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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"}],"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). 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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). 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** Consumer with u(x1,x2)=α ln x1 + (1−α) ln x2, budget p1x1+p2x2 ≤ m, x ≥ 0. Derive Marshallian demands, indirect utility, budget residual; validate with an independent numerical 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, numerical max utility on the budget line.\nMeaningful under: 0<α<1, p1,p2>0, m>0 (then u strictly increasing and strictly concave on R²₊₊, Inada at boundary → unique interior optimum, budget binds).\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; plus protocol files out/exclusions.csv, out/state/*.\n\n**Information rules.** Only data/parameters.csv. Numerical validation must maximise utility directly, not use the closed form.\n\n**Invalidity / impossibility.** Missing/duplicate/non-numeric parameters; α∉(0,1), non-positive prices or income (closed form invalid or not unique); 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":217,"cache_read_input_tokens":5934,"output_tokens":1049,"output_tokens_details":{"thinking_tokens":134},"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":217},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXjyaL8Hh915jEbCg12b","requestRef":"518085b3-7e21-4ef4-98ea-ade9947572c6","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"0a69e539-8196-4164-82c7-f7e17cfe58b1","timestamp":"2026-10-30T03:51:25.720Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}29{"parentUuid":"0a69e539-8196-4164-82c7-f7e17cfe58b1","isSidechain":false,"promptId":"94374b6b-ef1f-4be4-a414-eaf4b9cb7868","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01Ardws1kp2h5pKmWqPjJvKC","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"c1092508-df24-45aa-870b-2517a9016318","timestamp":"2026-10-30T03:51:25.752Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"0a69e539-8196-4164-82c7-f7e17cfe58b1","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020/out/state","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}30{"type":"api-request-blob","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","hash":"f7439dc393313b8cc68f0df035ce1f0af90857d6a5714650bc924c8471bfefc4","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01Ardws1kp2h5pKmWqPjJvKC","name":"Bash","input":{"command":"mkdir -p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** Consumer with u(x1,x2)=α ln x1 + (1−α) ln x2, budget p1x1+p2x2 ≤ m, x ≥ 0. Derive Marshallian demands, indirect utility, budget residual; validate with an independent numerical 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, numerical max utility on the budget line.\nMeaningful under: 0<α<1, p1,p2>0, m>0 (then u strictly increasing and strictly concave on R²₊₊, Inada at boundary → unique interior optimum, budget binds).\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; plus protocol files out/exclusions.csv, out/state/*.\n\n**Information rules.** Only data/parameters.csv. Numerical validation must maximise utility directly, not use the closed form.\n\n**Invalidity / impossibility.** Missing/duplicate/non-numeric parameters; α∉(0,1), non-positive prices or income (closed form invalid or not unique); 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"}}]}}31{"type":"api-request","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","id":"24e0e854-d07e-418c-b926-7f2712a6fcc6","timestamp":"2026-10-30T03:51:25.755Z","version":"2.1.314","querySource":"sdk","shapeHash":"54de31b1820d9b6b1dbb75b73b59d66ab108fd72b286485fb0bb8306e7aa9124","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":"518085b3-7e21-4ef4-98ea-ade9947572c6","keep":8,"tail":["f7439dc393313b8cc68f0df035ce1f0af90857d6a5714650bc924c8471bfefc4","43e7cbb08fe45af362343f1f6fdda2320ae53b5f581eff4ad7d33246fe53fcc3"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",9,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"4e21cc8d637a3386988af26568b0061ac60bd15981255bb420da7b44db1a3c9e"}32{"parentUuid":"c1092508-df24-45aa-870b-2517a9016318","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXjzGeXASSAEx4sQ8HMk","type":"message","role":"assistant","content":[{"type":"text","text":"Now the analysis script (includes audit, baseline numerical check, closed form)."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1064,"cache_read_input_tokens":6151,"output_tokens":2707,"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":1064},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXjzGNAYJm3BZbdpVq5S","requestRef":"24e0e854-d07e-418c-b926-7f2712a6fcc6","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"e1a87da9-56bc-43a2-aaec-ffbf8dfae3fc","timestamp":"2026-10-30T03:51:26.819Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020/out/state","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}33{"parentUuid":"e1a87da9-56bc-43a2-aaec-ffbf8dfae3fc","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXjzGeXASSAEx4sQ8HMk","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01D925H19Lym5Q4V9RnsxULQ","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-dev-01: Cobb-Douglas consumer. Closed-form Marshallian demands + independent\nnumerical validation. Reads only data/parameters.csv; writes out/results.json and\nout/exclusions.csv. Deterministic: no randomness is used (random_seed = null).\"\"\"\nimport json, os, hashlib\nimport numpy as np\nimport pandas as pd\nfrom scipy.optimize import minimize_scalar, minimize\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDATA = os.path.join(ROOT, \"data\", \"parameters.csv\")\nOUT = os.path.join(ROOT, \"out\")\n\n# ---------------- data audit ----------------\nraw = pd.read_csv(DATA)\nn_raw = len(raw)\nissues = []\nrequired = [\"alpha\", \"p1\", \"p2\", \"m\"]\ndups = raw[\"parameter\"][raw[\"parameter\"].duplicated()].tolist()\nif dups:\n issues.append({\"issue\": f\"duplicate parameter rows: {dups}\", \"handling\": \"fatal; not resolved\"})\nmissing = [k for k in required if k not in set(raw[\"parameter\"])]\nif missing:\n issues.append({\"issue\": f\"missing parameters: {missing}\", \"handling\": \"fatal\"})\nvals = pd.to_numeric(raw[\"value\"], errors=\"coerce\")\nif vals.isna().any():\n issues.append({\"issue\": \"non-numeric values\", \"handling\": \"fatal\"})\nextra = [k for k in raw[\"parameter\"] if k not in required]\nif extra:\n issues.append({\"issue\": f\"unexpected parameters {extra}\", \"handling\": \"ignored\"})\nused = raw[raw[\"parameter\"].isin(required)]\npd.DataFrame([{\"step\": 1, \"rule\": \"keep rows whose parameter is in {alpha,p1,p2,m}\",\n \"n_before\": n_raw, \"n_after\": len(used), \"n_removed\": n_raw - len(used),\n \"rationale\": \"only these parameters enter the model\"}]).to_csv(\n os.path.join(OUT, \"exclusions.csv\"), index=False)\n\nP = dict(zip(used[\"parameter\"], pd.to_numeric(used[\"value\"]).astype(float)))\na, p1, p2, m = P[\"alpha\"], P[\"p1\"], P[\"p2\"], P[\"m\"]\nvalid = (0 < a < 1) and p1 > 0 and p2 > 0 and m > 0\nif not valid:\n issues.append({\"issue\": \"parameters outside 0<alpha<1, p>0, m>0\", \"handling\": \"closed form not reported\"})\n\ndef u(x1, x2):\n return a * np.log(x1) + (1 - a) * np.log(x2)\n\n# ---------------- independent numerical maximisation (no closed form) ----------------\n# (i) 1-D: substitute the budget line x2 = (m - p1 x1)/p2, maximise over x1 in (0, m/p1)\n# with a bounded Brent search (strict monotonicity => budget binds; checked below in (iii)).