spb/wp29_uqo

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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 user's own instructions about these lines, such as a CLAUDE.md or memory rule, take precedence over this reminder, but do not add attribution lines this reminder leaves out):\n- End git commit messages with:\nCo-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>\n- End pull request descriptions with:\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n</system-reminder>"}],"renderedRole":"user","renderedBesideToolResult":true,"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3"}12{"parentUuid":"bb6c41a9-9090-4efa-8079-5aa9fd8e0533","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoWeRPqufK5wEs4XJpz","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":4,"cache_creation_input_tokens":2209,"cache_read_input_tokens":1504,"output_tokens":135,"output_tokens_details":{"thinking_tokens":20},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":2209},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":467,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXoWeEjFGtQgLyGnnUQx","requestRef":"86a41928-1527-4269-88d0-90dc1ad6e7ff","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"9327971f-d0b4-4c5f-9ae9-8a472ebeff96","timestamp":"2026-10-30T04:37:39.750Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"9327971f-d0b4-4c5f-9ae9-8a472ebeff96","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoWeRPqufK5wEs4XJpz","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01KKctG3bVetkcFAPn41ieZj","name":"Bash","input":{"command":"cat TASK.md; 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The Bellman equation is V(y) = max_{0<c<y} { ln c + β V((y − c)^α) }. This model has a known closed-form solution for the optimal consumption policy c(y) and the value function V(y). The estimands are: the closed-form policy at three evaluation points of y; the policy obtained by value-function iteration (VFI) on the prescribed grid at the same points; the maximum absolute discrepancy between them over the evaluation points; the closed-form and numerical value function at y = 1; the savings rate implied by the closed form; and the contraction modulus of the Bellman operator in the sup norm.\n\n## Inputs\n- `data/model.csv` — columns `parameter`, `value`, `description`: `alpha`, `beta`, the grid specification (`y_min`, `y_max`, `grid_points`, `grid_spacing` = log, i.e. points equally spaced in ln y), the VFI stopping tolerance `vfi_tolerance` (sup-norm change between successive value functions), and the three evaluation points `eval_y_1`, `eval_y_2`, `eval_y_3`. Theoretical parameters, not observed data.\n\n## Information-availability rules\n- Use only `data/model.csv` and solve the model on the prescribed grid with the prescribed parameters; if any deviation from the prescribed design is necessary, record it in `data_issues`.\n- The numerical policy must come from the VFI, not from the closed form; the closed form must be derived (e.g. guess-and-verify on the Bellman equation) and stated in the report.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F5-conf-04\" |\n| `c_closed_y05`, `c_closed_y1`, `c_closed_y2` | number | units of output | closed-form optimal consumption at y = 0.5, 1.0, 2.0 |\n| `c_num_y05`, `c_num_y1`, `c_num_y2` | number | units of output | VFI consumption policy at y = 0.5, 1.0, 2.0 (interpolated on the grid if the point is not a grid node) |\n| `max_abs_error_policy` | number | units of output | max over the three evaluation points of \\|c_num − c_closed\\| |\n| `value_closed_y1` | number | utils | closed-form V(1) |\n| `value_num_y1` | number | utils | VFI value function at y = 1 |\n| `savings_rate_closed_form` | number | — | closed-form (y − c)/y (the baseline quantity) |\n| `contraction_modulus` | number | — | modulus of the Bellman operator as a contraction in the sup norm |\n| `grid_points_used` | integer | — | number of grid points actually used |\n| `n_iterations` | integer | — | VFI iterations until the stopping rule was met |\n| `final_sup_change` | number | utils | sup-norm change at the last iteration |\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 or design deviations and how handled (empty list if none) |\n| `n_input_rows` | object | — | {\"model.csv\": rows read} |\n| `n_analysed` | integer or null | — | number of grid points |\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. State explicitly the assumptions of the closed form (log utility, Cobb–Douglas technology, full depreciation, interior solution), why the Bellman operator is a contraction and with what modulus, and the scope of the numerical validation (which grid, which parameter point, what the discretisation error depends on).\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.\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}]. Each claim's status must be justified by the listed results keys.\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels available). Do not modify `data/`.\n- This task is designed to be completed in well under 20 minutes of work; the VFI on the prescribed grid runs in seconds when vectorised.\nbundle.json\ndata\ngate_spec.json\nTASK.md\n\n./data:\nmodel.csv","is_error":true,"tool_use_id":"toolu_01KKctG3bVetkcFAPn41ieZj"}]},"uuid":"da4dc56b-69dc-4b1b-93a1-dc8e371b51ac","timestamp":"2026-10-30T04:37:40.475Z","toolUseResult":"Error: Exit code 1\n# F5-conf-04 — Value-function iteration against a closed-form policy (optimal growth with log utility)\n\n## Scientific question\nA planner maximises Σ_t β^t ln c_t subject to y_{t+1} = (y_t − c_t)^α, 0 < c_t < y_t, with full depreciation and productivity normalised to one. The Bellman equation is V(y) = max_{0<c<y} { ln c + β V((y − c)^α) }. This model has a known closed-form solution for the optimal consumption policy c(y) and the value function V(y). The estimands are: the closed-form policy at three evaluation points of y; the policy obtained by value-function iteration (VFI) on the prescribed grid at the same points; the maximum absolute discrepancy between them over the evaluation points; the closed-form and numerical value function at y = 1; the savings rate implied by the closed form; and the contraction modulus of the Bellman operator in the sup norm.\n\n## Inputs\n- `data/model.csv` — columns `parameter`, `value`, `description`: `alpha`, `beta`, the grid specification (`y_min`, `y_max`, `grid_points`, `grid_spacing` = log, i.e. points equally spaced in ln y), the VFI stopping tolerance `vfi_tolerance` (sup-norm change between successive value functions), and the three evaluation points `eval_y_1`, `eval_y_2`, `eval_y_3`. Theoretical parameters, not observed data.\n\n## Information-availability rules\n- Use only `data/model.csv` and solve the model on the prescribed grid with the prescribed parameters; if any deviation from the prescribed design is necessary, record it in `data_issues`.\n- The numerical policy must come from the VFI, not from the closed form; the closed form must be derived (e.g. guess-and-verify on the Bellman equation) and stated in the report.