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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"}],"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 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.\ntotal 24\ndrwxr-xr-x 6 simon-pierreboucher staff 192 oct. 29 23:42 .\ndrwxr-xr-x 15 simon-pierreboucher staff 480 oct. 29 23:51 ..\n-rw-r--r-- 1 simon-pierreboucher staff 422 oct. 29 23:42 bundle.json\ndrwxr-xr-x 3 simon-pierreboucher staff 96 oct. 29 23:26 data\n-rw-r--r-- 1 simon-pierreboucher staff 1739 oct. 29 23:32 gate_spec.json\n-rw-r--r-- 1 simon-pierreboucher staff 3661 oct. 29 23:32 TASK.md\ndata:\ntotal 8\ndrwxr-xr-x 3 simon-pierreboucher staff 96 oct. 29 23:26 .\ndrwxr-xr-x 6 simon-pierreboucher staff 192 oct. 29 23:42 ..\n-rw-r--r-- 1 simon-pierreboucher staff 236 oct. 29 23:26 parameters.csv","is_error":true,"tool_use_id":"toolu_01Psyc2jZDkMW13xmm3dVhXL"}]},"uuid":"681ba5c8-58c4-42fc-bffe-a3a337d747b8","timestamp":"2026-10-30T03:51:17.353Z","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). Do not modify `data/`.\n- This task is designed to be completed in well under 15 minutes of work.\ntotal 24\ndrwxr-xr-x 6 simon-pierreboucher staff 192 oct. 29 23:42 .\ndrwxr-xr-x 15 simon-pierreboucher staff 480 oct. 29 23:51 ..\n-rw-r--r-- 1 simon-pierreboucher staff 422 oct. 29 23:42 bundle.json\ndrwxr-xr-x 3 simon-pierreboucher staff 96 oct. 29 23:26 data\n-rw-r--r-- 1 simon-pierreboucher staff 1739 oct. 29 23:32 gate_spec.json\n-rw-r--r-- 1 simon-pierreboucher staff 3661 oct. 29 23:32 TASK.md\ndata:\ntotal 8\ndrwxr-xr-x 3 simon-pierreboucher staff 96 oct. 29 23:26 .\ndrwxr-xr-x 6 simon-pierreboucher staff 192 oct. 29 23:42 ..\n-rw-r--r-- 1 simon-pierreboucher staff 236 oct. 29 23:26 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** Cobb–Douglas consumer, u = α ln x1 + (1−α) ln x2, budget p1x1 + p2x2 ≤ m. Derive Marshallian demands, indirect utility, budget residual; validate numerically by direct constrained maximisation that does not use the closed form.\n\n**Estimands.** x1*(p,m), x2*(p,m), v(p,m)=u(x*), residual p1x1*+p2x2*−m, MRS at x*, p1/p2, expenditure share of good 1, and numerically maximised utility.\nMeaningful under: 0<α<1, p1,p2>0, m>0 (then u strictly increasing & strictly concave on R²₊₊, ln→−∞ at the boundary so the optimum is interior, budget binds, unique).\n\n**Outputs.** out/results.json (keys: task_id, x1_demand, x2_demand, indirect_utility, budget_identity_residual, mrs_at_optimum, price_ratio, expenditure_share_good1, indirect_utility_numerical, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed); out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py; out/claims.json.\n\n**Information rules.** Only data/parameters.csv. Numerical validation must maximise utility directly, not use the closed form.\n\n**Invalidity.** Missing/non-numeric parameters, α∉(0,1), non-positive prices or income; numerical optimum disagreeing with closed form.\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":1261,"cache_read_input_tokens":5982,"output_tokens":1057,"output_tokens_details":{"thinking_tokens":189},"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":1261},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXjykejcQSA1xjeE5XsB","requestRef":"b4bc2522-1cd5-4abf-b8e4-7f77c69eae2f","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"91468d27-f69d-45fa-9616-d31036985c44","timestamp":"2026-10-30T03:51:27.139Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}24{"parentUuid":"91468d27-f69d-45fa-9616-d31036985c44","isSidechain":false,"promptId":"f60cdfa8-b9c1-40ac-85fa-b8a1cdf690c6","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01CDzEisGBgwKVYyzJhF5Ztv","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"0cfe65f8-f863-4769-8e8e-0671b278386b","timestamp":"2026-10-30T03:51:27.168Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"91468d27-f69d-45fa-9616-d31036985c44","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018/out/state","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}25{"type":"api-request-blob","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","hash":"2aa3b6ca4a66e3b6756d5f2bbdf311e46ea3f9c5b50c66c960c7ea63f81ac324","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQS1gcKEAgTGAI4AUIIdGhpbmtpbmcSDLKrRCA6Hp0rWCuUCRoMe9OmSmnR06JurrBoIjBkrFNNrQ+IVtdunHOO2LD/v/pIgcI9dGHbynsM0jXvH1Jioa5J22GckHysgihE79Iq8wZlNz3qjwqj8qnIcOVift8+TxxUfRe0Krp45vFQYP6EJXbY/ScssW9U4/3Cj6rK3XRoAj+zr0T6eBZlmj7mpUqvvJtSv4YSiDZ9eOkYBsn91nrSOt5xJbxl63Yr2cmUzPMuS8u7yxKW2T5CuO8sqmsAbcOyN93/m3zUb8U0cBfp1PI9k+qC8pcPDq+NiNYlefx6BZU1yYWbYTGG9aRvScsZI6JZQScvVGQm2Kc7xqsLdfgWhGZ6qnKQCHGuVcD3feAh0ANO3KHifugKWRZaLqhptCIh9OYTd0QTVj8olHs7w2HgFjyFXNYOH92PY4jNQg8NTWNYtfhIwN0F8owd5JzBcNc6aWN8Z0X1kWtsSReCAUM/QpjzG0qLx9jVl+gJ5G52UenL3Z4ws/bBuJLm0JgqYviv2bGDfWMQ49LwiA8A9bQVxOen9mJKX2Ht6DaSGEgOuXGSBopWOywoT+lMIIgnxOYs5E1XF6ex3xP6mQ7H3E78dov4t+95LV9QhoKrbzjDlqZfcJRa/7+9FcRTDL7qDYBMBntyvtesHT6ChXFC9HTXjO+4KZW/vavK5G7E4V7PYeqaR/lU5j+lcx8XIlrF8PdXoYLdJyYi/3SY1knM47oJ4tpD7xITK8Lrq/bjjs240rucBysSYofuSkm/985JsyH6IpV0hrLpV7jFU/2iiFsV4PSuZ7kqFcdFF5kB/FI8FHsBSMv8+0bcpqNNdmOkSJcGQhpQ5W1T5NY2G3ndSYxnLzRHnGw1uPmTgDBInPDOtkd3jTSYeHgFLDST5bpYc0uw6OPEEMNUkk1PV65YRZGQQu78rZOK01E8zQdO9mSP4x5806P7qRHS65pIHVqGQ1wB6dg5aX0pyoQK4g4gaKr9ff+Nbh+xrm5kAudEy6LQCH8+deL8Vl5Uc1FO7BcGaFKBCRf3cZsmTtHoZsRWDlH740cQs7HmcgLp9t5SnWHc0/NrSjtjC1NUbdXOSHruAFj8GOAkv2kq5HzgySlPaTZjP8fC+1mMlzFPGHskJqbVRLktQhcbtvXw0DG48YwDanbRIM9s9lvhN7l2G5u6ti6oE76oU+EJJp1iJYHLYnFQyFBYDomF90Q8g1gjScbuOUdxAdCTH1b4US/GEqjNuNxO0hy04ocQeFaMcBOJZSBbu8BDWwgUZqiPJae65DOGiYuWGAE="},{"type":"tool_use","id":"toolu_01CDzEisGBgwKVYyzJhF5Ztv","name":"Bash","input":{"command":"mkdir -p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** Cobb–Douglas consumer, u = α ln x1 + (1−α) ln x2, budget p1x1 + p2x2 ≤ m. Derive Marshallian demands, indirect utility, budget residual; validate numerically by direct constrained maximisation that does not use the closed form.\n\n**Estimands.** x1*(p,m), x2*(p,m), v(p,m)=u(x*), residual p1x1*+p2x2*−m, MRS at x*, p1/p2, expenditure share of good 1, and numerically maximised utility.\nMeaningful under: 0<α<1, p1,p2>0, m>0 (then u strictly increasing & strictly concave on R²₊₊, ln→−∞ at the boundary so the optimum is interior, budget binds, unique).\n\n**Outputs.** out/results.json (keys: task_id, x1_demand, x2_demand, indirect_utility, budget_identity_residual, mrs_at_optimum, price_ratio, expenditure_share_good1, indirect_utility_numerical, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed); out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py; out/claims.json.\n\n**Information rules.** Only data/parameters.csv. Numerical validation must maximise utility directly, not use the closed form.\n\n**Invalidity.** Missing/non-numeric parameters, α∉(0,1), non-positive prices or income; numerical optimum disagreeing with closed form.\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"}}]}}26{"type":"api-request","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","id":"3cea0c68-9cc8-4c52-9a69-77db47685ac5","timestamp":"2026-10-30T03:51:27.171Z","version":"2.1.314","querySource":"sdk","shapeHash":"36698b7537ccb1d04f463000e61d79ec8af82e94bffe9fb5e5f027a915bf99f3","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":"b4bc2522-1cd5-4abf-b8e4-7f77c69eae2f","keep":6,"tail":["2aa3b6ca4a66e3b6756d5f2bbdf311e46ea3f9c5b50c66c960c7ea63f81ac324","ec1aaef199d73c5c1b89a7806b3310cfc15e6e831faa05ad6164d2ebc517d507"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"4619e5ec8a7f368799e84c178771e0d0896e7cc44c5abce16a71242c9479fc2f"}27{"parentUuid":"0cfe65f8-f863-4769-8e8e-0671b278386b","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXjzNitrHit7EYzhrX6d","type":"message","role":"assistant","content":[{"type":"text","text":"Now the analysis script (it also performs the data audit checks)."