spb/wp29_uqo

1{"type":"atis-latch","atis":"","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e"}2{"type":"queue-operation","operation":"enqueue","timestamp":"2026-10-30T04:36:43.081Z","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","content":"Begin"}3{"type":"queue-operation","operation":"dequeue","timestamp":"2026-10-30T04:36:43.087Z","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e"}4{"parentUuid":null,"isSidechain":false,"promptId":"1c50b31a-0240-4fbb-9eb0-20840a459bfb","type":"user","message":{"role":"user","content":"Begin"},"uuid":"ad1cbe6d-1c06-4bc1-87dd-01bc11048fbf","timestamp":"2026-10-30T04:36:43.091Z","permissionMode":"default","promptSource":"sdk","turnOrigin":"sdk","turnPosition":{"promptIndex":0,"turnIndex":1},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}5{"type":"api-request-shape","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","shapeHash":"82483642b97bb27a79f8911d058b21de56088dceec9d4a64e63418ec73b440c8","timestamp":"2026-10-30T04:36:43.104Z","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/RC0124\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"}],"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/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e"}12{"parentUuid":"117c2eea-8b2c-4668-8731-9f4064e94df1","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoSae5adzH5UfrMXMcb","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":2603,"cache_read_input_tokens":1504,"output_tokens":135,"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":2603},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":448,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXoSaNxQMtRAbVxc3gD4","requestRef":"1e54f173-5f82-408d-9c9d-01d3aa363d49","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"8abeb2bf-3fd2-4497-b3d8-1d8d32ca855a","timestamp":"2026-10-30T04:36:44.494Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"8abeb2bf-3fd2-4497-b3d8-1d8d32ca855a","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoSae5adzH5UfrMXMcb","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01SMkvCBTGvpazxjzeoxSVCL","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.\ntotal 32\ndrwxr-xr-x   6 simon-pierreboucher  staff   192 oct.  29 23:42 .\ndrwxr-xr-x  78 simon-pierreboucher  staff  2496 oct.  30 00:36 ..\n-rw-r--r--   1 simon-pierreboucher  staff   419 oct.  29 23:42 bundle.json\ndrwxr-xr-x   3 simon-pierreboucher  staff    96 oct.  29 23:28 data\n-rw-r--r--   1 simon-pierreboucher  staff  2193 oct.  29 23:32 gate_spec.json\n-rw-r--r--   1 simon-pierreboucher  staff  4470 oct.  29 23:32 TASK.md\n\n./data:\ntotal 8\ndrwxr-xr-x  3 simon-pierreboucher  staff   96 oct.  29 23:28 .\ndrwxr-xr-x  6 simon-pierreboucher  staff  192 oct.  29 23:42 ..\n-rw-r--r--  1 simon-pierreboucher  staff  597 oct.  29 23:39 model.csv","is_error":true,"tool_use_id":"toolu_01SMkvCBTGvpazxjzeoxSVCL"}]},"uuid":"dbbb25c5-5267-4e0d-920f-58f9ccfa6593","timestamp":"2026-10-30T04:36:45.197Z","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 vectorised.\ntotal 32\ndrwxr-xr-x   6 simon-pierreboucher  staff   192 oct.  29 23:42 .\ndrwxr-xr-x  78 simon-pierreboucher  staff  2496 oct.  30 00:36 ..\n-rw-r--r--   1 simon-pierreboucher  staff   419 oct.  29 23:42 bundle.json\ndrwxr-xr-x   3 simon-pierreboucher  staff    96 oct.  29 23:28 data\n-rw-r--r--   1 simon-pierreboucher  staff  2193 oct.  29 23:32 gate_spec.json\n-rw-r--r--   1 simon-pierreboucher  staff  4470 oct.  29 23:32 TASK.md\n\n./data:\ntotal 8\ndrwxr-xr-x  3 simon-pierreboucher  staff   96 oct.  29 23:28 .\ndrwxr-xr-x  6 simon-pierreboucher  staff  192 oct.  29 23:42 ..\n-rw-r--r--  1 simon-pierreboucher  staff  597 oct.  29 23:39 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-p out/state && cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-04: VFI vs closed-form policy, optimal growth with log utility.\nReads only data/model.csv; writes out/results.json (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\"])\nN = int(float(p[\"grid_points\"])); spacing = str(p[\"grid_spacing\"]).strip()\ntol = float(p[\"vfi_tolerance\"])\nevals = [float(p[\"eval_y_1\"]), float(p[\"eval_y_2\"]), float(p[\"eval_y_3\"])]\nassert spacing == \"log\"\n\ndata_issues = []\n\n# ---- Closed form (guess V = A + B ln y, verified in report) ----\nab = alpha * beta\ns_closed = ab                                   # savings rate (y-c)/y\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)\n\n# ---- VFI on the prescribed log grid; choice of next-period output y' on the same grid ----\ny = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))\nk_next = y ** (1.0 / alpha)                     # capital needed to produce y' = k^alpha\nC = y[:, None] - k_next[None, :]                # consumption for (y, y')\nfeasible = C > 0\nU = np.full(C.shape, -np.inf)\nU[feasible] = np.log(C[feasible])\nV = np.zeros(N)\nn_iter = 0; sup_change = np.inf\nwhile sup_change >= tol:\n    RHS = U + beta * V[None, :]\n    V_new = RHS.max(axis=1)\n    sup_change = float(np.max(np.abs(V_new - V)))\n    V = V_new; n_iter += 1\n    if n_iter > 100000:\n        raise RuntimeError(\"VFI did not converge\")\npol_idx = (U + beta * V[None, :]).argmax(axis=1)\nc_grid = y - k_next[pol_idx]\n# check that the upper/lower bound of the choice grid never binds\nn_bind_upper = int(np.sum(pol_idx == N - 1)); n_bind_lower = int(np.sum(pol_idx == 0))\nif n_bind_upper or n_bind_lower:\n    data_issues.append({\"issue\": f\"choice grid bound binds at {n_bind_lower} (lower) / {n_bind_upper} (upper) grid points\",\n                        \"handling\": \"reported; affects policy near grid edges only\"})\n\nlny = np.log(y)\ninterp = lambda f, x: float(np.interp(np.log(x), lny, f))   # linear in ln y\non_grid = [bool(np.any(np.isclose(y, e, rtol=0, atol=1e-12))) for e in evals]\noff = [e for e, g in zip(evals, on_grid) if not g]\nif off:\n    data_issues.append({\"issue\": f\"evaluation points {off} are not nodes of the prescribed log grid\",\n                        \"handling\": \"VFI policy and value interpolated linearly in ln y between adjacent grid nodes (as allowed by TASK.md)\"})\n\nc_num = [interp(c_grid, e) for e in evals]\nc_cl = [float(c_closed(e)) for e in evals]\nmax_err = float(max(abs(a - b) for a, b in zip(c_num, c_cl)))\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)),\n    \"value_num_y1\": interp(V, 1.0),\n    \"savings_rate_closed_form\": float(s_closed),\n    \"contraction_modulus\": beta,\n    \"grid_points_used\": N,\n    \"n_iterations\": n_iter,\n    \"final_sup_change\": sup_change,\n    \"feasibility\": \"complete\",\n    \"feasibility_reason\": None,\n    \"data_issues\": data_issues,\n    \"n_input_rows\": {\"model.csv\": int(len(df))},\n    \"n_analysed\": N,\n    \"random_seed\": None,\n    # supplementary diagnostics\n    \"baseline_savings_rate_closed_form\": float(s_closed),\n    \"diag_closed_form_A\": float(A), \"diag_closed_form_B\": float(B),\n    \"diag_grid_log_step\": float(lny[1] - lny[0]),\n    \"diag_max_abs_value_error_grid\": float(np.max(np.abs(V - V_closed(y)))),\n    \"diag_max_abs_policy_error_grid\": float(np.max(np.abs(c_grid - c_closed(y)))),\n    \"diag_mean_savings_rate_num_grid\": float(np.mean(1 - c_grid / y)),\n    \"diag_stopping_error_bound\": float(beta * sup_change / (1 - beta)),\n    \"diag_choice_bound_binds\": n_bind_lower + n_bind_upper,\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)\npd.DataFrame([{\"step\": \"none\", \"rule\": \"no filtering applied; all 10 parameter rows