\n# (ii) dense grid on the budget line (1,000,001 points) as a derivative-free check.\n# (iii) 2-D SLSQP with the inequality budget constraint (does not impose binding).\ndef neg_u_line(x1):\n return -u(x1, (m - p1 * x1) / p2)\neps = 1e-12 * m / p1\nr1 = minimize_scalar(neg_u_line, bounds=(eps, m / p1 - eps), method=\"bounded\",\n options={\"xatol\": 1e-12})\nx1_num, v_num = float(r1.x), float(-r1.fun)\nx2_num = (m - p1 * x1_num) / p2\ngrid = np.linspace(0, m / p1, 1_000_001)[1:-1]\nvg = u(grid, (m - p1 * grid) / p2)\nig = int(np.argmax(vg)); x1_grid, v_grid = float(grid[ig]), float(vg[ig])\nx0 = np.array([0.5 * m / (2 * p1), 0.5 * m / (2 * p2)]) # arbitrary feasible start\nr3 = minimize(lambda x: -u(x[0], x[1]), x0, method=\"SLSQP\",\n bounds=[(1e-9, None), (1e-9, None)],\n constraints=[{\"type\": \"ineq\", \"fun\": lambda x: m - p1 * x[0] - p2 * x[1]}],\n options={\"ftol\": 1e-14, \"maxiter\": 1000})\nx_slsqp, v_slsqp = r3.x.astype(float), float(-r3.fun)\n\n# ---------------- closed form (derived from FOCs; see report) ----------------\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)\n\nresults = {\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": x1 if valid else None,\n \"x2_demand\": x2 if valid else None,\n \"indirect_utility\": v if valid else None,\n \"budget_identity_residual\": resid if valid else None,\n \"mrs_at_optimum\": mrs if valid else None,\n \"price_ratio\": p1 / p2,\n \"expenditure_share_good1\": p1 * x1 / m if valid else None,\n \"indirect_utility_numerical\": v_num,\n \"feasibility\": \"complete\" if valid and not missing and not dups else \"infeasible\",\n \"feasibility_reason\": None if valid else \"parameters violate assumptions\",\n \"data_issues\": issues,\n \"n_input_rows\": {\"parameters.csv\": int(n_raw)},\n \"n_analysed\": int(len(used)),\n \"random_seed\": None,\n \"validation_details\": {\n \"input_sha256\": hashlib.sha256(open(DATA, \"rb\").read()).hexdigest(),\n \"brent_x1\": x1_num, \"brent_x2\": x2_num, \"brent_converged\": bool(r1.success),\n \"grid_points\": int(grid.size), \"grid_x1\": x1_grid, \"grid_utility\": v_grid,\n \"grid_step_x1\": float(grid[1] - grid[0]),\n \"slsqp_x1\": float(x_slsqp[0]), \"slsqp_x2\": float(x_slsqp[1]),\n \"slsqp_utility\": v_slsqp, \"slsqp_success\": bool(r3.success),\n \"slsqp_budget_slack\": float(m - p1 * x_slsqp[0] - p2 * x_slsqp[1]),\n \"abs_diff_utility_closed_vs_brent\": abs(v - v_num),\n \"abs_diff_x1_closed_vs_brent\": abs(x1 - x1_num),\n \"abs_diff_utility_closed_vs_grid\": abs(v - v_grid),\n \"abs_diff_utility_closed_vs_slsqp\": abs(v - v_slsqp),\n \"mrs_minus_price_ratio\": mrs - p1 / p2,\n },\n}\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n json.dump(results, f, indent=2, sort_keys=False)\nprint(json.dumps({k: results[k] for k in [\"x1_demand\", \"x2_demand\", \"indirect_utility\",\n \"indirect_utility_numerical\", \"budget_identity_residual\", \"mrs_at_optimum\", \"price_ratio\"]}, indent=1))\nEOF\n~/wp29/venv/bin/python out/analysis.py && cat out/results.json out/exclusions.csv","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":1064,"cache_read_input_tokens":6151,"output_tokens":2707,"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":1064},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXjzGNAYJm3BZbdpVq5S","requestRef":"24e0e854-d07e-418c-b926-7f2712a6fcc6","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"17405d99-5d9c-4be1-bbf8-031cf01fbe76","timestamp":"2026-10-30T03:51:46.424Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020/out/state","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}34{"parentUuid":"17405d99-5d9c-4be1-bbf8-031cf01fbe76","isSidechain":false,"promptId":"94374b6b-ef1f-4be4-a414-eaf4b9cb7868","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/RP0020/out/state/out/analysis.py': [Errno 2] No such file or directory","is_error":true,"tool_use_id":"toolu_01D925H19Lym5Q4V9RnsxULQ"}]},"uuid":"3a57208b-7ac3-4056-b9d5-102fa1f5453a","timestamp":"2026-10-30T03:51:46.490Z","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/RP0020/out/state/out/analysis.py': [Errno 2] No such file or directory","sandboxed":false,"sourceToolAssistantUUID":"17405d99-5d9c-4be1-bbf8-031cf01fbe76","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020/out/state","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}35{"type":"api-request-blob","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","hash":"ace03bab6ecab6f289cc28c991e802e9a5ba0396a1c890234b7dab55f0836881","message":{"role":"assistant","content":[{"type":"text","text":"Now the analysis script (includes audit, baseline numerical check, closed form)."},{"type":"tool_use","id":"toolu_01D925H19Lym5Q4V9RnsxULQ","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-dev-01: Cobb-Douglas consumer. Closed-form Marshallian demands + independent\nnumerical validation. Reads only data/parameters.csv; writes out/results.json and\nout/exclusions.csv. Deterministic: no randomness is used (random_seed = null).\"\"\"\nimport json, os, hashlib\nimport numpy as np\nimport pandas as pd\nfrom scipy.optimize import minimize_scalar, minimize\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDATA = os.path.join(ROOT, \"data\", \"parameters.csv\")\nOUT = os.path.join(ROOT, \"out\")\n\n# ---------------- data audit ----------------\nraw = pd.read_csv(DATA)\nn_raw = len(raw)\nissues = []\nrequired = [\"alpha\", \"p1\", \"p2\", \"m\"]\ndups = raw[\"parameter\"][raw[\"parameter\"].duplicated()].tolist()\nif dups:\n issues.append({\"issue\": f\"duplicate parameter rows: {dups}\", \"handling\": \"fatal; not resolved\"})\nmissing = [k for k in required if k not in set(raw[\"parameter\"])]\nif missing:\n issues.append({\"issue\": f\"missing parameters: {missing}\", \"handling\": \"fatal\"})\nvals = pd.to_numeric(raw[\"value\"], errors=\"coerce\")\nif vals.isna().any():\n issues.append({\"issue\": \"non-numeric values\", \"handling\": \"fatal\"})\nextra = [k for k in raw[\"parameter\"] if k not in required]\nif extra:\n issues.append({\"issue\": f\"unexpected parameters {extra}\", \"handling\": \"ignored\"})\nused = raw[raw[\"parameter\"].isin(required)]\npd.DataFrame([{\"step\": 1, \"rule\": \"keep rows whose parameter is in {alpha,p1,p2,m}\",\n \"n_before\": n_raw, \"n_after\": len(used), \"n_removed\": n_raw - len(used),\n \"rationale\": \"only these parameters enter the model\"}]).to_csv(\n os.path.join(OUT, \"exclusions.csv\"), index=False)\n\nP = dict(zip(used[\"parameter\"], pd.to_numeric(used[\"value\"]).astype(float)))\na, p1, p2, m = P[\"alpha\"], P[\"p1\"], P[\"p2\"], P[\"m\"]\nvalid = (0 < a < 1) and p1 > 0 and p2 > 0 and m > 0\nif not valid:\n issues.append({\"issue\": \"parameters outside 0<alpha<1, p>0, m>0\", \"handling\": \"closed form not reported\"})\n\ndef u(x1, x2):\n return a * np.log(x1) + (1 - a) * np.log(x2)\n\n# ---------------- independent numerical maximisation (no closed form) ----------------\n# (i) 1-D: substitute the budget line x2 = (m - p1 x1)/p2, maximise over x1 in (0, m/p1)\n# with a bounded Brent search (strict monotonicity => budget binds; checked below in (iii)).\n# (ii) dense grid on the budget line (1,000,001 points) as a derivative-free check.\n# (iii) 2-D SLSQP with the inequality budget constraint (does not impose binding).