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It is the complete and only authoritative description of what is required: the scientific question, the inputs under `data/`, the required output files and their exact keys, and the information-availability rules.\n- There is no network access. Use the Python interpreter `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels, matplotlib are installed). Standard shell tools are available. Do not try to install packages.\n- Write every deliverable under `./out/`. The required deliverables are listed in `TASK.md`; at minimum they always include `out/results.json`, `out/report.md`, and a replication entry point `out/analysis.py` that regenerates `out/results.json` from `data/` when run with `~/wp29/venv/bin/python out/analysis.py` from the workspace root.\n- You are working alone and unattended; nobody will answer questions. Make reasonable, documented decisions.\n\nIntegrity rules (identical for every task):\n- Never fabricate numbers, data, results, or references. Every number in `out/results.json` and `out/report.md` must be produced by code you ran on the provided inputs.\n- Respect the information-availability rules in `TASK.md` exactly (for example, never use information that would not have been available at the stated decision time).\n- If part of the task cannot be completed as specified, say so explicitly in `out/report.md`, explain why, and still write every required file (use `null` for values you could not legitimately produce). An honest statement of a limitation is always preferred to a fabricated or guessed value.\n- Do not modify anything under `data/`.\n- When you are done, end with a brief plain-text summary of what you produced and any limitations.\n\nComplete the task described in `TASK.md` by following this research protocol. The protocol adds no scientific information to the task; it organizes how you work and what evidence you leave behind.\n\nPHASES (execute in order; a phase is eligible only when its dependencies are satisfied):\n\nP0 Scope and contract (depends on: nothing)\n- Read `TASK.md` completely. In `out/state/contract.md`, restate in your own words: the scientific question; the quantity or quantities to be estimated (the estimands) and the assumptions under which they are meaningful; every required output file and key; the information-availability rules; what would make the task impossible or the result invalid.\n- Write the initial phase ledger `out/state/phases.json`: a JSON object mapping each phase id (P0 … P5) to {\"status\": \"pending\"|\"running\"|\"passed\"|\"failed\"|\"blocked\"|\"stale\"|\"skipped_optional\", \"checks\": [], \"notes\": \"\"}. Keep it current as you work. A phase may only be set to \"passed\" when the checks listed for it in this protocol have actually been executed and their outcome recorded in \"checks\".\n\nP1 Data audit and provenance (depends on: P0)\n- Inspect every input file: compute and record its SHA-256, row and column counts, schema, units, date ranges, missing values, duplicates and anomalies in `out/state/data_audit.md`.\n- Keep an exclusion ledger in `out/exclusions.csv` (columns: step, rule, n_before, n_after, n_removed, rationale) for every filtering step you apply, so that n_raw − total removed = n_analysed.\n- Identify any input that violates the information-availability rules and decide, in writing, how you will handle it.\n\nP2 Baseline (depends on: P1)\n- Before any elaborate method, compute the simplest valid baseline that answers the question (for example a naïve or unconditional estimate), with the same evaluation rule used later. Record it in `out/results.json` under the keys the task requires, or under `baseline_*` keys when the task does not name them.\n\nP3 Method and computation (depends on: P2)\n- Implement the analysis in `out/analysis.py` so that it reads only `data/`, writes `out/results.json` deterministically (fix every random seed you use and record it), and prints nothing that contradicts the written results. Any figure or table must be generated by this script.\n\nP4 Verification (depends on: P3)\n- Re-run `out/analysis.py` from a clean state and confirm it regenerates `out/results.json` with identical values. Record the check in `out/state/phases.json` under P4.\n- Check internal consistency: identities that must hold (for example counts that must add up, standard errors that must be positive, confidence intervals that must contain their estimates, date orderings that must respect the information rules), units, and magnitudes against the baseline. Record every check and its outcome in `out/state/checks.md`. A failed check must be fixed or honestly reported, never silently ignored.\n\nP5 Reporting (depends on: P4)\n- Write `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. Every quantitative statement must cite the key of `out/results.json` it comes from.\n- Write `out/claims.json`: a list of the central claims of your report, each as {\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}. Do not state a claim in the report that is not in this ledger.\n- Set the final statuses in `out/state/phases.json`.\n\nSTOPPING RULES\n- Stop and declare the task complete only when every phase P0–P5 is \"passed\" with recorded checks. If a phase is \"blocked\" (missing information, impossible requirement, violated availability rule), stop, set the status, explain in `out/report.md` (section Limitations and open issues) and still write every required file with `null` for values you could not legitimately produce.\n- Do not spend effort on extensions that the task does not require.\n\nRECOVERY RULES\n- Append a short dated entry to `out/state/log.md` after each phase transition and after any important decision, so that work can be resumed by reading `out/state/`.\n- If you discover that an upstream input or decision changed after a downstream phase passed, mark the downstream phases \"stale\" and redo them; do not reuse stale results.\n- If you are interrupted and later resumed, first read `out/state/` and continue from the last consistent state; never re-run expensive steps that already have recorded, unchanged outputs.\n\nEXECUTABLE GATES (additional, mandatory)\n- A read-only gate program is provided at `~/wp29/gates/pgar_gate.py`. Run it from the workspace root as `~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .` It checks the output contract of `TASK.md` (required files, keys, types, finite values, report sections, the claims ledger, the phase ledger, the exclusion ledger) and reproducibility (it re-runs `out/analysis.py` in a temporary copy and compares the regenerated `out/results.json` with yours). It never checks scientific correctness and it contains no reference answers.