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1{"type":"atis-latch","atis":"","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a"}2{"type":"queue-operation","operation":"enqueue","timestamp":"2026-10-30T04:37:38.846Z","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","content":"Begin"}3{"type":"queue-operation","operation":"dequeue","timestamp":"2026-10-30T04:37:38.853Z","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a"}4{"parentUuid":null,"isSidechain":false,"promptId":"5e5f89b6-9097-4581-beb4-9f594e0311cb","type":"user","message":{"role":"user","content":"Begin"},"uuid":"7cbd9ff4-f775-4f71-a6cb-afa851f71f2d","timestamp":"2026-10-30T04:37:38.858Z","permissionMode":"default","promptSource":"sdk","turnOrigin":"sdk","turnPosition":{"promptIndex":0,"turnIndex":1},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}5{"type":"api-request-shape","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","shapeHash":"9ceecb5141a3f1ecdb407a5cfd6f6d6f1a3c9481250e80a9eb800ca10dfd7ee1","timestamp":"2026-10-30T04:37:38.873Z","version":"2.1.314","shape":{"system":[{"type":"text","text":"You are Claude Code, Anthropic's official CLI for Claude, running within the Claude Agent SDK."},{"type":"text","text":"CWD: /Users/simon-pierreboucher/wp29/runs/RC0129\nDate: 2026-10-30\n\nYou are a research assistant executing one bounded scientific task inside the current working directory, which is your workspace.\n\nEnvironment facts (identical for every task):\n- The task statement is the file `TASK.md` in the workspace. It is the complete and only authoritative description of what is required: the scientific question, the inputs under `data/`, the required output files and their exact keys, and the information-availability rules.\n- There is no network access. Use the Python interpreter `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels, matplotlib are installed). Standard shell tools are available. Do not try to install packages.\n- Write every deliverable under `./out/`. The required deliverables are listed in `TASK.md`; at minimum they always include `out/results.json`, `out/report.md`, and a replication entry point `out/analysis.py` that regenerates `out/results.json` from `data/` when run with `~/wp29/venv/bin/python out/analysis.py` from the workspace root.\n- You are working alone and unattended; nobody will answer questions. Make reasonable, documented decisions.\n\nIntegrity rules (identical for every task):\n- Never fabricate numbers, data, results, or references. Every number in `out/results.json` and `out/report.md` must be produced by code you ran on the provided inputs.\n- Respect the information-availability rules in `TASK.md` exactly (for example, never use information that would not have been available at the stated decision time).\n- If part of the task cannot be completed as specified, say so explicitly in `out/report.md`, explain why, and still write every required file (use `null` for values you could not legitimately produce). An honest statement of a limitation is always preferred to a fabricated or guessed value.\n- Do not modify anything under `data/`.\n- When you are done, end with a brief plain-text summary of what you produced and any limitations.\n\nComplete the task described in `TASK.md` by following this research protocol. The protocol adds no scientific information to the task; it organizes how you work and what evidence you leave behind.\n\nPHASES (execute in order; a phase is eligible only when its dependencies are satisfied):\n\nP0 Scope and contract (depends on: nothing)\n- Read `TASK.md` completely. In `out/state/contract.md`, restate in your own words: the scientific question; the quantity or quantities to be estimated (the estimands) and the assumptions under which they are meaningful; every required output file and key; the information-availability rules; what would make the task impossible or the result invalid.\n- Write the initial phase ledger `out/state/phases.json`: a JSON object mapping each phase id (P0 … P5) to {\"status\": \"pending\"|\"running\"|\"passed\"|\"failed\"|\"blocked\"|\"stale\"|\"skipped_optional\", \"checks\": [], \"notes\": \"\"}. Keep it current as you work. A phase may only be set to \"passed\" when the checks listed for it in this protocol have actually been executed and their outcome recorded in \"checks\".\n\nP1 Data audit and provenance (depends on: P0)\n- Inspect every input file: compute and record its SHA-256, row and column counts, schema, units, date ranges, missing values, duplicates and anomalies in `out/state/data_audit.md`.\n- Keep an exclusion ledger in `out/exclusions.csv` (columns: step, rule, n_before, n_after, n_removed, rationale) for every filtering step you apply, so that n_raw − total removed = n_analysed.\n- Identify any input that violates the information-availability rules and decide, in writing, how you will handle it.\n\nP2 Baseline (depends on: P1)\n- Before any elaborate method, compute the simplest valid baseline that answers the question (for example a naïve or unconditional estimate), with the same evaluation rule used later. Record it in `out/results.json` under the keys the task requires, or under `baseline_*` keys when the task does not name them.\n\nP3 Method and computation (depends on: P2)\n- Implement the analysis in `out/analysis.py` so that it reads only `data/`, writes `out/results.json` deterministically (fix every random seed you use and record it), and prints nothing that contradicts the written results. Any figure or table must be generated by this script.\n\nP4 Verification (depends on: P3)\n- Re-run `out/analysis.py` from a clean state and confirm it regenerates `out/results.json` with identical values. Record the check in `out/state/phases.json` under P4.\n- Check internal consistency: identities that must hold (for example counts that must add up, standard errors that must be positive, confidence intervals that must contain their estimates, date orderings that must respect the information rules), units, and magnitudes against the baseline. Record every check and its outcome in `out/state/checks.md`. A failed check must be fixed or honestly reported, never silently ignored.\n\nP5 Reporting (depends on: P4)\n- Write `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. Every quantitative statement must cite the key of `out/results.json` it comes from.\n- Write `out/claims.json`: a list of the central claims of your report, each as {\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}. Do not state a claim in the report that is not in this ledger.\n- Set the final statuses in `out/state/phases.json`.\n\nSTOPPING RULES\n- Stop and declare the task complete only when every phase P0–P5 is \"passed\" with recorded checks. If a phase is \"blocked\" (missing information, impossible requirement, violated availability rule), stop, set the status, explain in `out/report.md` (section Limitations and open issues) and still write every required file with `null` for values you could not legitimately produce.\n- Do not spend effort on extensions that the task does not require.