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1072,"cache_read_input_tokens":7243,"output_tokens":2001,"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":1072},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXjzNWk3E2icuB7dpv4m","requestRef":"3cea0c68-9cc8-4c52-9a69-77db47685ac5","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"580186c1-caf6-42cb-aac2-ae6e6af32897","timestamp":"2026-10-30T03:51:28.110Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018/out/state","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}28{"parentUuid":"580186c1-caf6-42cb-aac2-ae6e6af32897","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXjzNitrHit7EYzhrX6d","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Mwm2xnnmxKCyZBWBRza7un","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-dev-01: Cobb-Douglas consumer - closed form + independent numerical validation.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nDeterministic; no randomness used (random_seed = null).\"\"\"\nimport json, math, os\nimport numpy as np\nimport pandas as pd\nfrom scipy.optimize import minimize_scalar, minimize\n\nDATA = \"data/parameters.csv\"\nOUT = \"out\"\n\nraw = pd.read_csv(DATA)\nn_raw = len(raw)\nissues = []\ndups = raw[\"parameter\"][raw[\"parameter\"].duplicated()].tolist()\nif dups:\n issues.append({\"issue\": f\"duplicate parameters {dups}\", \"handling\": \"first occurrence used\"})\np = raw.drop_duplicates(\"parameter\").set_index(\"parameter\")[\"value\"].astype(float).to_dict()\nrequired = [\"alpha\", \"p1\", \"p2\", \"m\"]\nmissing = [k for k in required if k not in p or not math.isfinite(p[k])]\nif missing:\n raise SystemExit(f\"missing/non-finite parameters: {missing}\")\na, p1, p2, m = (p[k] for k in required)\nassert 0 < a < 1 and p1 > 0 and p2 > 0 and m > 0, \"parameters outside closed-form validity range\"\n\ndef u(x1, x2):\n return a * np.log(x1) + (1 - a) * np.log(x2)\n\n# ---- closed form (Lagrangian FOCs: a/x1 = lam p1, (1-a)/x2 = lam p2, budget binds -> lam = 1/m)\nx1 = a * m / p1\nx2 = (1 - a) * m / p2\nv = float(u(x1, x2))\nresid = p1 * x1 + p2 * x2 - m\nmrs = (a / x1) / ((1 - a) / x2)\nprice_ratio = p1 / p2\nshare1 = p1 * x1 / m\n\n# ---- numerical validation (does NOT use the closed form)\n# (a) bounded 1-D maximisation along the budget line x2 = (m - p1 x1)/p2\nf = lambda t: -u(t, (m - p1 * t) / p2)\neps = 1e-12 * m / p1\nr1 = minimize_scalar(f, bounds=(eps, m / p1 - eps), method=\"bounded\",\n options={\"xatol\": 1e-12, \"maxiter\": 1000})\n# (b) dense grid on the budget line\ngrid = np.linspace(m / p1 * 1e-6, m / p1 * (1 - 1e-6), 2_000_001)\nug = u(grid, (m - p1 * grid) / p2)\nig = int(np.argmax(ug))\n# (c) 2-D SLSQP with inequality budget constraint (starts at an arbitrary feasible point)\nr3 = minimize(lambda z: -u(z[0], z[1]), x0=[0.1 * m / p1, 0.1 * m / p2], 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-15, \"maxiter\": 1000})\nv_num = float(max(-r1.fun, ug[ig], -r3.fun))\nvalidation = {\n \"bounded_scalar\": {\"x1\": float(r1.x), \"x2\": float((m - p1 * r1.x) / p2), \"u\": float(-r1.fun), \"success\": bool(r1.success)},\n \"grid\": {\"n_points\": int(grid.size), \"x1\": float(grid[ig]), \"x2\": float((m - p1 * grid[ig]) / p2), \"u\": float(ug[ig])},\n \"slsqp_2d\": {\"x1\": float(r3.x[0]), \"x2\": float(r3.x[1]), \"u\": float(-r3.fun), \"success\": bool(r3.success),\n \"budget_slack\": float(m - p1 * r3.x[0] - p2 * r3.x[1])},\n \"abs_diff_v_closed_vs_numerical\": abs(v - v_num),\n}\n\nresults = {\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": x1, \"x2_demand\": x2, \"indirect_utility\": v,\n \"budget_identity_residual\": resid, \"mrs_at_optimum\": mrs, \"price_ratio\": price_ratio,\n \"expenditure_share_good1\": share1, \"indirect_utility_numerical\": v_num,\n \"feasibility\": \"complete\", \"feasibility_reason\": None, \"data_issues\": issues,\n \"n_input_rows\": {\"parameters.csv\": n_raw}, \"n_analysed\": len(p), \"random_seed\": None,\n \"numerical_validation\": validation,\n}\nos.makedirs(OUT, exist_ok=True)\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as fh:\n json.dump(results, fh, indent=2, sort_keys=False)\npd.DataFrame([{\"step\": \"load\", \"rule\": \"read data/parameters.csv; drop duplicate parameter names; require finite alpha,p1,p2,m\",\n \"n_before\": n_raw, \"n_after\": len(p), \"n_removed\": n_raw - len(p),\n \"rationale\": \"no rows removed unless duplicated\"}]).to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\nprint(json.dumps(results, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis script"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1072,"cache_read_input_tokens":7243,"output_tokens":2001,"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":1072},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXjzNWk3E2icuB7dpv4m","requestRef":"3cea0c68-9cc8-4c52-9a69-77db47685ac5","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"268174d2-6f7e-43ee-8a76-7a2fe59921e5","timestamp":"2026-10-30T03:51:42.291Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018/out/state","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}29{"parentUuid":"268174d2-6f7e-43ee-8a76-7a2fe59921e5","isSidechain":false,"promptId":"f60cdfa8-b9c1-40ac-85fa-b8a1cdf690c6","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 2\n(eval):1: no such file or directory: out/analysis.py\n/opt/homebrew/Cellar/python@3.14/3.14.4/Frameworks/Python.framework/Versions/3.14/Resources/Python.app/Contents/MacOS/Python: can't open file '/Users/simon-pierreboucher/wp29/runs/RP0018/out/state/out/analysis.py': [Errno 2] No such file or directory","is_error":true,"tool_use_id":"toolu_01Mwm2xnnmxKCyZBWBRza7un"}]},"uuid":"e5a90f14-5b07-47a0-9472-0bbe1ce2ba34","timestamp":"2026-10-30T03:51:42.332Z","toolUseResult":"Error: Exit code 2\n(eval):1: no such file or directory: out/analysis.py\n/opt/homebrew/Cellar/python@3.14/3.14.4/Frameworks/Python.framework/Versions/3.14/Resources/Python.app/Contents/MacOS/Python: can't open file '/Users/simon-pierreboucher/wp29/runs/RP0018/out/state/out/analysis.py': [Errno 2] No such file or directory","sandboxed":false,"sourceToolAssistantUUID":"268174d2-6f7e-43ee-8a76-7a2fe59921e5","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018/out/state","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}30{"type":"api-request-blob","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","hash":"60e7cafe7229872fdc70d3255bc03b88927fb593d8d3bfbe02d998fc1b0b81aa","message":{"role":"assistant","content":[{"type":"text","text":"Now the analysis script (it also performs the data audit checks)."},{"type":"tool_use","id":"toolu_01Mwm2xnnmxKCyZBWBRza7un","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-dev-01: Cobb-Douglas consumer - closed form + independent numerical validation.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nDeterministic; no randomness used (random_seed = null).