\n- You must run the gate at the end of P4 and again at the end of P5, and record each run's receipt (the gate writes `out/state/gate_receipts/<timestamp>.json`) in `out/state/phases.json`. You may not declare the task complete while the latest gate receipt reports `\"passed\": false`. Fix the reported problems and re-run the gate.\n- The controller will run the same gate after your session ends. If it fails, you will be resumed with the gate output and asked to fix the problems; each such cycle consumes your remaining budget.\n\nSEPARATE REVIEW (additional)\n- After the gate passes, a separate reviewer session that has not seen your work in progress will examine `TASK.md` and everything under `out/` and may return a list of issues (file `out/review/review.json`). You will then be resumed once to address them: fix what is justified, explain in `out/report.md` (Limitations and open issues) what you disagree with, re-run the gate, and update `out/claims.json` and `out/state/phases.json`. 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The estimands are the Marshallian demands x1*(p, m) and x2*(p, m), the indirect utility v(p, m) = u(x1*, x2*), and the budget identity residual p1 x1* + p2 x2* − m at the optimum. Derive the closed-form solution, state the assumptions under which it is the unique optimum, and validate it numerically by an independent constrained maximisation (grid search or a numerical optimiser on the budget line).\n\n## Inputs\n- `data/parameters.csv` — columns `parameter`, `value`, `description`; one row per parameter: `alpha` (exponent on good 1, dimensionless), `p1`, `p2` (prices, currency units per unit of good), `m` (income, currency units). These are given parameters of a theoretical exercise, not observed data.\n\n## Information-availability rules\n- Use only `data/parameters.csv`. No other input exists.\n- The closed-form expressions must be derived from the stated utility function; the numerical validation must not use the closed form (it must maximise utility directly).\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F5-dev-01\" |\n| `x1_demand` | number | units of good 1 | closed-form Marshallian demand for good 1 |\n| `x2_demand` | number | units of good 2 | closed-form Marshallian demand for good 2 |\n| `indirect_utility` | number | utils | u evaluated at the closed-form demands |\n| `budget_identity_residual` | number | currency units | p1·x1_demand + p2·x2_demand − m (should be numerically zero) |\n| `mrs_at_optimum` | number | — | marginal rate of substitution (∂u/∂x1)/(∂u/∂x2) at the closed-form demands |\n| `price_ratio` | number | — | p1/p2 |\n| `expenditure_share_good1` | number | — | p1·x1_demand / m |\n| `indirect_utility_numerical` | number | utils | maximum utility found by the independent numerical maximisation on the budget line (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 | — | {\"parameters.csv\": rows read} |\n| `n_analysed` | integer or null | — | number of parameter rows used |\n| `random_seed` | integer or null | — | seed used, if any |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. The Method section must state explicitly the assumptions under which the closed form holds (e.g. interior solution, strict monotonicity/concavity, parameter ranges) and the scope of the numerical validation (which parameter point it covers).\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` from `data/` only, deterministically. It must contain both the closed-form computation and the numerical validation.\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 15 minutes of work.\nbundle.json\ndata\ngate_spec.json\nTASK.md\n\n./data:\nparameters.csv","is_error":true,"tool_use_id":"toolu_01H1txfUb8ThXq9Ej1XqvyP5"}]},"uuid":"d2fe9ae8-5ffa-4e11-8ffb-f04e13224557","timestamp":"2026-10-30T03:51:00.649Z","toolUseResult":"Error: Exit code 1\n# F5-dev-01 — Cobb–Douglas consumer: closed-form demands with numerical validation\n\n## Scientific question\nA consumer with utility u(x1, x2) = α ln x1 + (1 − α) ln x2 chooses non-negative quantities of two goods subject to the budget constraint p1 x1 + p2 x2 ≤ m. The estimands are the Marshallian demands x1*(p, m) and x2*(p, m), the indirect utility v(p, m) = u(x1*, x2*), and the budget identity residual p1 x1* + p2 x2* − m at the optimum. Derive the closed-form solution, state the assumptions under which it is the unique optimum, and validate it numerically by an independent constrained maximisation (grid search or a numerical optimiser on the budget line).\n\n## Inputs\n- `data/parameters.csv` — columns `parameter`, `value`, `description`; one row per parameter: `alpha` (exponent on good 1, dimensionless), `p1`, `p2` (prices, currency units per unit of good), `m` (income, currency units). These are given parameters of a theoretical exercise, not observed data.\n\n## Information-availability rules\n- Use only `data/parameters.csv`. No other input exists.\n- The closed-form expressions must be derived from the stated utility function; the numerical validation must not use the closed form (it must maximise utility directly).\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F5-dev-01\" |\n| `x1_demand` | number | units of good 1 | closed-form Marshallian demand for good 1 |\n| `x2_demand` | number | units of good 2 | closed-form Marshallian demand for good 2 |\n| `indirect_utility` | number | utils | u evaluated at the closed-form demands |\n| `budget_identity_residual` | number | currency units | p1·x1_demand + p2·x2_demand − m (should be numerically zero) |\n| `mrs_at_optimum` | number | — | marginal rate of substitution (∂u/∂x1)/(∂u/∂x2) at the closed-form demands |\n| `price_ratio` | number | — | p1/p2 |\n| `expenditure_share_good1` | number | — | p1·x1_demand / m |\n| `indirect_utility_numerical` | number | utils | maximum utility found by the independent numerical maximisation on the budget line (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 | — | {\"parameters.csv\": rows read} |\n| `n_analysed` | integer or null | — | number of parameter rows used |\n| `random_seed` | integer or null | — | seed used, if any |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. The Method section must state explicitly the assumptions under which the closed form holds (e.g. interior solution, strict monotonicity/concavity, parameter ranges) and the scope of the numerical validation (which parameter point it covers).\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` from `data/` only, deterministically. It must contain both the closed-form computation and the numerical validation.