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F5-conf-04\" |\n| `c_closed_y05`, `c_closed_y1`, `c_closed_y2` | number | units of output | closed-form optimal consumption at y = 0.5, 1.0, 2.0 |\n| `c_num_y05`, `c_num_y1`, `c_num_y2` | number | units of output | VFI consumption policy at y = 0.5, 1.0, 2.0 (interpolated on the grid if the point is not a grid node) |\n| `max_abs_error_policy` | number | units of output | max over the three evaluation points of \\|c_num − c_closed\\| |\n| `value_closed_y1` | number | utils | closed-form V(1) |\n| `value_num_y1` | number | utils | VFI value function at y = 1 |\n| `savings_rate_closed_form` | number | — | closed-form (y − c)/y (the baseline quantity) |\n| `contraction_modulus` | number | — | modulus of the Bellman operator as a contraction in the sup norm |\n| `grid_points_used` | integer | — | number of grid points actually used |\n| `n_iterations` | integer | — | VFI iterations until the stopping rule was met |\n| `final_sup_change` | number | utils | sup-norm change at the last iteration |\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 or design deviations and how handled (empty list if none) |\n| `n_input_rows` | object | — | {\"model.csv\": rows read} |\n| `n_analysed` | integer or null | — | number of grid points |\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. State explicitly the assumptions of the closed form (log utility, Cobb–Douglas technology, full depreciation, interior solution), why the Bellman operator is a contraction and with what modulus, and the scope of the numerical validation (which grid, which parameter point, what the discretisation error depends on).\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.\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}]. Each claim's status must be justified by the listed results keys.\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels available). 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Compare closed-form policy/value with VFI on prescribed log grid.\n**Estimands:** closed-form c(y)=(1-alpha*beta)y at y=0.5,1,2; VFI policy at same points (linear interpolation between grid nodes); max abs policy error; V(1) closed form and VFI; savings rate alpha*beta; contraction modulus (beta, Blackwell sufficient conditions on bounded grid problem).\n**Assumptions:** log utility, Cobb-Douglas, full depreciation, interior solution, 0<alpha<1, 0<beta<1.\n**Outputs:** out/results.json (keys per TASK.md table), out/report.md (6 sections), out/analysis.py, out/claims.json; plus protocol state files and out/exclusions.csv.\n**Info rules:** only data/model.csv; prescribed grid (400 log-spaced points in [0.05,5]), tolerance 1e-8; numerical policy from VFI only; deviations into data_issues.\n**Invalidity:** missing parameters, infeasible grid (no feasible choice at some node), non-convergence, using closed form to construct numerical policy.\nEOF\ncat > out/state/log.md <<'EOF'\n- 2026-10-30 P0 passed: contract written.\nEOF","description":"Write contract and log"}},{"type":"tool_use","id":"toolu_01W3pMhDK9XigUMUPyd6SuWh","name":"Bash","input":{"command":"cat bundle.json | head -c 1500","description":"Peek at bundle.json"}}]}}29{"type":"api-request-blob","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","hash":"9966c104c62e9e9e24d69d9c4ddac955287295811710295e9a469217cdb00668","message":{"role":"user","content":[{"tool_use_id":"toolu_017W9UTjA7X9DdGLYZaKoT2d","type":"tool_result","content":"{\n  \"task_id\": \"F5-conf-04\",\n  \"required_files\": [\n    \"out/results.json\",\n    \"out/report.md\",\n    \"out/analysis.py\",\n    \"out/claims.json\"\n  ],\n  \"results_keys\": {\n    \"task_id\": {\n      \"type\": \"string\",\n      \"nullable\": false\n    },\n    \"c_closed_y05\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"c_closed_y1\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"c_closed_y2\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"c_num_y05\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"c_num_y1\": {","is_error":false},{"tool_use_id":"toolu_01W3pMhDK9XigUMUPyd6SuWh","type":"tool_result","content":"{\n  \"task_id\": \"F5-conf-04\",\n  \"family\": \"F5\",\n  \"split\": \"conf\",\n  \"version\": \"1.0\",\n  \"created_utc\": \"2026-10-30T03:42:22.079893+00:00\",\n  \"files\": {\n    \"TASK.md\": \"7723e3dc76d5ee4831121d96c79e04c503d90569ba31c5a92d4c31bb24f0f3d2\",\n    \"gate_spec.json\": \"857972db0a035afd491bcfe1b5dc15095377a1fa6374a474f0e37cf424fb3860\",\n    \"data/model.csv\": \"098123961451e4f9a2e76afdbc83aec78066fc713d0645659c09b77b1636195b\"\n  }\n}","is_error":false}]}}30{"type":"api-request","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","id":"c10773cb-e43a-42c9-b85d-ee93891cfc30","timestamp":"2026-10-30T04:37:59.247Z","version":"2.1.314","querySource":"sdk","shapeHash":"00b73950d6ad4c2832fef6e39a3d997af555e3dd0e57b0a449ec5bdb5e48e0dd","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":"64954eef-ff13-42f3-b617-387d5f018662","keep":6,"tail":["f274996aa31ae8af83cfcd278eadde0611494913fbf6bdee2d88b4c09ab8204a","9966c104c62e9e9e24d69d9c4ddac955287295811710295e9a469217cdb00668"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",1],"value":{"type":"ephemeral"}}],"requestDigest":"44c12edbfcb067cb3675cc92561c8c50e274e9201e10b463e202a7d75b673818"}31{"parentUuid":"c18deae3-ce30-48cc-ac67-68c9c6b1a685","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoYC7B5RrRYUxx9SAkn","type":"message","role":"assistant","content":[{"type":"text","text":"Hash matches the bundle. Now the data audit and the analysis script."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2212,"cache_read_input_tokens":6007,"output_tokens":2768,"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":2212},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXoYBq3rgDjVjf9t9vPZ","requestRef":"c10773cb-e43a-42c9-b85d-ee93891cfc30","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"bbccd189-57a1-4969-92ce-5ba48e902f86","timestamp":"2026-10-30T04:38:00.325Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}32{"parentUuid":"bbccd189-57a1-4969-92ce-5ba48e902f86","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoYC7B5RrRYUxx9SAkn","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01DR64p4fJKN2T9yRVsJdXtH","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n- `data/model.csv`: SHA-256 098123961451e4f9a2e76afdbc83aec78066fc713d0645659c09b77b1636195b (matches bundle.json). 10 data rows x 3 columns (parameter, value, description). No missing values, no duplicate parameter names.\n- Parameters: alpha=0.36, beta=0.95, y_min=0.05, y_max=5.0, grid_points=400, grid_spacing=log, vfi_tolerance=1e-8, eval points 0.5, 1.0, 2.0.\n- `value` column mixes numeric and the string \"log\" (grid_spacing) -> parsed per row; not an anomaly.\n- Checks: 0<alpha<1, 0<beta<1, y_min<y_max, eval points inside grid. Steady state y* = (alpha*beta)^(alpha/(1-alpha)) ~ 0.547 lies inside grid; optimal next-period output from any y in [0.05,5] lies in [~0.23, ~1.21], inside grid, so truncation does not bind.\n- Eval points 0.5, 1.0, 2.0 are not grid nodes on the 400-point log grid -> linear interpolation (in ln y) of the VFI policy, as allowed by TASK.md.\n- No information-availability violations: the file contains only theoretical parameters.\n- Exclusions: none (out/exclusions.csv records the single \"parse\" step with 0 removed).\nEOF\ncat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-04: VFI vs closed form for Brock-Mirman growth with log utility.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nDeterministic; no random numbers used.