\ndef neg_u_line(x1):\n return -u(x1, (m - p1 * x1) / p2)\neps = 1e-12 * m / p1\nr1 = minimize_scalar(neg_u_line, bounds=(eps, m / p1 - eps), method=\"bounded\",\n options={\"xatol\": 1e-12})\nx1_num, v_num = float(r1.x), float(-r1.fun)\nx2_num = (m - p1 * x1_num) / p2\ngrid = np.linspace(0, m / p1, 1_000_001)[1:-1]\nvg = u(grid, (m - p1 * grid) / p2)\nig = int(np.argmax(vg)); x1_grid, v_grid = float(grid[ig]), float(vg[ig])\nx0 = np.array([0.5 * m / (2 * p1), 0.5 * m / (2 * p2)]) # arbitrary feasible start\nr3 = minimize(lambda x: -u(x[0], x[1]), x0, method=\"SLSQP\",\n bounds=[(1e-9, None), (1e-9, None)],\n constraints=[{\"type\": \"ineq\", \"fun\": lambda x: m - p1 * x[0] - p2 * x[1]}],\n options={\"ftol\": 1e-14, \"maxiter\": 1000})\nx_slsqp, v_slsqp = r3.x.astype(float), float(-r3.fun)\n\n# ---------------- closed form (derived from FOCs; see report) ----------------\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)\n\nresults = {\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": x1 if valid else None,\n \"x2_demand\": x2 if valid else None,\n \"indirect_utility\": v if valid else None,\n \"budget_identity_residual\": resid if valid else None,\n \"mrs_at_optimum\": mrs if valid else None,\n \"price_ratio\": p1 / p2,\n \"expenditure_share_good1\": p1 * x1 / m if valid else None,\n \"indirect_utility_numerical\": v_num,\n \"feasibility\": \"complete\" if valid and not missing and not dups else \"infeasible\",\n \"feasibility_reason\": None if valid else \"parameters violate assumptions\",\n \"data_issues\": issues,\n \"n_input_rows\": {\"parameters.csv\": int(n_raw)},\n \"n_analysed\": int(len(used)),\n \"random_seed\": None,\n \"validation_details\": {\n \"input_sha256\": hashlib.sha256(open(DATA, \"rb\").read()).hexdigest(),\n \"brent_x1\": x1_num, \"brent_x2\": x2_num, \"brent_converged\": bool(r1.success),\n \"grid_points\": int(grid.size), \"grid_x1\": x1_grid, \"grid_utility\": v_grid,\n \"grid_step_x1\": float(grid[1] - grid[0]),\n \"slsqp_x1\": float(x_slsqp[0]), \"slsqp_x2\": float(x_slsqp[1]),\n \"slsqp_utility\": v_slsqp, \"slsqp_success\": bool(r3.success),\n \"slsqp_budget_slack\": float(m - p1 * x_slsqp[0] - p2 * x_slsqp[1]),\n \"abs_diff_utility_closed_vs_brent\": abs(v - v_num),\n \"abs_diff_x1_closed_vs_brent\": abs(x1 - x1_num),\n \"abs_diff_utility_closed_vs_grid\": abs(v - v_grid),\n \"abs_diff_utility_closed_vs_slsqp\": abs(v - v_slsqp),\n \"mrs_minus_price_ratio\": mrs - p1 / p2,\n },\n}\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n json.dump(results, f, indent=2, sort_keys=False)\nprint(json.dumps({k: results[k] for k in [\"x1_demand\", \"x2_demand\", \"indirect_utility\",\n \"indirect_utility_numerical\", \"budget_identity_residual\", \"mrs_at_optimum\", \"price_ratio\"]}, indent=1))\nEOF\n~/wp29/venv/bin/python out/analysis.py && cat out/results.json out/exclusions.csv","description":"Write and run analysis script"}}]}}36{"type":"api-request","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","id":"ea35268b-a023-451a-9e90-a58413e3aaef","timestamp":"2026-10-30T03:51:46.493Z","version":"2.1.314","querySource":"sdk","shapeHash":"54de31b1820d9b6b1dbb75b73b59d66ab108fd72b286485fb0bb8306e7aa9124","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":"24e0e854-d07e-418c-b926-7f2712a6fcc6","keep":10,"tail":["ace03bab6ecab6f289cc28c991e802e9a5ba0396a1c890234b7dab55f0836881","c3d838331c8fea487f46deb77607eb064e0b6137c4ec049588a3291a0c93acda"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",11,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"174a05afa0ea6de8aeb5cfba376a426a6fc8952c0633242c2c2471dd49294730"}37{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"3a57208b-7ac3-4056-b9d5-102fa1f5453a","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1"}38{"type":"atis-latch","atis":"","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1"}39{"parentUuid":"3a57208b-7ac3-4056-b9d5-102fa1f5453a","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk1oUDAUqiJSAkp2rXe","type":"message","role":"assistant","content":[{"type":"text","text":"The shell was still in out/state; rerunning from the workspace root."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2869,"cache_read_input_tokens":7215,"output_tokens":2805,"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":2869},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXk1oBquVGQY2fhzYe7q","requestRef":"ea35268b-a023-451a-9e90-a58413e3aaef","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"add23ddf-b474-430f-b4a7-62371bd4e78f","timestamp":"2026-10-30T03:51:47.865Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}40{"parentUuid":"add23ddf-b474-430f-b4a7-62371bd4e78f","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk1oUDAUqiJSAkp2rXe","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_011ryugdpBSU32pvC1MxJfXQ","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RP0020 && pwd","description":"Return to workspace root"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2869,"cache_read_input_tokens":7215,"output_tokens":2805,"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":2869},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXk1oBquVGQY2fhzYe7q","requestRef":"ea35268b-a023-451a-9e90-a58413e3aaef","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"c870b031-6ee3-4ffb-9282-975c7626aa9e","timestamp":"2026-10-30T03:51:48.517Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}41{"parentUuid":"c870b031-6ee3-4ffb-9282-975c7626aa9e","isSidechain":false,"promptId":"94374b6b-ef1f-4be4-a414-eaf4b9cb7868","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_011ryugdpBSU32pvC1MxJfXQ","type":"tool_result","content":"/Users/simon-pierreboucher/wp29/runs/RP0020","is_error":false}]},"uuid":"3cb75969-cca6-4be8-bc01-67c7f05f820f","timestamp":"2026-10-30T03:51:48.556Z","toolUseResult":{"stdout":"/Users/simon-pierreboucher/wp29/runs/RP0020","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"c870b031-6ee3-4ffb-9282-975c7626aa9e","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}42{"parentUuid":"3cb75969-cca6-4be8-bc01-67c7f05f820f","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk1oUDAUqiJSAkp2rXe","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01JuA1ghaKpqERvqq7C99ufc","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-dev-01: Cobb-Douglas consumer. Closed-form Marshallian demands + independent\nnumerical validation. Reads only data/parameters.csv; writes out/results.json and\nout/exclusions.csv. Deterministic: no randomness is used (random_seed = null).\"\"\"\nimport json, os, hashlib\nimport numpy as np\nimport pandas as pd\nfrom scipy.optimize import minimize_scalar, minimize\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDATA = os.path.join(ROOT, \"data\", \"parameters.csv\")\nOUT = os.path.join(ROOT, \"out\")\n\n# ---------------- data audit ----------------\nraw = pd.read_csv(DATA)\nn_raw = len(raw)\nissues = []\nrequired = [\"alpha\", \"p1\", \"p2\", \"m\"]\ndups = raw[\"parameter\"][raw[\"parameter\"].duplicated()].tolist()\nif dups:\n issues.append({\"issue\": f\"duplicate parameter rows: {dups}\", \"handling\": \"fatal; not resolved\"})\nmissing = [k for k in required if k not in set(raw[\"parameter\"])]\nif missing:\n issues.append({\"issue\": f\"missing parameters: {missing}\", \"handling\": \"fatal\"})\nvals = pd.to_numeric(raw[\"value\"], errors=\"coerce\")\nif vals.isna().any():\n issues.append({\"issue\": \"non-numeric values\", \"handling\": \"fatal\"})\nextra = [k for k in raw[\"parameter\"] if k not in required]\nif extra:\n issues.append({\"issue\": f\"unexpected parameters {extra}\", \"handling\": \"ignored\"})\nused = raw[raw[\"parameter\"].isin(required)]\npd.DataFrame([{\"step\": 1, \"rule\": \"keep rows whose parameter is in {alpha,p1,p2,m}\",\n \"n_before\": n_raw, \"n_after\": len(used), \"n_removed\": n_raw - len(used),\n \"rationale\": \"only these parameters enter the model\"}]).to_csv(\n os.path.join(OUT, \"exclusions.csv\"), index=False)\n\nP = dict(zip(used[\"parameter\"], pd.to_numeric(used[\"value\"]).astype(float)))\na, p1, p2, m = P[\"alpha\"], P[\"p1\"], P[\"p2\"], P[\"m\"]\nvalid = (0 < a < 1) and p1 > 0 and p2 > 0 and m > 0\nif not valid:\n issues.append({\"issue\": \"parameters outside 0<alpha<1, p>0, m>0\", \"handling\": \"closed form not reported\"})\n\ndef u(x1, x2):\n return a * np.log(x1) + (1 - a) * np.log(x2)\n\n# ---------------- independent numerical maximisation (no closed form) ----------------\n# (i) 1-D: substitute the budget line x2 = (m - p1 x1)/p2, maximise over x1 in (0, m/p1)\n# with a bounded Brent search (strict monotonicity => budget binds; checked below in (iii)).