used\",\n               \"n_before\": len(df), \"n_after\": len(df), \"n_removed\": 0,\n               \"rationale\": \"inputs are model parameters, not observations\"}]).to_csv(\n    os.path.join(ROOT, \"out\", \"exclusions.csv\"), index=False)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis 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 \"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      \"issue\": \"evaluation points [0.5, 1.0, 2.0] are not nodes of the prescribed log grid\",\n      \"handling\": \"VFI policy and value interpolated linearly in ln y between adjacent grid nodes (as allowed by TASK.md)\"\n    }\n  ],\n  \"n_input_rows\": {\n    \"model.csv\": 10\n  },\n  \"n_analysed\": 400,\n  \"random_seed\": null,\n  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\"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      \"issue\": \"evaluation points [0.5, 1.0, 2.0] are not nodes of the prescribed log grid\",\n      \"handling\": \"VFI policy and value interpolated linearly in ln y between adjacent grid nodes (as allowed by TASK.md)\"\n    }\n  ],\n  \"n_input_rows\": {\n    \"model.csv\": 10\n  },\n  \"n_analysed\": 400,\n  \"random_seed\": null,\n  \"baseline_savings_rate_closed_form\": 0.34199999999999997,\n  \"diag_closed_form_A\": -19.524412221722393,\n  \"diag_closed_form_B\": 1.519756838905775,\n  \"diag_grid_log_step\": 0.011541779914757022,\n  \"diag_max_abs_value_error_grid\": 0.0004835155258184898,\n  \"diag_max_abs_policy_error_grid\": 0.02512152290513381,\n  \"diag_mean_savings_rate_num_grid\": 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-p out/state && cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-04: VFI vs closed-form policy, optimal growth with log utility.\nReads only data/model.csv; writes out/results.json (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\"])\nN = int(float(p[\"grid_points\"])); spacing = str(p[\"grid_spacing\"]).strip()\ntol = float(p[\"vfi_tolerance\"])\nevals = [float(p[\"eval_y_1\"]), float(p[\"eval_y_2\"]), float(p[\"eval_y_3\"])]\nassert spacing == \"log\"\n\ndata_issues = []\n\n# ---- Closed form (guess V = A + B ln y, verified in report) ----\nab = alpha * beta\ns_closed = ab                                   # savings rate (y-c)/y\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)\n\n# ---- VFI on the prescribed log grid; choice of next-period output y' on the same grid ----\ny = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))\nk_next = y ** (1.0 / alpha)                     # capital needed to produce y' = k^alpha\nC = y[:, None] - k_next[None, :]                # consumption for (y, y')\nfeasible = C > 0\nU = np.full(C.shape, -np.inf)\nU[feasible] = np.log(C[feasible])\nV = np.zeros(N)\nn_iter = 0; sup_change = np.inf\nwhile sup_change >= tol:\n    RHS = U + beta * V[None, :]\n    V_new = RHS.max(axis=1)\n    sup_change = float(np.max(np.abs(V_new - V)))\n    V = V_new; n_iter += 1\n    if n_iter > 100000:\n        raise RuntimeError(\"VFI did not converge\")\npol_idx = (U + beta * V[None, :]).argmax(axis=1)\nc_grid = y - k_next[pol_idx]\n# check that the upper/lower bound of the choice grid never binds\nn_bind_upper = int(np.sum(pol_idx == N - 1)); n_bind_lower = int(np.sum(pol_idx == 0))\nif n_bind_upper or n_bind_lower:\n    data_issues.append({\"issue\": f\"choice grid bound binds at {n_bind_lower} (lower) / {n_bind_upper} (upper) grid points\",\n                        \"handling\": \"reported; affects policy near grid edges only\"})\n\nlny = np.log(y)\ninterp = lambda f, x: float(np.interp(np.log(x), lny, f))   # linear in ln y\non_grid = [bool(np.any(np.isclose(y, e, rtol=0, atol=1e-12))) for e in evals]\noff = [e for e, g in zip(evals, on_grid) if not g]\nif off:\n    data_issues.append({\"issue\": f\"evaluation points {off} are not nodes of the prescribed log grid\",\n                        \"handling\": \"VFI policy and value interpolated linearly in ln y between adjacent grid nodes (as allowed by TASK.md)\"})\n\nc_num = [interp(c_grid, e) for e in evals]\nc_cl = [float(c_closed(e)) for e in evals]\nmax_err = float(max(abs(a - b) for a, b in zip(c_num, c_cl)))\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)),\n    \"value_num_y1\": interp(V, 1.0),\n    \"savings_rate_closed_form\": float(s_closed),\n    \"contraction_modulus\": beta,\n    \"grid_points_used\": N,\n    \"n_iterations\": n_iter,\n    \"final_sup_change\": sup_change,\n    \"feasibility\": \"complete\",\n    \"feasibility_reason\": None,\n    \"data_issues\": data_issues,\n    \"n_input_rows\": {\"model.csv\": int(len(df))},\n    \"n_analysed\": N,\n    \"random_seed\": None,\n    # supplementary diagnostics\n    \"baseline_savings_rate_closed_form\": float(s_closed),\n    \"diag_closed_form_A\": float(A), \"diag_closed_form_B\": float(B),\n    \"diag_grid_log_step\": float(lny[1] - lny[0]),\n    \"diag_max_abs_value_error_grid\": float(np.max(np.abs(V - V_closed(y)))),\n    \"diag_max_abs_policy_error_grid\": float(np.max(np.abs(c_grid - c_closed(y)))),\n    \"diag_mean_savings_rate_num_grid\": float(np.mean(1 - c_grid / y)),\n    \"diag_stopping_error_bound\": float(beta * sup_change / (1 - beta)),\n    \"diag_choice_bound_binds\": n_bind_lower + n_bind_upper,\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)\npd.DataFrame([{\"step\": \"none\", \"rule\": \"no filtering applied; all 10 parameter rows used\",\n               \"n_before\": len(df), \"n_after\": len(df), \"n_removed\": 0,\n               \"rationale\": \"inputs are model parameters, not observations\"}]).to_csv(\n    os.path.join(ROOT, \"out\", \"exclusions.csv\"), index=False)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis 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out/state\ncat > contract.md <<'EOF'\n# Contract (P0)\n**Question.** Deterministic optimal growth, log utility, y' = (y-c)^alpha (Cobb–Douglas, full depreciation, TFP=1). Compare the closed-form optimal consumption policy and value function with those produced by value-function iteration (VFI) on a prescribed log-spaced grid.\n**Estimands.** Closed-form c(y) at y=0.5,1,2; VFI c(y) at the same points (interpolated if off-grid); max abs policy discrepancy over the 3 points; closed-form and VFI V(1); closed-form savings rate (y-c)/y; sup-norm contraction modulus of the Bellman operator. Meaningful under: log utility, Cobb-Douglas, full depreciation, interior solution, 0<alpha<1, 0<beta<1.\n**Outputs.** out/results.json (keys per TASK.md table: task_id, c_closed_y05/y1/y2, c_num_y05/y1/y2, max_abs_error_policy, value_closed_y1, value_num_y1, savings_rate_closed_form, contraction_modulus, grid_points_used, n_iterations, final_sup_change, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed), out/report.md (6 sections), out/analysis.py, out/claims.json, plus protocol files.\n**Information rules.** Use only data/model.csv; prescribed grid and parameters; deviations recorded in data_issues; numerical policy from VFI only; closed form derived and stated.\n**Invalidity.** Missing parameters; grid that cannot contain the optimal choices (bound binding); VFI not converging; using closed form to produce the numerical policy.\nEOF\ncat > 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 parameters.\n- Values: 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_y = 0.5, 1.0, 2.0. `value` column mixes numbers and the string \"log\" (parsed as strings, cast per parameter).\n- Units: y and c in units of output; V in utils.