spb/wp29_uqo

1{"type":"atis-latch","atis":"","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746"}2{"type":"queue-operation","operation":"enqueue","timestamp":"2026-10-30T04:38:38.282Z","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","content":"Begin"}3{"type":"queue-operation","operation":"dequeue","timestamp":"2026-10-30T04:38:38.289Z","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746"}4{"parentUuid":null,"isSidechain":false,"promptId":"98c76955-6ef3-4dd0-ad59-6beeb3568c50","type":"user","message":{"role":"user","content":"Begin"},"uuid":"43ecd681-edfc-41dc-9837-779a428c021d","timestamp":"2026-10-30T04:38:38.294Z","permissionMode":"default","promptSource":"sdk","turnOrigin":"sdk","turnPosition":{"promptIndex":0,"turnIndex":1},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}5{"type":"api-request-shape","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","shapeHash":"74261e6e7cd56f87bea65087889d4ddf98044e0fbeb6aae5c04c10263b2c127e","timestamp":"2026-10-30T04:38:38.308Z","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/RC0130\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/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746"}12{"parentUuid":"04ed7878-2405-425d-adbd-3ab56750a0dd","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXob5PSGcMLeYj7QU7Hs","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":117,"output_tokens_details":{"thinking_tokens":15},"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":479,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXob5CGmgkJNDXHKPjnm","requestRef":"68f10443-1970-4c06-9fcf-17ba2ea1c605","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"55979bf5-2fcd-4ed2-a61c-218f9ae11009","timestamp":"2026-10-30T04:38:39.283Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"55979bf5-2fcd-4ed2-a61c-218f9ae11009","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXob5PSGcMLeYj7QU7Hs","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Fnp9AMjxUqE8yr6b6egWh7","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  83 simon-pierreboucher  staff  2656 oct.  30 00:38 ..\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\ndata:\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_01Fnp9AMjxUqE8yr6b6egWh7"}]},"uuid":"d2f20070-56ff-49e9-a7ef-6794498983a4","timestamp":"2026-10-30T04:38:39.863Z","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  83 simon-pierreboucher  staff  2656 oct.  30 00:38 ..\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\ndata:\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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-n \"exclusion\\|phases\\|claims\\|receipt\" ~/wp29/gates/pgar_gate.py | head -60","description":"Inspect gate 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a receipt to <workspace_dir>/out/state/gate_receipts/<utc>.json and exits 0 if passed, 1 otherwise.\n106:    # 4. claims\n107:    claims, cerr = _load_json(os.path.join(ws, \"out\", \"claims.json\"))\n108:    if \"claims_reference_existing_keys\" in fam or os.path.exists(os.path.join(ws, \"out\", \"claims.json\")):\n109:        if not isinstance(claims, list) or not claims:\n110:            add(\"claims_json\", False, f\"out/claims.json {cerr or 'must be a non-empty list'}\")\n113:            for i, c in enumerate(claims):\n121:            add(\"claims_json\", not bad, \"; \".join(bad) if bad else f\"{len(claims)} claims, all keys resolve\")\n123:    pl_path = os.path.join(ws, \"out\", \"state\", \"phases.json\")\n127:            add(\"phase_ledger\", False, f\"phases.json {perr or 'not an object'}\")\n137:                bad.append(f\"phases not terminal: {not_done}\")\n139:    # 6. exclusion ledger\n140:    ex_path = os.path.join(ws, \"out\", \"exclusions.csv\")\n141:    if \"exclusion_ledger_sums\" in fam and os.path.exists(ex_path):\n153:            add(\"exclusion_ledger\", not bad, \"; \".join(bad) if bad else f\"{len(rows)} steps consistent\")\n155:            add(\"exclusion_ledger\", False, f\"unreadable: {e}\")\n215:    receipt = {\"gate_version\": GATE_VERSION, \"workspace\": ws, \"utc\": datetime.datetime.now(datetime.timezone.utc).isoformat(),\n218:        d = os.path.join(ws, \"out\", \"state\", \"gate_receipts\"); os.makedirs(d, exist_ok=True)\n221:            json.dump(receipt, fh, indent=1)\n222:        receipt[\"receipt_path\"] = path\n223:        receipt[\"receipt_sha256\"] = hashlib.sha256(open(path, \"rb\").read()).hexdigest()\n225:        receipt[\"receipt_path\"] = None; receipt[\"receipt_error\"] = str(e)\n226:    return receipt\n245:        print(f\"receipt: {r.get('receipt_path')}\")","is_error":false}]},"uuid":"25493c08-68a3-43bb-9b70-0117efa85122","timestamp":"2026-10-30T04:38:56.182Z","toolUseResult":{"stdout":"7:Writes a receipt to <workspace_dir>/out/state/gate_receipts/<utc>.json and exits 0 if passed, 1 otherwise.