\n\nRECOVERY RULES\n- Append a short dated entry to `out/state/log.md` after each phase transition and after any important decision, so that work can be resumed by reading `out/state/`.\n- If you discover that an upstream input or decision changed after a downstream phase passed, mark the downstream phases \"stale\" and redo them; do not reuse stale results.\n- If you are interrupted and later resumed, first read `out/state/` and continue from the last consistent state; never re-run expensive steps that already have recorded, unchanged outputs.\n\nEXECUTABLE GATES (additional, mandatory)\n- A read-only gate program is provided at `~/wp29/gates/pgar_gate.py`. Run it from the workspace root as `~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .` It checks the output contract of `TASK.md` (required files, keys, types, finite values, report sections, the claims ledger, the phase ledger, the exclusion ledger) and reproducibility (it re-runs `out/analysis.py` in a temporary copy and compares the regenerated `out/results.json` with yours). It never checks scientific correctness and it contains no reference answers.\n- You must run the gate at the end of P4 and again at the end of P5, and record each run's receipt (the gate writes `out/state/gate_receipts/<timestamp>.json`) in `out/state/phases.json`. You may not declare the task complete while the latest gate receipt reports `\"passed\": false`. Fix the reported problems and re-run the gate.\n- The controller will run the same gate after your session ends. If it fails, you will be resumed with the gate output and asked to fix the problems; each such cycle consumes your remaining budget.\n\nSEPARATE REVIEW (additional)\n- After the gate passes, a separate reviewer session that has not seen your work in progress will examine `TASK.md` and everything under `out/` and may return a list of issues (file `out/review/review.json`). You will then be resumed once to address them: fix what is justified, explain in `out/report.md` (Limitations and open issues) what you disagree with, re-run the gate, and update `out/claims.json` and `out/state/phases.json`. The reviewer has no reference answers; its role is to challenge unsupported claims, violated information rules, unverified computations, and inconsistencies between your report and your results.\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/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a"}12{"parentUuid":"809d0d86-21c1-4c14-81a7-58b834254736","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoWpbqBKKdb8ksiTYs7","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":2811,"cache_read_input_tokens":1504,"output_tokens":146,"output_tokens_details":{"thinking_tokens":23},"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":2811},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":424,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXoWpKTSCp2B4u84H4bT","requestRef":"6265c590-c5e8-4362-b53d-a78b424313a7","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"63140303-b28a-43cb-b774-146486258eb7","timestamp":"2026-10-30T04:37:41.526Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"63140303-b28a-43cb-b774-146486258eb7","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoWpbqBKKdb8ksiTYs7","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_012qfSCNbdshwFkqLqqVeCzw","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_012qfSCNbdshwFkqLqqVeCzw"}]},"uuid":"c861f6d6-eb2c-4655-8c32-7c3a8148c5ed","timestamp":"2026-10-30T04:37:42.205Z","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). 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 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 },\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\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"c_num_y2\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"max_abs_error_policy\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"value_closed_y1\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"value_num_y1\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"savings_rate_closed_form\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"contraction_modulus\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    },\n    \"final_sup_change\": {\n      \"type\": \"number\",\n      \"nullable\": false\n    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Compare the closed-form\npolicy/value with those obtained by discrete value-function iteration (VFI) on a prescribed log-spaced grid.\n\n**Estimands.** Closed-form c(y) at y=0.5,1,2; VFI c(y) at the same points (interpolated if off-grid); max |c_num-c_closed|\nover the 3 points; closed-form V(1) and VFI V(1); closed-form savings rate (alpha*beta); contraction modulus of the Bellman\noperator in sup norm (beta, via Blackwell, on the bounded/compact grid problem). Meaningful under: log utility,\nCobb–Douglas technology, full depreciation, interior optimum, 0<alpha<1, 0<beta<1.\n\n**Outputs.** out/results.json with keys task_id, c_closed_y05, c_closed_y1, c_closed_y2, c_num_y05, c_num_y1, c_num_y2,\nmax_abs_error_policy, value_closed_y1, value_num_y1, savings_rate_closed_form, contraction_modulus, grid_points_used,\nn_iterations, final_sup_change, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed;\nout/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues);\nout/analysis.py; out/claims.json; plus protocol files (out/state/*, out/exclusions.csv).\n\n**Information rules.** Use only data/model.csv; prescribed grid/parameters (deviations -> data_issues). 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-p out/state && cat > out/state/contract.md <<'EOF'\n# Contract (P0)\n**Question.** Brock–Mirman optimal growth with log utility, y' = (y-c)^alpha, full depreciation, A=1. Compare the closed-form\npolicy/value with those obtained by discrete value-function iteration (VFI) on a prescribed log-spaced grid.\n\n**Estimands.** Closed-form c(y) at y=0.5,1,2; VFI c(y) at the same points (interpolated if off-grid); max |c_num-c_closed|\nover the 3 points; closed-form V(1) and VFI V(1); closed-form savings rate (alpha*beta); contraction modulus of the Bellman\noperator in sup norm (beta, via Blackwell, on the bounded/compact grid problem). Meaningful under: log utility,\nCobb–Douglas technology, full depreciation, interior optimum, 0<alpha<1, 0<beta<1.\n\n**Outputs.** out/results.json with keys task_id, c_closed_y05, c_closed_y1, c_closed_y2, c_num_y05, c_num_y1, c_num_y2,\nmax_abs_error_policy, value_closed_y1, value_num_y1, savings_rate_closed_form, contraction_modulus, grid_points_used,\nn_iterations, final_sup_change, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed;\nout/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues);\nout/analysis.py; out/claims.json; plus protocol files (out/state/*, out/exclusions.csv).\n\n**Information rules.** Use only data/model.csv; prescribed grid/parameters (deviations -> data_issues). 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> 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\nReads only data/model.csv; deterministic (no randomness).