\n- Anomaly: log step = ln(100)/399 = 0.01154; 0.5, 1.0, 2.0 are NOT grid nodes (e.g. ln(1) lies at index 259.55). Handling: linear interpolation in ln y (allowed by TASK.md), recorded in data_issues.\n- Grid adequacy: closed-form steady state y* = (alpha*beta)^(alpha/(1-alpha)) ≈ 0.547 inside grid; optimal y' at y_max=5 is (0.342*5)^0.36 ≈ 1.21 and at y_min=0.05 is ≈ 0.23, both inside grid, so the choice bounds should not bind (verified in code: diag_choice_bound_binds = 0).\n- No information-availability violations: only theoretical parameters.\n- Exclusions: none (out/exclusions.csv, 10 -> 10).\nEOF\ncat > log.md <<'EOF'\n# Log\n- 2026-10-30 P0 passed: contract written.\n- 2026-10-30 P1 passed: data audited, evaluation points off-grid -> linear interpolation in ln y.\n- 2026-10-30 Decision: VFI with discrete choice of next-period output y' on the same 400-point grid (c = y - y'^(1/alpha)), V0 = 0, stop when sup|V_{n+1}-V_n| < 1e-8. 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Compare the closed-form optimal consumption policy and value function with those produced by value-function iteration (VFI) on a prescribed log-spaced grid.\n**Estimands.** Closed-form c(y) at y=0.5,1,2; VFI c(y) at the same points (interpolated if off-grid); max abs policy discrepancy over the 3 points; closed-form and VFI V(1); closed-form savings rate (y-c)/y; sup-norm contraction modulus of the Bellman operator. Meaningful under: log utility, Cobb-Douglas, full depreciation, interior solution, 0<alpha<1, 0<beta<1.\n**Outputs.** out/results.json (keys per TASK.md table: task_id, c_closed_y05/y1/y2, c_num_y05/y1/y2, max_abs_error_policy, value_closed_y1, value_num_y1, savings_rate_closed_form, contraction_modulus, grid_points_used, n_iterations, final_sup_change, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed), out/report.md (6 sections), out/analysis.py, out/claims.json, plus protocol files.\n**Information rules.** Use only data/model.csv; prescribed grid and parameters; deviations recorded in data_issues; numerical policy from VFI only; closed form derived and stated.\n**Invalidity.** Missing parameters; grid that cannot contain the optimal choices (bound binding); VFI not converging; using closed form to produce the numerical policy.\nEOF\ncat > 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 parameters.\n- Values: 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_y = 0.5, 1.0, 2.0. `value` column mixes numbers and the string \"log\" (parsed as strings, cast per parameter).\n- Units: y and c in units of output; V in utils.\n- Anomaly: log step = ln(100)/399 = 0.01154; 0.5, 1.0, 2.0 are NOT grid nodes (e.g. ln(1) lies at index 259.55). Handling: linear interpolation in ln y (allowed by TASK.md), recorded in data_issues.\n- Grid adequacy: closed-form steady state y* = (alpha*beta)^(alpha/(1-alpha)) ≈ 0.547 inside grid; optimal y' at y_max=5 is (0.342*5)^0.36 ≈ 1.21 and at y_min=0.05 is ≈ 0.23, both inside grid, so the choice bounds should not bind (verified in code: diag_choice_bound_binds = 0).\n- No information-availability violations: only theoretical parameters.\n- Exclusions: none (out/exclusions.csv, 10 -> 10).\nEOF\ncat > log.md <<'EOF'\n# Log\n- 2026-10-30 P0 passed: contract written.\n- 2026-10-30 P1 passed: data audited, evaluation points off-grid -> linear interpolation in ln y.\n- 2026-10-30 Decision: VFI with discrete choice of next-period output y' on the same 400-point grid (c = y - y'^(1/alpha)), V0 = 0, stop when sup|V_{n+1}-V_n| < 1e-8. No randomness (random_seed null).\n- 2026-10-30 P2 passed: baseline = closed-form savings rate alpha*beta = 0.342 (baseline_savings_rate_closed_form).\n- 2026-10-30 P3 passed: analysis.py written and run.\nEOF","description":"Write contract, audit, 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verification: rerun from clean, check consistency."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1688,"cache_read_input_tokens":11955,"output_tokens":777,"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":1688},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXoWGgCcaetQUVJa1eEP","requestRef":"d1070adb-895e-4743-ace1-324a2783b2ff","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"99ad8d76-f3c4-442b-9e0b-56d7e01c6a6a","timestamp":"2026-10-30T04:37:34.734Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124/out/state","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}36{"parentUuid":"99ad8d76-f3c4-442b-9e0b-56d7e01c6a6a","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoWGxZVnJ8wk9sRqxdR","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01JfG9qb8wePsBP5QXvC6jz6","name":"Bash","input":{"command":"cp out/results.json /tmp/r1.json && rm out/results.json && ~/wp29/venv/bin/python out/analysis.py >/dev/null && cmp out/results.json /tmp/r1.json && echo IDENTICAL\n~/wp29/venv/bin/python - <<'EOF'\nimport json,numpy as np\nr=json.load(open('out/results.json'))\na,b=0.36,0.95\nprint(\"c_closed==(1-ab)y\", np.allclose([r['c_closed_y05'],r['c_closed_y1'],r['c_closed_y2']],[0.5*(1-a*b),(1-a*b),2*(1-a*b)]))\ne=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']))\nprint(\"max err consistent\",np.isclose(e,r['max_abs_error_policy']))\n# Bellman verification of closed form at random points with continuous maximisation\nfrom scipy.optimize import minimize_scalar\nA,B=r['diag_closed_form_A'],r['diag_closed_form_B']\nV=lambda y:A+B*np.log(y)\nfor y in [0.3,1,3]:\n    f=lambda c:-(np.log(c)+b*V((y-c)**a))\n    o=minimize_scalar(f,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(\"final_sup<tol\",r['final_sup_change']<1e-8, \"value gap\",r['value_num_y1']-r['value_closed_y1'])\nprint(\"rel policy err\",[ (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":1688,"cache_read_input_tokens":11955,"output_tokens":777,"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":1688},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXoWGgCcaetQUVJa1eEP","requestRef":"d1070adb-895e-4743-ace1-324a2783b2ff","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"1a9894ae-1ee0-415d-8a46-a114829730b2","timestamp":"2026-10-30T04:37:40.387Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124/out/state","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}37{"parentUuid":"1a9894ae-1ee0-415d-8a46-a114829730b2","isSidechain":false,"promptId":"1c50b31a-0240-4fbb-9eb0-20840a459bfb","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 1\ncp: out/results.json: No such file or directory\nTraceback (most recent call last):\n  File \"<stdin>\", line 2, in <module>\nFileNotFoundError: [Errno 2] No such file or directory: 'out/results.json'","is_error":true,"tool_use_id":"toolu_01JfG9qb8wePsBP5QXvC6jz6"}]},"uuid":"8afb0bdf-b4d5-40eb-8798-f5eeffe7af42","timestamp":"2026-10-30T04:37:40.489Z","toolUseResult":"Error: Exit code 1\ncp: out/results.json: No such file or directory\nTraceback (most recent call last):\n  File \"<stdin>\", line 2, in <module>\nFileNotFoundError: [Errno 2] No such file or directory: 'out/results.json'","sandboxed":false,"sourceToolAssistantUUID":"1a9894ae-1ee0-415d-8a46-a114829730b2","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124/out/state","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}38{"type":"api-request-blob","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","hash":"eb04ac4ebc2c0087c380601ffa8f137f89a97007c85aba7f803f5e5025fd67d7","message":{"role":"assistant","content":[{"type":"text","text":"Now verification: rerun from clean, check consistency."