\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\n\nos.makedirs(\"out\", exist_ok=True)\ndf = pd.read_csv(\"data/model.csv\")\nn_rows = len(df)\np = dict(zip(df[\"parameter\"], df[\"value\"]))\nalpha = float(p[\"alpha\"]); beta = float(p[\"beta\"])\ny_min = float(p[\"y_min\"]); y_max = float(p[\"y_max\"]); N = int(float(p[\"grid_points\"]))\nspacing = str(p[\"grid_spacing\"]).strip(); tol = float(p[\"vfi_tolerance\"])\nevals = [float(p[\"eval_y_1\"]), float(p[\"eval_y_2\"]), float(p[\"eval_y_3\"])]\nassert spacing == \"log\" and 0 < alpha < 1 and 0 < beta < 1 and y_min < y_max\ndata_issues = []\n\n# ---------- closed form (guess V = A + B ln y, verified in report) ----------\nab = alpha * beta\nB = 1.0 / (1.0 - ab)\nA = (np.log(1.0 - ab) + ab * B * np.log(ab)) / (1.0 - beta)\nc_closed = lambda y: (1.0 - ab) * y\nV_closed = lambda y: A + B * np.log(y)\nsavings_rate = ab\n\n# ---------- VFI on prescribed grid ----------\n# State y on log grid; control = next-period output y' chosen on the same grid.\n# Consumption implied: c = y - y'^(1/alpha) (capital k = y'^(1/alpha)).\ngrid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))\nk_needed = grid ** (1.0 / alpha)                     # capital required for each y'\nC = grid[:, None] - k_needed[None, :]                # rows: y, cols: y'\nfeasible = C > 0\nassert feasible.any(axis=1).all(), \"some grid node has no feasible choice\"\nU = np.full_like(C, -np.inf); U[feasible] = np.log(C[feasible])\nV = np.zeros(N); n_iter = 0; sup = np.inf\nwhile sup >= tol:\n    V_new = np.max(U + beta * V[None, :], axis=1)\n    sup = float(np.max(np.abs(V_new - V))); V = V_new; n_iter += 1\n    if n_iter > 100000:\n        raise RuntimeError(\"VFI did not converge\")\nidx = np.argmax(U + beta * V[None, :], axis=1)\nc_pol = C[np.arange(N), idx]\nlg = np.log(grid)\ninterp = lambda f, y: float(np.interp(np.log(y), lg, f))   # linear in ln y\nc_num = [interp(c_pol, y) for y in evals]\nc_cl = [float(c_closed(y)) for y in evals]\nmax_err = float(max(abs(a - b) for a, b in zip(c_num, c_cl)))\nv_num_1 = interp(V, 1.0)\nfor y in evals:\n    if not np.any(np.isclose(grid, y, rtol=0, atol=1e-12)):\n        data_issues.append({\"issue\": f\"evaluation point y={y} is not a grid node\",\n                            \"handling\": \"VFI policy/value linearly interpolated in ln y between adjacent grid nodes\"})\ndata_issues.append({\"issue\": \"VFI control is discretised: next-period output y' restricted to the 400-point grid\",\n                    \"handling\": \"standard discrete-choice VFI on the prescribed grid; no off-grid optimisation, so policy error reflects grid spacing\"})\n\n# diagnostics (not required keys)\ndiag = {\n    \"grid_log_step\": float(lg[1] - lg[0]),\n    \"max_abs_error_policy_on_grid\": float(np.max(np.abs(c_pol - c_closed(grid)))),\n    \"max_abs_error_value_on_grid\": float(np.max(np.abs(V - V_closed(grid)))),\n    \"vfi_error_bound_beta_over_1mbeta_times_sup\": float(beta / (1 - beta) * sup),\n    \"steady_state_y\": float(ab ** (alpha / (1 - alpha))),\n    \"choice_index_min_max\": [int(idx.min()), int(idx.max())],\n    \"closed_form_A\": float(A), \"closed_form_B\": float(B),\n}\n\nres = {\n    \"task_id\": \"F5-conf-04\",\n    \"c_closed_y05\": c_cl[0], \"c_closed_y1\": c_cl[1], \"c_closed_y2\": c_cl[2],\n    \"c_num_y05\": c_num[0], \"c_num_y1\": c_num[1], \"c_num_y2\": c_num[2],\n    \"max_abs_error_policy\": max_err,\n    \"value_closed_y1\": float(V_closed(1.0)), \"value_num_y1\": v_num_1,\n    \"savings_rate_closed_form\": float(savings_rate),\n    \"baseline_savings_rate\": float(savings_rate),\n    \"contraction_modulus\": beta,\n    \"grid_points_used\": int(N), \"n_iterations\": int(n_iter), \"final_sup_change\": sup,\n    \"feasibility\": \"complete\", \"feasibility_reason\": None,\n    \"data_issues\": data_issues,\n    \"n_input_rows\": {\"model.csv\": int(n_rows)},\n    \"n_analysed\": int(N), \"random_seed\": None,\n    \"diagnostics\": diag,\n}\nwith open(\"out/results.json\", \"w\") as f:\n    json.dump(res, f, indent=2)\npd.DataFrame([{\"step\": \"parse\", \"rule\": \"read all parameter rows\", \"n_before\": n_rows,\n               \"n_after\": n_rows, \"n_removed\": 0, \"rationale\": \"no rows excluded\"}]).to_csv(\"out/exclusions.csv\", index=False)\nprint(json.dumps({k: v for k, v in res.items() if k not in (\"data_issues\", \"diagnostics\")}, indent=1))\nEOF\n~/wp29/venv/bin/python out/analysis.py && cat out/results.json | sed -n '/diagnostics/,$p'","description":"Write audit and analysis script, run it"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2212,"cache_read_input_tokens":6007,"output_tokens":2768,"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":2212},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXoYBq3rgDjVjf9t9vPZ","requestRef":"c10773cb-e43a-42c9-b85d-ee93891cfc30","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"7aa16ea6-6d34-44a1-97f7-230c4519673a","timestamp":"2026-10-30T04:38:21.442Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}33{"parentUuid":"7aa16ea6-6d34-44a1-97f7-230c4519673a","isSidechain":false,"promptId":"d9e40f02-b150-4304-95c6-b81a056882bd","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01DR64p4fJKN2T9yRVsJdXtH","type":"tool_result","content":"{\n \"task_id\": \"F5-conf-04\",\n \"c_closed_y05\": 0.329,\n \"c_closed_y1\": 0.658,\n \"c_closed_y2\": 1.316,\n \"c_num_y05\": 0.32881774872035086,\n \"c_num_y1\": 0.6589935200017671,\n \"c_num_y2\": 1.309625047452993,\n \"max_abs_error_policy\": 0.006374952547007151,\n \"value_closed_y1\": -19.524412221722393,\n \"value_num_y1\": -19.52475624982261,\n \"savings_rate_closed_form\": 0.34199999999999997,\n \"baseline_savings_rate\": 0.34199999999999997,\n \"contraction_modulus\": 0.95,\n \"grid_points_used\": 400,\n \"n_iterations\": 361,\n \"final_sup_change\": 9.996650618404601e-09,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"n_input_rows\": {\n  \"model.csv\": 10\n },\n \"n_analysed\": 400,\n \"random_seed\": null\n}\n  \"diagnostics\": {\n    \"grid_log_step\": 0.011541779914757022,\n    \"max_abs_error_policy_on_grid\": 0.02512152290513381,\n    \"max_abs_error_value_on_grid\": 0.0004835155258184898,\n    \"vfi_error_bound_beta_over_1mbeta_times_sup\": 1.8993636174968724e-07,\n    \"steady_state_y\": 0.5468770327603131,\n    \"choice_index_min_max\": [\n      133,\n      276\n    ],\n    \"closed_form_A\": -19.524412221722393,\n    \"closed_form_B\": 1.519756838905775\n  }\n}","is_error":false}]},"uuid":"508e85ab-baf1-4ac5-9ae3-ce65bf081245","timestamp":"2026-10-30T04:38:21.693Z","toolUseResult":{"stdout":"{\n \"task_id\": \"F5-conf-04\",\n \"c_closed_y05\": 0.329,\n \"c_closed_y1\": 0.658,\n \"c_closed_y2\": 1.316,\n \"c_num_y05\": 0.32881774872035086,\n \"c_num_y1\": 0.6589935200017671,\n \"c_num_y2\": 1.309625047452993,\n \"max_abs_error_policy\": 0.006374952547007151,\n \"value_closed_y1\": -19.524412221722393,\n \"value_num_y1\": -19.52475624982261,\n \"savings_rate_closed_form\": 0.34199999999999997,\n \"baseline_savings_rate\": 0.34199999999999997,\n \"contraction_modulus\": 0.95,\n \"grid_points_used\": 400,\n \"n_iterations\": 361,\n \"final_sup_change\": 9.996650618404601e-09,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"n_input_rows\": {\n  \"model.csv\": 10\n },\n \"n_analysed\": 400,\n \"random_seed\": null\n}\n  \"diagnostics\": {\n    \"grid_log_step\": 0.011541779914757022,\n    \"max_abs_error_policy_on_grid\": 0.02512152290513381,\n    \"max_abs_error_value_on_grid\": 0.0004835155258184898,\n    \"vfi_error_bound_beta_over_1mbeta_times_sup\": 1.8993636174968724e-07,\n    \"steady_state_y\": 0.5468770327603131,\n    \"choice_index_min_max\": [\n      133,\n      276\n    ],\n    \"closed_form_A\": -19.524412221722393,\n    \"closed_form_B\": 1.519756838905775\n  }\n}","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"7aa16ea6-6d34-44a1-97f7-230c4519673a","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}34{"type":"api-request-blob","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","hash":"4fca6de0db7e1cbc60852dbd814abd159a4a8628abb09d3e9215a480309052b4","message":{"role":"assistant","content":[{"type":"text","text":"Hash matches the bundle. Now the data audit and the analysis script."