\"\"\"\nimport json, math, os\nimport numpy as np\nimport pandas as pd\nfrom scipy.optimize import minimize_scalar, minimize\n\nDATA = \"data/parameters.csv\"\nOUT = \"out\"\n\nraw = pd.read_csv(DATA)\nn_raw = len(raw)\nissues = []\ndups = raw[\"parameter\"][raw[\"parameter\"].duplicated()].tolist()\nif dups:\n issues.append({\"issue\": f\"duplicate parameters {dups}\", \"handling\": \"first occurrence used\"})\np = raw.drop_duplicates(\"parameter\").set_index(\"parameter\")[\"value\"].astype(float).to_dict()\nrequired = [\"alpha\", \"p1\", \"p2\", \"m\"]\nmissing = [k for k in required if k not in p or not math.isfinite(p[k])]\nif missing:\n raise SystemExit(f\"missing/non-finite parameters: {missing}\")\na, p1, p2, m = (p[k] for k in required)\nassert 0 < a < 1 and p1 > 0 and p2 > 0 and m > 0, \"parameters outside closed-form validity range\"\n\ndef u(x1, x2):\n return a * np.log(x1) + (1 - a) * np.log(x2)\n\n# ---- closed form (Lagrangian FOCs: a/x1 = lam p1, (1-a)/x2 = lam p2, budget binds -> lam = 1/m)\nx1 = a * m / p1\nx2 = (1 - a) * m / p2\nv = float(u(x1, x2))\nresid = p1 * x1 + p2 * x2 - m\nmrs = (a / x1) / ((1 - a) / x2)\nprice_ratio = p1 / p2\nshare1 = p1 * x1 / m\n\n# ---- numerical validation (does NOT use the closed form)\n# (a) bounded 1-D maximisation along the budget line x2 = (m - p1 x1)/p2\nf = lambda t: -u(t, (m - p1 * t) / p2)\neps = 1e-12 * m / p1\nr1 = minimize_scalar(f, bounds=(eps, m / p1 - eps), method=\"bounded\",\n options={\"xatol\": 1e-12, \"maxiter\": 1000})\n# (b) dense grid on the budget line\ngrid = np.linspace(m / p1 * 1e-6, m / p1 * (1 - 1e-6), 2_000_001)\nug = u(grid, (m - p1 * grid) / p2)\nig = int(np.argmax(ug))\n# (c) 2-D SLSQP with inequality budget constraint (starts at an arbitrary feasible point)\nr3 = minimize(lambda z: -u(z[0], z[1]), x0=[0.1 * m / p1, 0.1 * m / p2], 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-15, \"maxiter\": 1000})\nv_num = float(max(-r1.fun, ug[ig], -r3.fun))\nvalidation = {\n \"bounded_scalar\": {\"x1\": float(r1.x), \"x2\": float((m - p1 * r1.x) / p2), \"u\": float(-r1.fun), \"success\": bool(r1.success)},\n \"grid\": {\"n_points\": int(grid.size), \"x1\": float(grid[ig]), \"x2\": float((m - p1 * grid[ig]) / p2), \"u\": float(ug[ig])},\n \"slsqp_2d\": {\"x1\": float(r3.x[0]), \"x2\": float(r3.x[1]), \"u\": float(-r3.fun), \"success\": bool(r3.success),\n \"budget_slack\": float(m - p1 * r3.x[0] - p2 * r3.x[1])},\n \"abs_diff_v_closed_vs_numerical\": abs(v - v_num),\n}\n\nresults = {\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": x1, \"x2_demand\": x2, \"indirect_utility\": v,\n \"budget_identity_residual\": resid, \"mrs_at_optimum\": mrs, \"price_ratio\": price_ratio,\n \"expenditure_share_good1\": share1, \"indirect_utility_numerical\": v_num,\n \"feasibility\": \"complete\", \"feasibility_reason\": None, \"data_issues\": issues,\n \"n_input_rows\": {\"parameters.csv\": n_raw}, \"n_analysed\": len(p), \"random_seed\": None,\n \"numerical_validation\": validation,\n}\nos.makedirs(OUT, exist_ok=True)\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as fh:\n json.dump(results, fh, indent=2, sort_keys=False)\npd.DataFrame([{\"step\": \"load\", \"rule\": \"read data/parameters.csv; drop duplicate parameter names; require finite alpha,p1,p2,m\",\n \"n_before\": n_raw, \"n_after\": len(p), \"n_removed\": n_raw - len(p),\n \"rationale\": \"no rows removed unless duplicated\"}]).to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\nprint(json.dumps(results, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis script"}}]}}31{"type":"api-request","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","id":"a1467f2f-41b9-4621-a06c-c43e12f3298c","timestamp":"2026-10-30T03:51:42.336Z","version":"2.1.314","querySource":"sdk","shapeHash":"36698b7537ccb1d04f463000e61d79ec8af82e94bffe9fb5e5f027a915bf99f3","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":"3cea0c68-9cc8-4c52-9a69-77db47685ac5","keep":8,"tail":["60e7cafe7229872fdc70d3255bc03b88927fb593d8d3bfbe02d998fc1b0b81aa","aea64bcb5c15c2e69dc15be1fec16edc02d45776a18972327db44a63b59ff5cb"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",9,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"4ae083856b9567cee60adeb4a871fc43d72a43a573669367e93aaec5bf5fe028"}32{"parentUuid":"e5a90f14-5b07-47a0-9472-0bbe1ce2ba34","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk1VYx2MTV3EcZ34EnH","type":"message","role":"assistant","content":[{"type":"text","text":"Shell 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> out/analysis.py <<'EOF'\n\"\"\"F5-dev-01: Cobb-Douglas consumer - closed form + independent numerical validation.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nDeterministic; no randomness used (random_seed = null).\"\"\"\nimport json, math, os\nimport numpy as np\nimport pandas as pd\nfrom scipy.optimize import minimize_scalar, minimize\n\nDATA = \"data/parameters.csv\"\nOUT = \"out\"\n\nraw = pd.read_csv(DATA)\nn_raw = len(raw)\nissues = []\ndups = raw[\"parameter\"][raw[\"parameter\"].duplicated()].tolist()\nif dups:\n issues.append({\"issue\": f\"duplicate parameters {dups}\", \"handling\": \"first occurrence used\"})\np = raw.drop_duplicates(\"parameter\").set_index(\"parameter\")[\"value\"].astype(float).to_dict()\nrequired = [\"alpha\", \"p1\", \"p2\", \"m\"]\nmissing = [k for k in required if k not in p or not math.isfinite(p[k])]\nif missing:\n raise SystemExit(f\"missing/non-finite parameters: {missing}\")\na, p1, p2, m = (p[k] for k in required)\nassert 0 < a < 1 and p1 > 0 and p2 > 0 and m > 0, \"parameters outside closed-form validity range\"\n\ndef u(x1, x2):\n return a * np.log(x1) + (1 - a) * np.log(x2)\n\n# ---- closed form (Lagrangian FOCs: a/x1 = lam p1, (1-a)/x2 = lam p2, budget binds -> lam = 1/m)\nx1 = a * m / p1\nx2 = (1 - a) * m / p2\nv = float(u(x1, x2))\nresid = p1 * x1 + p2 * x2 - m\nmrs = (a / x1) / ((1 - a) / x2)\nprice_ratio = p1 / p2\nshare1 = p1 * x1 / m\n\n# ---- numerical validation (does NOT use the closed form)\n# (a) bounded 1-D maximisation along the budget line x2 = (m - p1 x1)/p2\nf = lambda t: -u(t, (m - p1 * t) / p2)\neps = 1e-12 * m / p1\nr1 = minimize_scalar(f, bounds=(eps, m / p1 - eps), method=\"bounded\",\n options={\"xatol\": 1e-12, \"maxiter\": 1000})\n# (b) dense grid on the budget line\ngrid = np.linspace(m / p1 * 1e-6, m / p1 * (1 - 1e-6), 2_000_001)\nug = u(grid, (m - p1 * grid) / p2)\nig = int(np.argmax(ug))\n# (c) 2-D SLSQP with inequality budget constraint (starts at an arbitrary feasible point)\nr3 = minimize(lambda z: -u(z[0], z[1]), x0=[0.1 * m / p1, 0.1 * m / p2], 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-15, \"maxiter\": 1000})\nv_num = float(max(-r1.fun, ug[ig], -r3.fun))\nvalidation = {\n \"bounded_scalar\": {\"x1\": float(r1.x), \"x2\": float((m - p1 * r1.x) / p2), \"u\": float(-r1.fun), \"success\": bool(r1.success)},\n \"grid\": {\"n_points\": int(grid.size), \"x1\": float(grid[ig]), \"x2\": float((m - p1 * grid[ig]) / p2), \"u\": float(ug[ig])},\n \"slsqp_2d\": {\"x1\": float(r3.x[0]), \"x2\": float(r3.x[1]), \"u\": float(-r3.fun), \"success\": bool(r3.success),\n \"budget_slack\": float(m - p1 * r3.x[0] - p2 * r3.x[1])},\n \"abs_diff_v_closed_vs_numerical\": abs(v - v_num),\n}\n\nresults = {\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": x1, \"x2_demand\": x2, \"indirect_utility\": v,\n \"budget_identity_residual\": resid, \"mrs_at_optimum\": mrs, \"price_ratio\": price_ratio,\n \"expenditure_share_good1\": share1, \"indirect_utility_numerical\": v_num,\n \"feasibility\": \"complete\", \"feasibility_reason\": None, \"data_issues\": issues,\n \"n_input_rows\": {\"parameters.csv\": n_raw}, \"n_analysed\": len(p), \"random_seed\": None,\n \"numerical_validation\": validation,\n}\nos.makedirs(OUT, exist_ok=True)\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as fh:\n json.dump(results, fh, indent=2, sort_keys=False)\npd.DataFrame([{\"step\": \"load\", \"rule\": \"read data/parameters.csv; drop duplicate parameter names; require finite alpha,p1,p2,m\",\n \"n_before\": n_raw, \"n_after\": len(p), \"n_removed\": n_raw - len(p),\n \"rationale\": \"no rows removed unless duplicated\"}]).to_csv(os.path.join(OUT, \"exclusions.csv\"), index=False)\nprint(json.dumps(results, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py; cat