\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\ndf = pd.read_csv(os.path.join(ROOT, \"data\", \"model.csv\"))\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\"])]\ndata_issues = []\nassert spacing == \"log\"\nassert 0 < alpha < 1 and 0 < beta < 1\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 / (1.0 - ab)) * 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  # (y - c)/y\n\n# ---------------- VFI on the prescribed grid (discrete choice of next-period y on the grid) ----\ngrid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))\nk_needed = grid ** (1.0 / alpha)           # investment needed to reach y' = grid[j]\nC = grid[:, None] - k_needed[None, :]       # consumption for (y_i, y'_j)\nfeasible = C > 0\nU = np.full(C.shape, -np.inf)\nU[feasible] = np.log(C[feasible])\nn_infeasible_pairs = int((~feasible).sum())\n\nV = np.zeros(N)\nn_iter = 0\nsup_change = np.inf\nmax_iter = 100000\nwhile sup_change >= tol and n_iter < max_iter:\n    V_new = np.max(U + beta * V[None, :], axis=1)\n    sup_change = float(np.max(np.abs(V_new - V)))\n    V = V_new\n    n_iter += 1\nconverged = sup_change < tol\npol_idx = np.argmax(U + beta * V[None, :], axis=1)\nc_pol = grid - k_needed[pol_idx]\nbound_hits = int(np.sum((pol_idx == 0) | (pol_idx == N - 1)))\nif bound_hits:\n    data_issues.append({\"issue\": f\"policy hits grid bound at {bound_hits} nodes\",\n                        \"handling\": \"reported; results at such nodes may be distorted by truncation\"})\n\n# interpolation at evaluation points: linear in ln y (grid is uniform in ln y)\nlg = np.log(grid)\ndef interp(vals, y):\n    assert y_min <= y <= y_max\n    return float(np.interp(np.log(y), lg, vals))\non_node = [bool(np.min(np.abs(lg - np.log(y))) < 1e-12) for y in evals]\n\nc_num = [interp(c_pol, y) for y in evals]\nc_cf = [float(c_closed(y)) for y in evals]\nmax_err = float(max(abs(a - b) for a, b in zip(c_num, c_cf)))\nV_num_1 = interp(V, 1.0)\n\n# diagnostics (not required keys; printed only)\nerr_grid_c = float(np.max(np.abs(c_pol - c_closed(grid))))\nerr_grid_V = float(np.max(np.abs(V - V_closed(grid))))\nprint(f\"grid step in ln y = {lg[1]-lg[0]:.6f}; eval points on nodes: {on_node}\")\nprint(f\"VFI iterations={n_iter}, final sup change={sup_change:.3e}, converged={converged}\")\nprint(f\"policy bound hits={bound_hits}; infeasible (y,y') pairs={n_infeasible_pairs}\")\nprint(f\"max |c_vfi - c_closed| over all grid nodes = {err_grid_c:.3e}; max |V_vfi - V_closed| = {err_grid_V:.3e}\")\n\nif not all(on_node):\n    pass  # interpolation is allowed by TASK.md; documented in report\n\nres = {\n    \"task_id\": \"F5-conf-04\",\n    \"c_closed_y05\": c_cf[0], \"c_closed_y1\": c_cf[1], \"c_closed_y2\": c_cf[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)),\n    \"value_num_y1\": V_num_1,\n    \"savings_rate_closed_form\": float(savings_rate),\n    \"contraction_modulus\": beta,\n    \"grid_points_used\": int(N),\n    \"n_iterations\": int(n_iter),\n    \"final_sup_change\": float(sup_change),\n    \"feasibility\": \"complete\" if converged else \"partial\",\n    \"feasibility_reason\": None if converged else \"VFI did not reach tolerance within max_iter\",\n    \"data_issues\": data_issues,\n    \"n_input_rows\": {\"model.csv\": int(len(df))},\n    \"n_analysed\": int(N),\n    \"random_seed\": None,\n    \"diagnostics\": {\n        \"grid_step_log_y\": float(lg[1] - lg[0]),\n        \"eval_points_on_grid_nodes\": on_node,\n        \"policy_grid_bound_hits\": bound_hits,\n        \"max_abs_policy_error_all_nodes\": err_grid_c,\n        \"max_abs_value_error_all_nodes\": err_grid_V,\n        \"initial_guess\": \"V0 = 0\",\n        \"choice_variable\": \"next-period output y' restricted to grid\",\n        \"interpolation\": \"linear in ln y\",\n    },\n}\nos.makedirs(os.path.join(ROOT, \"out\"), exist_ok=True)\nwith open(os.path.join(ROOT, \"out\", \"results.json\"), \"w\") as f:\n    json.dump(res, f, indent=2)\nprint(json.dumps({k: v for k, v in res.items() if k != \"diagnostics\"}, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis script"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2156,"cache_read_input_tokens":7903,"output_tokens":2398,"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":2156},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXoYhL5afqVvemRTPESw","requestRef":"173b5cba-0c55-4923-8ab8-7c9e62d2b0c8","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"c2c76e5d-7de9-4fde-b0a9-b5d94ec38d57","timestamp":"2026-10-30T04:38:24.799Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}36{"parentUuid":"c2c76e5d-7de9-4fde-b0a9-b5d94ec38d57","isSidechain":false,"promptId":"5e5f89b6-9097-4581-beb4-9f594e0311cb","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01YJstfpAd4MM3SqYPrbcibf","type":"tool_result","content":"grid step in ln y = 0.011542; eval points on nodes: [False, False, False]\nVFI iterations=361, final sup change=9.997e-09, converged=True\npolicy bound hits=0; infeasible (y,y') pairs=64632\nmax |c_vfi - c_closed| over all grid nodes = 2.512e-02; max |V_vfi - V_closed| = 4.835e-04\n{\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  \"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  \"data_issues\": [],\n  \"n_input_rows\": {\n    \"model.csv\": 10\n  },\n  \"n_analysed\": 400,\n  \"random_seed\": null\n}","is_error":false}]},"uuid":"0ddca5d0-2ced-47cf-abbd-5b34e0250863","timestamp":"2026-10-30T04:38:25.124Z","toolUseResult":{"stdout":"grid step in ln y = 0.011542; eval points on nodes: [False, False, False]\nVFI iterations=361, final sup change=9.997e-09, converged=True\npolicy bound hits=0; infeasible (y,y') pairs=64632\nmax |c_vfi - c_closed| over all grid nodes = 2.512e-02; max |V_vfi - V_closed| = 4.835e-04\n{\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  \"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  \"data_issues\": [],\n  \"n_input_rows\": {\n    \"model.csv\": 10\n  },\n  \"n_analysed\": 400,\n  \"random_seed\": null\n}","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"c2c76e5d-7de9-4fde-b0a9-b5d94ec38d57","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}37{"type":"api-request-blob","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","hash":"babc2bce97bbbe03089e99f44bc7ada315028134973a620917de9fd4fdd6a36b","message":{"role":"assistant","content":[{"type":"text","text":"Now the analysis script."},{"type":"tool_use","id":"toolu_01YJstfpAd4MM3SqYPrbcibf","name":"Bash","input":{"command":"cat > 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\nReads only data/model.csv; deterministic (no randomness).