\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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on good 1 in u(x1,x2) = alpha*ln(x1) + (1-alpha)*ln(x2)\"\np1,2.5,price of good 1 (currency units per unit)\np2,4.0,price of good 2 (currency units per unit)\nm,120.0,income (currency units)\na04798ade7a0f774f1e4651a0c7f99752f4c4df6eb3d4dc275694601ed994722 data/parameters.csv\n{\n \"task_id\": \"F5-dev-01\",\n \"required_files\": [\n \"out/results.json\",\n \"out/report.md\",\n \"out/analysis.py\",\n \"out/claims.json\"\n ],\n \"results_keys\": {\n \"task_id\": {\n \"type\": \"string\",\n \"nullable\": false\n },\n \"x1_demand\": {\n \"type\": \"number\",\n \"nullable\": false\n },\n \"x2_demand\": {\n \"type\": \"number\",\n \"nullable\": false\n },\n \"indirect_utility\": {\n \"type\": \"number\",\n \"nullable\": false\n },\n \"budget_identity_residual\": {\n \"type\": \"number\",\n \"nullable\": false\n },\n \"mrs_at_optimum\": {\n \"type\": \"number\",\n \"nullable\": false\n },\n \"price_ratio\": {\n \"type\": \"number\",\n \"nullable\": false\n },\n \"expenditure_share_good1\": {\n \"type\": \"number\",\n \"nullable\": false\n },\n \"indirect_utility_numerical\": {\n \"type\": \"number\",\n \"nullable\": false\n },\n \"feasibility\": {\n \"type\": \"string\",\n \"nullable\": false\n },\n \"feasibility_reason\": {\n \"type\": \"string\",\n \"nullable\": true\n },\n \"data_issues\": {\n \"type\": \"array\",\n \"nullable\": false\n },\n \"n_input_rows\": {\n \"type\": \"object\",\n \"nullable\": false\n },\n \"n_analysed\": {\n \"type\": \"integer\",\n \"nullable\": true\n },\n \"random_seed\": {\n \"type\": \"integer\",\n \"nullable\": true\n }\n },\n \"report_sections\": [\n \"Question\",\n \"Data and exclusions\",\n \"Method\",\n \"Results\",\n \"Uncertainty\",\n \"Limitations and open issues\"\n ],\n \"family_checks\": [\n \"claims_reference_existing_keys\",\n \"phase_ledger_consistent\"\n ],\n \"ci_pairs\": [],\n \"positive_keys\": [],\n \"chronology_pairs\": [],\n \"analysis_timeout_s\": 300,\n \"reproducibility_tolerance_rel\": 1e-06\n}{\n \"task_id\": 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0) — F5-dev-01\n\n**Question.** A consumer maximises u(x1,x2) = α ln x1 + (1−α) ln x2 s.t. p1x1 + p2x2 ≤ m, x ≥ 0. Derive the closed-form\nMarshallian demands, evaluate them at the given parameters, and validate numerically by maximising u directly on the budget line\n(without using the closed form).\n\n**Estimands** (at the single parameter point in data/parameters.csv): x1*(p,m), x2*(p,m), v(p,m)=u(x*), budget residual\np1x1*+p2x2*−m, MRS at x*, p1/p2, expenditure share of good 1, and the numerically found maximum utility.\n\n**Assumptions for meaningfulness/uniqueness.** 0<α<1, p1>0, p2>0, m>0. Then u is strictly increasing (budget binds), strictly\nconcave on R²₊₊, and ln x → −∞ as x→0 (interior solution); the feasible set is compact and convex, so the optimum exists and is unique.\n\n**Outputs.** out/results.json (keys: task_id, x1_demand, x2_demand, indirect_utility, budget_identity_residual, mrs_at_optimum,\nprice_ratio, expenditure_share_good1, indirect_utility_numerical, feasibility, feasibility_reason, data_issues, n_input_rows,\nn_analysed, random_seed); out/report.md (sections Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open\nissues); out/analysis.py; out/claims.json; plus protocol files (state/, exclusions.csv).\n\n**Information rules.** Only data/parameters.csv. Numerical validation must not use the closed form.\n\n**Invalidity conditions.** Missing/non-numeric parameters, α∉(0,1), non-positive prices or income (closed form would not be the\nunique interior optimum / problem ill-posed).\nEOF\ncat > phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully; contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P2\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P3\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P4\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P5\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"}}\nEOF\necho \"- 2026-10-29 P0 passed: contract written.\" > log.md","description":"Write contract, phase ledger, log"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1265,"cache_read_input_tokens":5877,"output_tokens":1120,"output_tokens_details":{"thinking_tokens":137},"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":1265},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXjxZu3q7T2cyLjwFzC4","requestRef":"e2917e44-99e8-4670-b6d9-3da6a46b715d","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"c17e1e00-85fc-44fd-8c56-5f036c7afbe2","timestamp":"2026-10-30T03:51:12.553Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0019","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","version":"2.1.314","gitBranch":"HEAD"}25{"parentUuid":"c17e1e00-85fc-44fd-8c56-5f036c7afbe2","isSidechain":false,"promptId":"6070ab8e-4224-4cd9-9696-2dc3cd90dce8","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01TNRuSFKsmBTbYUwh5CCG2N","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"3ae882aa-9d90-4d14-a9a8-60387dfd7f80","timestamp":"2026-10-30T03:51:12.588Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"c17e1e00-85fc-44fd-8c56-5f036c7afbe2","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0019/out/state","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","version":"2.1.314","gitBranch":"HEAD"}26{"type":"api-request-blob","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","hash":"61b5c63ce8611a8da90eb848abc6cf1cf671f9142f1716f68955cfa73e3923ae","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01TNRuSFKsmBTbYUwh5CCG2N","name":"Bash","input":{"command":"mkdir -p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0) — F5-dev-01\n\n**Question.** A consumer maximises u(x1,x2) = α ln x1 + (1−α) ln x2 s.t. p1x1 + p2x2 ≤ m, x ≥ 0. Derive the closed-form\nMarshallian demands, evaluate them at the given parameters, and validate numerically by maximising u directly on the budget line\n(without using the closed form).\n\n**Estimands** (at the single parameter point in data/parameters.csv): x1*(p,m), x2*(p,m), v(p,m)=u(x*), budget residual\np1x1*+p2x2*−m, MRS at x*, p1/p2, expenditure share of good 1, and the numerically found maximum utility.\n\n**Assumptions for meaningfulness/uniqueness.** 0<α<1, p1>0, p2>0, m>0. Then u is strictly increasing (budget binds), strictly\nconcave on R²₊₊, and ln x → −∞ as x→0 (interior solution); the feasible set is compact and convex, so the optimum exists and is unique.\n\n**Outputs.** out/results.json (keys: task_id, x1_demand, x2_demand, indirect_utility, budget_identity_residual, mrs_at_optimum,\nprice_ratio, expenditure_share_good1, indirect_utility_numerical, feasibility, feasibility_reason, data_issues, n_input_rows,\nn_analysed, random_seed); out/report.md (sections Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open\nissues); out/analysis.py; out/claims.json; plus protocol files (state/, exclusions.csv).