\n# (ii) dense grid on the budget line (1,000,001 points) as a derivative-free check.\n# (iii) 2-D SLSQP with the inequality budget constraint (does not impose binding).\ndef neg_u_line(x1):\n return -u(x1, (m - p1 * x1) / p2)\neps = 1e-12 * m / p1\nr1 = minimize_scalar(neg_u_line, bounds=(eps, m / p1 - eps), method=\"bounded\",\n options={\"xatol\": 1e-12})\nx1_num, v_num = float(r1.x), float(-r1.fun)\nx2_num = (m - p1 * x1_num) / p2\ngrid = np.linspace(0, m / p1, 1_000_001)[1:-1]\nvg = u(grid, (m - p1 * grid) / p2)\nig = int(np.argmax(vg)); x1_grid, v_grid = float(grid[ig]), float(vg[ig])\nx0 = np.array([0.5 * m / (2 * p1), 0.5 * m / (2 * p2)]) # arbitrary feasible start\nr3 = minimize(lambda x: -u(x[0], x[1]), x0, method=\"SLSQP\",\n bounds=[(1e-9, None), (1e-9, None)],\n constraints=[{\"type\": \"ineq\", \"fun\": lambda x: m - p1 * x[0] - p2 * x[1]}],\n options={\"ftol\": 1e-14, \"maxiter\": 1000})\nx_slsqp, v_slsqp = r3.x.astype(float), float(-r3.fun)\n\n# ---------------- closed form (derived from FOCs; see report) ----------------\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)\n\nresults = {\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": x1 if valid else None,\n \"x2_demand\": x2 if valid else None,\n \"indirect_utility\": v if valid else None,\n \"budget_identity_residual\": resid if valid else None,\n \"mrs_at_optimum\": mrs if valid else None,\n \"price_ratio\": p1 / p2,\n \"expenditure_share_good1\": p1 * x1 / m if valid else None,\n \"indirect_utility_numerical\": v_num,\n \"feasibility\": \"complete\" if valid and not missing and not dups else \"infeasible\",\n \"feasibility_reason\": None if valid else \"parameters violate assumptions\",\n \"data_issues\": issues,\n \"n_input_rows\": {\"parameters.csv\": int(n_raw)},\n \"n_analysed\": int(len(used)),\n \"random_seed\": None,\n \"validation_details\": {\n \"input_sha256\": hashlib.sha256(open(DATA, \"rb\").read()).hexdigest(),\n \"brent_x1\": x1_num, \"brent_x2\": x2_num, \"brent_converged\": bool(r1.success),\n \"grid_points\": int(grid.size), \"grid_x1\": x1_grid, \"grid_utility\": v_grid,\n \"grid_step_x1\": float(grid[1] - grid[0]),\n \"slsqp_x1\": float(x_slsqp[0]), \"slsqp_x2\": float(x_slsqp[1]),\n \"slsqp_utility\": v_slsqp, \"slsqp_success\": bool(r3.success),\n \"slsqp_budget_slack\": float(m - p1 * x_slsqp[0] - p2 * x_slsqp[1]),\n \"abs_diff_utility_closed_vs_brent\": abs(v - v_num),\n \"abs_diff_x1_closed_vs_brent\": abs(x1 - x1_num),\n \"abs_diff_utility_closed_vs_grid\": abs(v - v_grid),\n \"abs_diff_utility_closed_vs_slsqp\": abs(v - v_slsqp),\n \"mrs_minus_price_ratio\": mrs - p1 / p2,\n },\n}\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n json.dump(results, f, indent=2, sort_keys=False)\nprint(json.dumps({k: results[k] for k in [\"x1_demand\", \"x2_demand\", \"indirect_utility\",\n \"indirect_utility_numerical\", \"budget_identity_residual\", \"mrs_at_optimum\", \"price_ratio\"]}, indent=1))\nEOF\n~/wp29/venv/bin/python out/analysis.py && cat out/results.json out/exclusions.csv","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":2869,"cache_read_input_tokens":7215,"output_tokens":2805,"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":2869},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXk1oBquVGQY2fhzYe7q","requestRef":"ea35268b-a023-451a-9e90-a58413e3aaef","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"55651e61-d72d-41a6-8694-2f66ded24148","timestamp":"2026-10-30T03:52:05.154Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}43{"parentUuid":"55651e61-d72d-41a6-8694-2f66ded24148","isSidechain":false,"promptId":"94374b6b-ef1f-4be4-a414-eaf4b9cb7868","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01JuA1ghaKpqERvqq7C99ufc","type":"tool_result","content":"{\n \"x1_demand\": 16.8,\n \"x2_demand\": 19.5,\n \"indirect_utility\": 2.9182520128635305,\n \"indirect_utility_numerical\": 2.9182520128635305,\n \"budget_identity_residual\": 0.0,\n \"mrs_at_optimum\": 0.625,\n \"price_ratio\": 0.625\n}\n{\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": 16.8,\n \"x2_demand\": 19.5,\n \"indirect_utility\": 2.9182520128635305,\n \"budget_identity_residual\": 0.0,\n \"mrs_at_optimum\": 0.625,\n \"price_ratio\": 0.625,\n \"expenditure_share_good1\": 0.35,\n \"indirect_utility_numerical\": 2.9182520128635305,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [],\n \"n_input_rows\": {\n \"parameters.csv\": 4\n },\n \"n_analysed\": 4,\n \"random_seed\": null,\n \"validation_details\": {\n \"input_sha256\": \"a04798ade7a0f774f1e4651a0c7f99752f4c4df6eb3d4dc275694601ed994722\",\n \"brent_x1\": 16.800000228799448,\n \"brent_x2\": 19.499999857000347,\n \"brent_converged\": true,\n \"grid_points\": 999999,\n \"grid_x1\": 16.8,\n \"grid_utility\": 2.9182520128635305,\n \"grid_step_x1\": 4.8e-05,\n \"slsqp_x1\": 16.800000138855022,\n \"slsqp_x2\": 19.49999991321561,\n \"slsqp_utility\": 2.9182520128635305,\n \"slsqp_success\": true,\n \"slsqp_budget_slack\": 0.0,\n \"abs_diff_utility_closed_vs_brent\": 0.0,\n \"abs_diff_x1_closed_vs_brent\": 2.287994469440946e-07,\n \"abs_diff_utility_closed_vs_grid\": 0.0,\n \"abs_diff_utility_closed_vs_slsqp\": 0.0,\n \"mrs_minus_price_ratio\": 0.0\n }\n}step,rule,n_before,n_after,n_removed,rationale\n1,\"keep rows whose parameter is in {alpha,p1,p2,m}\",4,4,0,only these parameters enter the model","is_error":false}]},"uuid":"09480bdb-d39f-4b4d-bf24-1a8432516bb1","timestamp":"2026-10-30T03:52:05.547Z","toolUseResult":{"stdout":"{\n \"x1_demand\": 16.8,\n \"x2_demand\": 19.5,\n \"indirect_utility\": 2.9182520128635305,\n \"indirect_utility_numerical\": 2.9182520128635305,\n \"budget_identity_residual\": 0.0,\n \"mrs_at_optimum\": 0.625,\n \"price_ratio\": 0.625\n}\n{\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": 16.8,\n \"x2_demand\": 19.5,\n \"indirect_utility\": 2.9182520128635305,\n \"budget_identity_residual\": 0.0,\n \"mrs_at_optimum\": 0.625,\n \"price_ratio\": 0.625,\n \"expenditure_share_good1\": 0.35,\n \"indirect_utility_numerical\": 2.9182520128635305,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [],\n \"n_input_rows\": {\n \"parameters.csv\": 4\n },\n \"n_analysed\": 4,\n \"random_seed\": null,\n \"validation_details\": {\n \"input_sha256\": \"a04798ade7a0f774f1e4651a0c7f99752f4c4df6eb3d4dc275694601ed994722\",\n \"brent_x1\": 16.800000228799448,\n \"brent_x2\": 19.499999857000347,\n \"brent_converged\": true,\n \"grid_points\": 999999,\n \"grid_x1\": 16.8,\n \"grid_utility\": 2.9182520128635305,\n \"grid_step_x1\": 4.8e-05,\n \"slsqp_x1\": 16.800000138855022,\n \"slsqp_x2\": 19.49999991321561,\n \"slsqp_utility\": 2.9182520128635305,\n \"slsqp_success\": true,\n \"slsqp_budget_slack\": 0.0,\n \"abs_diff_utility_closed_vs_brent\": 0.0,\n \"abs_diff_x1_closed_vs_brent\": 2.287994469440946e-07,\n \"abs_diff_utility_closed_vs_grid\": 0.0,\n \"abs_diff_utility_closed_vs_slsqp\": 0.0,\n \"mrs_minus_price_ratio\": 0.0\n }\n}step,rule,n_before,n_after,n_removed,rationale\n1,\"keep rows whose parameter is in {alpha,p1,p2,m}\",4,4,0,only these parameters enter the model","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"55651e61-d72d-41a6-8694-2f66ded24148","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}44{"type":"api-request-blob","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","hash":"da946b8eaeca6acf356de9ce8c1d766e3561018d1f9d0a3723de104b1b48f398","message":{"role":"assistant","content":[{"type":"text","text":"The shell was still in out/state; rerunning from the workspace root."