},{"type":"tool_use","id":"toolu_01JfG9qb8wePsBP5QXvC6jz6","name":"Bash","input":{"command":"cp out/results.json /tmp/r1.json && rm out/results.json && ~/wp29/venv/bin/python out/analysis.py >/dev/null && cmp out/results.json /tmp/r1.json && echo IDENTICAL\n~/wp29/venv/bin/python - <<'EOF'\nimport json,numpy as np\nr=json.load(open('out/results.json'))\na,b=0.36,0.95\nprint(\"c_closed==(1-ab)y\", np.allclose([r['c_closed_y05'],r['c_closed_y1'],r['c_closed_y2']],[0.5*(1-a*b),(1-a*b),2*(1-a*b)]))\ne=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']))\nprint(\"max err consistent\",np.isclose(e,r['max_abs_error_policy']))\n# Bellman verification of closed form at random points with continuous maximisation\nfrom scipy.optimize import minimize_scalar\nA,B=r['diag_closed_form_A'],r['diag_closed_form_B']\nV=lambda y:A+B*np.log(y)\nfor y in [0.3,1,3]:\n    f=lambda c:-(np.log(c)+b*V((y-c)**a))\n    o=minimize_scalar(f,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(\"final_sup<tol\",r['final_sup_change']<1e-8, \"value gap\",r['value_num_y1']-r['value_closed_y1'])\nprint(\"rel policy err\",[ (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"}}]}}39{"type":"api-request","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","id":"32f684c3-a105-415f-a741-3a8817483f1a","timestamp":"2026-10-30T04:37:40.491Z","version":"2.1.314","querySource":"sdk","shapeHash":"82483642b97bb27a79f8911d058b21de56088dceec9d4a64e63418ec73b440c8","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":"d1070adb-895e-4743-ace1-324a2783b2ff","keep":10,"tail":["eb04ac4ebc2c0087c380601ffa8f137f89a97007c85aba7f803f5e5025fd67d7","00ae19e5f7aa8aedb453462ce2e661a9cdcfdfbfe41214fd1de25afe71d4a32f"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",11,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"a4e9050874ed45877ab8fc12b60e67f489720899c0803b04e7e526539a27f00d"}40{"parentUuid":"8afb0bdf-b4d5-40eb-8798-f5eeffe7af42","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoWow9QiXXYRuZoP7Ch","type":"message","role":"assistant","content":[{"type":"text","text":"Wrong cwd after earlier `cd`."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":872,"cache_read_input_tokens":13643,"output_tokens":782,"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":872},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXoWof21bzsDQRwo7otL","requestRef":"32f684c3-a105-415f-a741-3a8817483f1a","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"102adb68-418f-411d-a57c-07363f649534","timestamp":"2026-10-30T04:37:42.128Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124/out/state","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}41{"parentUuid":"102adb68-418f-411d-a57c-07363f649534","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoWow9QiXXYRuZoP7Ch","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01UksCTM59ttYa4EdLNASQxV","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0124 && cp out/results.json /tmp/r1.json && rm out/results.json && ~/wp29/venv/bin/python out/analysis.py >/dev/null && cmp out/results.json /tmp/r1.json && echo IDENTICAL\n~/wp29/venv/bin/python - <<'EOF'\nimport json,numpy as np\nr=json.load(open('out/results.json'))\na,b=0.36,0.95\nprint(\"c_closed==(1-ab)y\", np.allclose([r['c_closed_y05'],r['c_closed_y1'],r['c_closed_y2']],[0.5*(1-a*b),(1-a*b),2*(1-a*b)]))\ne=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']))\nprint(\"max err consistent\",np.isclose(e,r['max_abs_error_policy']))\nfrom scipy.optimize import minimize_scalar\nA,B=r['diag_closed_form_A'],r['diag_closed_form_B']\nV=lambda y:A+B*np.log(y)\nfor y in [0.3,1,3]:\n    f=lambda c:-(np.log(c)+b*V((y-c)**a))\n    o=minimize_scalar(f,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(\"final_sup<tol\",r['final_sup_change']<1e-8, \"value gap\",r['value_num_y1']-r['value_closed_y1'])\nprint(\"rel policy err\",[ (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":872,"cache_read_input_tokens":13643,"output_tokens":782,"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":872},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXoWof21bzsDQRwo7otL","requestRef":"32f684c3-a105-415f-a741-3a8817483f1a","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"924a1bed-ac0a-41a4-ab6d-a31a6190de64","timestamp":"2026-10-30T04:37:46.817Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124/out/state","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}42{"parentUuid":"924a1bed-ac0a-41a4-ab6d-a31a6190de64","isSidechain":false,"promptId":"1c50b31a-0240-4fbb-9eb0-20840a459bfb","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01UksCTM59ttYa4EdLNASQxV","type":"tool_result","content":"IDENTICAL\nc_closed==(1-ab)y True\nmax err consistent True\n0.3 argmax 0.19740000019735232 closed 0.1974 TV-V 0.0\n1 argmax 0.6579999792181229 closed 0.658 TV-V 0.0\n3 argmax 1.9740000019746047 closed 1.9740000000000002 TV-V 3.552713678800501e-15\nfinal_sup<tol True value gap -0.0003440281002156098\nrel policy err [-0.0005539552572922775, 0.001509908817275246, -0.004844188865506954]","is_error":false}]},"uuid":"801bce8e-3c8b-4fe7-be73-01f77e4104c4","timestamp":"2026-10-30T04:37:47.255Z","toolUseResult":{"stdout":"IDENTICAL\nc_closed==(1-ab)y True\nmax err consistent True\n0.3 argmax 0.19740000019735232 closed 0.1974 TV-V 0.0\n1 argmax 0.6579999792181229 closed 0.658 TV-V 0.0\n3 argmax 1.9740000019746047 closed 1.9740000000000002 TV-V 3.552713678800501e-15\nfinal_sup<tol True value gap -0.0003440281002156098\nrel policy err [-0.0005539552572922775, 0.001509908817275246, -0.004844188865506954]","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"924a1bed-ac0a-41a4-ab6d-a31a6190de64","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}43{"type":"api-request-blob","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","hash":"31092bf30dfad7c1c21e321ce3c1f2bb65805643aebed088d0c0e5aac5100b01","message":{"role":"assistant","content":[{"type":"text","text":"Wrong cwd after earlier `cd`."},{"type":"tool_use","id":"toolu_01UksCTM59ttYa4EdLNASQxV","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0124 && cp out/results.json /tmp/r1.json && rm out/results.json && ~/wp29/venv/bin/python out/analysis.py >/dev/null && cmp out/results.json /tmp/r1.json && echo IDENTICAL\n~/wp29/venv/bin/python - <<'EOF'\nimport json,numpy as np\nr=json.load(open('out/results.json'))\na,b=0.36,0.95\nprint(\"c_closed==(1-ab)y\", np.allclose([r['c_closed_y05'],r['c_closed_y1'],r['c_closed_y2']],[0.5*(1-a*b),(1-a*b),2*(1-a*b)]))\ne=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']))\nprint(\"max err consistent\",np.isclose(e,r['max_abs_error_policy']))\nfrom scipy.optimize import minimize_scalar\nA,B=r['diag_closed_form_A'],r['diag_closed_form_B']\nV=lambda y:A+B*np.log(y)\nfor y in [0.3,1,3]:\n    f=lambda c:-(np.log(c)+b*V((y-c)**a))\n    o=minimize_scalar(f,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(\"final_sup<tol\",r['final_sup_change']<1e-8, \"value gap\",r['value_num_y1']-r['value_closed_y1'])\nprint(\"rel policy err\",[ (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"}}]}}44{"type":"api-request","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","id":"358c7c82-54a0-4100-b63e-67bf9956fd6e","timestamp":"2026-10-30T04:37:47.257Z","version":"2.1.314","querySource":"sdk","shapeHash":"82483642b97bb27a79f8911d058b21de56088dceec9d4a64e63418ec73b440c8","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":"32f684c3-a105-415f-a741-3a8817483f1a","keep":12,"tail":["31092bf30dfad7c1c21e321ce3c1f2bb65805643aebed088d0c0e5aac5100b01","c1c7d7c3a57c3eeeca5fcc8e0bc57b826cb9fd66782db269534b4951ea068978"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",13,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"bcdb00fe39fbb6a6bdf913bf31645f6caf5219c6fa3ebc34f73057690b4519db"}45{"parentUuid":"801bce8e-3c8b-4fe7-be73-01f77e4104c4","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoXJvA76BADR7mCa38N","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":983,"cache_read_input_tokens":14515,"output_tokens":1081,"output_tokens_details":{"thinking_tokens":80},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":983},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":829,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXoXJeYS8SLxfxXPAXu6","requestRef":"358c7c82-54a0-4100-b63e-67bf9956fd6e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6e2784bd-5e30-4a9f-b175-5a8252c27442","timestamp":"2026-10-30T04:37:49.760Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}46{"parentUuid":"6e2784bd-5e30-4a9f-b175-5a8252c27442","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoXJvA76BADR7mCa38N","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_018R7oa5bbYRMwmdiAKR3szk","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0124\ncat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Clean re-run of out/analysis.py regenerates byte-identical out/results.json (cmp) — PASS.\n2. c_closed values equal (1-alpha*beta)*y at y=0.5,1,2 — PASS.\n3. max_abs_error_policy equals max |c_num - c_closed| over the three points — PASS.\n4. Closed form verified as Bellman fixed point by independent continuous maximisation (scipy bounded) at y=0.3,1,3: argmax matches (1-alpha*beta)y to ~2e-8, |TV - V| <= 4e-15 — PASS.\n5. final_sup_change (9.997e-9) < vfi_tolerance (1e-8) — PASS.\n6. Choice-grid bounds never bind (diag_choice_bound_binds = 0) — PASS.\n7. Magnitudes: relative policy errors -0.06%, +0.15%, -0.48%; value gap at y=1 = -3.4e-4 utils (≈ diag_max_abs_value_error_grid order), mean numerical savings rate on grid 0.34202 vs baseline 0.342 — PASS (consistent with grid-discretisation error, log step 0.0115).\n8. contraction_modulus = beta = 0.95 in (0,1) — PASS.\n9. Exclusion ledger: 10 rows in, 0 removed, 10 out — PASS.\nEOF\ncat > out/state/phases.json <<'EOF'\n{\n \"P0\": {\"status\": \"passed\", \"checks\": [\"contract.md written covering question, estimands, outputs, rules, invalidity\"], \"notes\": \"\"},\n \"P1\": {\"status\": \"passed\", \"checks\": [\"sha256 matches bundle.json\", \"10 rows x 3 cols, no missing/duplicates\", \"eval points off-grid recorded\", \"grid adequacy vs closed-form choices checked\"], \"notes\": \"\"},\n \"P2\": {\"status\": \"passed\", \"checks\": [\"baseline_savings_rate_closed_form = alpha*beta computed by analysis.py\"], \"notes\": \"\"},\n \"P3\": {\"status\": \"passed\", \"checks\": [\"analysis.py runs, writes results.json, no randomness\"], \"notes\": \"\"},\n \"P4\": {\"status\": \"running\", \"checks\": [\"clean re-run byte-identical\", \"consistency checks 1-9 in checks.md all PASS\"], \"notes\": \"\"},\n \"P5\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"}\n}\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Write checks and phases, run gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":983,"cache_read_input_tokens":14515,"output_tokens":1081,"output_tokens_details":{"thinking_tokens":80},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":983},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXoXJeYS8SLxfxXPAXu6","requestRef":"358c7c82-54a0-4100-b63e-67bf9956fd6e","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"dbadb67b-6386-48c0-bb94-af3603ce8551","timestamp":"2026-10-30T04:37:57.078Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}47{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"dbadb67b-6386-48c0-bb94-af3603ce8551","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e"}48{"type":"atis-latch","atis":"","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e"}49{"parentUuid":"dbadb67b-6386-48c0-bb94-af3603ce8551","isSidechain":false,"promptId":"1c50b31a-0240-4fbb-9eb0-20840a459bfb","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 1\nPGAR GATE pgar_gate/1.0 — FAILED (10 of 35 checks failed)\n  [ok] file:out/results.json: present\n  [FAIL] file:out/report.md: missing or empty\n  [ok] file:out/analysis.py: present\n  [FAIL] file:out/claims.json: missing or empty\n  [ok] results_json: parsed\n  [ok] key:task_id: ok\n  [ok] key: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: ['P4', 'P5']\n  [ok] reproducibility: regenerated in 0.2s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0124/out/state/gate_receipts/20261030T043757.347619Z.json","is_error":true,"tool_use_id":"toolu_018R7oa5bbYRMwmdiAKR3szk"}]},"uuid":"e4f49f25-ca65-4d1d-b781-c521d8122d96","timestamp":"2026-10-30T04:37:57.352Z","toolUseResult":"Error: Exit code 1\nPGAR GATE pgar_gate/1.0 — FAILED (10 of 35 checks failed)\n  [ok] file:out/results.json: present\n  [FAIL] file:out/report.md: missing or empty\n  [ok] file:out/analysis.py: present\n  [FAIL] file:out/claims.json: missing or empty\n  [ok] results_json: parsed\n  [ok] key:task_id: ok\n  [ok] key: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: ['P4', 'P5']\n  [ok] reproducibility: regenerated in 0.2s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0124/out/state/gate_receipts/20261030T043757.347619Z.json","sandboxed":false,"sourceToolAssistantUUID":"dbadb67b-6386-48c0-bb94-af3603ce8551","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}50{"type":"api-request-blob","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","hash":"4b7b92eafd1384516209aca150035ba1d136b8bdd5578d8527d87be5bd422cc4","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_018R7oa5bbYRMwmdiAKR3szk","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0124\ncat > out/state/checks.md <<'EOF'\n# Verification checks (P4)\n1. Clean re-run of out/analysis.py regenerates byte-identical out/results.json (cmp) — PASS.\n2. c_closed values equal (1-alpha*beta)*y at y=0.5,1,2 — PASS.\n3. max_abs_error_policy equals max |c_num - c_closed| over the three points — PASS.\n4. Closed form verified as Bellman fixed point by independent continuous maximisation (scipy bounded) at y=0.3,1,3: argmax matches (1-alpha*beta)y to ~2e-8, |TV - V| <= 4e-15 — PASS.\n5. final_sup_change (9.997e-9) < vfi_tolerance (1e-8) — PASS.\n6. Choice-grid bounds never bind (diag_choice_bound_binds = 0) — PASS.\n7. Magnitudes: relative policy errors -0.06%, +0.15%, -0.48%; value gap at y=1 = -3.4e-4 utils (≈ diag_max_abs_value_error_grid order), mean numerical savings rate on grid 0.34202 vs baseline 0.342 — PASS (consistent with grid-discretisation error, log step 0.0115).\n8. contraction_modulus = beta = 0.95 in (0,1) — PASS.\n9. Exclusion ledger: 10 rows in, 0 removed, 10 out — PASS.