\n\n**Information rules.** Only data/parameters.csv. Numerical validation must not use the closed form.\n\n**Invalidity conditions.** Missing/non-numeric parameters, α∉(0,1), non-positive prices or income (closed form would not be the\nunique interior optimum / problem ill-posed).\nEOF\ncat > phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully; contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P2\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P3\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P4\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P5\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"}}\nEOF\necho \"- 2026-10-29 P0 passed: contract written.\" > log.md","description":"Write contract, phase ledger, 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No exclusions needed.\nEOF\ncat > out/exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n1,keep rows with parameter in {alpha,p1,p2,m} and finite numeric value satisfying 0<alpha<1 and p1,p2,m>0,4,4,0,all four parameter rows valid; none removed\nEOF\necho \"- 2026-10-29 P1 passed: data audited (4 rows, valid, no exclusions).\" >> out/state/log.md","description":"Write data audit and exclusion ledger"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":269,"cache_read_input_tokens":9358,"output_tokens":605,"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_011CgXjymcn4P6NabdyRuPKr","requestRef":"5191445a-7e85-4463-b8a5-b9f662ec4d33","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"b9228719-ca09-4709-ba4d-65d064c1d5a5","timestamp":"2026-10-30T03:51:24.236Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0019","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","version":"2.1.314","gitBranch":"HEAD"}39{"parentUuid":"b9228719-ca09-4709-ba4d-65d064c1d5a5","isSidechain":false,"promptId":"6070ab8e-4224-4cd9-9696-2dc3cd90dce8","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_014zuZg2Nnv3vTndY3A1ET4f","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"aa1816fb-7bfb-4975-8b07-c7bbda563ad0","timestamp":"2026-10-30T03:51:24.291Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"b9228719-ca09-4709-ba4d-65d064c1d5a5","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0019","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","version":"2.1.314","gitBranch":"HEAD"}40{"type":"api-request-blob","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","hash":"952f772d1fffbc9741e36a5ec1c0470fe7930ff7a940a48e10d07e4b7c3ca592","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_014zuZg2Nnv3vTndY3A1ET4f","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n\n| file | SHA-256 | rows | cols |\n|---|---|---|---|\n| data/parameters.csv | a04798ade7a0f774f1e4651a0c7f99752f4c4df6eb3d4dc275694601ed994722 | 4 (+header) | 3 (parameter: str, value: float64, description: str) |\n\n- Matches the hash in bundle.json.\n- Values: alpha = 0.35 (dimensionless), p1 = 2.5, p2 = 4.0 (currency/unit), m = 120.0 (currency).\n- Missing values: 0. 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> out/analysis.py <<'EOF'\n\"\"\"F5-dev-01: Cobb-Douglas consumer. Closed-form Marshallian demands + independent numerical validation.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nReads only data/parameters.csv; writes out/results.json. Fully deterministic (no randomness; random_seed = null).\n\"\"\"\nimport json, math, os\nimport numpy as np\nimport pandas as pd\nfrom scipy.optimize import minimize_scalar, minimize\n\nDATA = os.path.join(\"data\", \"parameters.csv\")\nOUT = os.path.join(\"out\", \"results.json\")\n\nraw = pd.read_csv(DATA)\nn_raw = len(raw)\nissues = []\nif raw[\"parameter\"].duplicated().any():\n issues.append({\"issue\": \"duplicate parameter names\", \"handling\": \"first occurrence used\"})\npar = raw.drop_duplicates(\"parameter\").set_index(\"parameter\")[\"value\"].astype(float)\nneeded = [\"alpha\", \"p1\", \"p2\", \"m\"]\nmissing = [k for k in needed if k not in par.index or not np.isfinite(par[k])]\nif missing:\n raise SystemExit(f\"missing/non-finite parameters: {missing}\")\nalpha, p1, p2, m = (float(par[k]) for k in needed)\nif not (0 < alpha < 1 and p1 > 0 and p2 > 0 and m > 0):\n raise SystemExit(\"parameters outside the range where the interior closed form is the unique optimum\")\nn_analysed = int(sum(raw[\"parameter\"].isin(needed)))\n\n\ndef u(x1, x2):\n return alpha * np.log(x1) + (1 - alpha) * np.log(x2)\n\n\n# ---------- Closed form (Lagrangian FOCs: alpha/x1 = lam p1, (1-alpha)/x2 = lam p2, budget binds => lam = 1/m) ----------\nx1 = alpha * m / p1\nx2 = (1 - alpha) * m / p2\nv = float(u(x1, x2))\nresid = p1 * x1 + p2 * x2 - m\nmrs = (alpha / x1) / ((1 - alpha) / x2)\nprice_ratio = p1 / p2\nshare1 = p1 * x1 / m\n\n# ---------- Independent numerical validation (does NOT use the closed form) ----------\n# Budget line (monotone utility => budget binds): x1 in (0, m/p1), x2 = (m - p1 x1)/p2.\ndef neg_u_line(x1v):\n return -u(x1v, (m - p1 * x1v) / p2)\n\nub = m / p1\n# (a) dense grid search on the budget line\ngrid = np.linspace(ub * 1e-6, ub * (1 - 1e-6), 2_000_001)\nvals = -neg_u_line(grid)\ni = int(np.argmax(vals))\nx1_grid, v_grid = float(grid[i]), float(vals[i])\n# (b) bounded scalar optimiser (Brent) on the budget line\nres_b = minimize_scalar(neg_u_line, bounds=(ub * 1e-9, ub * (1 - 1e-9)), method=\"bounded\",\n options={\"xatol\": 1e-12})\nx1_brent, v_brent = float(res_b.x), float(-res_b.fun)\n# (c) 2-D SLSQP with the inequality budget constraint (checks that the budget binds without imposing it)\nres_s = minimize(lambda z: -u(z[0], z[1]), x0=np.array([1.0, 1.0]), method=\"SLSQP\",\n bounds=[(1e-9, None), (1e-9, None)],\n constraints=[{\"type\": \"ineq\", \"fun\": lambda z: m - p1 * z[0] - p2 * z[1]}],\n options={\"ftol\": 1e-14, \"maxiter\": 1000})\nv_slsqp = float(-res_s.fun)\n\nv_num = max(v_grid, v_brent, v_slsqp) # best utility found numerically\nx1_num = x1_brent\nx2_num = (m - p1 * x1_num) / p2\n\nresults = {\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": x1,\n \"x2_demand\": x2,\n \"indirect_utility\": v,\n \"budget_identity_residual\": resid,\n \"mrs_at_optimum\": mrs,\n \"price_ratio\": price_ratio,\n \"expenditure_share_good1\": share1,\n \"indirect_utility_numerical\": v_num,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": None,\n \"data_issues\": issues,\n \"n_input_rows\": {\"parameters.csv\": n_raw},\n \"n_analysed\": n_analysed,\n \"random_seed\": None,\n # diagnostics of the numerical validation\n \"numerical_x1_brent\": x1_num,\n \"numerical_x2_brent\": x2_num,\n \"numerical_x1_grid\": x1_grid,\n \"numerical_utility_grid\": v_grid,\n \"numerical_utility_brent\": v_brent,\n \"numerical_utility_slsqp\": v_slsqp,\n \"numerical_x_slsqp\": [float(res_s.x[0]), float(res_s.x[1])],\n \"numerical_slsqp_budget_slack\": float(m - p1 * res_s.x[0] - p2 * res_s.x[1]),\n \"utility_gap_numerical_minus_closed_form\": v_num - v,\n \"max_abs_demand_gap_x1\": max(abs(x1_num - x1), abs(x1_grid - x1), abs(float(res_s.x[0]) - x1)),\n \"max_abs_demand_gap_x2\": max(abs(x2_num - x2), abs(float(res_s.x[1]) - x2)),\n}\nwith open(OUT, \"w\") as f:\n json.dump(results, f, indent=2)\nprint(f\"x1*={x1:.6f} x2*={x2:.6f} v={v:.10f} v_num={v_num:.10f} residual={resid:.3e} MRS={mrs:.6f} 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x2*=19.500000 v=2.9182520129 v_num=2.9182520129 residual=0.000e+00 MRS=0.625000 p1/p2=0.625000\n{\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": 16.8,\n \"x2_demand\": 19.5,\n \"indirect_utility\": 2.9182520128635305,\n \"budget_identity_residual\": 0.0,\n \"mrs_at_optimum\": 0.625,\n \"price_ratio\": 0.625,\n \"expenditure_share_good1\": 0.35,\n \"indirect_utility_numerical\": 2.9182520128635305,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [],\n \"n_input_rows\": {\n \"parameters.csv\": 4\n },\n \"n_analysed\": 4,\n \"random_seed\": null,\n \"numerical_x1_brent\": 16.800000228802414,\n \"numerical_x2_brent\": 19.499999856998492,\n \"numerical_x1_grid\": 16.799990400048,\n \"numerical_utility_grid\": 2.9182520128634426,\n \"numerical_utility_brent\": 2.9182520128635305,\n \"numerical_utility_slsqp\": 2.9182520128635296,\n \"numerical_x_slsqp\": [\n 16.80000070212138,\n 19.49999956117413\n ],\n \"numerical_slsqp_budget_slack\": 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Fully deterministic (no randomness; random_seed = null).\n\"\"\"\nimport json, math, os\nimport numpy as np\nimport pandas as pd\nfrom scipy.optimize import minimize_scalar, minimize\n\nDATA = os.path.join(\"data\", \"parameters.csv\")\nOUT = os.path.join(\"out\", \"results.json\")\n\nraw = pd.read_csv(DATA)\nn_raw = len(raw)\nissues = []\nif raw[\"parameter\"].duplicated().any():\n issues.append({\"issue\": \"duplicate parameter names\", \"handling\": \"first occurrence used\"})\npar = raw.drop_duplicates(\"parameter\").set_index(\"parameter\")[\"value\"].astype(float)\nneeded = [\"alpha\", \"p1\", \"p2\", \"m\"]\nmissing = [k for k in needed if k not in par.index or not np.isfinite(par[k])]\nif missing:\n raise SystemExit(f\"missing/non-finite parameters: {missing}\")\nalpha, p1, p2, m = (float(par[k]) for k in needed)\nif not (0 < alpha < 1 and p1 > 0 and p2 > 0 and m > 0):\n raise SystemExit(\"parameters outside the range where the interior closed form is the unique optimum\")\nn_analysed = int(sum(raw[\"parameter\"].isin(needed)))\n\n\ndef u(x1, x2):\n return alpha * np.log(x1) + (1 - alpha) * np.log(x2)\n\n\n# ---------- Closed form (Lagrangian FOCs: alpha/x1 = lam p1, (1-alpha)/x2 = lam p2, budget binds => lam = 1/m) ----------\nx1 = alpha * m / p1\nx2 = (1 - alpha) * m / p2\nv = float(u(x1, x2))\nresid = p1 * x1 + p2 * x2 - m\nmrs = (alpha / x1) / ((1 - alpha) / x2)\nprice_ratio = p1 / p2\nshare1 = p1 * x1 / m\n\n# ---------- Independent numerical validation (does NOT use the closed form) ----------\n# Budget line (monotone utility => budget binds): x1 in (0, m/p1), x2 = (m - p1 x1)/p2.\ndef neg_u_line(x1v):\n return -u(x1v, (m - p1 * x1v) / p2)\n\nub = m / p1\n# (a) dense grid search on the budget line\ngrid = np.linspace(ub * 1e-6, ub * (1 - 1e-6), 2_000_001)\nvals = -neg_u_line(grid)\ni = int(np.argmax(vals))\nx1_grid, v_grid = float(grid[i]), float(vals[i])\n# (b) bounded scalar optimiser (Brent) on the budget line\nres_b = minimize_scalar(neg_u_line, bounds=(ub * 1e-9, ub * (1 - 1e-9)), method=\"bounded\",\n options={\"xatol\": 1e-12})\nx1_brent, v_brent = float(res_b.x), float(-res_b.fun)\n# (c) 2-D SLSQP with the inequality budget constraint (checks that the budget binds without imposing it)\nres_s = minimize(lambda z: -u(z[0], z[1]), x0=np.array([1.0, 1.0]), method=\"SLSQP\",\n bounds=[(1e-9, None), (1e-9, None)],\n constraints=[{\"type\": \"ineq\", \"fun\": lambda z: m - p1 * z[0] - p2 * z[1]}],\n options={\"ftol\": 1e-14, \"maxiter\": 1000})\nv_slsqp = float(-res_s.fun)\n\nv_num = max(v_grid, v_brent, v_slsqp) # best utility found numerically\nx1_num = x1_brent\nx2_num = (m - p1 * x1_num) / p2\n\nresults = {\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": x1,\n \"x2_demand\": x2,\n \"indirect_utility\": v,\n \"budget_identity_residual\": resid,\n \"mrs_at_optimum\": mrs,\n \"price_ratio\": price_ratio,\n \"expenditure_share_good1\": share1,\n \"indirect_utility_numerical\": v_num,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": None,\n \"data_issues\": issues,\n \"n_input_rows\": {\"parameters.csv\": n_raw},\n \"n_analysed\": n_analysed,\n \"random_seed\": None,\n # diagnostics of the numerical validation\n \"numerical_x1_brent\": x1_num,\n \"numerical_x2_brent\": x2_num,\n \"numerical_x1_grid\": x1_grid,\n \"numerical_utility_grid\": v_grid,\n \"numerical_utility_brent\": v_brent,\n \"numerical_utility_slsqp\": v_slsqp,\n \"numerical_x_slsqp\": [float(res_s.x[0]), float(res_s.x[1])],\n \"numerical_slsqp_budget_slack\": float(m - p1 * res_s.x[0] - p2 * res_s.x[1]),\n \"utility_gap_numerical_minus_closed_form\": v_num - v,\n \"max_abs_demand_gap_x1\": max(abs(x1_num - x1), abs(x1_grid - x1), abs(float(res_s.x[0]) - x1)),\n \"max_abs_demand_gap_x2\": max(abs(x2_num - x2), abs(float(res_s.x[1]) - x2)),\n}\nwith open(OUT, \"w\") as f:\n json.dump(results, f, indent=2)\nprint(f\"x1*={x1:.6f} x2*={x2:.6f} v={v:.10f} v_num={v_num:.10f} residual={resid:.3e} MRS={mrs:.6f} 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GATE pgar_gate/1.0 — FAILED (10 of 29 checks failed)\n [ok] file:out/results.json: present\n [FAIL] file:out/report.md: missing or empty\n [ok] file:out/analysis.py: present\n [FAIL] file:out/claims.json: missing or empty\n [ok] results_json: parsed\n [ok] key:task_id: ok\n [ok] key:x1_demand: ok\n [ok] key:x2_demand: ok\n [ok] key:indirect_utility: ok\n [ok] key:budget_identity_residual: ok\n [ok] key:mrs_at_optimum: ok\n [ok] key:price_ratio: ok\n [ok] key:expenditure_share_good1: ok\n [ok] key:indirect_utility_numerical: ok\n [ok] key:feasibility: ok\n [ok] key:feasibility_reason: ok\n [ok] key:data_issues: ok\n [ok] key:n_input_rows: ok\n [ok] key:n_analysed: ok\n [ok] key:random_seed: ok\n [FAIL] section:Question: heading not found\n [FAIL] section:Data and exclusions: heading not found\n [FAIL] section:Method: heading not found\n [FAIL] section:Results: heading not found\n [FAIL] section:Uncertainty: heading not found\n [FAIL] section:Limitations and open issues: heading not found\n [FAIL] claims_json: out/claims.json missing\n [FAIL] phase_ledger: phases not terminal: ['P1', 'P2', 'P3', 'P4', 'P5']\n [ok] reproducibility: regenerated in 0.3s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RP0019/out/state/gate_receipts/20261030T035155.297365Z.json\n20261030T035155.297365Z.json","is_error":false}]},"uuid":"f06fd476-2b65-41a9-9a0d-87973331fa3f","timestamp":"2026-10-30T03:51:55.304Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — FAILED (10 of 29 checks failed)\n [ok] file:out/results.json: present\n [FAIL] file:out/report.md: missing or empty\n [ok] file:out/analysis.py: present\n [FAIL] file:out/claims.json: missing or empty\n [ok] results_json: parsed\n [ok] key:task_id: ok\n [ok] key:x1_demand: ok\n [ok] key:x2_demand: ok\n [ok] key:indirect_utility: ok\n [ok] key:budget_identity_residual: ok\n [ok] key:mrs_at_optimum: ok\n [ok] key:price_ratio: ok\n [ok] key:expenditure_share_good1: ok\n [ok] key:indirect_utility_numerical: ok\n [ok] key:feasibility: ok\n [ok] key:feasibility_reason: ok\n [ok] key:data_issues: ok\n [ok] key:n_input_rows: ok\n [ok] key:n_analysed: ok\n [ok] key:random_seed: ok\n [FAIL] section:Question: heading not found\n [FAIL] section:Data and exclusions: heading not found\n [FAIL] section:Method: heading not found\n [FAIL] section:Results: heading not found\n [FAIL] section:Uncertainty: heading not found\n [FAIL] section:Limitations and open issues: heading not found\n [FAIL] claims_json: out/claims.json missing\n [FAIL] phase_ledger: phases not terminal: ['P1', 'P2', 'P3', 'P4', 'P5']\n [ok] reproducibility: regenerated in 0.3s; identical within tolerance\nreceipt: 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failures are P5 deliverables (expected at end of P4). Writing the report, claims and ledger."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1255,"cache_read_input_tokens":13869,"output_tokens":2861,"output_tokens_details":{"thinking_tokens":32},"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":1255},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXk2TXvt2CZRKbijSZWH","requestRef":"abe32fca-6a10-4531-954e-e2fcd81a37d2","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"fab372ec-94dd-4231-bbb3-15b8a910609c","timestamp":"2026-10-30T03:51:57.503Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0019","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","version":"2.1.314","gitBranch":"HEAD"}62{"parentUuid":"fab372ec-94dd-4231-bbb3-15b8a910609c","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk2TooTw1fFcGDdxuo2","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01WEf1NU4YjaLBLucivZ1mCK","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-dev-01 — Cobb–Douglas consumer: closed-form demands with numerical validation\n\n## Question\nA consumer with u(x1,x2) = α ln x1 + (1−α) ln x2 chooses x1, x2 ≥ 0 subject to p1x1 + p2x2 ≤ m. We derive the Marshallian\ndemands, the indirect utility and the budget residual in closed form, evaluate them at the parameters in `data/parameters.csv`,\nand validate them by an independent numerical maximisation of u that does not use the closed form.\n\n## Data and exclusions\n`data/parameters.csv` (SHA-256 a04798ad…4722, matches bundle.json) has 4 rows (`n_input_rows`): α = 0.35, p1 = 2.5, p2 = 4.0,\nm = 120. No missing values, duplicates or out-of-range values; `data_issues` is empty and no rows were excluded\n(`out/exclusions.csv`), so all 4 rows are used (`n_analysed` = 4). Audit details: `out/state/data_audit.md`.\n\n## Method\n**Assumptions under which the closed form is the unique optimum:** 0 < α < 1, p1 > 0, p2 > 0, m > 0 (all hold here, checked in\nthe script). Then (i) u is strictly increasing in both goods on R²₊₊, so the budget constraint binds; (ii) u is strictly concave\n(sum of strictly concave logs with positive weights), so any optimum is unique; (iii) ln x → −∞ as x → 0⁺, so the corner solutions\nare never optimal and the solution is interior (the non-negativity constraints are slack); (iv) the budget set is compact, so an\noptimum exists.\n\n**Derivation.** Lagrangian L = α ln x1 + (1−α) ln x2 + λ(m − p1x1 − p2x2). FOCs: α/x1 = λp1, (1−α)/x2 = λp2. Hence p1x1 = α/λ,\np2x2 = (1−α)/λ; summing and using the binding budget gives λ = 1/m. Therefore\nx1* = αm/p1, x2* = (1−α)m/p2, v(p,m) = α ln(αm/p1) + (1−α) ln((1−α)m/p2). Implications: MRS = (α/x1)/((1−α)/x2) = p1/p2 at the\noptimum, and the expenditure share of good 1 is α.\n\n**Numerical validation (independent of the closed form).** Implemented in `out/analysis.py`, using only u, the prices and the income:\n(a) grid search over 2,000,001 points of x1 ∈ (0, m/p1) on the budget line x2 = (m − p1x1)/p2; (b) bounded Brent minimisation of −u\non the same line (xatol 1e-12); (c) 2-D SLSQP on −u with the *inequality* budget constraint and positivity bounds, started at (1,1),\nwhich tests that the budget binds rather than imposing it. `indirect_utility_numerical` is the largest utility found across the\nthree. **Scope:** the validation covers only the single parameter point in `data/parameters.csv` (α = 0.35, p1 = 2.5, p2 = 4,\nm = 120); the general formula is established by the derivation, not by the numerics. No randomness is used (`random_seed` = null).\n\n## Results\n- Demand for good 1: `x1_demand` = 16.8 units; demand for good 2: `x2_demand` = 19.5 units.\n- Indirect utility: `indirect_utility` = 2.9182520129 utils.\n- Budget residual: `budget_identity_residual` = 0.0 currency units.\n- Tangency: `mrs_at_optimum` = 0.625 = `price_ratio` = 0.625.\n- Expenditure share of good 1: `expenditure_share_good1` = 0.35 (= α).\n- Numerical maximum: `indirect_utility_numerical` = 2.9182520129; `utility_gap_numerical_minus_closed_form` = 0.0. Individual\n methods: `numerical_utility_grid` = 2.91825201286344, `numerical_utility_brent` = 2.91825201286353, `numerical_utility_slsqp`\n = 2.91825201286353. Numerical maximisers agree with the closed-form demands to within `max_abs_demand_gap_x1` = 9.6e-6 (set by\n grid spacing) and `max_abs_demand_gap_x2` = 4.4e-7; SLSQP's budget slack is `numerical_slsqp_budget_slack` = 2.8e-14 (budget binds).\n- `feasibility` = \"complete\".\n\n## Uncertainty\nThis is a deterministic theoretical exercise with given parameters; there is no sampling uncertainty. The only uncertainty is\nnumerical: floating-point rounding (residual exactly 0.0 here) and optimiser/grid tolerance. Because utility is flat near the\noptimum, demand discrepancies of order 1e-6–1e-5 (`max_abs_demand_gap_x1`, `max_abs_demand_gap_x2`) translate into utility\ndiscrepancies at or below ~1e-13 (`numerical_utility_grid` vs `indirect_utility`).\n\n## Limitations and open issues\n- The numerical validation covers one parameter point only; it does not by itself prove the formula for other parameters (the\n analytic derivation does, under the stated assumptions).