},{"type":"tool_use","id":"toolu_01DR64p4fJKN2T9yRVsJdXtH","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n- `data/model.csv`: SHA-256 098123961451e4f9a2e76afdbc83aec78066fc713d0645659c09b77b1636195b (matches bundle.json). 10 data rows x 3 columns (parameter, value, description). No missing values, no duplicate parameter names.\n- Parameters: alpha=0.36, beta=0.95, y_min=0.05, y_max=5.0, grid_points=400, grid_spacing=log, vfi_tolerance=1e-8, eval points 0.5, 1.0, 2.0.\n- `value` column mixes numeric and the string \"log\" (grid_spacing) -> parsed per row; not an anomaly.\n- Checks: 0<alpha<1, 0<beta<1, y_min<y_max, eval points inside grid. Steady state y* = (alpha*beta)^(alpha/(1-alpha)) ~ 0.547 lies inside grid; optimal next-period output from any y in [0.05,5] lies in [~0.23, ~1.21], inside grid, so truncation does not bind.\n- Eval points 0.5, 1.0, 2.0 are not grid nodes on the 400-point log grid -> linear interpolation (in ln y) of the VFI policy, as allowed by TASK.md.\n- No information-availability violations: the file contains only theoretical parameters.\n- Exclusions: none (out/exclusions.csv records the single \"parse\" step with 0 removed).\nEOF\ncat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-04: VFI vs closed form for Brock-Mirman growth with log utility.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nDeterministic; no random numbers used.\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\n\nos.makedirs(\"out\", exist_ok=True)\ndf = pd.read_csv(\"data/model.csv\")\nn_rows = len(df)\np = dict(zip(df[\"parameter\"], df[\"value\"]))\nalpha = float(p[\"alpha\"]); beta = float(p[\"beta\"])\ny_min = float(p[\"y_min\"]); y_max = float(p[\"y_max\"]); N = int(float(p[\"grid_points\"]))\nspacing = str(p[\"grid_spacing\"]).strip(); tol = float(p[\"vfi_tolerance\"])\nevals = [float(p[\"eval_y_1\"]), float(p[\"eval_y_2\"]), float(p[\"eval_y_3\"])]\nassert spacing == \"log\" and 0 < alpha < 1 and 0 < beta < 1 and y_min < y_max\ndata_issues = []\n\n# ---------- closed form (guess V = A + B ln y, verified in report) ----------\nab = alpha * beta\nB = 1.0 / (1.0 - ab)\nA = (np.log(1.0 - ab) + ab * B * np.log(ab)) / (1.0 - beta)\nc_closed = lambda y: (1.0 - ab) * y\nV_closed = lambda y: A + B * np.log(y)\nsavings_rate = ab\n\n# ---------- VFI on prescribed grid ----------\n# State y on log grid; control = next-period output y' chosen on the same grid.\n# Consumption implied: c = y - y'^(1/alpha) (capital k = y'^(1/alpha)).\ngrid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))\nk_needed = grid ** (1.0 / alpha)                     # capital required for each y'\nC = grid[:, None] - k_needed[None, :]                # rows: y, cols: y'\nfeasible = C > 0\nassert feasible.any(axis=1).all(), \"some grid node has no feasible choice\"\nU = np.full_like(C, -np.inf); U[feasible] = np.log(C[feasible])\nV = np.zeros(N); n_iter = 0; sup = np.inf\nwhile sup >= tol:\n    V_new = np.max(U + beta * V[None, :], axis=1)\n    sup = float(np.max(np.abs(V_new - V))); V = V_new; n_iter += 1\n    if n_iter > 100000:\n        raise RuntimeError(\"VFI did not converge\")\nidx = np.argmax(U + beta * V[None, :], axis=1)\nc_pol = C[np.arange(N), idx]\nlg = np.log(grid)\ninterp = lambda f, y: float(np.interp(np.log(y), lg, f))   # linear in ln y\nc_num = [interp(c_pol, y) for y in evals]\nc_cl = [float(c_closed(y)) for y in evals]\nmax_err = float(max(abs(a - b) for a, b in zip(c_num, c_cl)))\nv_num_1 = interp(V, 1.0)\nfor y in evals:\n    if not np.any(np.isclose(grid, y, rtol=0, atol=1e-12)):\n        data_issues.append({\"issue\": f\"evaluation point y={y} is not a grid node\",\n                            \"handling\": \"VFI policy/value linearly interpolated in ln y between adjacent grid nodes\"})\ndata_issues.append({\"issue\": \"VFI control is discretised: next-period output y' restricted to the 400-point grid\",\n                    \"handling\": \"standard discrete-choice VFI on the prescribed grid; no off-grid optimisation, so policy error reflects grid spacing\"})\n\n# diagnostics (not required keys)\ndiag = {\n    \"grid_log_step\": float(lg[1] - lg[0]),\n    \"max_abs_error_policy_on_grid\": float(np.max(np.abs(c_pol - c_closed(grid)))),\n    \"max_abs_error_value_on_grid\": float(np.max(np.abs(V - V_closed(grid)))),\n    \"vfi_error_bound_beta_over_1mbeta_times_sup\": float(beta / (1 - beta) * sup),\n    \"steady_state_y\": float(ab ** (alpha / (1 - alpha))),\n    \"choice_index_min_max\": [int(idx.min()), int(idx.max())],\n    \"closed_form_A\": float(A), \"closed_form_B\": float(B),\n}\n\nres = {\n    \"task_id\": \"F5-conf-04\",\n    \"c_closed_y05\": c_cl[0], \"c_closed_y1\": c_cl[1], \"c_closed_y2\": c_cl[2],\n    \"c_num_y05\": c_num[0], \"c_num_y1\": c_num[1], \"c_num_y2\": c_num[2],\n    \"max_abs_error_policy\": max_err,\n    \"value_closed_y1\": float(V_closed(1.0)), \"value_num_y1\": v_num_1,\n    \"savings_rate_closed_form\": float(savings_rate),\n    \"baseline_savings_rate\": float(savings_rate),\n    \"contraction_modulus\": beta,\n    \"grid_points_used\": int(N), \"n_iterations\": int(n_iter), \"final_sup_change\": sup,\n    \"feasibility\": \"complete\", \"feasibility_reason\": None,\n    \"data_issues\": data_issues,\n    \"n_input_rows\": {\"model.csv\": int(n_rows)},\n    \"n_analysed\": int(N), \"random_seed\": None,\n    \"diagnostics\": diag,\n}\nwith open(\"out/results.json\", \"w\") as f:\n    json.dump(res, f, indent=2)\npd.DataFrame([{\"step\": \"parse\", \"rule\": \"read all parameter rows\", \"n_before\": n_rows,\n               \"n_after\": n_rows, \"n_removed\": 0, \"rationale\": \"no rows excluded\"}]).to_csv(\"out/exclusions.csv\", index=False)\nprint(json.dumps({k: v for k, v in res.items() if k not in (\"data_issues\", \"diagnostics\")}, indent=1))\nEOF\n~/wp29/venv/bin/python out/analysis.py && cat out/results.json | sed -n '/diagnostics/,$p'","description":"Write audit and analysis script, run