\nEOF\ncat > out/state/phases.json <<'EOF'\n{\n \"P0\": {\"status\": \"passed\", \"checks\": [\"contract.md written covering question, estimands, outputs, rules, invalidity\"], \"notes\": \"\"},\n \"P1\": {\"status\": \"passed\", \"checks\": [\"sha256 matches bundle.json\", \"10 rows x 3 cols, no missing/duplicates\", \"eval points off-grid recorded\", \"grid adequacy vs closed-form choices checked\"], \"notes\": \"\"},\n \"P2\": {\"status\": \"passed\", \"checks\": [\"baseline_savings_rate_closed_form = alpha*beta computed by analysis.py\"], \"notes\": \"\"},\n \"P3\": {\"status\": \"passed\", \"checks\": [\"analysis.py runs, writes results.json, no randomness\"], \"notes\": \"\"},\n \"P4\": {\"status\": \"running\", \"checks\": [\"clean re-run byte-identical\", \"consistency checks 1-9 in checks.md all PASS\"], \"notes\": \"\"},\n \"P5\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"}\n}\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Write checks and phases, run gate"}}]}}51{"type":"api-request","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","id":"d07aa824-000f-4930-8205-c3d04538c381","timestamp":"2026-10-30T04:37:57.355Z","version":"2.1.314","querySource":"sdk","shapeHash":"82483642b97bb27a79f8911d058b21de56088dceec9d4a64e63418ec73b440c8","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":"358c7c82-54a0-4100-b63e-67bf9956fd6e","keep":14,"tail":["4b7b92eafd1384516209aca150035ba1d136b8bdd5578d8527d87be5bd422cc4","5c7e2eef9feb44e13ede32d3700104139cc368cd2aba95f932b23e7613f48273"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",15,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"ff5addea0a0ae7cb1fbe074104614225823e0d577d8944b660d9f044b32d7741"}52{"parentUuid":"e4f49f25-ca65-4d1d-b781-c521d8122d96","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoY45UQ3XiynJyJQ2xs","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":1836,"cache_read_input_tokens":15498,"output_tokens":3601,"output_tokens_details":{"thinking_tokens":60},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1836},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":800,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXoY3o6wRrLY1hhxGevP","requestRef":"d07aa824-000f-4930-8205-c3d04538c381","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"ca05980f-9bb7-41a7-858d-1118a2d1e190","timestamp":"2026-10-30T04:37:59.727Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}53{"parentUuid":"ca05980f-9bb7-41a7-858d-1118a2d1e190","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoY45UQ3XiynJyJQ2xs","type":"message","role":"assistant","content":[{"type":"text","text":"P4-relevant checks (keys, reproducibility) pass; the remaining failures are P5 deliverables. Writing report and claims."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1836,"cache_read_input_tokens":15498,"output_tokens":3601,"output_tokens_details":{"thinking_tokens":60},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1836},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXoY3o6wRrLY1hhxGevP","requestRef":"d07aa824-000f-4930-8205-c3d04538c381","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"2013c0cd-2953-4a8d-812a-6214b5b4f574","timestamp":"2026-10-30T04:37:59.730Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}54{"parentUuid":"2013c0cd-2953-4a8d-812a-6214b5b4f574","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoY45UQ3XiynJyJQ2xs","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_019VCUPpLjLmSBM4K8ZaUQZn","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0124\ncat > out/report.md <<'EOF'\n# F5-conf-04 — VFI against the closed-form policy (log-utility optimal growth)\n\n## Question\nA planner maximises Σ β^t ln c_t subject to y_{t+1} = (y_t − c_t)^α (Cobb–Douglas, full depreciation, productivity 1). We derive the closed-form policy and value function, solve the Bellman equation numerically by value-function iteration (VFI) on the prescribed grid, and compare the two at y = 0.5, 1, 2 (policy) and y = 1 (value).\n\n## Data and exclusions\nOnly `data/model.csv` (10 parameter rows, `n_input_rows`; SHA-256 checked, see `out/state/data_audit.md`): α = 0.36, β = 0.95, 400 grid points log-spaced on [0.05, 5] (`grid_points_used` = `n_analysed` = 400), tolerance 1e-8. No rows excluded (`out/exclusions.csv`). One design issue (`data_issues`): the evaluation points 0.5, 1, 2 are not grid nodes (log step = `diag_grid_log_step` ≈ 0.01154), so the VFI policy and value are linearly interpolated in ln y between adjacent nodes, as TASK.md allows. No other deviation from the prescribed design.\n\n## Method\n**Closed form (guess and verify).** Assumptions: log utility, Cobb–Douglas technology y' = k^α with 0<α<1, full depreciation, productivity 1, 0<β<1, interior solution 0<c<y. Guess V(y) = A + B ln y. The FOC of max_c {ln c + β(A + Bα ln(y−c))} gives 1/c = αβB/(y−c), i.e. c = y/(1+αβB). Matching the coefficient on ln y gives B = 1 + αβB ⇒ B = 1/(1−αβ), hence\n\n c(y) = (1 − αβ) y,  savings rate (y−c)/y = αβ,\n A = [ln(1−αβ) + (αβ/(1−αβ)) ln(αβ)] / (1−β).\n\nWith α=0.36, β=0.95: B = `diag_closed_form_B` ≈ 1.5198, A = `diag_closed_form_A` ≈ −19.524. The solution was verified numerically as a Bellman fixed point by independent continuous maximisation (`out/state/checks.md`, check 4). The interior solution holds for every y>0 because c/y = 1−αβ ∈ (0,1).\n\n**Contraction.** The Bellman operator T satisfies Blackwell's sufficient conditions on bounded functions: monotonicity (V ≤ W ⇒ TV ≤ TW) and discounting (T(V+a) = TV + βa). Hence it is a contraction in the sup norm with modulus β (`contraction_modulus` = 0.95). On the finite grid with discrete choice, utility is bounded, so this applies directly to the discretised operator, guaranteeing a unique fixed point and geometric convergence from any start.\n\n**VFI.** State: the 400 log-spaced y nodes. Control: next-period output y' chosen from the same grid, with consumption c = y − y'^{1/α} (infeasible pairs c ≤ 0 excluded). V_0 = 0; iterate V_{n+1}(y) = max_{y'} {ln c + β V_n(y')} until sup|V_{n+1} − V_n| < 1e-8. The policy c(y) on the grid comes from the argmax of the converged VFI (never from the closed form), then is interpolated linearly in ln y at the evaluation points. Choice-grid bounds never bind (`diag_choice_bound_binds` = 0). No randomness (`random_seed` = null). Baseline: the closed-form savings rate (`baseline_savings_rate_closed_form`).\n\n## Results\n| y | closed form c | VFI c |\n|---|---|---|\n| 0.5 | 0.3290 (`c_closed_y05`) | 0.32882 (`c_num_y05`) |\n| 1.0 | 0.6580 (`c_closed_y1`) | 0.65899 (`c_num_y1`) |\n| 2.0 | 1.3160 (`c_closed_y2`) | 1.30963 (`c_num_y2`) |\n\n- Maximum absolute policy discrepancy over the three points: 0.00637 units of output (`max_abs_error_policy`), attained at y = 2 (≈0.5% relative).\n- V(1): closed form −19.52441 (`value_closed_y1`), VFI −19.52476 (`value_num_y1`); gap ≈ 3.4e-4 utils.\n- Closed-form savings rate αβ = 0.342 (`savings_rate_closed_form`); the average VFI savings rate over grid nodes is 0.34202 (`diag_mean_savings_rate_num_grid`).\n- VFI converged in 361 iterations (`n_iterations`) with final sup-norm change 9.997e-9 (`final_sup_change`) < 1e-8.\n- Over all grid nodes: max |V_num − V_closed| = 4.8e-4 (`diag_max_abs_value_error_grid`), max |c_num − c_closed| = 0.0251 (`diag_max_abs_policy_error_grid`).\n\n## Uncertainty\nThe problem is deterministic; there is no sampling uncertainty. The only errors are numerical:\n(i) stopping error: by the contraction property, ‖V_n − V*_grid‖ ≤ β/(1−β)·`final_sup_change` ≈ 1.9e-7 (`diag_stopping_error_bound`), negligible relative to (ii);\n(ii) discretisation error: the control y' is restricted to grid nodes (log step ≈ 0.0115), so the chosen y' can be off by up to half a step in ln y', which shifts consumption by roughly (k/α)·Δln y'/2 — growing with y (hence the largest error at y = 2 and the larger grid-wide max at high y); plus linear interpolation error between nodes at the evaluation points. The value function is much more accurate than the policy (envelope/first-order-condition argument: value errors are second order in policy errors).