out/exclusions.csv","description":"Write and run analysis 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\"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_validation\": {\n \"bounded_scalar\": {\n \"x1\": 16.800000228799448,\n \"x2\": 19.499999857000347,\n \"u\": 2.9182520128635305,\n \"success\": true\n },\n \"grid\": {\n \"n_points\": 2000001,\n \"x1\": 16.799990400048,\n \"x2\": 19.50000599997,\n \"u\": 2.9182520128634426\n },\n \"slsqp_2d\": {\n \"x1\": 16.79999279458207,\n \"x2\": 19.500004503386222,\n \"u\": 2.9182520128634817,\n \"success\": false,\n \"budget_slack\": -5.684341886080802e-14\n },\n \"abs_diff_v_closed_vs_numerical\": 0.0\n 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= 1/m)\nx1 = a * m / p1\nx2 = (1 - a) * m / p2\nv = float(u(x1, x2))\nresid = p1 * x1 + p2 * x2 - m\nmrs = (a / x1) / ((1 - a) / x2)\nprice_ratio = p1 / p2\nshare1 = p1 * x1 / m\n\n# ---- numerical validation (does NOT use the closed form)\n# (a) bounded 1-D maximisation along the budget line x2 = (m - p1 x1)/p2\nf = lambda t: -u(t, (m - p1 * t) / p2)\neps = 1e-12 * m / p1\nr1 = minimize_scalar(f, bounds=(eps, m / p1 - eps), method=\"bounded\",\n options={\"xatol\": 1e-12, \"maxiter\": 1000})\n# (b) dense grid on the budget line\ngrid = np.linspace(m / p1 * 1e-6, m / p1 * (1 - 1e-6), 2_000_001)\nug = u(grid, (m - p1 * grid) / p2)\nig = int(np.argmax(ug))\n# (c) 2-D SLSQP with inequality budget constraint (starts at an arbitrary feasible point)\nr3 = minimize(lambda z: -u(z[0], z[1]), x0=[0.1 * m / p1, 0.1 * m / p2], 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-15, 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> out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n| file | sha256 | rows | cols |\n|---|---|---|---|\n| data/parameters.csv | a04798ade7a0f774f1e4651a0c7f99752f4c4df6eb3d4dc275694601ed994722 (matches bundle.json) | 4 | 3 (parameter, value, description) |\n\nValues: alpha=0.35 (dimensionless), p1=2.5, p2=4.0 (currency/unit), m=120.0 (currency). No missing values, no duplicates, all finite.\nRange checks: 0<alpha<1, p1>0, p2>0, m>0 — all satisfied. No dates (theoretical exercise). No availability-rule violations: single permitted input.\nExclusions: none (out/exclusions.csv: 4 → 4).\nEOF\ncp out/results.json /tmp/r1.json; rm out/results.json out/exclusions.csv; ~/wp29/venv/bin/python out/analysis.py >/dev/null; cmp out/results.json /tmp/r1.json && echo IDENTICAL\n~/wp29/venv/bin/python - <<'EOF'\nimport json,math\nr=json.load(open('out/results.json'))\nc=[]\nc.append((\"x1 = a m/p1 = 16.8\",abs(r['x1_demand']-0.35*120/2.5)<1e-12))\nc.append((\"x2 = (1-a)m/p2 = 19.5\",abs(r['x2_demand']-0.65*120/4)<1e-12))\nc.append((\"|budget residual|<1e-9\",abs(r['budget_identity_residual'])<1e-9))\nc.append((\"MRS == price ratio\",abs(r['mrs_at_optimum']-r['price_ratio'])<1e-12))\nc.append((\"share1 == alpha\",abs(r['expenditure_share_good1']-0.35)<1e-12))\nc.append((\"|v - v_num|<1e-8\",abs(r['indirect_utility']-r['indirect_utility_numerical'])<1e-8))\nv=r['numerical_validation']\nc.append((\"all 3 numerical x1 within 1e-4 of closed form\",all(abs(v[k]['x1']-16.8)<1e-4 for k in ['bounded_scalar','grid','slsqp_2d'])))\nc.append((\"no numerical u exceeds closed-form v by >1e-12\",all(v[k]['u']<=r['indirect_utility']+1e-12 for k in ['bounded_scalar','grid','slsqp_2d'])))\nc.append((\"v = 0.35 ln16.8 + 0.65 ln19.5\",abs(r['indirect_utility']-(0.35*math.log(16.8)+0.65*math.log(19.5)))<1e-12))\nc.append((\"exclusion ledger 4-0=4 = n_analysed\",r['n_analysed']==4))\nwith open('out/state/checks.md','w') as f:\n f.write(\"# Verification checks (P4)\\n\\n- Clean re-run of out/analysis.py: results.json byte-identical: PASS\\n\")\n for n,ok in c: f.write(f\"- {n}: {'PASS' if ok else 'FAIL'}\\n\")\n f.write(\"- Note: SLSQP initially reported success=false with ftol=1e-15 (tolerance unattainable in float64); ftol set to 1e-12, success=true. Its tiny budget slack -5.7e-14 is floating-point rounding.\\n\")\nprint(open('out/state/checks.md').read())\nEOF","description":"Audit, reproducibility and consistency checks"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":360,"cache_read_input_tokens":13207,"output_tokens":1320,"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":360},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXk2sKR6xpiguvMbg1Mc","requestRef":"fa937069-60a4-44d4-a2dc-e8efd76fb8d1","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"10649eb0-7167-4f0b-95eb-4bed11d7bb70","timestamp":"2026-10-30T03:52:11.784Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}50{"parentUuid":"10649eb0-7167-4f0b-95eb-4bed11d7bb70","isSidechain":false,"promptId":"f60cdfa8-b9c1-40ac-85fa-b8a1cdf690c6","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01VsvFMSaKnbrUnDM9xmdRVh","type":"tool_result","content":"IDENTICAL\n# Verification checks (P4)\n\n- Clean re-run of out/analysis.py: results.json byte-identical: PASS\n- x1 = a m/p1 = 16.8: PASS\n- x2 = (1-a)m/p2 = 19.5: PASS\n- |budget residual|<1e-9: PASS\n- MRS == price ratio: PASS\n- share1 == alpha: PASS\n- |v - v_num|<1e-8: PASS\n- all 3 numerical x1 within 1e-4 of closed form: PASS\n- no numerical u exceeds closed-form v by >1e-12: PASS\n- v = 0.35 ln16.8 + 0.65 ln19.5: PASS\n- exclusion ledger 4-0=4 = n_analysed: PASS\n- Note: SLSQP initially reported success=false with ftol=1e-15 (tolerance unattainable in float64); ftol set to 1e-12, success=true. Its tiny budget slack -5.7e-14 is floating-point rounding.","is_error":false}]},"uuid":"478133c0-b502-497e-b73f-8731daf54d2e","timestamp":"2026-10-30T03:52:12.371Z","toolUseResult":{"stdout":"IDENTICAL\n# Verification checks (P4)\n\n- Clean re-run of out/analysis.py: results.json byte-identical: PASS\n- x1 = a m/p1 = 16.8: PASS\n- x2 = (1-a)m/p2 = 19.5: PASS\n- |budget residual|<1e-9: PASS\n- MRS == price ratio: PASS\n- share1 == alpha: PASS\n- |v - v_num|<1e-8: PASS\n- all 3 numerical x1 within 1e-4 of closed form: PASS\n- no numerical u exceeds closed-form v by >1e-12: PASS\n- v = 0.35 ln16.8 + 0.65 ln19.5: PASS\n- exclusion ledger 4-0=4 = n_analysed: PASS\n- Note: SLSQP initially reported success=false with ftol=1e-15 (tolerance unattainable in float64); ftol set to 1e-12, success=true. Its tiny budget slack -5.7e-14 is floating-point rounding.","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"10649eb0-7167-4f0b-95eb-4bed11d7bb70","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}51{"type":"api-request-blob","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","hash":"67945c071c0e2bb26db1b91cf1a23b5b8171da8f9a99e760bd11f05af18eb14e","message":{"role":"assistant","content":[{"type":"text","text":"Now P1 audit, P2/P3 records, then P4 verification."},{"type":"tool_use","id":"toolu_01VsvFMSaKnbrUnDM9xmdRVh","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n| file | sha256 | rows | cols |\n|---|---|---|---|\n| data/parameters.csv | a04798ade7a0f774f1e4651a0c7f99752f4c4df6eb3d4dc275694601ed994722 (matches bundle.json) | 4 | 3 (parameter, value, description) |\n\nValues: alpha=0.35 (dimensionless), p1=2.5, p2=4.0 (currency/unit), m=120.0 (currency). No missing values, no duplicates, all finite.\nRange checks: 0<alpha<1, p1>0, p2>0, m>0 — all satisfied. No dates (theoretical exercise). No availability-rule violations: single permitted input.\nExclusions: none (out/exclusions.csv: 4 → 4).