},{"type":"tool_use","id":"toolu_011ryugdpBSU32pvC1MxJfXQ","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RP0020 && pwd","description":"Return to workspace root"}},{"type":"tool_use","id":"toolu_01JuA1ghaKpqERvqq7C99ufc","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-dev-01: Cobb-Douglas consumer. Closed-form Marshallian demands + independent\nnumerical validation. Reads only data/parameters.csv; writes out/results.json and\nout/exclusions.csv. Deterministic: no randomness is used (random_seed = null).\"\"\"\nimport json, os, hashlib\nimport numpy as np\nimport pandas as pd\nfrom scipy.optimize import minimize_scalar, minimize\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nDATA = os.path.join(ROOT, \"data\", \"parameters.csv\")\nOUT = os.path.join(ROOT, \"out\")\n\n# ---------------- data audit ----------------\nraw = pd.read_csv(DATA)\nn_raw = len(raw)\nissues = []\nrequired = [\"alpha\", \"p1\", \"p2\", \"m\"]\ndups = raw[\"parameter\"][raw[\"parameter\"].duplicated()].tolist()\nif dups:\n issues.append({\"issue\": f\"duplicate parameter rows: {dups}\", \"handling\": \"fatal; not resolved\"})\nmissing = [k for k in required if k not in set(raw[\"parameter\"])]\nif missing:\n issues.append({\"issue\": f\"missing parameters: {missing}\", \"handling\": \"fatal\"})\nvals = pd.to_numeric(raw[\"value\"], errors=\"coerce\")\nif vals.isna().any():\n issues.append({\"issue\": \"non-numeric values\", \"handling\": \"fatal\"})\nextra = [k for k in raw[\"parameter\"] if k not in required]\nif extra:\n issues.append({\"issue\": f\"unexpected parameters {extra}\", \"handling\": \"ignored\"})\nused = raw[raw[\"parameter\"].isin(required)]\npd.DataFrame([{\"step\": 1, \"rule\": \"keep rows whose parameter is in {alpha,p1,p2,m}\",\n \"n_before\": n_raw, \"n_after\": len(used), \"n_removed\": n_raw - len(used),\n \"rationale\": \"only these parameters enter the model\"}]).to_csv(\n os.path.join(OUT, \"exclusions.csv\"), index=False)\n\nP = dict(zip(used[\"parameter\"], pd.to_numeric(used[\"value\"]).astype(float)))\na, p1, p2, m = P[\"alpha\"], P[\"p1\"], P[\"p2\"], P[\"m\"]\nvalid = (0 < a < 1) and p1 > 0 and p2 > 0 and m > 0\nif not valid:\n issues.append({\"issue\": \"parameters outside 0<alpha<1, p>0, m>0\", \"handling\": \"closed form not reported\"})\n\ndef u(x1, x2):\n return a * np.log(x1) + (1 - a) * np.log(x2)\n\n# ---------------- independent numerical maximisation (no closed form) ----------------\n# (i) 1-D: substitute the budget line x2 = (m - p1 x1)/p2, maximise over x1 in (0, m/p1)\n# with a bounded Brent search (strict monotonicity => budget binds; checked below in (iii)).\n# (ii) dense grid on the budget line (1,000,001 points) as a derivative-free check.\n# (iii) 2-D SLSQP with the inequality budget constraint (does not impose binding).\ndef neg_u_line(x1):\n return -u(x1, (m - p1 * x1) / p2)\neps = 1e-12 * m / p1\nr1 = minimize_scalar(neg_u_line, bounds=(eps, m / p1 - eps), method=\"bounded\",\n options={\"xatol\": 1e-12})\nx1_num, v_num = float(r1.x), float(-r1.fun)\nx2_num = (m - p1 * x1_num) / p2\ngrid = np.linspace(0, m / p1, 1_000_001)[1:-1]\nvg = u(grid, (m - p1 * grid) / p2)\nig = int(np.argmax(vg)); x1_grid, v_grid = float(grid[ig]), float(vg[ig])\nx0 = np.array([0.5 * m / (2 * p1), 0.5 * m / (2 * p2)]) # arbitrary feasible start\nr3 = minimize(lambda x: -u(x[0], x[1]), x0, method=\"SLSQP\",\n bounds=[(1e-9, None), (1e-9, None)],\n constraints=[{\"type\": \"ineq\", \"fun\": lambda x: m - p1 * x[0] - p2 * x[1]}],\n options={\"ftol\": 1e-14, \"maxiter\": 1000})\nx_slsqp, v_slsqp = r3.x.astype(float), float(-r3.fun)\n\n# ---------------- closed form (derived from FOCs; see report) ----------------\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)\n\nresults = {\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": x1 if valid else None,\n \"x2_demand\": x2 if valid else None,\n \"indirect_utility\": v if valid else None,\n \"budget_identity_residual\": resid if valid else None,\n \"mrs_at_optimum\": mrs if valid else None,\n \"price_ratio\": p1 / p2,\n \"expenditure_share_good1\": p1 * x1 / m if valid else None,\n \"indirect_utility_numerical\": v_num,\n \"feasibility\": \"complete\" if valid and not missing and not dups else \"infeasible\",\n \"feasibility_reason\": None if valid else \"parameters violate assumptions\",\n \"data_issues\": issues,\n \"n_input_rows\": {\"parameters.csv\": int(n_raw)},\n \"n_analysed\": int(len(used)),\n \"random_seed\": None,\n \"validation_details\": {\n \"input_sha256\": hashlib.sha256(open(DATA, \"rb\").read()).hexdigest(),\n \"brent_x1\": x1_num, \"brent_x2\": x2_num, \"brent_converged\": bool(r1.success),\n \"grid_points\": int(grid.size), \"grid_x1\": x1_grid, \"grid_utility\": v_grid,\n \"grid_step_x1\": float(grid[1] - grid[0]),\n \"slsqp_x1\": float(x_slsqp[0]), \"slsqp_x2\": float(x_slsqp[1]),\n \"slsqp_utility\": v_slsqp, \"slsqp_success\": bool(r3.success),\n \"slsqp_budget_slack\": float(m - p1 * x_slsqp[0] - p2 * x_slsqp[1]),\n \"abs_diff_utility_closed_vs_brent\": abs(v - v_num),\n \"abs_diff_x1_closed_vs_brent\": abs(x1 - x1_num),\n \"abs_diff_utility_closed_vs_grid\": abs(v - v_grid),\n \"abs_diff_utility_closed_vs_slsqp\": abs(v - v_slsqp),\n \"mrs_minus_price_ratio\": mrs - p1 / p2,\n },\n}\nwith open(os.path.join(OUT, \"results.json\"), \"w\") as f:\n json.dump(results, f, indent=2, sort_keys=False)\nprint(json.dumps({k: results[k] for k in [\"x1_demand\", \"x2_demand\", \"indirect_utility\",\n \"indirect_utility_numerical\", \"budget_identity_residual\", \"mrs_at_optimum\", \"price_ratio\"]}, indent=1))\nEOF\n~/wp29/venv/bin/python out/analysis.py && cat out/results.json out/exclusions.csv","description":"Write and run analysis script"}}]}}45{"type":"api-request-blob","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","hash":"da7bb97924a99e6fa7332d974020fbd5edd9f16d8ca69d2afa216310bcc12194","message":{"role":"user","content":[{"tool_use_id":"toolu_011ryugdpBSU32pvC1MxJfXQ","type":"tool_result","content":"/Users/simon-pierreboucher/wp29/runs/RP0020","is_error":false},{"tool_use_id":"toolu_01JuA1ghaKpqERvqq7C99ufc","type":"tool_result","content":"{\n \"x1_demand\": 16.8,\n \"x2_demand\": 19.5,\n \"indirect_utility\": 2.9182520128635305,\n \"indirect_utility_numerical\": 2.9182520128635305,\n \"budget_identity_residual\": 0.0,\n \"mrs_at_optimum\": 0.625,\n \"price_ratio\": 0.625\n}\n{\n \"task_id\": \"F5-dev-01\",\n \"x1_demand\": 16.8,\n \"x2_demand\": 19.5,\n \"indirect_utility\": 2.9182520128635305,\n \"budget_identity_residual\": 0.0,\n \"mrs_at_optimum\": 0.625,\n \"price_ratio\": 0.625,\n \"expenditure_share_good1\": 0.35,\n \"indirect_utility_numerical\": 2.9182520128635305,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [],\n \"n_input_rows\": {\n \"parameters.csv\": 4\n },\n \"n_analysed\": 4,\n \"random_seed\": null,\n \"validation_details\": {\n \"input_sha256\": \"a04798ade7a0f774f1e4651a0c7f99752f4c4df6eb3d4dc275694601ed994722\",\n \"brent_x1\": 16.800000228799448,\n \"brent_x2\": 19.499999857000347,\n \"brent_converged\": true,\n \"grid_points\": 999999,\n \"grid_x1\": 16.8,\n \"grid_utility\": 2.9182520128635305,\n \"grid_step_x1\": 4.8e-05,\n \"slsqp_x1\": 16.800000138855022,\n \"slsqp_x2\": 19.49999991321561,\n \"slsqp_utility\": 2.9182520128635305,\n \"slsqp_success\": true,\n \"slsqp_budget_slack\": 0.0,\n \"abs_diff_utility_closed_vs_brent\": 0.0,\n \"abs_diff_x1_closed_vs_brent\": 2.287994469440946e-07,\n \"abs_diff_utility_closed_vs_grid\": 0.0,\n \"abs_diff_utility_closed_vs_slsqp\": 0.0,\n \"mrs_minus_price_ratio\": 0.0\n }\n}step,rule,n_before,n_after,n_removed,rationale\n1,\"keep rows whose parameter is in {alpha,p1,p2,m}\",4,4,0,only these parameters enter the 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Now verification: clean re-run and consistency checks."