\n\n## Limitations and open issues\n- Scope of the validation: one parameter point (α=0.36, β=0.95), one grid (400 log-spaced points on [0.05, 5]), discrete choice on the same grid, linear interpolation in ln y. The discrepancy figures are specific to this design; they would shrink with a finer grid or a continuous-choice (interpolated) maximisation, which were not run because they are not part of the prescribed design.\n- Policy errors at the evaluation points partly reflect where 0.5, 1, 2 fall between grid nodes (they are not nodes; see `data_issues`); the reported errors are not monotone in y for that reason.\n- The closed form relies on log utility, Cobb–Douglas output, full depreciation and productivity normalised to one; it does not extend to partial depreciation or CRRA ≠ 1.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The closed-form policy is c(y) = (1-alpha*beta) y, giving consumption 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 reproduces the closed-form policy at the three evaluation points with a maximum absolute discrepancy of about 0.0064 units of output (largest at y = 2).\",\"results_keys\":[\"c_num_y05\",\"c_num_y1\",\"c_num_y2\",\"max_abs_error_policy\",\"grid_points_used\"],\"status\":\"supported\",\"caveat\":\"Discretisation and interpolation error specific to this grid and parameter point.\"},\n {\"id\":\"C3\",\"text\":\"The VFI value at y = 1 (-19.52476) matches the closed-form V(1) (-19.52441) to about 3.4e-4 utils.\",\"results_keys\":[\"value_num_y1\",\"value_closed_y1\"],\"status\":\"supported\",\"caveat\":\"Evaluated by interpolation since y = 1 is not a grid node.\"},\n {\"id\":\"C4\",\"text\":\"The Bellman operator is a sup-norm contraction with modulus beta = 0.95; VFI converged in 361 iterations with final sup change below 1e-8, implying a stopping error bound of about 1.9e-7.\",\"results_keys\":[\"contraction_modulus\",\"n_iterations\",\"final_sup_change\",\"diag_stopping_error_bound\"],\"status\":\"supported\",\"caveat\":\"Blackwell conditions apply to bounded functions; satisfied on the finite discrete grid.\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P4']['status']='passed'\np['P4']['checks'].append(\"gate run 1 receipt out/state/gate_receipts/20261030T043757.347619Z.json: all results-key and reproducibility checks ok; only failures were P5 deliverables (report, claims) and non-terminal phase ledger\")\np['P5']['status']='passed'\np['P5']['checks']=[\"report.md with 6 sections citing results keys\",\"claims.json with 4 claims referencing existing keys\",\"final gate run (receipt recorded below)\"]\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P4 passed (gate run 1: only P5 items missing). P5: report and claims written.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Write report, claims, update ledger, rerun gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1836,"cache_read_input_tokens":15498,"output_tokens":3601,"output_tokens_details":{"thinking_tokens":60},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1836},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXoY3o6wRrLY1hhxGevP","requestRef":"d07aa824-000f-4930-8205-c3d04538c381","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"b0feb828-1434-4036-8a09-3a5e686854de","timestamp":"2026-10-30T04:38:27.613Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}55{"parentUuid":"b0feb828-1434-4036-8a09-3a5e686854de","isSidechain":false,"promptId":"1c50b31a-0240-4fbb-9eb0-20840a459bfb","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_019VCUPpLjLmSBM4K8ZaUQZn","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 35 checks failed)\n  [ok] file:out/results.json: present\n  [ok] file:out/report.md: present\n  [ok] file:out/analysis.py: present\n  [ok] file:out/claims.json: present\n  [ok] results_json: parsed\n  [ok] key:task_id: ok\n  [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  [ok] section:Question: present\n  [ok] section:Data and exclusions: present\n  [ok] section:Method: present\n  [ok] section:Results: present\n  [ok] section:Uncertainty: present\n  [ok] section:Limitations and open issues: present\n  [ok] claims_json: 4 claims, all keys resolve\n  [ok] phase_ledger: consistent\n  [ok] reproducibility: regenerated in 0.2s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0124/out/state/gate_receipts/20261030T043827.897724Z.json","is_error":false}]},"uuid":"5bc7cb99-ef9e-4fd6-a71d-cee7a4db6b7a","timestamp":"2026-10-30T04:38:27.903Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 35 checks failed)\n  [ok] file:out/results.json: present\n  [ok] file:out/report.md: present\n  [ok] file:out/analysis.py: present\n  [ok] file:out/claims.json: present\n  [ok] results_json: parsed\n  [ok] key:task_id: ok\n  [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  [ok] section:Question: present\n  [ok] section:Data and exclusions: present\n  [ok] section:Method: present\n  [ok] section:Results: present\n  [ok] section:Uncertainty: present\n  [ok] section:Limitations and open issues: present\n  [ok] claims_json: 4 claims, all keys resolve\n  [ok] phase_ledger: consistent\n  [ok] reproducibility: regenerated in 0.2s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0124/out/state/gate_receipts/20261030T043827.897724Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"b0feb828-1434-4036-8a09-3a5e686854de","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0124","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","version":"2.1.314","gitBranch":"HEAD"}56{"type":"api-request-blob","sessionId":"f60adb53-fb95-4bac-9975-53cbe3be4a9e","hash":"929f475c1836c00c17f36d6063563afdbde6df228a1bab81257ba4e3e0c91a81","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"P4-relevant checks (keys, reproducibility) pass; the remaining failures are P5 deliverables. Writing report and claims."},{"type":"tool_use","id":"toolu_019VCUPpLjLmSBM4K8ZaUQZn","name":"Bash","input":{"command":"cd /Users/simon-pierreboucher/wp29/runs/RC0124\ncat > out/report.md <<'EOF'\n# F5-conf-04 — VFI against the closed-form policy (log-utility optimal growth)\n\n## Question\nA planner maximises Σ β^t ln c_t subject to y_{t+1} = (y_t − c_t)^α (Cobb–Douglas, full depreciation, productivity 1). We derive the closed-form policy and value function, solve the Bellman equation numerically by value-function iteration (VFI) on the prescribed grid, and compare the two at y = 0.5, 1, 2 (policy) and y = 1 (value).\n\n## Data and exclusions\nOnly `data/model.csv` (10 parameter rows, `n_input_rows`; SHA-256 checked, see `out/state/data_audit.md`): α = 0.36, β = 0.95, 400 grid points log-spaced on [0.05, 5] (`grid_points_used` = `n_analysed` = 400), tolerance 1e-8. No rows excluded (`out/exclusions.csv`). One design issue (`data_issues`): the evaluation points 0.5, 1, 2 are not grid nodes (log step = `diag_grid_log_step` ≈ 0.01154), so the VFI policy and value are linearly interpolated in ln y between adjacent nodes, as TASK.md allows. No other deviation from the prescribed design.\n\n## Method\n**Closed form (guess and verify).** Assumptions: log utility, Cobb–Douglas technology y' = k^α with 0<α<1, full depreciation, productivity 1, 0<β<1, interior solution 0<c<y. Guess V(y) = A + B ln y. The FOC of max_c {ln c + β(A + Bα ln(y−c))} gives 1/c = αβB/(y−c), i.e. c = y/(1+αβB). Matching the coefficient on ln y gives B = 1 + αβB ⇒ B = 1/(1−αβ), hence\n\n c(y) = (1 − αβ) y,  savings rate (y−c)/y = αβ,\n A = [ln(1−αβ) + (αβ/(1−αβ)) ln(αβ)] / (1−β).\n\nWith α=0.36, β=0.95: B = `diag_closed_form_B` ≈ 1.5198, A = `diag_closed_form_A` ≈ −19.524. The solution was verified numerically as a Bellman fixed point by independent continuous maximisation (`out/state/checks.md`, check 4). The interior solution holds for every y>0 because c/y = 1−αβ ∈ (0,1).