\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\ndf = pd.read_csv(os.path.join(ROOT, \"data\", \"model.csv\"))\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\"])]\ndata_issues = []\nassert spacing == \"log\"\nassert 0 < alpha < 1 and 0 < beta < 1\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 / (1.0 - ab)) * 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  # (y - c)/y\n\n# ---------------- VFI on the prescribed grid (discrete choice of next-period y on the grid) ----\ngrid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))\nk_needed = grid ** (1.0 / alpha)           # investment needed to reach y' = grid[j]\nC = grid[:, None] - k_needed[None, :]       # consumption for (y_i, y'_j)\nfeasible = C > 0\nU = np.full(C.shape, -np.inf)\nU[feasible] = np.log(C[feasible])\nn_infeasible_pairs = int((~feasible).sum())\n\nV = np.zeros(N)\nn_iter = 0\nsup_change = np.inf\nmax_iter = 100000\nwhile sup_change >= tol and n_iter < max_iter:\n    V_new = np.max(U + beta * V[None, :], axis=1)\n    sup_change = float(np.max(np.abs(V_new - V)))\n    V = V_new\n    n_iter += 1\nconverged = sup_change < tol\npol_idx = np.argmax(U + beta * V[None, :], axis=1)\nc_pol = grid - k_needed[pol_idx]\nbound_hits = int(np.sum((pol_idx == 0) | (pol_idx == N - 1)))\nif bound_hits:\n    data_issues.append({\"issue\": f\"policy hits grid bound at {bound_hits} nodes\",\n                        \"handling\": \"reported; results at such nodes may be distorted by truncation\"})\n\n# interpolation at evaluation points: linear in ln y (grid is uniform in ln y)\nlg = np.log(grid)\ndef interp(vals, y):\n    assert y_min <= y <= y_max\n    return float(np.interp(np.log(y), lg, vals))\non_node = [bool(np.min(np.abs(lg - np.log(y))) < 1e-12) for y in evals]\n\nc_num = [interp(c_pol, y) for y in evals]\nc_cf = [float(c_closed(y)) for y in evals]\nmax_err = float(max(abs(a - b) for a, b in zip(c_num, c_cf)))\nV_num_1 = interp(V, 1.0)\n\n# diagnostics (not required keys; printed only)\nerr_grid_c = float(np.max(np.abs(c_pol - c_closed(grid))))\nerr_grid_V = float(np.max(np.abs(V - V_closed(grid))))\nprint(f\"grid step in ln y = {lg[1]-lg[0]:.6f}; eval points on nodes: {on_node}\")\nprint(f\"VFI iterations={n_iter}, final sup change={sup_change:.3e}, converged={converged}\")\nprint(f\"policy bound hits={bound_hits}; infeasible (y,y') pairs={n_infeasible_pairs}\")\nprint(f\"max |c_vfi - c_closed| over all grid nodes = {err_grid_c:.3e}; max |V_vfi - V_closed| = {err_grid_V:.3e}\")\n\nif not all(on_node):\n    pass  # interpolation is allowed by TASK.md; documented in report\n\nres = {\n    \"task_id\": \"F5-conf-04\",\n    \"c_closed_y05\": c_cf[0], \"c_closed_y1\": c_cf[1], \"c_closed_y2\": c_cf[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)),\n    \"value_num_y1\": V_num_1,\n    \"savings_rate_closed_form\": float(savings_rate),\n    \"contraction_modulus\": beta,\n    \"grid_points_used\": int(N),\n    \"n_iterations\": int(n_iter),\n    \"final_sup_change\": float(sup_change),\n    \"feasibility\": \"complete\" if converged else \"partial\",\n    \"feasibility_reason\": None if converged else \"VFI did not reach tolerance within max_iter\",\n    \"data_issues\": data_issues,\n    \"n_input_rows\": {\"model.csv\": int(len(df))},\n    \"n_analysed\": int(N),\n    \"random_seed\": None,\n    \"diagnostics\": {\n        \"grid_step_log_y\": float(lg[1] - lg[0]),\n        \"eval_points_on_grid_nodes\": on_node,\n        \"policy_grid_bound_hits\": bound_hits,\n        \"max_abs_policy_error_all_nodes\": err_grid_c,\n        \"max_abs_value_error_all_nodes\": err_grid_V,\n        \"initial_guess\": \"V0 = 0\",\n        \"choice_variable\": \"next-period output y' restricted to grid\",\n        \"interpolation\": \"linear in ln y\",\n    },\n}\nos.makedirs(os.path.join(ROOT, \"out\"), exist_ok=True)\nwith open(os.path.join(ROOT, \"out\", \"results.json\"), \"w\") as f:\n    json.dump(res, f, indent=2)\nprint(json.dumps({k: v for k, v in res.items() if k != \"diagnostics\"}, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis script"}}]}}38{"type":"api-request","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","id":"58169a52-9769-4cc4-b124-6ce026b8cff3","timestamp":"2026-10-30T04:38:25.128Z","version":"2.1.314","querySource":"sdk","shapeHash":"9ceecb5141a3f1ecdb407a5cfd6f6d6f1a3c9481250e80a9eb800ca10dfd7ee1","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":"173b5cba-0c55-4923-8ab8-7c9e62d2b0c8","keep":10,"tail":["babc2bce97bbbe03089e99f44bc7ada315028134973a620917de9fd4fdd6a36b","922f45f7b17e71e48bb71aad0047d6c4359351071c2a6dc93a12cd80da09a7cb"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",11,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"97604701c73b689af5b43220cd17d3dd13afa12dce9b999403728a5251e3beab"}39{"parentUuid":"0ddca5d0-2ced-47cf-abbd-5b34e0250863","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoa6oUoCdP7E3mxKcNv","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":2890,"cache_read_input_tokens":10059,"output_tokens":983,"output_tokens_details":{"thinking_tokens":177},"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":2890},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1715,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXoa6RffrFxUL7uYGyCL","requestRef":"58169a52-9769-4cc4-b124-6ce026b8cff3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"82574f4f-1f87-4259-859a-6122dc56f68a","timestamp":"2026-10-30T04:38:27.816Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}40{"parentUuid":"82574f4f-1f87-4259-859a-6122dc56f68a","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoa6oUoCdP7E3mxKcNv","type":"message","role":"assistant","content":[{"type":"text","text":"Converged; no grid-bound hits. Now audit, exclusions, checks."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2890,"cache_read_input_tokens":10059,"output_tokens":983,"output_tokens_details":{"thinking_tokens":177},"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":2890},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXoa6RffrFxUL7uYGyCL","requestRef":"58169a52-9769-4cc4-b124-6ce026b8cff3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"9c6c6e6d-26ce-4fa1-9a72-c743d354fa2c","timestamp":"2026-10-30T04:38:27.817Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}41{"parentUuid":"9c6c6e6d-26ce-4fa1-9a72-c743d354fa2c","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoa6oUoCdP7E3mxKcNv","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01B3Bxg2R4oaTsRNGUY7b42o","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n- File: data/model.csv, SHA-256 098123961451e4f9a2e76afdbc83aec78066fc713d0645659c09b77b1636195b (matches bundle.json).\n- 10 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,\n  eval points 0.5, 1.0, 2.0 (units of output). value column is mixed (string 'log'), parsed per parameter.\n- Anomalies: none. All eval points lie inside [y_min, y_max] but none is a grid node (ln-step 0.011542) -> linear\n  interpolation in ln y, as permitted by TASK.md.\n- Feasibility of grid: deterministic steady state y* = (alpha*beta)^(alpha/(1-alpha)) ~= 0.547 is inside the grid; the optimal\n  next-period y from y_min (0.231) and y_max (1.21) are interior, so the grid bounds should not bind (confirmed: 0 bound hits).\n- Some (y, y') pairs are infeasible (need investment >= y); they are assigned -inf utility, not removed from the grid.\n- Information-availability: theoretical parameters only, no violation. No exclusions applied.\nEOF\nprintf \"step,rule,n_before,n_after,n_removed,rationale\\n0,none (all parameter rows used; all 400 grid points analysed),10,10,0,no filtering needed for theoretical parameter file\\n\" > out/exclusions.csv\ncat > out/state/checks.md <<'EOF'\n# Checks\nEOF\necho \"- 2026-10-30 P1 passed: audit done, no exclusions. P2 baseline = closed form (savings rate alpha*beta). P3: analysis.py written, VFI converged in 361 iterations.