it"}}]}}35{"type":"api-request","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","id":"866c1f21-d51b-4dbd-832b-40a17cec00f4","timestamp":"2026-10-30T04:38:21.696Z","version":"2.1.314","querySource":"sdk","shapeHash":"00b73950d6ad4c2832fef6e39a3d997af555e3dd0e57b0a449ec5bdb5e48e0dd","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":"c10773cb-e43a-42c9-b85d-ee93891cfc30","keep":8,"tail":["4fca6de0db7e1cbc60852dbd814abd159a4a8628abb09d3e9215a480309052b4","5d4d2daa3813c8a6c233429e6a9c28b1447ea2d37fb6839f14c80e547be9deb5"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",9,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"dc0ddb5a6de447f8bc79d2cd1750249de33c4a2876eff5bde2aebbb90df32994"}36{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"508e85ab-baf1-4ac5-9ae3-ce65bf081245","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3"}37{"type":"atis-latch","atis":"","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3"}38{"parentUuid":"508e85ab-baf1-4ac5-9ae3-ce65bf081245","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoZr4xp193UVndtrBAR","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":3354,"cache_read_input_tokens":8219,"output_tokens":1235,"output_tokens_details":{"thinking_tokens":38},"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":3354},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":549,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXoZqoqgCrp6QXbVmaeu","requestRef":"866c1f21-d51b-4dbd-832b-40a17cec00f4","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"8993332a-4b8f-4623-adf1-b4017df031e5","timestamp":"2026-10-30T04:38:23.359Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}39{"parentUuid":"8993332a-4b8f-4623-adf1-b4017df031e5","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoZr4xp193UVndtrBAR","type":"message","role":"assistant","content":[{"type":"text","text":"Choices are interior (indices 133–276 of 0–399), so the grid bounds never bind. Now I'll run the verification."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":3354,"cache_read_input_tokens":8219,"output_tokens":1235,"output_tokens_details":{"thinking_tokens":38},"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":3354},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXoZqoqgCrp6QXbVmaeu","requestRef":"866c1f21-d51b-4dbd-832b-40a17cec00f4","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f389f0ac-4371-4ef1-a57b-3fcb2a999de3","timestamp":"2026-10-30T04:38:23.362Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}40{"parentUuid":"f389f0ac-4371-4ef1-a57b-3fcb2a999de3","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoZr4xp193UVndtrBAR","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Hjwk7RhfE6XA2tCs7TvTFD","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\n~/wp29/venv/bin/python - <<'EOF'\nimport json,math\nr=json.load(open(\"out/results.json\"))\na,b=0.36,0.95\nchk=[]\nchk.append((\"closed c = (1-ab)y\", all(abs(r[k]-(1-a*b)*y)<1e-12 for k,y in [(\"c_closed_y05\",.5),(\"c_closed_y1\",1),(\"c_closed_y2\",2)])))\nchk.append((\"max err recomputed\", abs(r[\"max_abs_error_policy\"]-max(abs(r[\"c_num_y05\"]-r[\"c_closed_y05\"]),abs(r[\"c_num_y1\"]-r[\"c_closed_y1\"]),abs(r[\"c_num_y2\"]-r[\"c_closed_y2\"])))<1e-15))\nchk.append((\"final_sup < tol\", r[\"final_sup_change\"]<1e-8))\nchk.append((\"policy error <= on-grid max\", r[\"max_abs_error_policy\"]<=r[\"diagnostics\"][\"max_abs_error_policy_on_grid\"]))\nchk.append((\"value err small vs |V|\", abs(r[\"value_num_y1\"]-r[\"value_closed_y1\"])/abs(r[\"value_closed_y1\"])<1e-4))\n# Bellman verification of closed form at random points via fine continuous maximisation\nA=r[\"diagnostics\"][\"closed_form_A\"];B=r[\"diagnostics\"][\"closed_form_B\"]\nimport numpy as np\nok=True\nfor y in [0.1,0.5,1,2,4]:\n    c=np.linspace(1e-6,y-1e-9,200001); rhs=np.max(np.log(c)+b*(A+B*a*np.log(y-c)))\n    ok&= abs(rhs-(A+B*math.log(y)))<1e-6\nchk.append((\"closed form satisfies Bellman eq (fine continuous check)\",bool(ok)))\nchk.append((\"savings rate = alpha*beta\", abs(r[\"savings_rate_closed_form\"]-a*b)<1e-15))\nchk.append((\"modulus in (0,1)\",0<r[\"contraction_modulus\"]<1))\nchk.append((\"n_analysed == grid_points_used == 400\", r[\"n_analysed\"]==r[\"grid_points_used\"]==400))\nchk.append((\"choices interior to grid\", r[\"diagnostics\"][\"choice_index_min_max\"][0]>0 and r[\"diagnostics\"][\"choice_index_min_max\"][1]<399))\nwith open(\"out/state/checks.md\",\"w\") as f:\n    f.write(\"# Verification checks (P4)\\n- Clean re-run of out/analysis.py: results.json byte-identical: PASS\\n- exclusions: n_raw 10 - removed 0 = 10 rows parsed: PASS\\n\")\n    for n,o in chk: f.write(f\"- {n}: {'PASS' if o else 'FAIL'}\\n\"); print(n,o)\nEOF","description":"Rerun from clean state and run 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":3354,"cache_read_input_tokens":8219,"output_tokens":1235,"output_tokens_details":{"thinking_tokens":38},"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":3354},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXoZqoqgCrp6QXbVmaeu","requestRef":"866c1f21-d51b-4dbd-832b-40a17cec00f4","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"44cda1e6-adb9-4ec6-b2e1-1a84271cdaa1","timestamp":"2026-10-30T04:38:32.064Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}41{"parentUuid":"44cda1e6-adb9-4ec6-b2e1-1a84271cdaa1","isSidechain":false,"promptId":"d9e40f02-b150-4304-95c6-b81a056882bd","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01Hjwk7RhfE6XA2tCs7TvTFD","type":"tool_result","content":"IDENTICAL\nclosed c = (1-ab)y True\nmax err recomputed True\nfinal_sup < tol True\npolicy error <= on-grid max True\nvalue err small vs |V| True\nclosed form satisfies Bellman eq (fine continuous check) True\nsavings rate = alpha*beta True\nmodulus in (0,1) True\nn_analysed == grid_points_used == 400 True\nchoices interior to grid True","is_error":false}]},"uuid":"f6abce0d-0cf2-4fa4-8752-3affb0944ece","timestamp":"2026-10-30T04:38:32.331Z","toolUseResult":{"stdout":"IDENTICAL\nclosed c = (1-ab)y True\nmax err recomputed True\nfinal_sup < tol True\npolicy error <= on-grid max True\nvalue err small vs |V| True\nclosed form satisfies Bellman eq (fine continuous check) True\nsavings rate = alpha*beta True\nmodulus in (0,1) True\nn_analysed == grid_points_used == 400 True\nchoices interior to grid True","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"44cda1e6-adb9-4ec6-b2e1-1a84271cdaa1","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}42{"type":"api-request-blob","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","hash":"daef09a38558ac524bf68c24ef74ec96e999f156704bb2e059216ae6aa01697a","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"Choices are interior (indices 133–276 of 0–399), so the grid bounds never bind. Now I'll run the verification."},{"type":"tool_use","id":"toolu_01Hjwk7RhfE6XA2tCs7TvTFD","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\n~/wp29/venv/bin/python - <<'EOF'\nimport json,math\nr=json.load(open(\"out/results.json\"))\na,b=0.36,0.95\nchk=[]\nchk.append((\"closed c = (1-ab)y\", all(abs(r[k]-(1-a*b)*y)<1e-12 for k,y in [(\"c_closed_y05\",.5),(\"c_closed_y1\",1),(\"c_closed_y2\",2)])))\nchk.append((\"max err recomputed\", abs(r[\"max_abs_error_policy\"]-max(abs(r[\"c_num_y05\"]-r[\"c_closed_y05\"]),abs(r[\"c_num_y1\"]-r[\"c_closed_y1\"]),abs(r[\"c_num_y2\"]-r[\"c_closed_y2\"])))<1e-15))\nchk.append((\"final_sup < tol\", r[\"final_sup_change\"]<1e-8))\nchk.append((\"policy error <= on-grid max\", r[\"max_abs_error_policy\"]<=r[\"diagnostics\"][\"max_abs_error_policy_on_grid\"]))\nchk.append((\"value err small vs |V|\", abs(r[\"value_num_y1\"]-r[\"value_closed_y1\"])/abs(r[\"value_closed_y1\"])<1e-4))\n# Bellman verification of closed form at random points via fine continuous maximisation\nA=r[\"diagnostics\"][\"closed_form_A\"];B=r[\"diagnostics\"][\"closed_form_B\"]\nimport numpy as np\nok=True\nfor y in [0.1,0.5,1,2,4]:\n    c=np.linspace(1e-6,y-1e-9,200001); rhs=np.max(np.log(c)+b*(A+B*a*np.log(y-c)))\n    ok&= abs(rhs-(A+B*math.log(y)))<1e-6\nchk.append((\"closed form satisfies Bellman eq (fine continuous check)\",bool(ok)))\nchk.append((\"savings rate = alpha*beta\", abs(r[\"savings_rate_closed_form\"]-a*b)<1e-15))\nchk.append((\"modulus in (0,1)\",0<r[\"contraction_modulus\"]<1))\nchk.append((\"n_analysed == grid_points_used == 400\", r[\"n_analysed\"]==r[\"grid_points_used\"]==400))\nchk.append((\"choices interior to grid\", r[\"diagnostics\"][\"choice_index_min_max\"][0]>0 and r[\"diagnostics\"][\"choice_index_min_max\"][1]<399))\nwith open(\"out/state/checks.md\",\"w\") as f:\n    f.write(\"# Verification checks (P4)\\n- Clean re-run of out/analysis.py: results.json byte-identical: PASS\\n- exclusions: n_raw 10 - removed 0 = 10 rows parsed: PASS\\n\")\n    for n,o in chk: f.write(f\"- {n}: {'PASS' if o else 'FAIL'}\\n\"); print(n,o)\nEOF","description":"Rerun from clean state and run consistency checks"}}]}}43{"type":"api-request","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","id":"6e9e7248-f842-4cfd-be44-822a654200f3","timestamp":"2026-10-30T04:38:32.333Z","version":"2.1.314","querySource":"sdk","shapeHash":"00b73950d6ad4c2832fef6e39a3d997af555e3dd0e57b0a449ec5bdb5e48e0dd","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":"866c1f21-d51b-4dbd-832b-40a17cec00f4","keep":10,"tail":["daef09a38558ac524bf68c24ef74ec96e999f156704bb2e059216ae6aa01697a","e11e2a10289a2282e0f8e01a2e93e7b2d68997a53c81d76534cb879d4942aa00"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",11,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"f0e0b5abe2cdb4480dfd1a4c8883483719944b264b6327940d0dfe6124362b2b"}44{"parentUuid":"f6abce0d-0cf2-4fa4-8752-3affb0944ece","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoadb9qsNv7Vh7GwjCj","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":1373,"cache_read_input_tokens":11573,"output_tokens":3688,"output_tokens_details":{"thinking_tokens":87},"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":1373},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":826,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXoadHYpWC1rqoPW8XhH","requestRef":"6e9e7248-f842-4cfd-be44-822a654200f3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"4b09dc98-ed42-4fd4-8523-094556521e47","timestamp":"2026-10-30T04:38:36.623Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}45{"parentUuid":"4b09dc98-ed42-4fd4-8523-094556521e47","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoadb9qsNv7Vh7GwjCj","type":"message","role":"assistant","content":[{"type":"text","text":"All checks pass. Next I'll write the report, claims and final state."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1373,"cache_read_input_tokens":11573,"output_tokens":3688,"output_tokens_details":{"thinking_tokens":87},"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":1373},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXoadHYpWC1rqoPW8XhH","requestRef":"6e9e7248-f842-4cfd-be44-822a654200f3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"248f11ee-3866-4d42-9b2b-2fce86f8af53","timestamp":"2026-10-30T04:38:36.625Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}46{"parentUuid":"248f11ee-3866-4d42-9b2b-2fce86f8af53","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoadb9qsNv7Vh7GwjCj","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01VdR93wsrreTYbSmD1veXoC","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-conf-04 — VFI vs closed-form policy, optimal growth with log utility\n\n## Question\nA planner maximises Σ β^t ln c_t subject to y_{t+1} = (y_t − c_t)^α. This report compares the closed-form optimal consumption policy and value function with the ones obtained by value-function iteration (VFI) on the prescribed grid. The parameter point is α = 0.36, β = 0.95.\n\n## Data and exclusions\n- The only input is `data/model.csv`: 10 parameter rows (`n_input_rows`). Its SHA-256 matches the bundle.\n- No rows were excluded (`out/exclusions.csv`).\n- Grid: 400 points equally spaced in ln y on [0.05, 5] (`grid_points_used`, `n_analysed`). VFI stopping tolerance: 1e-8 in the sup norm.\n- Design notes, recorded in `data_issues`:\n  1. The evaluation points 0.5, 1.0 and 2.0 are not grid nodes. VFI policy and value are therefore interpolated linearly in ln y between neighbouring nodes.\n  2. The control (next-period output y′) is restricted to the same grid. This is standard discrete VFI, with no off-grid optimisation.\n- No random numbers are used (`random_seed` = null).\n\n## Method\n**Closed form (guess and verify).** Assumptions: log utility, Cobb–Douglas technology y′ = k^α with productivity 1, full depreciation, 0 < α < 1, 0 < β < 1, and an interior solution 0 < c < y.\n- Guess V(y) = A + B ln y. The Bellman right-hand side becomes ln c + β(A + Bα ln(y − c)).\n- The first-order condition 1/c = αβB/(y − c) gives c = y/(1 + αβB).\n- Matching the coefficients on ln y gives B = 1 + αβB, so B = 1/(1 − αβ).\n- Policy: **c(y) = (1 − αβ) y**. Savings rate: **(y − c)/y = αβ**.\n- Constant: **A = [ln(1 − αβ) + (αβ/(1 − αβ)) ln(αβ)] / (1 − β)**.\n- I also checked numerically that this V satisfies the Bellman equation, by brute-force continuous maximisation at y ∈ {0.1, 0.5, 1, 2, 4} (`out/state/checks.md`).\n\n**Contraction.** The Bellman operator T is monotone (v ≤ w implies Tv ≤ Tw) and discounts (T(v + a) = Tv + βa). By Blackwell's sufficient conditions it is a contraction in the sup norm with modulus β.\n- This argument applies on the bounded grid problem: the state space is compact, and at every node there is a feasible choice with c bounded away from 0, so the return is bounded. The infinite-domain log-utility problem has unbounded returns, so there the argument needs a weighted-norm extension or the closed-form verification instead.\n- As a check, the optimal y′ = (αβy)^α maps [0.05, 5] into roughly [0.23, 1.21]. The grid truncation therefore never binds (VFI choice indices stay between 133 and 399 − 123).\n\n**VFI.**\n- Start from V₀ = 0 and iterate V_{n+1}(y_i) = max_j { ln(y_i − y_j^{1/α}) + β V_n(y_j) } over feasible j, until the sup change is below 1e-8.\n- Read the policy off the argmax: c = y_i − y_j^{1/α}.\n- Implementation: `out/analysis.py`, vectorised.\n\n## Results\n| quantity | closed form | VFI |\n|---|---|---|\n| c(0.5) | 0.329 (`c_closed_y05`) | 0.32882 (`c_num_y05`) |\n| c(1.0) | 0.658 (`c_closed_y1`) | 0.65899 (`c_num_y1`) |\n| c(2.0) | 1.316 (`c_closed_y2`) | 1.30963 (`c_num_y2`) |\n| V(1) | −19.52441 (`value_closed_y1`) | −19.52476 (`value_num_y1`) |\n\n- Maximum absolute policy error over the three points: 0.00637 (`max_abs_error_policy`). It occurs at y = 2, about 0.5% of consumption.\n- Savings rate implied by the closed form: αβ = 0.342 (`savings_rate_closed_form`, also stored as `baseline_savings_rate`).\n- Contraction modulus: 0.95 (`contraction_modulus`).\n- VFI converged in 361 iterations (`n_iterations`), with a final sup change of 9.997e-9 (`final_sup_change`).\n- Diagnostics:\n  - Largest policy error at any grid node: 0.0251 (`diagnostics.max_abs_error_policy_on_grid`), at high y.\n  - Largest value error at any grid node: 4.8e-4 (`diagnostics.max_abs_error_value_on_grid`).\n\n## Uncertainty\nThe model is deterministic, so there is no sampling uncertainty. The numerical error has two sources:\n1. **Iteration truncation.** It is bounded by β/(1 − β) × final sup change ≈ 1.9e-7 utils (`diagnostics.vfi_error_bound_beta_over_1mbeta_times_sup`). This is negligible.\n2. **Discretisation.** This is the dominant source.\n   - The chosen y′ can be off by up to half a log step (Δ ln y = 0.0115, `diagnostics.grid_log_step`).