},{"type":"tool_use","id":"toolu_01HM2KKMdPVQFRNW4iLS1p5v","name":"Bash","input":{"command":"cp out/results.json /tmp/r1.json; rm out/results.json out/exclusions.csv; ~/wp29/venv/bin/python out/analysis.py >/dev/null; cmp /tmp/r1.json out/results.json && echo IDENTICAL; shasum -a 256 out/results.json\n~/wp29/venv/bin/python - <<'EOF'\nimport json; r=json.load(open('out/results.json'))\na,p1,p2,m=0.35,2.5,4.0,120.0\nimport math\nchk={\n \"x>0\": r[\"x1_demand\"]>0 and r[\"x2_demand\"]>0,\n \"residual~0\": abs(r[\"budget_identity_residual\"])<1e-9,\n \"mrs==price_ratio\": abs(r[\"mrs_at_optimum\"]-r[\"price_ratio\"])<1e-12,\n \"share==alpha\": abs(r[\"expenditure_share_good1\"]-a)<1e-12,\n \"v_closed>=v_num-1e-12\": r[\"indirect_utility\"]>=r[\"indirect_utility_numerical\"]-1e-12,\n \"|v-v_num|<1e-10\": abs(r[\"indirect_utility\"]-r[\"indirect_utility_numerical\"])<1e-10,\n \"v formula a ln(a m/p1)+(1-a)ln((1-a)m/p2)\": abs(r[\"indirect_utility\"]-(a*math.log(a*m/p1)+(1-a)*math.log((1-a)*m/p2)))<1e-12,\n \"brent x1 within 1e-6\": r[\"validation_details\"][\"abs_diff_x1_closed_vs_brent\"]<1e-6,\n \"slsqp budget binds\": abs(r[\"validation_details\"][\"slsqp_budget_slack\"])<1e-8,\n \"n_raw-removed==n_analysed\": 4-0==r[\"n_analysed\"],\n}\nfor k,v in chk.items(): print(k, v)\nEOF","description":"Clean rerun, compare, consistency checks"}}]}}52{"type":"api-request","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","id":"93f4ec1b-fce1-412e-83aa-b8d9b02c6cbb","timestamp":"2026-10-30T03:52:13.872Z","version":"2.1.314","querySource":"sdk","shapeHash":"54de31b1820d9b6b1dbb75b73b59d66ab108fd72b286485fb0bb8306e7aa9124","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":"ed7a722c-6830-4e9d-a3f3-93ec223d7239","keep":14,"tail":["890409c3b8c4040274af5833d3944070b73a9c98d88cb121d74173003f908953","1983bd1a29587164daf45cbb4c12df711517352a8ae6e0cf190f7a8ce2a59c84"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",15,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"ab2b496083fdba37494aa04747b8d3d486d70a9801548cf40ec66122e3e1ec02"}53{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"05fdd522-b60e-4dfe-a6ed-8e08f4bf9d1d","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1"}54{"type":"atis-latch","atis":"","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1"}55{"parentUuid":"05fdd522-b60e-4dfe-a6ed-8e08f4bf9d1d","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk3pS4KNcSdYiZ8Ymcz","type":"message","role":"assistant","content":[{"type":"text","text":"Now the state docs, report and claims."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1052,"cache_read_input_tokens":13801,"output_tokens":3340,"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":1052},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXk3p6D7hwRQX2oCUA39","requestRef":"93f4ec1b-fce1-412e-83aa-b8d9b02c6cbb","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"acb312e2-54dd-4f6a-8dde-b01b70f2a41b","timestamp":"2026-10-30T03:52:15.205Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}56{"parentUuid":"acb312e2-54dd-4f6a-8dde-b01b70f2a41b","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk3pS4KNcSdYiZ8Ymcz","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01H83YKLD65N64Bge3hs1U9W","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n| file | SHA-256 | 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 values numeric, no unexpected parameters, LF line endings, no dates (not applicable).\nAssumption checks: 0<alpha<1, p1>0, p2>0, m>0 all hold.\nInformation availability: the only input is the permitted file; no violations. (`gate_spec.json`/`bundle.json` in the workspace root are not task inputs and were not used by the analysis.)\nExclusions: none (out/exclusions.csv: 4 → 4).\nEOF\ncat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n| check | outcome |\n|---|---|\n| Clean re-run (deleted results.json, exclusions.csv; re-ran) gives byte-identical results.json (sha256 923215d3…) | PASS |\n| x1_demand, x2_demand > 0 (interior) | PASS |\n| |budget_identity_residual| < 1e-9 (exactly 0.0) | PASS |\n| mrs_at_optimum == price_ratio (0.625) | PASS |\n| expenditure_share_good1 == alpha (0.35) | PASS |\n| indirect_utility equals α ln(αm/p1)+(1−α) ln((1−α)m/p2) | PASS |\n| indirect_utility_numerical (Brent on budget line) ≤ indirect_utility + 1e-12 and |diff| < 1e-10 (diff 0.0) | PASS |\n| Brent x1 within 1e-6 of closed form (2.3e-7) | PASS |\n| Grid (999,999 interior points) and 2-D SLSQP with inequality budget give same utility to machine precision; SLSQP budget slack 0 (budget binds) | PASS |\n| Counts: n_raw 4 − removed 0 = n_analysed 4 | PASS |\n| Note: grid maximiser equals 16.8 exactly because 16.8 is a grid node (step 4.8e-5); utility agreement to 0.0 reflects flatness of u near the optimum (second-order), so the x-distance (2.3e-7) is the more informative metric. | noted |\nEOF\ncat > 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 check them against an independent numerical maximisation.\n\n## Data and exclusions\nInput: `data/parameters.csv` (4 rows, `n_input_rows`; SHA-256 a04798ad…, recorded in `validation_details.input_sha256`). α = 0.35, p1 = 2.5, p2 = 4.0, m = 120. No missing, duplicated or non-numeric values (`data_issues` = []). No rows excluded; 4 rows used (`n_analysed`; see `out/exclusions.csv`). These are given theoretical parameters, not observed data.\n\n## Method\n**Assumptions for the closed form to be the unique optimum:** 0 < α < 1, p1 > 0, p2 > 0, m > 0 (all hold here). Then u is strictly increasing in each good (local non-satiation ⇒ budget binds), strictly concave on R²₊₊, and satisfies ∂u/∂xi → ∞ as xi → 0 with u → −∞ on the boundary, so the optimum is interior. A strictly concave objective on a convex compact-relevant feasible set has at most one maximiser, so the KKT point is the unique global optimum.\n\n**Derivation.** Lagrangian L = α ln x1 + (1−α) ln x2 + λ(m − p1x1 − p2x2). FOCs: α/x1 = λp1, (1−α)/x2 = λp2, budget binding. Dividing, MRS = αx2/((1−α)x1) = p1/p2. Substituting into the budget: p1x1 + p2·(1−α)p1x1/(αp2) = m ⇒ p1x1/α = m ⇒ λ = 1/m and\nx1* = αm/p1, x2* = (1−α)m/p2, v(p,m) = α ln(αm/p1) + (1−α) ln((1−α)m/p2).\n\n**Numerical validation (does not use the closed form).** At the single parameter point in the file only: (i) bounded Brent maximisation of u(x1, (m−p1x1)/p2) over x1 ∈ (0, m/p1) — this is the reported `indirect_utility_numerical`; (ii) a 999,999-point interior grid on the budget line; (iii) 2-D SLSQP on u with the inequality budget constraint and non-negativity bounds (does not impose that the budget binds). No randomness is used (`random_seed` = null). Code: `out/analysis.py`.\n\n## Results\n- x1* = 16.8 units of good 1 (`x1_demand`); x2* = 19.5 units of good 2 (`x2_demand`).\n- v = 2.9182520128635305 utils (`indirect_utility`).\n- Budget residual = 0.0 currency units (`budget_identity_residual`).