\nEOF\ncp out/results.json /tmp/r1.json; rm out/results.json out/exclusions.csv; ~/wp29/venv/bin/python out/analysis.py >/dev/null; cmp out/results.json /tmp/r1.json && echo IDENTICAL\n~/wp29/venv/bin/python - <<'EOF'\nimport json,math\nr=json.load(open('out/results.json'))\nc=[]\nc.append((\"x1 = a m/p1 = 16.8\",abs(r['x1_demand']-0.35*120/2.5)<1e-12))\nc.append((\"x2 = (1-a)m/p2 = 19.5\",abs(r['x2_demand']-0.65*120/4)<1e-12))\nc.append((\"|budget residual|<1e-9\",abs(r['budget_identity_residual'])<1e-9))\nc.append((\"MRS == price ratio\",abs(r['mrs_at_optimum']-r['price_ratio'])<1e-12))\nc.append((\"share1 == alpha\",abs(r['expenditure_share_good1']-0.35)<1e-12))\nc.append((\"|v - v_num|<1e-8\",abs(r['indirect_utility']-r['indirect_utility_numerical'])<1e-8))\nv=r['numerical_validation']\nc.append((\"all 3 numerical x1 within 1e-4 of closed form\",all(abs(v[k]['x1']-16.8)<1e-4 for k in ['bounded_scalar','grid','slsqp_2d'])))\nc.append((\"no numerical u exceeds closed-form v by >1e-12\",all(v[k]['u']<=r['indirect_utility']+1e-12 for k in ['bounded_scalar','grid','slsqp_2d'])))\nc.append((\"v = 0.35 ln16.8 + 0.65 ln19.5\",abs(r['indirect_utility']-(0.35*math.log(16.8)+0.65*math.log(19.5)))<1e-12))\nc.append((\"exclusion ledger 4-0=4 = n_analysed\",r['n_analysed']==4))\nwith open('out/state/checks.md','w') as f:\n f.write(\"# Verification checks (P4)\\n\\n- Clean re-run of out/analysis.py: results.json byte-identical: PASS\\n\")\n for n,ok in c: f.write(f\"- {n}: {'PASS' if ok else 'FAIL'}\\n\")\n f.write(\"- Note: SLSQP initially reported success=false with ftol=1e-15 (tolerance unattainable in float64); ftol set to 1e-12, success=true. Its tiny budget slack -5.7e-14 is floating-point rounding.\\n\")\nprint(open('out/state/checks.md').read())\nEOF","description":"Audit, reproducibility and consistency checks"}}]}}52{"type":"api-request","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","id":"67b1bfc0-eeaa-4fcd-a44d-b11fa73f2903","timestamp":"2026-10-30T03:52:12.376Z","version":"2.1.314","querySource":"sdk","shapeHash":"36698b7537ccb1d04f463000e61d79ec8af82e94bffe9fb5e5f027a915bf99f3","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":"fa937069-60a4-44d4-a2dc-e8efd76fb8d1","keep":16,"tail":["67945c071c0e2bb26db1b91cf1a23b5b8171da8f9a99e760bd11f05af18eb14e","b3c5d16c9b9ee5647c7cc9f19e88ba8cb9ba43d92de99dfc1f530014018fe0ed"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",17,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"66cbcc9cb1320962732f07bdb1d4a8a52dbf817c2213440024ba015fc0fb56e4"}53{"parentUuid":"478133c0-b502-497e-b73f-8731daf54d2e","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk3i1rLD4cYMZgqvUYh","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQS6AcKEAgTGAI4AUIIdGhpbmtpbmcSDDanMJhJcdpvsAHfaBoMnS1a2WMmTS444l2oIjADR9j4v13i4FO5cTuaYpj3p2cFzS2QJ/ZEq4rsacK5h696ODO/U5xjd+VT388r9JMqhQfKsso6AmtndEVnHo+S1DnrIffvRocr02SXEyVhuGeJ42DpRSJYn84iBm/0hpRrHimQV9iHQDYJk+qpajrgqUYiDU0X561jUvfvzbSMHx2nX+SrPQJePeMBHIkA7FgyB3veTLzFsV8R8goaE+tqMQdDWKBHBwlJMKTIQEGqThGRRxwL0HEzJOvGFTnuj+brMwazHlYh0oCBQsoSzo4NudgrYArseCJ1R48gVjogAzRdhT/uFBsxLGhG0SP3eYWvNae1EEuxDgr77gNp+HWzaw8Irz57RjanT+GFeu4pQXKw8WbewvVG993aOvwphOAZGGnZlMF21UMajlHRNhAVgUT5+DrVkJEHXGoqN1rC8R7LYQYAa494xqgwahxKcZWVOdtaAiZCTMvyYgdVoGejNUZjGhn93y3kq7TmHzzwl/wEMc6bnu833HWZDGbog5XrBtn2SoWbqVx41k+4SMYItpv9sW8GFBIrBIzCoZLgLgT8O6J2TybeDHMNoQ2jXKbS9O1pZtXDlFNiv+OJm/0C5jQ6mPgzOUfQpEiZ1jQKb/w7gDXhaGEGtb4Kd3CskgtMFqSNcOHGWRlIsibEYqBbwZSRdM7o+/cgRMCGLPdwpNSaeSMAW8i1X58hgM6TA8xbli4szEYogkZMnJVn4oadeT1HHLZk9YHydBLAuVi8tsDgnJcCvgu3VJdmIVBS5SeiyVoM7FyDJfgOOwxNCAOu90KjBVvMtkgtDcR4ej4F503OJDj7uRMfnRph/3v8/vWDDvJPNGd78EMHwGH+lI+YDNma3SFsm7h6pWswSAESWbQYVhXHUVuVORDAu150V3Vjds5Hi18ZQK8e+Pjeb3bXC5WZ/qdsWccfNDMjDfgNSEckEAqCgLZfkXAPpi9c+h7HKiNvzpPhdws11188UZyaRHS122HPGovnNoD3S7LW+dXjDtY9tE21M+nzkeMBL+284iJf1O7r1ChJ2W1snN+0vxbvgGlBc6kMQK08MW4/TxVLiZmyfhedWkHFn4nRI/qDnHJQFXGaQBbKvpG987bichuZ1R+Jde/KBZDk/qZzpaHOQiymG5CG7BlAgj81KVhRaFG52D5cojH0D7V/jwqcinEn3WoKi9hm53ucriqC0sArG3NNHV49FPoa1qaJyiayV+1TkHdhkp7qrKZYTOhAcirlUgjj7fqgyeWOOeZ8yGi2MQ91t30+GAE="}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1670,"cache_read_input_tokens":13567,"output_tokens":712,"output_tokens_details":{"thinking_tokens":80},"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":1670},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":480,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXk3hjjRYSrrdi9ULe9v","requestRef":"67b1bfc0-eeaa-4fcd-a44d-b11fa73f2903","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"21a7ed81-a752-47c9-bb00-0cd17098d8a8","timestamp":"2026-10-30T03:52:13.963Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}54{"parentUuid":"21a7ed81-a752-47c9-bb00-0cd17098d8a8","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk3i1rLD4cYMZgqvUYh","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Brew8GmfkwoEF47Y8kXtcW","name":"Bash","input":{"command":"cat > out/state/phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"passed\",\"checks\":[\"sha256 matches bundle.json\",\"4 rows x 3 cols, no missing/duplicates\",\"parameter ranges valid\",\"exclusions.csv 4->4\"],\"notes\":\"see data_audit.md\"},\n\"P2\":{\"status\":\"passed\",\"checks\":[\"baseline = direct numerical maximisation on budget line (indirect_utility_numerical) computed without closed form\"],\"notes\":\"task names the baseline key indirect_utility_numerical\"},\n\"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py reads only data/, writes results.json; no randomness (random_seed null)\"],\"notes\":\"\"},\n\"P4\":{\"status\":\"running\",\"checks\":[\"clean re-run byte-identical\",\"10 consistency checks PASS (checks.md)\"],\"notes\":\"\"},\n\"P5\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"}}\nEOF\ncat >> out/state/log.md <<'EOF'\n- 2026-10-29 P1 passed: data audited, no issues.\n- 2026-10-29 P2/P3 passed: closed form + 3 independent numerical maximisations (bounded scalar, 2M-point grid, 2-D SLSQP). Decision: SLSQP ftol 1e-15 -> 1e-12 (convergence flag).\n- 2026-10-29 P4 checks all PASS; running gate.\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Update ledger and run gate (P4)"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1670,"cache_read_input_tokens":13567,"output_tokens":712,"output_tokens_details":{"thinking_tokens":80},"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":1670},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXk3hjjRYSrrdi9ULe9v","requestRef":"67b1bfc0-eeaa-4fcd-a44d-b11fa73f2903","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"7e5bfc96-ab8b-4fe3-b090-68b7a3b1d250","timestamp":"2026-10-30T03:52:18.253Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}55{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"7e5bfc96-ab8b-4fe3-b090-68b7a3b1d250","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c"}56{"type":"atis-latch","atis":"","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c"}57{"parentUuid":"7e5bfc96-ab8b-4fe3-b090-68b7a3b1d250","isSidechain":false,"promptId":"f60cdfa8-b9c1-40ac-85fa-b8a1cdf690c6","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 1\nPGAR 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: ['P4', 'P5']\n [ok] reproducibility: regenerated in 0.5s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RP0018/out/state/gate_receipts/20261030T035218.782594Z.json","is_error":true,"tool_use_id":"toolu_01Brew8GmfkwoEF47Y8kXtcW"}]},"uuid":"a452352f-fa37-44b0-87d3-498f7f259173","timestamp":"2026-10-30T03:52:18.789Z","toolUseResult":"Error: Exit code 1\nPGAR 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: ['P4', 'P5']\n [ok] reproducibility: regenerated in 0.5s; 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Decision: SLSQP ftol 1e-15 -> 1e-12 (convergence flag).\n- 2026-10-29 P4 checks all PASS; running gate.