\n- The closed form is not valid outside 0 < α < 1, p1, p2, m > 0; the script stops with an error in that case rather than reporting\n values.\n- The reported `indirect_utility_numerical` is the maximum over three methods; the Brent and closed-form values coincide to the last\n printed digit, so the gap reported is 0.0 at double precision.\n- Extra diagnostic keys (prefixed `numerical_`, `utility_gap_…`, `max_abs_demand_gap_…`) are included in `out/results.json` beyond\n the required ones.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"Under 0<alpha<1 and positive prices and income, the unique optimum is x1*=alpha*m/p1, x2*=(1-alpha)*m/p2; at the given parameters x1*=16.8 and x2*=19.5.\",\"results_keys\":[\"x1_demand\",\"x2_demand\"],\"status\":\"supported\",\"caveat\":\"Analytic derivation; numerical evaluation at a single parameter point.\"},\n {\"id\":\"C2\",\"text\":\"Indirect utility at the closed-form demands is 2.9182520129 utils and the budget binds exactly (residual 0.0).\",\"results_keys\":[\"indirect_utility\",\"budget_identity_residual\"],\"status\":\"supported\",\"caveat\":\"Residual is subject to floating-point rounding; exactly 0.0 here.\"},\n {\"id\":\"C3\",\"text\":\"At the optimum the MRS equals the price ratio (0.625) and the expenditure share of good 1 equals alpha (0.35).\",\"results_keys\":[\"mrs_at_optimum\",\"price_ratio\",\"expenditure_share_good1\"],\"status\":\"supported\",\"caveat\":\"\"},\n {\"id\":\"C4\",\"text\":\"Independent numerical maximisation (grid, Brent, SLSQP with inequality budget) reaches the same maximum utility as the closed form, with demand gaps at most ~1e-5.\",\"results_keys\":[\"indirect_utility_numerical\",\"utility_gap_numerical_minus_closed_form\",\"max_abs_demand_gap_x1\",\"max_abs_demand_gap_x2\",\"numerical_slsqp_budget_slack\"],\"status\":\"supported\",\"caveat\":\"Validation covers only the single parameter point in data/parameters.csv.\"}\n]\nEOF\necho \"- 2026-10-29 P2 passed (numerical baseline), P3 passed (analysis.py), P4 passed (repro identical, checks.md, gate run 1 failures only P5 artifacts). P5 report+claims written.\" >> out/state/log.md","description":"Write report, claims, log"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1255,"cache_read_input_tokens":13869,"output_tokens":2861,"output_tokens_details":{"thinking_tokens":32},"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":1255},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXk2TXvt2CZRKbijSZWH","requestRef":"abe32fca-6a10-4531-954e-e2fcd81a37d2","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"e8a8c32a-5136-46c7-b6f0-4515adeea359","timestamp":"2026-10-30T03:52:19.256Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0019","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","version":"2.1.314","gitBranch":"HEAD"}63{"parentUuid":"e8a8c32a-5136-46c7-b6f0-4515adeea359","isSidechain":false,"promptId":"6070ab8e-4224-4cd9-9696-2dc3cd90dce8","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01WEf1NU4YjaLBLucivZ1mCK","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"9a68982b-85fb-435e-95e5-704b1c8a4c34","timestamp":"2026-10-30T03:52:19.312Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"e8a8c32a-5136-46c7-b6f0-4515adeea359","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0019","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","version":"2.1.314","gitBranch":"HEAD"}64{"type":"api-request-blob","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","hash":"ea78b74991e395a1711b89c920800ae596545e5ff545e7c79f2a50ceafbcc3b4","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"Remaining failures are P5 deliverables (expected at end of P4). Writing the report, claims and ledger."},{"type":"tool_use","id":"toolu_01WEf1NU4YjaLBLucivZ1mCK","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-dev-01 — Cobb–Douglas consumer: closed-form demands with numerical validation\n\n## Question\nA consumer with u(x1,x2) = α ln x1 + (1−α) ln x2 chooses x1, x2 ≥ 0 subject to p1x1 + p2x2 ≤ m. We derive the Marshallian\ndemands, the indirect utility and the budget residual in closed form, evaluate them at the parameters in `data/parameters.csv`,\nand validate them by an independent numerical maximisation of u that does not use the closed form.\n\n## Data and exclusions\n`data/parameters.csv` (SHA-256 a04798ad…4722, matches bundle.json) has 4 rows (`n_input_rows`): α = 0.35, p1 = 2.5, p2 = 4.0,\nm = 120. No missing values, duplicates or out-of-range values; `data_issues` is empty and no rows were excluded\n(`out/exclusions.csv`), so all 4 rows are used (`n_analysed` = 4). Audit details: `out/state/data_audit.md`.\n\n## Method\n**Assumptions under which the closed form is the unique optimum:** 0 < α < 1, p1 > 0, p2 > 0, m > 0 (all hold here, checked in\nthe script). Then (i) u is strictly increasing in both goods on R²₊₊, so the budget constraint binds; (ii) u is strictly concave\n(sum of strictly concave logs with positive weights), so any optimum is unique; (iii) ln x → −∞ as x → 0⁺, so the corner solutions\nare never optimal and the solution is interior (the non-negativity constraints are slack); (iv) the budget set is compact, so an\noptimum exists.\n\n**Derivation.** Lagrangian L = α ln x1 + (1−α) ln x2 + λ(m − p1x1 − p2x2). FOCs: α/x1 = λp1, (1−α)/x2 = λp2. Hence p1x1 = α/λ,\np2x2 = (1−α)/λ; summing and using the binding budget gives λ = 1/m. Therefore\nx1* = αm/p1, x2* = (1−α)m/p2, v(p,m) = α ln(αm/p1) + (1−α) ln((1−α)m/p2). Implications: MRS = (α/x1)/((1−α)/x2) = p1/p2 at the\noptimum, and the expenditure share of good 1 is α.\n\n**Numerical validation (independent of the closed form).** Implemented in `out/analysis.py`, using only u, the prices and the income:\n(a) grid search over 2,000,001 points of x1 ∈ (0, m/p1) on the budget line x2 = (m − p1x1)/p2; (b) bounded Brent minimisation of −u\non the same line (xatol 1e-12); (c) 2-D SLSQP on −u with the *inequality* budget constraint and positivity bounds, started at (1,1),\nwhich tests that the budget binds rather than imposing it. `indirect_utility_numerical` is the largest utility found across the\nthree. **Scope:** the validation covers only the single parameter point in `data/parameters.csv` (α = 0.35, p1 = 2.5, p2 = 4,\nm = 120); the general formula is established by the derivation, not by the numerics. No randomness is used (`random_seed` = null).\n\n## Results\n- Demand for good 1: `x1_demand` = 16.8 units; demand for good 2: `x2_demand` = 19.5 units.\n- Indirect utility: `indirect_utility` = 2.9182520129 utils.\n- Budget residual: `budget_identity_residual` = 0.0 currency units.\n- Tangency: `mrs_at_optimum` = 0.625 = `price_ratio` = 0.625.\n- Expenditure share of good 1: `expenditure_share_good1` = 0.35 (= α).