\n- MRS at optimum = 0.625 = p1/p2 = 0.625 (`mrs_at_optimum`, `price_ratio`).\n- Expenditure share of good 1 = 0.35 = α (`expenditure_share_good1`).\n- Numerical maximum utility = 2.9182520128635305 (`indirect_utility_numerical`), identical to the closed form in double precision (`validation_details.abs_diff_utility_closed_vs_brent` = 0). Brent maximiser x1 = 16.8000002 (`validation_details.brent_x1`, |diff| ≈ 2.3e-7, `validation_details.abs_diff_x1_closed_vs_brent`). Grid and SLSQP agree (`validation_details.grid_utility`, `validation_details.slsqp_utility`); SLSQP leaves zero budget slack (`validation_details.slsqp_budget_slack`), confirming the budget binds.\n- `feasibility` = \"complete\".\n\n## Uncertainty\nThis is a deterministic theoretical exercise; there is no sampling uncertainty. The only uncertainty is numerical: optimiser tolerance gives x1 errors of order 1e-7 (`validation_details.abs_diff_x1_closed_vs_brent`). Utility differences are 0 to machine precision because u is flat (second-order) near the optimum, so utility agreement is a weaker test than the agreement of the maximisers.\n\n## Limitations and open issues\n- Validation covers only the single parameter point (α=0.35, p1=2.5, p2=4, m=120); the general formula is supported by the analytical derivation, not by a numerical sweep.\n- The grid maximiser coincides exactly with 16.8 because 16.8 is a grid node (step 4.8e-5, `validation_details.grid_step_x1`); this is a coincidence of the grid, not extra precision.\n- The closed form does not apply for α ∉ (0,1) or non-positive prices/income; the script would then report null for the closed-form keys.\n- Extra diagnostic keys are stored under `validation_details` in results.json beyond the required keys.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"Under 0<alpha<1, p>0, m>0 the unique optimum is x1*=alpha m/p1=16.8 and x2*=(1-alpha)m/p2=19.5.\",\"results_keys\":[\"x1_demand\",\"x2_demand\"],\"status\":\"supported\",\"caveat\":\"Uniqueness is analytical; numerical check at one parameter point.\"},\n {\"id\":\"C2\",\"text\":\"Indirect utility at the optimum is 2.9182520128635305 utils.\",\"results_keys\":[\"indirect_utility\"],\"status\":\"supported\",\"caveat\":\"\"},\n {\"id\":\"C3\",\"text\":\"The budget binds exactly at the closed-form demands (residual 0).\",\"results_keys\":[\"budget_identity_residual\",\"validation_details\"],\"status\":\"supported\",\"caveat\":\"SLSQP slack also 0.\"},\n {\"id\":\"C4\",\"text\":\"At the optimum 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\":\"C5\",\"text\":\"An independent numerical maximisation on the budget line reproduces the closed-form utility to machine precision and the maximiser to ~2e-7.\",\"results_keys\":[\"indirect_utility_numerical\",\"validation_details\"],\"status\":\"supported\",\"caveat\":\"Utility agreement is weak evidence due to flatness; covers only the given parameter point.\"}\n]\nEOF\n~/wp29/venv/bin/python -c \"import json;json.load(open('out/claims.json'))\" && echo ok","description":"Write audit, checks, report, claims"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1052,"cache_read_input_tokens":13801,"output_tokens":3340,"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":1052},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXk3p6D7hwRQX2oCUA39","requestRef":"93f4ec1b-fce1-412e-83aa-b8d9b02c6cbb","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"74b26a63-ddcc-41e6-b95f-81f03b0ba151","timestamp":"2026-10-30T03:52:41.890Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}57{"parentUuid":"74b26a63-ddcc-41e6-b95f-81f03b0ba151","isSidechain":false,"promptId":"94374b6b-ef1f-4be4-a414-eaf4b9cb7868","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01H83YKLD65N64Bge3hs1U9W","type":"tool_result","content":"ok","is_error":false}]},"uuid":"96beb7e2-4145-4886-b6d0-df99f7a414f2","timestamp":"2026-10-30T03:52:41.968Z","toolUseResult":{"stdout":"ok","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"74b26a63-ddcc-41e6-b95f-81f03b0ba151","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RP0020","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","version":"2.1.314","gitBranch":"HEAD"}58{"type":"api-request-blob","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","hash":"f228ce3c483db9bde7a274df62614e3a458fe08b655230d3ddefa0ac948d6ad5","message":{"role":"assistant","content":[{"type":"text","text":"Now the state docs, report and claims."},{"type":"tool_use","id":"toolu_01H83YKLD65N64Bge3hs1U9W","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n| file | SHA-256 | 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 values numeric, no unexpected parameters, LF line endings, no dates (not applicable).\nAssumption checks: 0<alpha<1, p1>0, p2>0, m>0 all hold.\nInformation availability: the only input is the permitted file; no violations. (`gate_spec.json`/`bundle.json` in the workspace root are not task inputs and were not used by the analysis.)\nExclusions: none (out/exclusions.csv: 4 → 4).\nEOF\ncat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n| check | outcome |\n|---|---|\n| Clean re-run (deleted results.json, exclusions.csv; re-ran) gives byte-identical results.json (sha256 923215d3…) | PASS |\n| x1_demand, x2_demand > 0 (interior) | PASS |\n| |budget_identity_residual| < 1e-9 (exactly 0.0) | PASS |\n| mrs_at_optimum == price_ratio (0.625) | PASS |\n| expenditure_share_good1 == alpha (0.35) | PASS |\n| indirect_utility equals α ln(αm/p1)+(1−α) ln((1−α)m/p2) | PASS |\n| indirect_utility_numerical (Brent on budget line) ≤ indirect_utility + 1e-12 and |diff| < 1e-10 (diff 0.0) | PASS |\n| Brent x1 within 1e-6 of closed form (2.3e-7) | PASS |\n| Grid (999,999 interior points) and 2-D SLSQP with inequality budget give same utility to machine precision; SLSQP budget slack 0 (budget binds) | PASS |\n| Counts: n_raw 4 − removed 0 = n_analysed 4 | PASS |\n| Note: grid maximiser equals 16.8 exactly because 16.8 is a grid node (step 4.8e-5); utility agreement to 0.0 reflects flatness of u near the optimum (second-order), so the x-distance (2.3e-7) is the more informative metric. | noted |\nEOF\ncat > 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 check them against an independent numerical maximisation.\n\n## Data and exclusions\nInput: `data/parameters.csv` (4 rows, `n_input_rows`; SHA-256 a04798ad…, recorded in `validation_details.input_sha256`). α = 0.35, p1 = 2.5, p2 = 4.0, m = 120. No missing, duplicated or non-numeric values (`data_issues` = []). No rows excluded; 4 rows used (`n_analysed`; see `out/exclusions.csv`). These are given theoretical parameters, not observed data.\n\n## Method\n**Assumptions for the closed form to be the unique optimum:** 0 < α < 1, p1 > 0, p2 > 0, m > 0 (all hold here). Then u is strictly increasing in each good (local non-satiation ⇒ budget binds), strictly concave on R²₊₊, and satisfies ∂u/∂xi → ∞ as xi → 0 with u → −∞ on the boundary, so the optimum is interior. A strictly concave objective on a convex compact-relevant feasible set has at most one maximiser, so the KKT point is the unique global optimum.\n\n**Derivation.** Lagrangian L = α ln x1 + (1−α) ln x2 + λ(m − p1x1 − p2x2). FOCs: α/x1 = λp1, (1−α)/x2 = λp2, budget binding. Dividing, MRS = αx2/((1−α)x1) = p1/p2. Substituting into the budget: p1x1 + p2·(1−α)p1x1/(αp2) = m ⇒ p1x1/α = m ⇒ λ = 1/m and\nx1* = αm/p1, x2* = (1−α)m/p2, v(p,m) = α ln(αm/p1) + (1−α) ln((1−α)m/p2).\n\n**Numerical validation (does not use the closed form).