\" >> out/state/log.md","description":"Write audit, exclusions, log"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2890,"cache_read_input_tokens":10059,"output_tokens":983,"output_tokens_details":{"thinking_tokens":177},"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":2890},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXoa6RffrFxUL7uYGyCL","requestRef":"58169a52-9769-4cc4-b124-6ce026b8cff3","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"8abde9a1-472d-4ddb-b9a2-cc37fce52847","timestamp":"2026-10-30T04:38:34.829Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}42{"parentUuid":"8abde9a1-472d-4ddb-b9a2-cc37fce52847","isSidechain":false,"promptId":"5e5f89b6-9097-4581-beb4-9f594e0311cb","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01B3Bxg2R4oaTsRNGUY7b42o","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"de7d4397-772e-4a96-a5ff-5b8468986de3","timestamp":"2026-10-30T04:38:34.883Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"8abde9a1-472d-4ddb-b9a2-cc37fce52847","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}43{"type":"api-request-blob","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","hash":"0243128454cc70ce20d613473f9689b15009929835410003c5a1b2402102af34","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"Converged; no grid-bound hits. Now audit, exclusions, checks."},{"type":"tool_use","id":"toolu_01B3Bxg2R4oaTsRNGUY7b42o","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n- File: data/model.csv, SHA-256 098123961451e4f9a2e76afdbc83aec78066fc713d0645659c09b77b1636195b (matches bundle.json).\n- 10 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,\n  eval points 0.5, 1.0, 2.0 (units of output). value column is mixed (string 'log'), parsed per parameter.\n- Anomalies: none. All eval points lie inside [y_min, y_max] but none is a grid node (ln-step 0.011542) -> linear\n  interpolation in ln y, as permitted by TASK.md.\n- Feasibility of grid: deterministic steady state y* = (alpha*beta)^(alpha/(1-alpha)) ~= 0.547 is inside the grid; the optimal\n  next-period y from y_min (0.231) and y_max (1.21) are interior, so the grid bounds should not bind (confirmed: 0 bound hits).\n- Some (y, y') pairs are infeasible (need investment >= y); they are assigned -inf utility, not removed from the grid.\n- Information-availability: theoretical parameters only, no violation. No exclusions applied.\nEOF\nprintf \"step,rule,n_before,n_after,n_removed,rationale\\n0,none (all parameter rows used; all 400 grid points analysed),10,10,0,no filtering needed for theoretical parameter file\\n\" > out/exclusions.csv\ncat > out/state/checks.md <<'EOF'\n# Checks\nEOF\necho \"- 2026-10-30 P1 passed: audit done, no exclusions. P2 baseline = closed form (savings rate alpha*beta). P3: analysis.py written, VFI converged in 361 iterations.\" >> out/state/log.md","description":"Write audit, exclusions, 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out/results.json /tmp/r1.json; ~/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,numpy as np\nr=json.load(open('out/results.json'))\na,b=0.36,0.95\n# verify Bellman closed form numerically: V(y) = max_c ln c + b V((y-c)^a)\nB=1/(1-a*b); A=r['value_closed_y1']\nV=lambda y:A+B*np.log(y)\nfrom scipy.optimize import minimize_scalar\nfor y in [0.5,1,2]:\n    o=minimize_scalar(lambda c:-(np.log(c)+b*V((y-c)**a)),bounds=(1e-9,y-1e-9),method='bounded',options={'xatol':1e-12})\n    print(y,'argmax',o.x,'closed',(1-a*b)*y,'TV-V',-o.fun-V(y))\nprint('max err recompute', max(abs(r[f'c_num_{k}']-r[f'c_closed_{k}']) for k in ['y05','y1','y2'])==r['max_abs_error_policy'])\nprint('savings 1-c/y', 1-r['c_closed_y1']/1.0)\nprint('stopping-rule V error bound', 1e-8*b/(1-b), 'observed |dV1|', abs(r['value_num_y1']-r['value_closed_y1']))\nprint('rel policy errs',[ (r[f'c_num_{k}']-r[f'c_closed_{k}'])/r[f'c_closed_{k}'] for k in ['y05','y1','y2']])\nEOF","description":"Reproducibility and consistency checks"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":998,"cache_read_input_tokens":12949,"output_tokens":672,"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":998},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXoapA9KT4i1aEk1hw82","requestRef":"88972b39-752c-4fb1-b8cd-04d31a592460","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"a0984660-d654-433c-809b-26c6ae856f51","timestamp":"2026-10-30T04:38:40.537Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}46{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"a0984660-d654-433c-809b-26c6ae856f51","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a"}47{"type":"atis-latch","atis":"","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a"}48{"parentUuid":"a0984660-d654-433c-809b-26c6ae856f51","isSidechain":false,"promptId":"5e5f89b6-9097-4581-beb4-9f594e0311cb","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01GFmfEv98uNzPVTygf6tmCf","type":"tool_result","content":"IDENTICAL\n0.5 argmax 0.32899998496004007 closed 0.329 TV-V 0.0\n1 argmax 0.6579999792181229 closed 0.658 TV-V 0.0\n2 argmax 1.3159999817971206 closed 1.316 TV-V 0.0\nmax err recompute True\nsavings 1-c/y 0.34199999999999997\nstopping-rule V error bound 1.8999999999999982e-07 observed |dV1| 0.0003440281002156098\nrel policy errs [-0.0005539552572922775, 0.001509908817275246, -0.004844188865506954]","is_error":false}]},"uuid":"bc7b1de4-d9f4-419b-877b-22bbb26e75d9","timestamp":"2026-10-30T04:38:41.144Z","toolUseResult":{"stdout":"IDENTICAL\n0.5 argmax 0.32899998496004007 closed 0.329 TV-V 0.0\n1 argmax 0.6579999792181229 closed 0.658 TV-V 0.0\n2 argmax 1.3159999817971206 closed 1.316 TV-V 0.0\nmax err recompute True\nsavings 1-c/y 0.34199999999999997\nstopping-rule V error bound 1.8999999999999982e-07 observed |dV1| 0.0003440281002156098\nrel policy errs [-0.0005539552572922775, 0.001509908817275246, 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np\nr=json.load(open('out/results.json'))\na,b=0.36,0.95\n# verify Bellman closed form numerically: V(y) = max_c ln c + b V((y-c)^a)\nB=1/(1-a*b); A=r['value_closed_y1']\nV=lambda y:A+B*np.log(y)\nfrom scipy.optimize import minimize_scalar\nfor y in [0.5,1,2]:\n    o=minimize_scalar(lambda c:-(np.log(c)+b*V((y-c)**a)),bounds=(1e-9,y-1e-9),method='bounded',options={'xatol':1e-12})\n    print(y,'argmax',o.x,'closed',(1-a*b)*y,'TV-V',-o.fun-V(y))\nprint('max err recompute', max(abs(r[f'c_num_{k}']-r[f'c_closed_{k}']) for k in ['y05','y1','y2'])==r['max_abs_error_policy'])\nprint('savings 1-c/y', 1-r['c_closed_y1']/1.0)\nprint('stopping-rule V error bound', 1e-8*b/(1-b), 'observed |dV1|', abs(r['value_num_y1']-r['value_closed_y1']))\nprint('rel policy errs',[ (r[f'c_num_{k}']-r[f'c_closed_{k}'])/r[f'c_closed_{k}'] for k in ['y05','y1','y2']])\nEOF","description":"Reproducibility and consistency 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>> out/state/checks.md <<'EOF'\n- [PASS] Reproducibility: re-ran out/analysis.py; out/results.json byte-identical (cmp).