\n- Numerical maximum: `indirect_utility_numerical` = 2.9182520129; `utility_gap_numerical_minus_closed_form` = 0.0. Individual\n methods: `numerical_utility_grid` = 2.91825201286344, `numerical_utility_brent` = 2.91825201286353, `numerical_utility_slsqp`\n = 2.91825201286353. Numerical maximisers agree with the closed-form demands to within `max_abs_demand_gap_x1` = 9.6e-6 (set by\n grid spacing) and `max_abs_demand_gap_x2` = 4.4e-7; SLSQP's budget slack is `numerical_slsqp_budget_slack` = 2.8e-14 (budget binds).\n- `feasibility` = \"complete\".\n\n## Uncertainty\nThis is a deterministic theoretical exercise with given parameters; there is no sampling uncertainty. The only uncertainty is\nnumerical: floating-point rounding (residual exactly 0.0 here) and optimiser/grid tolerance. Because utility is flat near the\noptimum, demand discrepancies of order 1e-6–1e-5 (`max_abs_demand_gap_x1`, `max_abs_demand_gap_x2`) translate into utility\ndiscrepancies at or below ~1e-13 (`numerical_utility_grid` vs `indirect_utility`).\n\n## Limitations and open issues\n- The numerical validation covers one parameter point only; it does not by itself prove the formula for other parameters (the\n analytic derivation does, under the stated assumptions).\n- The closed form is not valid outside 0 < α < 1, p1, p2, m > 0; the script stops with an error in that case rather than reporting\n values.\n- The reported `indirect_utility_numerical` is the maximum over three methods; the Brent and closed-form values coincide to the last\n printed digit, so the gap reported is 0.0 at double precision.\n- Extra diagnostic keys (prefixed `numerical_`, `utility_gap_…`, `max_abs_demand_gap_…`) are included in `out/results.json` beyond\n the required ones.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"Under 0<alpha<1 and positive prices and income, the unique optimum is x1*=alpha*m/p1, x2*=(1-alpha)*m/p2; at the given parameters x1*=16.8 and x2*=19.5.\",\"results_keys\":[\"x1_demand\",\"x2_demand\"],\"status\":\"supported\",\"caveat\":\"Analytic derivation; numerical evaluation at a single parameter point.\"},\n {\"id\":\"C2\",\"text\":\"Indirect utility at the closed-form demands is 2.9182520129 utils and the budget binds exactly (residual 0.0).\",\"results_keys\":[\"indirect_utility\",\"budget_identity_residual\"],\"status\":\"supported\",\"caveat\":\"Residual is subject to floating-point rounding; exactly 0.0 here.\"},\n {\"id\":\"C3\",\"text\":\"At the optimum the MRS equals the price ratio (0.625) and the expenditure share of good 1 equals alpha (0.35).\",\"results_keys\":[\"mrs_at_optimum\",\"price_ratio\",\"expenditure_share_good1\"],\"status\":\"supported\",\"caveat\":\"\"},\n {\"id\":\"C4\",\"text\":\"Independent numerical maximisation (grid, Brent, SLSQP with inequality budget) reaches the same maximum utility as the closed form, with demand gaps at most ~1e-5.\",\"results_keys\":[\"indirect_utility_numerical\",\"utility_gap_numerical_minus_closed_form\",\"max_abs_demand_gap_x1\",\"max_abs_demand_gap_x2\",\"numerical_slsqp_budget_slack\"],\"status\":\"supported\",\"caveat\":\"Validation covers only the single parameter point in data/parameters.csv.\"}\n]\nEOF\necho \"- 2026-10-29 P2 passed (numerical baseline), P3 passed (analysis.py), P4 passed (repro identical, checks.md, gate run 1 failures only P5 artifacts). 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They agree, and the final gate run passed with 0 of 29 checks failing.\n\n**Results** at α = 0.35, p1 = 2.5, p2 = 4, m = 120:\n- **Demand for good 1:** x1* = αm/p1 = 16.8 units.\n- **Demand for good 2:** x2* = (1−α)m/p2 = 19.5 units.\n- **Indirect utility:** v = 2.9182520129 utils.\n- **Budget residual:** 0.0, so the budget is spent exactly.\n- **Tangency:** the marginal rate of substitution equals the price ratio, both 0.625.\n- **Spending share on good 1:** 0.35, which equals α as the formula predicts.\n\n**Assumptions:** the closed form is the unique optimum when 0 < α < 1 and prices and income are positive. Under those conditions utility always rises with more of either good (so the whole budget is spent), it is strictly concave (so there is only one optimum), and log utility rules out corner solutions. These are stated in the report's Method section, and the script stops with an error if a parameter falls outside these ranges.\n\n**Numerical check:** none of the three methods uses the closed form.\n- A grid search over 2,000,001 points on the budget line.\n- A bounded optimiser on the budget line.\n- A two-dimensional optimiser that is only told to stay within the budget. It still ended up spending all of it, which confirms the budget binds rather than assuming it.\n\nThe best utility the three found equals the closed-form value to double precision. The quantities they chose differ from the formula by at most about 1e-5, and that largest gap comes from the grid spacing.\n\nRe-running the script from scratch gives an identical `results.json`. The input file's hash matches the bundle, it has no data issues, and no rows were excluded (4 read, 4 used). No randomness is involved, so `random_seed` is null.\n\n**Limitations:**\n- The numerical check covers only the one parameter point in the file. The general formula rests on the derivation, not on the numbers.\n- `results.json` contains some extra diagnostic keys beyond the required ones; the report says so.\n\nFiles are in `out/`:\n- `analysis.py`\n- `results.json`\n- `report.md`\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":280,"cache_read_input_tokens":18696,"output_tokens":819,"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":280},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXk4svSLJe69XWLUkMyq","requestRef":"b17fa477-9e21-449e-b5d1-6b5009bf23fb","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"c663685c-2779-4d85-b1ed-2d602d0db338","timestamp":"2026-10-30T03:52:36.451Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0019","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","version":"2.1.314","gitBranch":"HEAD"}77{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"c663685c-2779-4d85-b1ed-2d602d0db338","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a"}78{"type":"cost-state","sessionId":"3eea0fc0-4407-4152-b5e0-05fb05f85f7a","totalCostUSD":0.3260052,"totalAPIDuration":95939,"totalAPIDurationWithoutRetries":95932,"totalToolDuration":2509,"totalLinesAdded":0,"totalLinesRemoved":0,"totalDuration":98566,"startTime":1793332257911,"modelUsage":{"claude-opus-5-5":{"inputTokens":28,"outputTokens":10575,"thinkingTokens":589,"cacheReadInputTokens":135166,"cacheCreationInputTokens":17472,"cacheCreationEphemeral5mInputTokens":17472,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.3260052}},"hasUnknownModelCost":false}79