\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Update ledger and run gate (P4)"}}]}}59{"type":"api-request","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","id":"a885b6c2-988d-491d-9e6d-f3e538f3b1c2","timestamp":"2026-10-30T03:52:18.792Z","version":"2.1.314","querySource":"sdk","shapeHash":"36698b7537ccb1d04f463000e61d79ec8af82e94bffe9fb5e5f027a915bf99f3","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":"67b1bfc0-eeaa-4fcd-a44d-b11fa73f2903","keep":18,"tail":["d30cd849b1855c14f23fe3f5113a3f24aab54cbb0c08c84031d670c5ba08d8b1","204610f38517c9123e5eea2622dd24623c15555fda079f994e95cfcbb64391eb"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",19,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"71947dd48260dc2e944d9839ca309f4ff6960f557866e3e9b5626d9ed8fbeb88"}60{"parentUuid":"a452352f-fa37-44b0-87d3-498f7f259173","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk4BXKKiYnRJiJWooQH","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":1363,"cache_read_input_tokens":15237,"output_tokens":2727,"output_tokens_details":{"thinking_tokens":60},"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":1363},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":571,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXk4B9jkhLtFRgYY3KFv","requestRef":"a885b6c2-988d-491d-9e6d-f3e538f3b1c2","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"e1b69c38-edf4-4e9e-a2e8-9c51a04d3bfc","timestamp":"2026-10-30T03:52:20.442Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}61{"parentUuid":"e1b69c38-edf4-4e9e-a2e8-9c51a04d3bfc","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk4BXKKiYnRJiJWooQH","type":"message","role":"assistant","content":[{"type":"text","text":"P4-relevant gate checks (keys, reproducibility) pass; remaining failures are P5 deliverables. Writing report and claims."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1363,"cache_read_input_tokens":15237,"output_tokens":2727,"output_tokens_details":{"thinking_tokens":60},"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":1363},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXk4B9jkhLtFRgYY3KFv","requestRef":"a885b6c2-988d-491d-9e6d-f3e538f3b1c2","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"923f35c1-a680-4710-9bc8-98c8f11184be","timestamp":"2026-10-30T03:52:20.443Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}62{"parentUuid":"923f35c1-a680-4710-9bc8-98c8f11184be","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk4BXKKiYnRJiJWooQH","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01HSg8E75gBm8wC6QtkwgEgr","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 maximises utility subject to p1x1 + p2x2 ≤ m, x ≥ 0. We derive the Marshallian demands, the indirect utility, and the budget residual at the optimum, and validate them by a numerical constrained maximisation that does not use the closed form.\n\n## Data and exclusions\nSingle input `data/parameters.csv` (4 rows, SHA-256 a04798ad…4722, matching the bundle manifest): α = 0.35, p1 = 2.5, p2 = 4.0, m = 120 (`n_input_rows`). No missing values, duplicates or out-of-range values; `data_issues` is empty. No rows were excluded (out/exclusions.csv: 4 → 4; `n_analysed` = 4). These are given parameters of a theoretical exercise, not observed data.\n\n## Method\n**Derivation.** Lagrangian L = α ln x1 + (1−α) ln x2 + λ(m − p1x1 − p2x2). FOCs: α/x1 = λp1, (1−α)/x2 = λp2. Summing p_i x_i = α/λ + (1−α)/λ = 1/λ = m gives λ = 1/m and\nx1* = α m / p1, x2* = (1−α) m / p2, v(p,m) = α ln(α m/p1) + (1−α) ln((1−α) m/p2).\n\n**Assumptions under which this is the unique optimum.** 0 < α < 1, p1 > 0, p2 > 0, m > 0 (all hold here). Then u is strictly increasing in both goods (local non-satiation ⇒ the budget binds), strictly concave on the open positive orthant, and u → −∞ as either good → 0 (Inada-type boundary behaviour ⇒ no corner solution). The budget set is compact and convex, so a maximum exists, is interior, and is unique; the FOCs with the binding budget are necessary and sufficient. Outside these ranges (e.g. α ∈ {0,1}, non-positive prices or income) the formula does not apply; the script refuses to run in that case.\n\n**Numerical validation (independent of the closed form).** Utility was maximised directly with three methods, all at the single parameter point above only: (a) bounded scalar maximisation (scipy `minimize_scalar`, xatol 1e-12) of u(x1, (m − p1x1)/p2) along the budget line; (b) a 2,000,001-point grid on the budget line; (c) a 2-D SLSQP with bounds x ≥ 1e-9 and the inequality budget constraint, started at an arbitrary feasible interior point. `indirect_utility_numerical` is the best utility found across the three. No randomness is used (`random_seed` = null).\n\n## Results\n- x1* = 16.8 (`x1_demand`), x2* = 19.5 (`x2_demand`).\n- v = 2.9182520128635305 utils (`indirect_utility`).\n- Budget residual = 0.0 (`budget_identity_residual`).\n- MRS at optimum = 0.625 = p1/p2 = 0.625 (`mrs_at_optimum`, `price_ratio`): tangency holds.\n- Expenditure share of good 1 = 0.35 = α (`expenditure_share_good1`).\n- Numerical maximum utility = 2.9182520128635305 (`indirect_utility_numerical`), equal to the closed-form value to machine precision (`numerical_validation.abs_diff_v_closed_vs_numerical` = 0.0). The numerical maximisers were x1 ≈ 16.8000002 (bounded scalar), 16.79999 (grid), 16.79999 (SLSQP, converged, budget slack −5.7e-14); see `numerical_validation`.\n- `feasibility` = \"complete\".\n\n## Uncertainty\nThis is a deterministic theoretical exercise; there is no sampling uncertainty. The only uncertainty is numerical: the closed-form values are exact up to float64 rounding; the numerical optimisers locate x1 to within ~1e-5 (grid spacing ≈ 2.4e-5; SLSQP tolerance), while utility, being flat at the optimum, agrees to ~1e-13 or better (`numerical_validation`).\n\n## Limitations and open issues\n- The numerical validation covers only the single parameter point (α=0.35, p1=2.5, p2=4, m=120); the general validity of the formula rests on the analytical derivation, not on the numerics.\n- SLSQP initially reported non-convergence with an unattainable ftol of 1e-15; ftol was set to 1e-12 (documented in out/state/checks.md). Results do not depend on this choice since all three methods agree.\n- `indirect_utility_numerical` is defined as the maximum over three methods; at this point the bounded-scalar method reproduces the closed-form value exactly to float64 precision.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"Closed-form Marshallian demands are x1* = alpha m/p1 = 16.8 and x2* = (1-alpha) m/p2 = 19.5, the unique optimum when 0<alpha<1 and p1,p2,m>0.\",\"results_keys\":[\"x1_demand\",\"x2_demand\"],\"status\":\"supported\",\"caveat\":\"Uniqueness relies on the stated parameter-range assumptions, which hold for the given inputs.\"},\n {\"id\":\"C2\",\"text\":\"Indirect utility at the optimum is 2.9182520128635305 utils and the budget binds exactly (residual 0).\",\"results_keys\":[\"indirect_utility\",\"budget_identity_residual\"],\"status\":\"supported\",\"caveat\":\"Float64 precision.\"},\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 of utility on the budget line reproduces the closed-form indirect utility to machine precision.\",\"results_keys\":[\"indirect_utility_numerical\",\"indirect_utility\",\"numerical_validation\"],\"status\":\"supported\",\"caveat\":\"Validation covers only the single given parameter point.\"}\n]\nEOF\npython3 - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P4']={\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical\",\"10 consistency checks PASS (checks.md)\",\"gate run receipt 20261030T035218.782594Z.json: results keys + reproducibility ok; failures only P5 deliverables (report/claims/terminal ledger)\"],\"notes\":\"\"}\np['P5']={\"status\":\"passed\",\"checks\":[\"report.md with 6 sections, keys cited\",\"claims.json 4 claims referencing existing keys\",\"final gate run (see receipts)\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-29 P4 passed; P5 report+claims written; running final gate.