\n- [PASS] Closed form verified independently: for y in {0.5,1,2}, a continuous bounded optimiser (scipy) applied to the Bellman RHS with V=A+B ln y returns argmax = (1-alpha*beta)y to 1e-8 and T V - V = 0 (fixed point).\n- [PASS] max_abs_error_policy equals max of the three |c_num - c_closed| (recomputed).\n- [PASS] savings_rate_closed_form = 1 - c_closed_y1/1 = alpha*beta = 0.342.\n- [PASS] VFI converged: final_sup_change 9.997e-9 < tol 1e-8 after 361 iterations; consistent with beta^n * initial gap (0.95^361 ~ 9e-9 x O(1) gap).\n- [PASS] Policy never at grid bounds (0 bound hits) -> no truncation distortion.\n- [PASS] Magnitudes: relative policy errors -0.06%, +0.15%, -0.48% at y=0.5,1,2, consistent with ln-grid step 0.0115 in y' (=> ~3.2% step in required investment, i.e. at most ~0.55% of y in consumption). |V_num(1) - V_closed(1)| = 3.4e-4, larger than the stopping-rule bound beta*tol/(1-beta)=1.9e-7, so the residual value gap is discretisation (and interpolation) error, not iteration error.\n- [PASS] Units: consumption in output units, values in utils; contraction modulus = beta = 0.95 in (0,1).\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . 2>&1 | tail -30","description":"Record checks and run 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 [ok] key:c_closed_y05: ok\n  [ok] key:c_closed_y1: ok\n  [ok] key:c_closed_y2: ok\n  [ok] key:c_num_y05: ok\n  [ok] key:c_num_y1: ok\n  [ok] key:c_num_y2: ok\n  [ok] key:max_abs_error_policy: ok\n  [ok] key:value_closed_y1: ok\n  [ok] key:value_num_y1: ok\n  [ok] key:savings_rate_closed_form: ok\n  [ok] key:contraction_modulus: ok\n  [ok] key:final_sup_change: ok\n  [ok] key:grid_points_used: ok\n  [ok] key:n_iterations: ok\n  [ok] key:feasibility: ok\n  [ok] key:feasibility_reason: ok\n  [ok] key:data_issues: ok\n  [ok] key:n_input_rows: ok\n  [ok] key:n_analysed: ok\n  [ok] key:random_seed: ok\n  [FAIL] section:Question: heading not found\n  [FAIL] section:Data and exclusions: heading not found\n  [FAIL] section:Method: heading not found\n  [FAIL] section:Results: heading not found\n  [FAIL] section:Uncertainty: heading not found\n  [FAIL] section:Limitations and open issues: heading not found\n  [FAIL] claims_json: out/claims.json missing\n  [FAIL] phase_ledger: phases not terminal: ['P1', 'P2', 'P3', 'P4', 'P5']\n  [ok] reproducibility: regenerated in 0.3s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0129/out/state/gate_receipts/20261030T043849.385560Z.json","is_error":false}]},"uuid":"e5e8e541-977a-47a2-a512-28b506f68d71","timestamp":"2026-10-30T04:38:49.393Z","toolUseResult":{"stdout":"  [ok] key:c_closed_y05: ok\n  [ok] key:c_closed_y1: ok\n  [ok] key:c_closed_y2: ok\n  [ok] key:c_num_y05: ok\n  [ok] key:c_num_y1: ok\n  [ok] key:c_num_y2: ok\n  [ok] key:max_abs_error_policy: ok\n  [ok] key:value_closed_y1: ok\n  [ok] key:value_num_y1: ok\n  [ok] key:savings_rate_closed_form: ok\n  [ok] key:contraction_modulus: ok\n  [ok] key:final_sup_change: ok\n  [ok] key:grid_points_used: ok\n  [ok] key:n_iterations: ok\n  [ok] key:feasibility: ok\n  [ok] key:feasibility_reason: ok\n  [ok] key:data_issues: ok\n  [ok] key:n_input_rows: ok\n  [ok] key:n_analysed: ok\n  [ok] key:random_seed: ok\n  [FAIL] section:Question: heading not found\n  [FAIL] section:Data and exclusions: heading not found\n  [FAIL] section:Method: heading not found\n  [FAIL] section:Results: heading not found\n  [FAIL] section:Uncertainty: heading not found\n  [FAIL] section:Limitations and open issues: heading not found\n  [FAIL] claims_json: out/claims.json missing\n  [FAIL] phase_ledger: phases not terminal: ['P1', 'P2', 'P3', 'P4', 'P5']\n  [ok] reproducibility: regenerated in 0.3s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0129/out/state/gate_receipts/20261030T043849.385560Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"20acb6ef-3692-483f-a6c4-662936113ccc","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}54{"type":"api-request-blob","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","hash":"4271fa2393369bbc7b5d76b8761f51e3a392e823ae467b6d800a0f1b4dfd8849","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_012mRipXmmT1md413kXi38cN","name":"Bash","input":{"command":"cat >> out/state/checks.md <<'EOF'\n- [PASS] Reproducibility: re-ran out/analysis.py; out/results.json byte-identical (cmp).\n- [PASS] Closed form verified independently: for y in {0.5,1,2}, a continuous bounded optimiser (scipy) applied to the Bellman RHS with V=A+B ln y returns argmax = (1-alpha*beta)y to 1e-8 and T V - V = 0 (fixed point).\n- [PASS] max_abs_error_policy equals max of the three |c_num - c_closed| (recomputed).\n- [PASS] savings_rate_closed_form = 1 - c_closed_y1/1 = alpha*beta = 0.342.\n- [PASS] VFI converged: final_sup_change 9.997e-9 < tol 1e-8 after 361 iterations; consistent with beta^n * initial gap (0.95^361 ~ 9e-9 x O(1) gap).\n- [PASS] Policy never at grid bounds (0 bound hits) -> no truncation distortion.\n- [PASS] Magnitudes: relative policy errors -0.06%, +0.15%, -0.48% at y=0.5,1,2, consistent with ln-grid step 0.0115 in y' (=> ~3.2% step in required investment, i.e. at most ~0.55% of y in consumption). |V_num(1) - V_closed(1)| = 3.4e-4, larger than the stopping-rule bound beta*tol/(1-beta)=1.9e-7, so the residual value gap is discretisation (and interpolation) error, not iteration error.\n- [PASS] Units: consumption in output units, values in utils; contraction modulus = beta = 0.95 in (0,1).\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . 2>&1 | tail -30","description":"Record checks and run 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failures (report/claims not yet written). Now the report and claims."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1452,"cache_read_input_tokens":14831,"output_tokens":3184,"output_tokens_details":{"thinking_tokens":32},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1452},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXobtC25a8tLL5rpJZt2","requestRef":"01ba20eb-6125-4f79-a131-472b98acd266","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"54c1149e-398d-4d03-88e5-0d0a9de20b53","timestamp":"2026-10-30T04:38:50.527Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0129","sessionId":"4ee83577-c6ff-495e-9937-52e4372fc03a","version":"2.1.314","gitBranch":"HEAD"}58{"parentUuid":"54c1149e-398d-4d03-88e5-0d0a9de20b53","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXobtTPcDjqat1qWS7R7","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Ag4wK8QtHYKr2p2dFAL4DS","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-conf-04 — VFI vs closed form, 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 (full depreciation, productivity 1). We derive the\nclosed-form policy and value function, solve the same problem by value-function iteration (VFI) on the prescribed grid,\nand compare them at y = 0.5, 1, 2 and (for the value) at y = 1. Parameters from `data/model.csv`: α = 0.36, β = 0.95.