the right place, which passed.\n\nFiles are in `out/`:\n- `results.json`\n- `counterexample.csv`\n- `argument.md`\n- `report.md`\n- `analysis.py`\n- `claims.json`\n- `exclusions.csv`\n- `state/` (contract, data audit, checks, phase ledger, log, gate receipts)"}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":269,"cache_read_input_tokens":21012,"output_tokens":982,"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":269},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXpooQyy9JfEmvVubzzx","requestRef":"0af9d0ca-dece-4764-a2c3-40a91ccb95f7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"aac591f4-02fe-413b-976f-a72c3701b338","timestamp":"2026-10-30T04:54:47.141Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0183","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","version":"2.1.314","gitBranch":"HEAD"}93{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"aac591f4-02fe-413b-976f-a72c3701b338","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a"}94{"type":"cost-state","sessionId":"37094023-396c-42b3-ad75-0a7e00cf356a","totalCostUSD":0.39416379999999995,"totalAPIDuration":119882,"totalAPIDurationWithoutRetries":119872,"totalToolDuration":4744,"totalLinesAdded":0,"totalLinesRemoved":0,"totalDuration":124791,"startTime":1793335962356,"modelUsage":{"claude-opus-5-5":{"inputTokens":32,"outputTokens":12743,"thinkingTokens":870,"cacheReadInputTokens":201454,"cacheCreationInputTokens":19777,"cacheCreationEphemeral5mInputTokens":19777,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.39416379999999995}},"hasUnknownModelCost":false}95