\n   - Because k = y′^{1/α}, a small error in y′ becomes an error of roughly (k/α)·Δ ln y′ in consumption. That error grows with y, which is why the policy error is largest at y = 2 and at the top of the grid.\n   - The policy error is first order in grid spacing. The value error is much smaller (second order, by the envelope theorem).\n   - Interpolating the policy between nodes adds a little more error.\n\n## Limitations and open issues\n- The validation covers one parameter point (α = 0.36, β = 0.95), one grid (400 log-spaced points on [0.05, 5]) and one tolerance (1e-8). I have not shown how the error shrinks as the grid is refined.\n- The discrete-choice VFI policy is a step function. A finer grid, or continuous optimisation of the control, would reduce the policy error. I did not do either, because the task prescribes this grid.\n- The contraction argument as stated applies to the bounded (truncated-grid) problem.\n- All required outputs were produced (`feasibility` = \"complete\").\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The closed-form policy is c(y)=(1-alpha*beta)y, giving c=0.329, 0.658, 1.316 at y=0.5, 1, 2 and a savings rate alpha*beta=0.342.\",\"results_keys\":[\"c_closed_y05\",\"c_closed_y1\",\"c_closed_y2\",\"savings_rate_closed_form\"],\"status\":\"supported\",\"caveat\":\"Requires log utility, Cobb-Douglas technology, full depreciation and an interior solution.\"},\n {\"id\":\"C2\",\"text\":\"VFI on the prescribed 400-point log grid reproduces the closed-form policy at the evaluation points to within 0.0064 (max abs error, at y=2).\",\"results_keys\":[\"c_num_y05\",\"c_num_y1\",\"c_num_y2\",\"max_abs_error_policy\"],\"status\":\"supported\",\"caveat\":\"Error comes from discretising the control on the grid and grows with y; single grid and parameter point.\"},\n {\"id\":\"C3\",\"text\":\"The VFI value at y=1 (-19.52476) matches the closed form (-19.52441) to about 3.4e-4 utils.\",\"results_keys\":[\"value_num_y1\",\"value_closed_y1\"],\"status\":\"supported\",\"caveat\":\"Interpolated in ln y; 1.0 is not a grid node.\"},\n {\"id\":\"C4\",\"text\":\"The Bellman operator is a sup-norm contraction with modulus beta=0.95; VFI met the 1e-8 tolerance after 361 iterations.\",\"results_keys\":[\"contraction_modulus\",\"n_iterations\",\"final_sup_change\"],\"status\":\"supported\",\"caveat\":\"The Blackwell argument applies to the bounded truncated-grid problem; log utility is unbounded on the full domain.\"}\n]\nEOF\ncat > out/state/phases.json <<'EOF'\n{\n \"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully; contract.md written with estimands, outputs, rules\"],\"notes\":\"\"},\n \"P1\":{\"status\":\"passed\",\"checks\":[\"SHA-256 matches bundle.json\",\"10 rows, no missing/duplicates\",\"eval points inside grid\",\"exclusion ledger: 0 removed\"],\"notes\":\"no availability violations\"},\n \"P2\":{\"status\":\"passed\",\"checks\":[\"baseline closed-form savings rate 0.342 recorded (savings_rate_closed_form, baseline_savings_rate)\"],\"notes\":\"\"},\n \"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py reads only data/, deterministic, no seed needed\",\"VFI converged 361 iterations\"],\"notes\":\"\"},\n \"P4\":{\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical results.json\",\"11 consistency checks PASS (see checks.md)\"],\"notes\":\"\"},\n \"P5\":{\"status\":\"passed\",\"checks\":[\"report.md has 6 required sections with key citations\",\"claims.json 4 claims all mapped to keys\"],\"notes\":\"\"}\n}\nEOF\ncat >> out/state/log.md <<'EOF'\n- 2026-10-30 P1 passed: data audit; hash verified; no exclusions.\n- 2026-10-30 P2 passed: baseline closed-form savings rate alpha*beta.\n- 2026-10-30 P3 passed: discrete-choice VFI (control y' on grid), linear interpolation in ln y at eval points; decision recorded in data_issues.\n- 2026-10-30 P4 passed: reproducible re-run, all checks PASS.\n- 2026-10-30 P5 passed: report and claims written. Task complete.\nEOF\nls out out/state","description":"Write report, claims, 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":1373,"cache_read_input_tokens":11573,"output_tokens":3688,"output_tokens_details":{"thinking_tokens":87},"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":1373},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXoadHYpWC1rqoPW8XhH","requestRef":"6e9e7248-f842-4cfd-be44-822a654200f3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"f96ae8dd-d814-4da1-977c-48fa8ed4a28b","timestamp":"2026-10-30T04:39:04.841Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}47{"parentUuid":"f96ae8dd-d814-4da1-977c-48fa8ed4a28b","isSidechain":false,"promptId":"d9e40f02-b150-4304-95c6-b81a056882bd","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01VdR93wsrreTYbSmD1veXoC","type":"tool_result","content":"out:\nanalysis.py\nclaims.json\nexclusions.csv\nreport.md\nresults.json\nstate\n\nout/state:\nchecks.md\ncontract.md\ndata_audit.md\nlog.md\nphases.json","is_error":false}]},"uuid":"5cb1c001-1189-4ce7-95e4-8c15653ac0ad","timestamp":"2026-10-30T04:39:04.910Z","toolUseResult":{"stdout":"out:\nanalysis.py\nclaims.json\nexclusions.csv\nreport.md\nresults.json\nstate\n\nout/state:\nchecks.md\ncontract.md\ndata_audit.md\nlog.md\nphases.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"f96ae8dd-d814-4da1-977c-48fa8ed4a28b","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0128","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","version":"2.1.314","gitBranch":"HEAD"}48{"type":"api-request-blob","sessionId":"5638f446-608b-4c7d-b6a6-50df51e080c3","hash":"c4983cf0032566c04da07e7ae65b9a3dbaf2b1653064677fcff09cdacd9e4345","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"All checks pass. Next I'll write the report, claims and final state."},{"type":"tool_use","id":"toolu_01VdR93wsrreTYbSmD1veXoC","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-conf-04 — VFI vs closed-form policy, optimal growth with log utility\n\n## Question\nA planner maximises Σ β^t ln c_t subject to y_{t+1} = (y_t − c_t)^α. This report compares the closed-form optimal consumption policy and value function with the ones obtained by value-function iteration (VFI) on the prescribed grid. The parameter point is α = 0.36, β = 0.95.\n\n## Data and exclusions\n- The only input is `data/model.csv`: 10 parameter rows (`n_input_rows`). Its SHA-256 matches the bundle.\n- No rows were excluded (`out/exclusions.csv`).\n- Grid: 400 points equally spaced in ln y on [0.05, 5] (`grid_points_used`, `n_analysed`). VFI stopping tolerance: 1e-8 in the sup norm.\n- Design notes, recorded in `data_issues`:\n  1. The evaluation points 0.5, 1.0 and 2.0 are not grid nodes. VFI policy and value are therefore interpolated linearly in ln y between neighbouring nodes.\n  2. The control (next-period output y′) is restricted to the same grid. This is standard discrete VFI, with no off-grid optimisation.\n- No random numbers are used (`random_seed` = null).\n\n## Method\n**Closed form (guess and verify).** Assumptions: log utility, Cobb–Douglas technology y′ = k^α with productivity 1, full depreciation, 0 < α < 1, 0 < β < 1, and an interior solution 0 < c < y.\n- Guess V(y) = A + B ln y. The Bellman right-hand side becomes ln c + β(A + Bα ln(y − c)).\n- The first-order condition 1/c = αβB/(y − c) gives c = y/(1 + αβB).\n- Matching the coefficients on ln y gives B = 1 + αβB, so B = 1/(1 − αβ).\n- Policy: **c(y) = (1 − αβ) y**. Savings rate: **(y − c)/y = αβ**.\n- Constant: **A = [ln(1 − αβ) + (αβ/(1 − αβ)) ln(αβ)] / (1 − β)**.