\n\n## Data and exclusions\n`data/model.csv` (10 rows, `n_input_rows`; SHA-256 0981239614…6195b) holds theoretical parameters only. No rows were\nexcluded (`out/exclusions.csv`); all 400 grid points were analysed (`grid_points_used`, `n_analysed`). No deviations\nfrom the prescribed design were needed (`data_issues` = []). None of the evaluation points is a grid node, so the VFI\npolicy and value are interpolated (linearly in ln y), as TASK.md allows. Audit details: `out/state/data_audit.md`.\n\n## Method\n**Closed form (guess-and-verify).** Guess V(y) = A + B ln y. The RHS of the Bellman equation is\nln c + β[A + Bα ln(y − c)]. The FOC 1/c = αβB/(y − c) gives c = y/(1 + αβB). Matching coefficients on ln y:\nB = 1 + αβB ⇒ B = 1/(1 − αβ), so c(y) = (1 − αβ) y and the savings rate is (y − c)/y = αβ. Matching constants:\nA = [ln(1 − αβ) + (αβ/(1 − αβ)) ln(αβ)] / (1 − β). The verification holds exactly; we also checked numerically that\na continuous optimiser applied to the Bellman RHS with this V returns c = (1 − αβ)y and TV = V (`out/state/checks.md`).\nAssumptions: log utility, Cobb–Douglas technology y' = k^α with 0<α<1, full depreciation, productivity normalised to 1,\ninterior solution (0 < c < y, guaranteed by the Inada property of ln and of k^α), 0<β<1, and the transversality condition\n(satisfied since V is A + B ln y with finite A, B and log output is stationary).\n\n**Contraction.** On the compact grid, with feasible choices and bounded utilities, the Bellman operator T satisfies\nBlackwell's sufficient conditions: monotonicity (V ≤ W ⇒ TV ≤ TW) and discounting (T(V + a) = TV + βa). Hence T is a\ncontraction in the sup norm with modulus β = 0.95 (`contraction_modulus`). (On the unbounded continuous domain ln c is\nunbounded; there the result is obtained on the restricted/compact state space or with weighted norms — the discretised\nproblem is bounded, which is what we iterate on.)\n\n**VFI.** Grid: 400 points equally spaced in ln y on [0.05, 5]. The choice variable is next-period output y' restricted\nto the grid; consumption is c = y − y'^{1/α}, and pairs with c ≤ 0 are infeasible (utility −∞). Start V0 = 0; iterate\nV_{n+1}(y_i) = max_j {ln c_ij + β V_n(y_j)} until sup|V_{n+1} − V_n| < 1e-8. The policy is the argmax at the final V.\nThe closed form is never used inside the VFI. No randomness (`random_seed` = null). Code: `out/analysis.py`.\n\n## Results\nThe baseline (closed form) gives a savings rate αβ = 0.342 (`savings_rate_closed_form`).\n\n| y | closed form c | VFI c | \n|---|---|---|\n| 0.5 | 0.329 (`c_closed_y05`) | 0.328818 (`c_num_y05`) |\n| 1.0 | 0.658 (`c_closed_y1`) | 0.658994 (`c_num_y1`) |\n| 2.0 | 1.316 (`c_closed_y2`) | 1.309625 (`c_num_y2`) |\n\n- Maximum absolute policy discrepancy over the three points: 0.00637 at y = 2 (`max_abs_error_policy`), i.e. below 0.5%\n  of consumption at each point.\n- V(1): closed form −19.52441 (`value_closed_y1`), VFI −19.52476 (`value_num_y1`); gap ≈ 3.4e-4 utils.\n- VFI converged in 361 iterations (`n_iterations`) with final sup-norm change 1.0e-8 < 1e-8 tolerance\n  (`final_sup_change`); `feasibility` = \"complete\".\n- Diagnostic (in `results.json` → `diagnostics`): no grid node chooses a boundary y'; across all 400 nodes the max policy\n  error is 0.025 (at large y, where c ≈ 3.3) and the max value error 4.8e-4.\n\n## Uncertainty\nThe problem is deterministic; there is no sampling uncertainty. Numerical error has two sources:\n(i) iteration error, bounded by β·tol/(1 − β) = 1.9e-7 utils in V (from `contraction_modulus` and the 1e-8 tolerance);\n(ii) discretisation/interpolation error: y' is restricted to a grid with ln-step 0.0115, so the required investment\ny'^{1/α} jumps by ≈ 3.2% per step, which bounds the consumption error to a fraction of a percent of y — consistent with\nthe observed relative errors (−0.06%, +0.15%, −0.48%). The V(1) gap (3.4e-4) far exceeds bound (i), so it is\ndiscretisation error. Errors shrink as the grid is refined (smaller ln-step), not by tightening the tolerance.\n\n## Limitations and open issues\n- Validation scope: a single parameter point (α = 0.36, β = 0.95), one grid (400 log-spaced points on [0.05, 5]), one\n  tolerance, discrete choice over grid nodes with linear-in-ln y interpolation at off-grid points. Other interpolation\n  schemes (e.g. continuous choice with interpolated V) would give different (typically smaller) discrepancies; we did not\n  run grid-refinement studies because the task does not require them.\n- The policy error is not monotone in y; it reflects where the evaluation point falls relative to grid nodes.\n- The contraction argument applies to the bounded discretised problem; the continuous log-utility problem is unbounded\n  and needs the standard restricted-domain argument.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"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 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, interior solution.\"},\n {\"id\":\"C2\",\"text\":\"VFI on the prescribed 400-point log grid converged in 361 iterations with final sup change below 1e-8.\",\"results_keys\":[\"n_iterations\",\"final_sup_change\",\"grid_points_used\",\"feasibility\"],\"status\":\"supported\",\"caveat\":\"Starting guess V0=0.\"},\n {\"id\":\"C3\",\"text\":\"VFI policy matches the closed form to within 0.0064 units of output (below 0.5% relative) at the three evaluation points.\",\"results_keys\":[\"c_num_y05\",\"c_num_y1\",\"c_num_y2\",\"max_abs_error_policy\"],\"status\":\"supported\",\"caveat\":\"Discrete choice on grid nodes plus linear-in-ln y interpolation; error depends on grid step.\"},\n {\"id\":\"C4\",\"text\":\"VFI value at y=1 (-19.52476) matches the closed form (-19.52441) to about 3.4e-4 utils, a gap dominated by discretisation rather than iteration error.\",\"results_keys\":[\"value_num_y1\",\"value_closed_y1\",\"contraction_modulus\",\"final_sup_change\"],\"status\":\"supported\",\"caveat\":\"Iteration error bound beta*tol/(1-beta)=1.9e-7.\"},\n {\"id\":\"C5\",\"text\":\"The Bellman operator is a sup-norm contraction with modulus beta=0.95 (Blackwell conditions on the bounded discretised problem).\",\"results_keys\":[\"contraction_modulus\"],\"status\":\"supported\",\"caveat\":\"Continuous log-utility problem is unbounded; argument applies on compact state space.\"}\n]\nEOF\necho \"- 2026-10-30 P4 checks recorded; gate run 1 (pre-report) failed only on report/claims/ledger. 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Now the report and claims."},{"type":"tool_use","id":"toolu_01Ag4wK8QtHYKr2p2dFAL4DS","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-conf-04 — VFI vs closed form, 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 (full depreciation, productivity 1). We derive the\nclosed-form policy and value function, solve the same problem by value-function iteration (VFI) on the prescribed grid,\nand compare them at y = 0.5, 1, 2 and (for the value) at y = 1. Parameters from `data/model.csv`: α = 0.36, β = 0.95.\n\n## Data and exclusions\n`data/model.csv` (10 rows, `n_input_rows`; SHA-256 0981239614…6195b) holds theoretical parameters only. No rows were\nexcluded (`out/exclusions.csv`); all 400 grid points were analysed (`grid_points_used`, `n_analysed`). No deviations\nfrom the prescribed design were needed (`data_issues` = []). None of the evaluation points is a grid node, so the VFI\npolicy and value are interpolated (linearly in ln y), as TASK.md allows. Audit details: `out/state/data_audit.md`.