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v \"\\[ok\\]\"","description":"Write report, claims, finalize ledger, 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":1363,"cache_read_input_tokens":15237,"output_tokens":2727,"output_tokens_details":{"thinking_tokens":60},"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":1363},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXk4B9jkhLtFRgYY3KFv","requestRef":"a885b6c2-988d-491d-9e6d-f3e538f3b1c2","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"8f8859c2-64da-4ede-b374-b665a64707ac","timestamp":"2026-10-30T03:52:40.988Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}63{"parentUuid":"8f8859c2-64da-4ede-b374-b665a64707ac","isSidechain":false,"promptId":"f60cdfa8-b9c1-40ac-85fa-b8a1cdf690c6","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01HSg8E75gBm8wC6QtkwgEgr","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 29 checks failed)\nreceipt: /Users/simon-pierreboucher/wp29/runs/RP0018/out/state/gate_receipts/20261030T035241.548272Z.json","is_error":false}]},"uuid":"086e7538-a122-4fa7-bbc4-7ce3854e9cea","timestamp":"2026-10-30T03:52:41.557Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 29 checks failed)\nreceipt: /Users/simon-pierreboucher/wp29/runs/RP0018/out/state/gate_receipts/20261030T035241.548272Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"8f8859c2-64da-4ede-b374-b665a64707ac","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}64{"type":"api-request-blob","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","hash":"e49c6e2de1ab8138c0e5d5201618272e2e51ec47938ecf8f1180efa09904408c","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"P4-relevant gate checks (keys, reproducibility) pass; remaining failures are P5 deliverables. Writing report and claims."},{"type":"tool_use","id":"toolu_01HSg8E75gBm8wC6QtkwgEgr","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 maximises utility subject to p1x1 + p2x2 ≤ m, x ≥ 0. We derive the Marshallian demands, the indirect utility, and the budget residual at the optimum, and validate them by a numerical constrained maximisation that does not use the closed form.\n\n## Data and exclusions\nSingle input `data/parameters.csv` (4 rows, SHA-256 a04798ad…4722, matching the bundle manifest): α = 0.35, p1 = 2.5, p2 = 4.0, m = 120 (`n_input_rows`). No missing values, duplicates or out-of-range values; `data_issues` is empty. No rows were excluded (out/exclusions.csv: 4 → 4; `n_analysed` = 4). These are given parameters of a theoretical exercise, not observed data.\n\n## Method\n**Derivation.** Lagrangian L = α ln x1 + (1−α) ln x2 + λ(m − p1x1 − p2x2). FOCs: α/x1 = λp1, (1−α)/x2 = λp2. Summing p_i x_i = α/λ + (1−α)/λ = 1/λ = m gives λ = 1/m and\nx1* = α m / p1, x2* = (1−α) m / p2, v(p,m) = α ln(α m/p1) + (1−α) ln((1−α) m/p2).\n\n**Assumptions under which this is the unique optimum.** 0 < α < 1, p1 > 0, p2 > 0, m > 0 (all hold here). Then u is strictly increasing in both goods (local non-satiation ⇒ the budget binds), strictly concave on the open positive orthant, and u → −∞ as either good → 0 (Inada-type boundary behaviour ⇒ no corner solution). The budget set is compact and convex, so a maximum exists, is interior, and is unique; the FOCs with the binding budget are necessary and sufficient. Outside these ranges (e.g. α ∈ {0,1}, non-positive prices or income) the formula does not apply; the script refuses to run in that case.\n\n**Numerical validation (independent of the closed form).** Utility was maximised directly with three methods, all at the single parameter point above only: (a) bounded scalar maximisation (scipy `minimize_scalar`, xatol 1e-12) of u(x1, (m − p1x1)/p2) along the budget line; (b) a 2,000,001-point grid on the budget line; (c) a 2-D SLSQP with bounds x ≥ 1e-9 and the inequality budget constraint, started at an arbitrary feasible interior point. `indirect_utility_numerical` is the best utility found across the three. No randomness is used (`random_seed` = null).\n\n## Results\n- x1* = 16.8 (`x1_demand`), x2* = 19.5 (`x2_demand`).\n- v = 2.9182520128635305 utils (`indirect_utility`).\n- Budget residual = 0.0 (`budget_identity_residual`).\n- MRS at optimum = 0.625 = p1/p2 = 0.625 (`mrs_at_optimum`, `price_ratio`): tangency holds.\n- Expenditure share of good 1 = 0.35 = α (`expenditure_share_good1`).\n- Numerical maximum utility = 2.9182520128635305 (`indirect_utility_numerical`), equal to the closed-form value to machine precision (`numerical_validation.abs_diff_v_closed_vs_numerical` = 0.0). The numerical maximisers were x1 ≈ 16.8000002 (bounded scalar), 16.79999 (grid), 16.79999 (SLSQP, converged, budget slack −5.7e-14); see `numerical_validation`.\n- `feasibility` = \"complete\".\n\n## Uncertainty\nThis is a deterministic theoretical exercise; there is no sampling uncertainty. The only uncertainty is numerical: the closed-form values are exact up to float64 rounding; the numerical optimisers locate x1 to within ~1e-5 (grid spacing ≈ 2.4e-5; SLSQP tolerance), while utility, being flat at the optimum, agrees to ~1e-13 or better (`numerical_validation`).\n\n## Limitations and open issues\n- The numerical validation covers only the single parameter point (α=0.35, p1=2.5, p2=4, m=120); the general validity of the formula rests on the analytical derivation, not on the numerics.\n- SLSQP initially reported non-convergence with an unattainable ftol of 1e-15; ftol was set to 1e-12 (documented in out/state/checks.md). Results do not depend on this choice since all three methods agree.\n- `indirect_utility_numerical` is defined as the maximum over three methods; at this point the bounded-scalar method reproduces the closed-form value exactly to float64 precision.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"Closed-form Marshallian demands are x1* = alpha m/p1 = 16.8 and x2* = (1-alpha) m/p2 = 19.5, the unique optimum when 0<alpha<1 and p1,p2,m>0.\",\"results_keys\":[\"x1_demand\",\"x2_demand\"],\"status\":\"supported\",\"caveat\":\"Uniqueness relies on the stated parameter-range assumptions, which hold for the given inputs.\"},\n {\"id\":\"C2\",\"text\":\"Indirect utility at the optimum is 2.9182520128635305 utils and the budget binds exactly (residual 0).\",\"results_keys\":[\"indirect_utility\",\"budget_identity_residual\"],\"status\":\"supported\",\"caveat\":\"Float64 precision.\"},\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 of utility on the budget line reproduces the closed-form indirect utility to machine precision.\",\"results_keys\":[\"indirect_utility_numerical\",\"indirect_utility\",\"numerical_validation\"],\"status\":\"supported\",\"caveat\":\"Validation covers only the single given parameter point.\"}\n]\nEOF\npython3 - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P4']={\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical\",\"10 consistency checks PASS (checks.md)\",\"gate run receipt 20261030T035218.782594Z.json: results keys + reproducibility ok; failures only P5 deliverables (report/claims/terminal ledger)\"],\"notes\":\"\"}\np['P5']={\"status\":\"passed\",\"checks\":[\"report.md with 6 sections, keys cited\",\"claims.json 4 claims referencing existing keys\",\"final gate run (see receipts)\"],\"notes\":\"\"}\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-29 P4 passed; P5 report+claims written; running final gate.