\n- I also checked numerically that this V satisfies the Bellman equation, by brute-force continuous maximisation at y ∈ {0.1, 0.5, 1, 2, 4} (`out/state/checks.md`).\n\n**Contraction.** The Bellman operator T is monotone (v ≤ w implies Tv ≤ Tw) and discounts (T(v + a) = Tv + βa). By Blackwell's sufficient conditions it is a contraction in the sup norm with modulus β.\n- This argument applies on the bounded grid problem: the state space is compact, and at every node there is a feasible choice with c bounded away from 0, so the return is bounded. The infinite-domain log-utility problem has unbounded returns, so there the argument needs a weighted-norm extension or the closed-form verification instead.\n- As a check, the optimal y′ = (αβy)^α maps [0.05, 5] into roughly [0.23, 1.21]. The grid truncation therefore never binds (VFI choice indices stay between 133 and 399 − 123).\n\n**VFI.**\n- Start from V₀ = 0 and iterate V_{n+1}(y_i) = max_j { ln(y_i − y_j^{1/α}) + β V_n(y_j) } over feasible j, until the sup change is below 1e-8.\n- Read the policy off the argmax: c = y_i − y_j^{1/α}.\n- Implementation: `out/analysis.py`, vectorised.\n\n## Results\n| quantity | closed form | VFI |\n|---|---|---|\n| c(0.5) | 0.329 (`c_closed_y05`) | 0.32882 (`c_num_y05`) |\n| c(1.0) | 0.658 (`c_closed_y1`) | 0.65899 (`c_num_y1`) |\n| c(2.0) | 1.316 (`c_closed_y2`) | 1.30963 (`c_num_y2`) |\n| V(1) | −19.52441 (`value_closed_y1`) | −19.52476 (`value_num_y1`) |\n\n- Maximum absolute policy error over the three points: 0.00637 (`max_abs_error_policy`). It occurs at y = 2, about 0.5% of consumption.\n- Savings rate implied by the closed form: αβ = 0.342 (`savings_rate_closed_form`, also stored as `baseline_savings_rate`).\n- Contraction modulus: 0.95 (`contraction_modulus`).\n- VFI converged in 361 iterations (`n_iterations`), with a final sup change of 9.997e-9 (`final_sup_change`).\n- Diagnostics:\n  - Largest policy error at any grid node: 0.0251 (`diagnostics.max_abs_error_policy_on_grid`), at high y.\n  - Largest value error at any grid node: 4.8e-4 (`diagnostics.max_abs_error_value_on_grid`).\n\n## Uncertainty\nThe model is deterministic, so there is no sampling uncertainty. The numerical error has two sources:\n1. **Iteration truncation.** It is bounded by β/(1 − β) × final sup change ≈ 1.9e-7 utils (`diagnostics.vfi_error_bound_beta_over_1mbeta_times_sup`). This is negligible.\n2. **Discretisation.** This is the dominant source.\n   - The chosen y′ can be off by up to half a log step (Δ ln y = 0.0115, `diagnostics.grid_log_step`).\n   - Because k = y′^{1/α}, a small error in y′ becomes an error of roughly (k/α)·Δ ln y′ in consumption. That error grows with y, which is why the policy error is largest at y = 2 and at the top of the grid.\n   - The policy error is first order in grid spacing. The value error is much smaller (second order, by the envelope theorem).\n   - Interpolating the policy between nodes adds a little more error.\n\n## Limitations and open issues\n- The validation covers one parameter point (α = 0.36, β = 0.95), one grid (400 log-spaced points on [0.05, 5]) and one tolerance (1e-8). I have not shown how the error shrinks as the grid is refined.\n- The discrete-choice VFI policy is a step function. A finer grid, or continuous optimisation of the control, would reduce the policy error. I did not do either, because the task prescribes this grid.\n- The contraction argument as stated applies to the bounded (truncated-grid) problem.\n- All required outputs were produced (`feasibility` = \"complete\").\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The closed-form policy is c(y)=(1-alpha*beta)y, giving c=0.329, 0.658, 1.316 at y=0.5, 1, 2 and a savings rate alpha*beta=0.342.\",\"results_keys\":[\"c_closed_y05\",\"c_closed_y1\",\"c_closed_y2\",\"savings_rate_closed_form\"],\"status\":\"supported\",\"caveat\":\"Requires log utility, Cobb-Douglas technology, full depreciation and an interior solution.\"},\n {\"id\":\"C2\",\"text\":\"VFI on the prescribed 400-point log grid reproduces the closed-form policy at the evaluation points to within 0.0064 (max abs error, at y=2).\",\"results_keys\":[\"c_num_y05\",\"c_num_y1\",\"c_num_y2\",\"max_abs_error_policy\"],\"status\":\"supported\",\"caveat\":\"Error comes from discretising the control on the grid and grows with y; single grid and parameter point.\"},\n {\"id\":\"C3\",\"text\":\"The VFI value at y=1 (-19.52476) matches the closed form (-19.52441) to about 3.4e-4 utils.\",\"results_keys\":[\"value_num_y1\",\"value_closed_y1\"],\"status\":\"supported\",\"caveat\":\"Interpolated in ln y; 1.0 is not a grid node.\"},\n {\"id\":\"C4\",\"text\":\"The Bellman operator is a sup-norm contraction with modulus beta=0.95; VFI met the 1e-8 tolerance after 361 iterations.\",\"results_keys\":[\"contraction_modulus\",\"n_iterations\",\"final_sup_change\"],\"status\":\"supported\",\"caveat\":\"The Blackwell argument applies to the bounded truncated-grid problem; log utility is unbounded on the full domain.\"}\n]\nEOF\ncat > out/state/phases.json <<'EOF'\n{\n \"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully; contract.md written with estimands, outputs, rules\"],\"notes\":\"\"},\n \"P1\":{\"status\":\"passed\",\"checks\":[\"SHA-256 matches bundle.json\",\"10 rows, no missing/duplicates\",\"eval points inside grid\",\"exclusion ledger: 0 removed\"],\"notes\":\"no availability violations\"},\n \"P2\":{\"status\":\"passed\",\"checks\":[\"baseline closed-form savings rate 0.342 recorded (savings_rate_closed_form, baseline_savings_rate)\"],\"notes\":\"\"},\n \"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py reads only data/, deterministic, no seed needed\",\"VFI converged 361 iterations\"],\"notes\":\"\"},\n \"P4\":{\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical results.json\",\"11 consistency checks PASS (see checks.md)\"],\"notes\":\"\"},\n \"P5\":{\"status\":\"passed\",\"checks\":[\"report.md has 6 required sections with key citations\",\"claims.json 4 claims all mapped to keys\"],\"notes\":\"\"}\n}\nEOF\ncat >> out/state/log.md <<'EOF'\n- 2026-10-30 P1 passed: data audit; hash verified; no exclusions.\n- 2026-10-30 P2 passed: baseline closed-form savings rate alpha*beta.\n- 2026-10-30 P3 passed: discrete-choice VFI (control y' on grid), linear interpolation in ln y at eval points; decision recorded in data_issues.\n- 2026-10-30 P4 passed: reproducible re-run, all checks PASS.\n- 2026-10-30 P5 passed: report and claims written. 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The two match closely. Re-running `out/analysis.py` from a clean state gives an identical `out/results.json`, and all 11 consistency checks passed.\n\n**Closed form**, found by guessing V(y) = A + B ln y and verifying it in the Bellman equation:\n- Consumption is c(y) = (1−αβ)y, so the savings rate is αβ = 0.342.\n- The value function has B = 1/(1−αβ) and A = [ln(1−αβ) + (αβ/(1−αβ)) ln(αβ)]/(1−β).\n- This holds under log utility, Cobb–Douglas technology, full depreciation and an interior solution.\n\n**VFI against closed form** (α = 0.36, β = 0.95, 400 points evenly spaced in ln y on [0.05, 5]):\n\n| | closed form | VFI |\n|---|---|---|\n| c(0.5) | 0.329 | 0.32882 |\n| c(1.0) | 0.658 | 0.65899 |\n| c(2.0) | 1.316 | 1.30963 |\n| V(1) | −19.52441 | −19.52476 |\n\n- **Largest policy error:** 0.0064, at y = 2 (about 0.5% of consumption). 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