\n\n## Method\n**Closed form (guess-and-verify).** Guess V(y) = A + B ln y. The RHS of the Bellman equation is\nln c + β[A + Bα ln(y − c)]. The FOC 1/c = αβB/(y − c) gives c = y/(1 + αβB). Matching coefficients on ln y:\nB = 1 + αβB ⇒ B = 1/(1 − αβ), so c(y) = (1 − αβ) y and the savings rate is (y − c)/y = αβ. Matching constants:\nA = [ln(1 − αβ) + (αβ/(1 − αβ)) ln(αβ)] / (1 − β). The verification holds exactly; we also checked numerically that\na continuous optimiser applied to the Bellman RHS with this V returns c = (1 − αβ)y and TV = V (`out/state/checks.md`).\nAssumptions: log utility, Cobb–Douglas technology y' = k^α with 0<α<1, full depreciation, productivity normalised to 1,\ninterior solution (0 < c < y, guaranteed by the Inada property of ln and of k^α), 0<β<1, and the transversality condition\n(satisfied since V is A + B ln y with finite A, B and log output is stationary).\n\n**Contraction.** On the compact grid, with feasible choices and bounded utilities, the Bellman operator T satisfies\nBlackwell's sufficient conditions: monotonicity (V ≤ W ⇒ TV ≤ TW) and discounting (T(V + a) = TV + βa). Hence T is a\ncontraction in the sup norm with modulus β = 0.95 (`contraction_modulus`). (On the unbounded continuous domain ln c is\nunbounded; there the result is obtained on the restricted/compact state space or with weighted norms — the discretised\nproblem is bounded, which is what we iterate on.)\n\n**VFI.** Grid: 400 points equally spaced in ln y on [0.05, 5]. The choice variable is next-period output y' restricted\nto the grid; consumption is c = y − y'^{1/α}, and pairs with c ≤ 0 are infeasible (utility −∞). Start V0 = 0; iterate\nV_{n+1}(y_i) = max_j {ln c_ij + β V_n(y_j)} until sup|V_{n+1} − V_n| < 1e-8. The policy is the argmax at the final V.\nThe closed form is never used inside the VFI. No randomness (`random_seed` = null). Code: `out/analysis.py`.\n\n## Results\nThe baseline (closed form) gives a savings rate αβ = 0.342 (`savings_rate_closed_form`).\n\n| y | closed form c | VFI c | \n|---|---|---|\n| 0.5 | 0.329 (`c_closed_y05`) | 0.328818 (`c_num_y05`) |\n| 1.0 | 0.658 (`c_closed_y1`) | 0.658994 (`c_num_y1`) |\n| 2.0 | 1.316 (`c_closed_y2`) | 1.309625 (`c_num_y2`) |\n\n- Maximum absolute policy discrepancy over the three points: 0.00637 at y = 2 (`max_abs_error_policy`), i.e. below 0.5%\n  of consumption at each point.\n- V(1): closed form −19.52441 (`value_closed_y1`), VFI −19.52476 (`value_num_y1`); gap ≈ 3.4e-4 utils.\n- VFI converged in 361 iterations (`n_iterations`) with final sup-norm change 1.0e-8 < 1e-8 tolerance\n  (`final_sup_change`); `feasibility` = \"complete\".\n- Diagnostic (in `results.json` → `diagnostics`): no grid node chooses a boundary y'; across all 400 nodes the max policy\n  error is 0.025 (at large y, where c ≈ 3.3) and the max value error 4.8e-4.\n\n## Uncertainty\nThe problem is deterministic; there is no sampling uncertainty. Numerical error has two sources:\n(i) iteration error, bounded by β·tol/(1 − β) = 1.9e-7 utils in V (from `contraction_modulus` and the 1e-8 tolerance);\n(ii) discretisation/interpolation error: y' is restricted to a grid with ln-step 0.0115, so the required investment\ny'^{1/α} jumps by ≈ 3.2% per step, which bounds the consumption error to a fraction of a percent of y — consistent with\nthe observed relative errors (−0.06%, +0.15%, −0.48%). The V(1) gap (3.4e-4) far exceeds bound (i), so it is\ndiscretisation error. Errors shrink as the grid is refined (smaller ln-step), not by tightening the tolerance.\n\n## Limitations and open issues\n- Validation scope: a single parameter point (α = 0.36, β = 0.95), one grid (400 log-spaced points on [0.05, 5]), one\n  tolerance, discrete choice over grid nodes with linear-in-ln y interpolation at off-grid points. Other interpolation\n  schemes (e.g. continuous choice with interpolated V) would give different (typically smaller) discrepancies; we did not\n  run grid-refinement studies because the task does not require them.\n- The policy error is not monotone in y; it reflects where the evaluation point falls relative to grid nodes.\n- The contraction argument applies to the bounded discretised problem; the continuous log-utility problem is unbounded\n  and needs the standard restricted-domain argument.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"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 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, interior solution.\"},\n {\"id\":\"C2\",\"text\":\"VFI on the prescribed 400-point log grid converged in 361 iterations with final sup change below 1e-8.\",\"results_keys\":[\"n_iterations\",\"final_sup_change\",\"grid_points_used\",\"feasibility\"],\"status\":\"supported\",\"caveat\":\"Starting guess V0=0.\"},\n {\"id\":\"C3\",\"text\":\"VFI policy matches the closed form to within 0.0064 units of output (below 0.5% relative) at the three evaluation points.\",\"results_keys\":[\"c_num_y05\",\"c_num_y1\",\"c_num_y2\",\"max_abs_error_policy\"],\"status\":\"supported\",\"caveat\":\"Discrete choice on grid nodes plus linear-in-ln y interpolation; error depends on grid step.\"},\n {\"id\":\"C4\",\"text\":\"VFI value at y=1 (-19.52476) matches the closed form (-19.52441) to about 3.4e-4 utils, a gap dominated by discretisation rather than iteration error.\",\"results_keys\":[\"value_num_y1\",\"value_closed_y1\",\"contraction_modulus\",\"final_sup_change\"],\"status\":\"supported\",\"caveat\":\"Iteration error bound beta*tol/(1-beta)=1.9e-7.\"},\n {\"id\":\"C5\",\"text\":\"The Bellman operator is a sup-norm contraction with modulus beta=0.95 (Blackwell conditions on the bounded discretised problem).\",\"results_keys\":[\"contraction_modulus\"],\"status\":\"supported\",\"caveat\":\"Continuous log-utility problem is unbounded; argument applies on compact state space.\"}\n]\nEOF\necho \"- 2026-10-30 P4 checks recorded; gate run 1 (pre-report) failed only on report/claims/ledger. 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Value-function iteration on the prescribed grid matches the closed form to within 0.0064 units of output at the three evaluation points. The final gate run passed (0 of 35 checks failed), and re-running `out/analysis.py` reproduces `out/results.json` exactly.\n\n**Closed form.** Guess-and-verify on the Bellman equation gives optimal consumption c(y) = (1 − αβ)·y and value function V(y) = A + ln y / (1 − αβ), where A is a constant derived in the report. With α = 0.36 and β = 0.95, this means saving 34.2% of output (αβ) and consuming the rest. I also checked numerically that this V reproduces itself when you apply the Bellman equation (it is a fixed point).\n\n**Numerical solution.** I used 400 points equally spaced in ln y on [0.05, 5], choosing next period's output from the grid points. It stopped after 361 iterations, when the largest change between successive value functions fell just below 1e-8. 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