\n\n**Contraction.** The Bellman operator T satisfies Blackwell's sufficient conditions on bounded functions: monotonicity (V ≤ W ⇒ TV ≤ TW) and discounting (T(V+a) = TV + βa). Hence it is a contraction in the sup norm with modulus β (`contraction_modulus` = 0.95). On the finite grid with discrete choice, utility is bounded, so this applies directly to the discretised operator, guaranteeing a unique fixed point and geometric convergence from any start.\n\n**VFI.** State: the 400 log-spaced y nodes. Control: next-period output y' chosen from the same grid, with consumption c = y − y'^{1/α} (infeasible pairs c ≤ 0 excluded). V_0 = 0; iterate V_{n+1}(y) = max_{y'} {ln c + β V_n(y')} until sup|V_{n+1} − V_n| < 1e-8. The policy c(y) on the grid comes from the argmax of the converged VFI (never from the closed form), then is interpolated linearly in ln y at the evaluation points. Choice-grid bounds never bind (`diag_choice_bound_binds` = 0). No randomness (`random_seed` = null). Baseline: the closed-form savings rate (`baseline_savings_rate_closed_form`).\n\n## Results\n| y | closed form c | VFI c |\n|---|---|---|\n| 0.5 | 0.3290 (`c_closed_y05`) | 0.32882 (`c_num_y05`) |\n| 1.0 | 0.6580 (`c_closed_y1`) | 0.65899 (`c_num_y1`) |\n| 2.0 | 1.3160 (`c_closed_y2`) | 1.30963 (`c_num_y2`) |\n\n- Maximum absolute policy discrepancy over the three points: 0.00637 units of output (`max_abs_error_policy`), attained at y = 2 (≈0.5% relative).\n- V(1): closed form −19.52441 (`value_closed_y1`), VFI −19.52476 (`value_num_y1`); gap ≈ 3.4e-4 utils.\n- Closed-form savings rate αβ = 0.342 (`savings_rate_closed_form`); the average VFI savings rate over grid nodes is 0.34202 (`diag_mean_savings_rate_num_grid`).\n- VFI converged in 361 iterations (`n_iterations`) with final sup-norm change 9.997e-9 (`final_sup_change`) < 1e-8.\n- Over all grid nodes: max |V_num − V_closed| = 4.8e-4 (`diag_max_abs_value_error_grid`), max |c_num − c_closed| = 0.0251 (`diag_max_abs_policy_error_grid`).\n\n## Uncertainty\nThe problem is deterministic; there is no sampling uncertainty. The only errors are numerical:\n(i) stopping error: by the contraction property, ‖V_n − V*_grid‖ ≤ β/(1−β)·`final_sup_change` ≈ 1.9e-7 (`diag_stopping_error_bound`), negligible relative to (ii);\n(ii) discretisation error: the control y' is restricted to grid nodes (log step ≈ 0.0115), so the chosen y' can be off by up to half a step in ln y', which shifts consumption by roughly (k/α)·Δln y'/2 — growing with y (hence the largest error at y = 2 and the larger grid-wide max at high y); plus linear interpolation error between nodes at the evaluation points. The value function is much more accurate than the policy (envelope/first-order-condition argument: value errors are second order in policy errors).\n\n## Limitations and open issues\n- Scope of the validation: one parameter point (α=0.36, β=0.95), one grid (400 log-spaced points on [0.05, 5]), discrete choice on the same grid, linear interpolation in ln y. The discrepancy figures are specific to this design; they would shrink with a finer grid or a continuous-choice (interpolated) maximisation, which were not run because they are not part of the prescribed design.\n- Policy errors at the evaluation points partly reflect where 0.5, 1, 2 fall between grid nodes (they are not nodes; see `data_issues`); the reported errors are not monotone in y for that reason.\n- The closed form relies on log utility, Cobb–Douglas output, full depreciation and productivity normalised to one; it does not extend to partial depreciation or CRRA ≠ 1.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The closed-form policy is c(y) = (1-alpha*beta) y, giving consumption 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 reproduces the closed-form policy at the three evaluation points with a maximum absolute discrepancy of about 0.0064 units of output (largest at y = 2).\",\"results_keys\":[\"c_num_y05\",\"c_num_y1\",\"c_num_y2\",\"max_abs_error_policy\",\"grid_points_used\"],\"status\":\"supported\",\"caveat\":\"Discretisation and interpolation error specific to this grid and parameter point.\"},\n {\"id\":\"C3\",\"text\":\"The VFI value at y = 1 (-19.52476) matches the closed-form V(1) (-19.52441) to about 3.4e-4 utils.\",\"results_keys\":[\"value_num_y1\",\"value_closed_y1\"],\"status\":\"supported\",\"caveat\":\"Evaluated by interpolation since y = 1 is not a grid node.\"},\n {\"id\":\"C4\",\"text\":\"The Bellman operator is a sup-norm contraction with modulus beta = 0.95; VFI converged in 361 iterations with final sup change below 1e-8, implying a stopping error bound of about 1.9e-7.\",\"results_keys\":[\"contraction_modulus\",\"n_iterations\",\"final_sup_change\",\"diag_stopping_error_bound\"],\"status\":\"supported\",\"caveat\":\"Blackwell conditions apply to bounded functions; satisfied on the finite discrete grid.\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open('out/state/phases.json'))\np['P4']['status']='passed'\np['P4']['checks'].append(\"gate run 1 receipt out/state/gate_receipts/20261030T043757.347619Z.json: all results-key and reproducibility checks ok; only failures were P5 deliverables (report, claims) and non-terminal phase ledger\")\np['P5']['status']='passed'\np['P5']['checks']=[\"report.md with 6 sections citing results keys\",\"claims.json with 4 claims referencing existing keys\",\"final gate run (receipt recorded below)\"]\njson.dump(p,open('out/state/phases.json','w'),indent=1)\nEOF\necho \"- 2026-10-30 P4 passed (gate run 1: only P5 items missing). 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The largest policy gap at the three evaluation points is about 0.0064 units of output. The final gate check passed with no failures, and a clean re-run of `out/analysis.py` reproduced `out/results.json` exactly.\n\n**Closed form.** I derived it by guessing V(y) = A + B ln y and checking it in the Bellman equation. This gives consumption c(y) = (1 − αβ)y and a savings rate of αβ = 0.342, with B = 1/(1 − αβ) ≈ 1.520 and A ≈ −19.524. An independent numerical maximisation at three points confirmed that this solution satisfies the Bellman equation. The Bellman operator shrinks distances by a factor of β = 0.95 at each step (it meets Blackwell's conditions), so that is the contraction modulus.\n\n**Numerical solution.** The value-function iteration starts from V = 0 and picks next-period output from the same 400 log-spaced points. It converged in 361 iterations, with a final change of 9.997e-9, just under the 1e-8 tolerance. The edges of the grid never constrained the choice. No randomness is involved.\n\n| y | closed form c | numerical c |\n|---|---|---|\n| 0.5 | 0.329 | 0.32882 |\n| 1.0 | 0.658 | 0.65899 |\n| 2.0 | 1.316 | 1.30963 |\n\n- **Largest policy gap:** 0.00637, at y = 2 (about 0.5%).\n- **Value at y = 1:** −19.52441 (closed form) against −19.52476 (numerical), a gap of about 3.4e-4.\n- **Error sources:** the error from stopping the iteration is at most about 1.9e-7, so nearly all the gap comes from the grid. Next-period output can only take grid values, and the policy has to be interpolated between grid points.\n\n**Limitations:**\n- None of the evaluation points (0.5, 1, 2) is a grid point, so the numerical policy and value there are interpolated linearly in ln y. This is listed under `data_issues`.\n- The comparison covers only this one parameter setting and this one grid. 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