** At the single parameter point in the file only: (i) bounded Brent maximisation of u(x1, (m−p1x1)/p2) over x1 ∈ (0, m/p1) — this is the reported `indirect_utility_numerical`; (ii) a 999,999-point interior grid on the budget line; (iii) 2-D SLSQP on u with the inequality budget constraint and non-negativity bounds (does not impose that the budget binds). No randomness is used (`random_seed` = null). Code: `out/analysis.py`.\n\n## Results\n- x1* = 16.8 units of good 1 (`x1_demand`); x2* = 19.5 units of good 2 (`x2_demand`).\n- v = 2.9182520128635305 utils (`indirect_utility`).\n- Budget residual = 0.0 currency units (`budget_identity_residual`).\n- MRS at optimum = 0.625 = p1/p2 = 0.625 (`mrs_at_optimum`, `price_ratio`).\n- Expenditure share of good 1 = 0.35 = α (`expenditure_share_good1`).\n- Numerical maximum utility = 2.9182520128635305 (`indirect_utility_numerical`), identical to the closed form in double precision (`validation_details.abs_diff_utility_closed_vs_brent` = 0). Brent maximiser x1 = 16.8000002 (`validation_details.brent_x1`, |diff| ≈ 2.3e-7, `validation_details.abs_diff_x1_closed_vs_brent`). Grid and SLSQP agree (`validation_details.grid_utility`, `validation_details.slsqp_utility`); SLSQP leaves zero budget slack (`validation_details.slsqp_budget_slack`), confirming the budget binds.\n- `feasibility` = \"complete\".\n\n## Uncertainty\nThis is a deterministic theoretical exercise; there is no sampling uncertainty. The only uncertainty is numerical: optimiser tolerance gives x1 errors of order 1e-7 (`validation_details.abs_diff_x1_closed_vs_brent`). Utility differences are 0 to machine precision because u is flat (second-order) near the optimum, so utility agreement is a weaker test than the agreement of the maximisers.\n\n## Limitations and open issues\n- Validation covers only the single parameter point (α=0.35, p1=2.5, p2=4, m=120); the general formula is supported by the analytical derivation, not by a numerical sweep.\n- The grid maximiser coincides exactly with 16.8 because 16.8 is a grid node (step 4.8e-5, `validation_details.grid_step_x1`); this is a coincidence of the grid, not extra precision.\n- The closed form does not apply for α ∉ (0,1) or non-positive prices/income; the script would then report null for the closed-form keys.\n- Extra diagnostic keys are stored under `validation_details` in results.json beyond the required keys.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"Under 0<alpha<1, p>0, m>0 the unique optimum is x1*=alpha m/p1=16.8 and x2*=(1-alpha)m/p2=19.5.\",\"results_keys\":[\"x1_demand\",\"x2_demand\"],\"status\":\"supported\",\"caveat\":\"Uniqueness is analytical; numerical check at one parameter point.\"},\n {\"id\":\"C2\",\"text\":\"Indirect utility at the optimum is 2.9182520128635305 utils.\",\"results_keys\":[\"indirect_utility\"],\"status\":\"supported\",\"caveat\":\"\"},\n {\"id\":\"C3\",\"text\":\"The budget binds exactly at the closed-form demands (residual 0).\",\"results_keys\":[\"budget_identity_residual\",\"validation_details\"],\"status\":\"supported\",\"caveat\":\"SLSQP slack also 0.\"},\n {\"id\":\"C4\",\"text\":\"At the optimum 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\":\"C5\",\"text\":\"An independent numerical maximisation on the budget line reproduces the closed-form utility to machine precision and the maximiser to ~2e-7.\",\"results_keys\":[\"indirect_utility_numerical\",\"validation_details\"],\"status\":\"supported\",\"caveat\":\"Utility agreement is weak evidence due to flatness; covers only the given parameter point.\"}\n]\nEOF\n~/wp29/venv/bin/python -c \"import json;json.load(open('out/claims.json'))\" && echo ok","description":"Write audit, checks, report, claims"}}]}}59{"type":"api-request","sessionId":"b3526ab7-883a-4530-802f-9781a18102c1","id":"55f04763-cbdf-4d93-b332-b91c3c04ce05","timestamp":"2026-10-30T03:52:41.971Z","version":"2.1.314","querySource":"sdk","shapeHash":"54de31b1820d9b6b1dbb75b73b59d66ab108fd72b286485fb0bb8306e7aa9124","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":"93f4ec1b-fce1-412e-83aa-b8d9b02c6cbb","keep":16,"tail":["f228ce3c483db9bde7a274df62614e3a458fe08b655230d3ddefa0ac948d6ad5","d735a8ca0933421bbf29d4169c5fa91ae2478619ea9e2b6009f804571799762e"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",17,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"5ba1cd93bacc05593db34f81af5f38d24f41a7e005435e117e8f63d840792770"}60{"parentUuid":"96beb7e2-4145-4886-b6d0-df99f7a414f2","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXk5tPVYFN3Nvp8aDXVL","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01KyMEa1bj8V3LKPiRiSvngM","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/dup/non-numeric\",\"parameter ranges valid\",\"exclusions.csv: 4->4\"],\"notes\":\"data_audit.md\"},\n \"P2\":{\"status\":\"passed\",\"checks\":[\"baseline numerical max (Brent on budget line) computed without closed form -> indirect_utility_numerical\"],\"notes\":\"\"},\n \"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py reads only data/, writes results.json deterministically, no RNG (seed null)\"],\"notes\":\"\"},\n \"P4\":{\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical results.json\",\"residual 0\",\"MRS==price ratio\",\"share==alpha\",\"closed vs numerical utility diff 0, x1 diff 2.3e-7\",\"SLSQP budget binds\",\"counts add up\"],\"notes\":\"checks.md\"},\n \"P5\":{\"status\":\"passed\",\"checks\":[\"report.md has all 6 sections with key citations\",\"claims.json valid, all report claims listed\"],\"notes\":\"\"}}\nEOF\ncat >> out/state/log.md <<'EOF'\n- 2026-10-29: P1 passed (clean data, no exclusions).\n- 2026-10-29: P2/P3 passed (analysis.py with Brent/grid/SLSQP validation + closed form).\n- 2026-10-29: P4 passed (identical re-run, all consistency checks pass).\n- 2026-10-29: P5 passed (report.md, claims.json). 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Re-running `out/analysis.py` from scratch gives an identical `out/results.json`, and all six protocol phases (P0–P5) are marked passed with their checks recorded.\n\n**Results** (α = 0.35, p1 = 2.5, p2 = 4, m = 120):\n\n| Quantity | Value |\n|---|---|\n| Demand for good 1, x1* = αm/p1 | 16.8 |\n| Demand for good 2, x2* = (1−α)m/p2 | 19.5 |\n| Indirect utility | 2.9182520128635305 utils |\n| Budget residual | 0.0 |\n| MRS at the optimum | 0.625, equal to p1/p2 |\n| Spending share on good 1 | 0.35, equal to α |\n\n**Assumptions:** the closed form is the unique optimum when 0 < α < 1 and prices and income are positive. Under those conditions utility always rises with more of either good, so the whole budget is spent. It is also strictly concave, and it falls without limit as either quantity approaches zero, so the best choice has positive amounts of both goods. The report sets out the full derivation.\n\n**Numerical check:** none of the three methods uses the formula; each maximises utility directly.\n- **One-dimensional search along the budget line:** this gives the reported numerical utility. It matches the formula to machine precision, and its x1 is about 2.3e-7 away from 16.8.\n- **Grid of about one million points on the budget line:** it lands exactly on 16.8, but only because 16.8 happens to be one of the grid points.\n- **Two-dimensional optimiser:** I only told it the budget was an upper limit, and it still spent all of it, which independently confirms the budget binds.\n\n**Limitations:**\n- The numerical check covers only the one parameter set in the file. That the formula holds in general rests on the derivation, not on testing other values.\n- Matching utilities is a weak test, because utility is nearly flat near the optimum. 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