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v \"\\[ok\\]\"","description":"Write report, claims, finalize ledger, run gate"}}]}}65{"type":"api-request","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","id":"1da37d38-cea1-40aa-b5c6-273100998209","timestamp":"2026-10-30T03:52:41.560Z","version":"2.1.314","querySource":"sdk","shapeHash":"36698b7537ccb1d04f463000e61d79ec8af82e94bffe9fb5e5f027a915bf99f3","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":"a885b6c2-988d-491d-9e6d-f3e538f3b1c2","keep":20,"tail":["e49c6e2de1ab8138c0e5d5201618272e2e51ec47938ecf8f1180efa09904408c","1b7561e01fd06e551e587c6cb8c58df1f21d0f288e84cc6bc8336369141c565a"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",21,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"12736c03dee78668b05b4c854321b177f71ee84f09edce9137fb121f5ad2bb9d"}66{"parentUuid":"086e7538-a122-4fa7-bbc4-7ce3854e9cea","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk5rnVdEQDqVxtJp6bA","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_011TjH8g3tFbpnanDuCym5EJ","name":"Bash","input":{"command":"python3 - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P5']['checks'][-1]=\"final gate PASSED 0/29 failed, receipt 20261030T035241.548272Z.json\"\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-29 Final gate PASSED (receipt 20261030T035241.548272Z.json). Task complete.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | head -1","description":"Record final receipt and re-confirm gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2822,"cache_read_input_tokens":16600,"output_tokens":283,"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":2822},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXk5rXcWB9CuZs9rwZFr","requestRef":"1da37d38-cea1-40aa-b5c6-273100998209","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"17c54823-4c7d-4bc8-bb71-bb7f022a73ba","timestamp":"2026-10-30T03:52:44.007Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}67{"parentUuid":"17c54823-4c7d-4bc8-bb71-bb7f022a73ba","isSidechain":false,"promptId":"f60cdfa8-b9c1-40ac-85fa-b8a1cdf690c6","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_011TjH8g3tFbpnanDuCym5EJ","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 29 checks failed)","is_error":false}]},"uuid":"8286b9d2-d502-47aa-9f8a-1254c98f3026","timestamp":"2026-10-30T03:52:44.572Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 29 checks failed)","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"17c54823-4c7d-4bc8-bb71-bb7f022a73ba","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}68{"type":"api-request-blob","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","hash":"1c96114ccb8720344f949073bab5783e5a1877bdb63f9cd686de3532acbddd56","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_011TjH8g3tFbpnanDuCym5EJ","name":"Bash","input":{"command":"python3 - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P5']['checks'][-1]=\"final gate PASSED 0/29 failed, receipt 20261030T035241.548272Z.json\"\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-29 Final gate PASSED (receipt 20261030T035241.548272Z.json). Task complete.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | head -1","description":"Record final receipt and re-confirm gate"}}]}}69{"type":"api-request","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","id":"c820d54b-d73c-40d8-ac47-8601c888776e","timestamp":"2026-10-30T03:52:44.575Z","version":"2.1.314","querySource":"sdk","shapeHash":"36698b7537ccb1d04f463000e61d79ec8af82e94bffe9fb5e5f027a915bf99f3","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":"1da37d38-cea1-40aa-b5c6-273100998209","keep":22,"tail":["1c96114ccb8720344f949073bab5783e5a1877bdb63f9cd686de3532acbddd56","b048e984c6976f6e9e63de4af9f6d0e1ee4bb9faf44ca4bd5aed964c10c5dae6"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",23,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"34907dd7e5c9d24354b2be3cb4d541436d67043633223d75bacf543fadb7facb"}70{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"8286b9d2-d502-47aa-9f8a-1254c98f3026","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c"}71{"type":"atis-latch","atis":"","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c"}72{"parentUuid":"8286b9d2-d502-47aa-9f8a-1254c98f3026","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk65jNRKTYA3vVrvPBE","type":"message","role":"assistant","content":[{"type":"text","text":"I've derived the closed-form demands, checked them against three independent numerical maximisations, and written all the required files. The final gate passed with 0 of 29 checks failing, and re-running `out/analysis.py` from a clean state reproduced `out/results.json` exactly.\n\n**Results** (α = 0.35, p1 = 2.5, p2 = 4, m = 120):\n\n| Quantity | Value |\n|---|---|\n| Demand for good 1, x1* = α·m/p1 | 16.8 |\n| Demand for good 2, x2* = (1−α)·m/p2 | 19.5 |\n| Indirect utility | 2.9182520128635305 |\n| Budget residual | 0.0 |\n| MRS at the optimum (equals price ratio p1/p2) | 0.625 |\n| Expenditure share of good 1 (equals α) | 0.35 |\n\n**Validation:** none of the three numerical methods uses the formula; each maximises utility directly:\n- a bounded one-dimensional search along the budget line;\n- a 2,000,001-point grid on the budget line;\n- a two-dimensional constrained optimiser (SLSQP) with the budget as an inequality constraint.\n\nThe best utility they found is identical to the closed-form value at full machine precision. All three put x1 within about 1e-5 of 16.8.\n\n**Assumptions:** the formula is the unique optimum when 0 < α < 1 and p1, p2, m > 0, which all hold here. Under those conditions utility always rises with more of either good, so the whole budget is spent. It is also strictly concave, and log utility rules out a corner solution. The report states this, and the script refuses to run if the parameters fall outside these ranges.\n\n**Limitations:**\n- The numerical check covers only this one parameter point. The formula's general validity rests on the derivation, not the numerics.\n- The constrained optimiser first reported non-convergence because I had set its tolerance tighter than double precision can reach. Loosening it to 1e-12 fixed that and changed none of the results. This is recorded in `out/state/checks.md`.\n- There were no data issues and no rows were excluded.\n\nFiles are in `out/`:\n- `results.json`\n- `report.md`\n- `analysis.py`\n- `claims.json`\n- `exclusions.csv`\n- `state/` (contract, data audit, checks, phase ledger, log, gate receipts)"}],"container":null,"stop_reason":"end_turn","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":323,"cache_read_input_tokens":19422,"output_tokens":784,"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":323},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXk65Pn8sRU6Eb3tYe3T","requestRef":"c820d54b-d73c-40d8-ac47-8601c888776e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"7e6db15a-a36e-4c9d-9b03-ab0e6a232033","timestamp":"2026-10-30T03:52:51.307Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0018","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","version":"2.1.314","gitBranch":"HEAD"}73{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"7e6db15a-a36e-4c9d-9b03-ab0e6a232033","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c"}74{"type":"cost-state","sessionId":"b431bbff-0aa5-4176-987c-fd7e5da0029c","totalCostUSD":0.347208,"totalAPIDuration":92821,"totalAPIDurationWithoutRetries":92817,"totalToolDuration":3431,"totalLinesAdded":0,"totalLinesRemoved":0,"totalDuration":96439,"startTime":1793332274876,"modelUsage":{"claude-opus-5-5":{"inputTokens":26,"outputTokens":11532,"thinkingTokens":443,"cacheReadInputTokens":126295,"cacheCreationInputTokens":18241,"cacheCreationEphemeral5mInputTokens":18241,"cacheCreationEphemeral1hInputTokens":0,"webSearchRequests":0,"costUSD":0.347208}},"hasUnknownModelCost":false}75