\n106:    # 4. claims\n107:    claims, cerr = _load_json(os.path.join(ws, \"out\", \"claims.json\"))\n108:    if \"claims_reference_existing_keys\" in fam or os.path.exists(os.path.join(ws, \"out\", \"claims.json\")):\n109:        if not isinstance(claims, list) or not claims:\n110:            add(\"claims_json\", False, f\"out/claims.json {cerr or 'must be a non-empty list'}\")\n113:            for i, c in enumerate(claims):\n121:            add(\"claims_json\", not bad, \"; \".join(bad) if bad else f\"{len(claims)} claims, all keys resolve\")\n123:    pl_path = os.path.join(ws, \"out\", \"state\", \"phases.json\")\n127:            add(\"phase_ledger\", False, f\"phases.json {perr or 'not an object'}\")\n137:                bad.append(f\"phases not terminal: {not_done}\")\n139:    # 6. exclusion ledger\n140:    ex_path = os.path.join(ws, \"out\", \"exclusions.csv\")\n141:    if \"exclusion_ledger_sums\" in fam and os.path.exists(ex_path):\n153:            add(\"exclusion_ledger\", not bad, \"; \".join(bad) if bad else f\"{len(rows)} steps consistent\")\n155:            add(\"exclusion_ledger\", False, f\"unreadable: {e}\")\n215:    receipt = {\"gate_version\": GATE_VERSION, \"workspace\": ws, \"utc\": datetime.datetime.now(datetime.timezone.utc).isoformat(),\n218:        d = os.path.join(ws, \"out\", \"state\", \"gate_receipts\"); os.makedirs(d, exist_ok=True)\n221:            json.dump(receipt, fh, indent=1)\n222:        receipt[\"receipt_path\"] = path\n223:        receipt[\"receipt_sha256\"] = hashlib.sha256(open(path, \"rb\").read()).hexdigest()\n225:        receipt[\"receipt_path\"] = None; receipt[\"receipt_error\"] = str(e)\n226:    return receipt\n245:        print(f\"receipt: {r.get('receipt_path')}\")","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"aafa5ad8-ecce-404c-8850-23f39ba89e7b","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}26{"type":"api-request-blob","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","hash":"948c02f80e9d9e6768afd627ff5fa5a36424e3d60dbb2196e972ac889e7ea6c8","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"tool_use","id":"toolu_01XW47czARxZqvnzuEzeGMji","name":"Bash","input":{"command":"grep -n \"exclusion\\|phases\\|claims\\|receipt\" ~/wp29/gates/pgar_gate.py | head -60","description":"Inspect gate checks"}}]}}27{"type":"api-request","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","id":"38095d37-3284-4824-9875-b35d2eb8dd9d","timestamp":"2026-10-30T04:38:56.185Z","version":"2.1.314","querySource":"sdk","shapeHash":"74261e6e7cd56f87bea65087889d4ddf98044e0fbeb6aae5c04c10263b2c127e","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":"107d20c0-d8ac-4808-9ed9-39d2da5b71dd","keep":6,"tail":["948c02f80e9d9e6768afd627ff5fa5a36424e3d60dbb2196e972ac889e7ea6c8","7c508847a5bfba0a13d1d693bab7820dd6ae341527f679cfe6ad96535b9c6b9c"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"1e274ecc2d0fd957e387198291e37aae6b92354e6963b68383e1cad51ab350c4"}28{"parentUuid":"25493c08-68a3-43bb-9b70-0117efa85122","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXocPqUEp1ZPLiJqha2Z","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01NNeLEUzdJBP5PFABHNKWbC","name":"Bash","input":{"command":"sed -n 100,160p ~/wp29/gates/pgar_gate.py","description":"Read gate ledger checks"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2178,"cache_read_input_tokens":7868,"output_tokens":102,"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":2178},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXocPZ72TKPyJxWnUW93","requestRef":"38095d37-3284-4824-9875-b35d2eb8dd9d","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"2a29fd02-9ccb-4672-9453-255ab430586e","timestamp":"2026-10-30T04:38:57.504Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}29{"parentUuid":"2a29fd02-9ccb-4672-9453-255ab430586e","isSidechain":false,"promptId":"98c76955-6ef3-4dd0-ad59-6beeb3568c50","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01NNeLEUzdJBP5PFABHNKWbC","type":"tool_result","content":"    except Exception:  # noqa: BLE001\n        pass\n    for s in spec.get(\"report_sections\", []):\n        ok = re.search(NUMERIC_RE + re.escape(s) + r\"\\s*$\", rep, re.M | re.I) is not None\n        add(f\"section:{s}\", ok, \"present\" if ok else \"heading not found\")\n    fam = set(spec.get(\"family_checks\", []))\n    # 4. claims\n    claims, cerr = _load_json(os.path.join(ws, \"out\", \"claims.json\"))\n    if \"claims_reference_existing_keys\" in fam or os.path.exists(os.path.join(ws, \"out\", \"claims.json\")):\n        if not isinstance(claims, list) or not claims:\n            add(\"claims_json\", False, f\"out/claims.json {cerr or 'must be a non-empty list'}\")\n        else:\n            bad = []\n            for i, c in enumerate(claims):\n                if not isinstance(c, dict) or not all(k in c for k in (\"id\", \"text\", \"results_keys\", \"status\")):\n                    bad.append(f\"#{i}: missing fields\"); continue\n                if c[\"status\"] not in (\"supported\", \"unsupported\", \"not_evaluated\"):\n                    bad.append(f\"{c.get('id')}: bad status {c['status']!r}\")\n                missing = [k for k in (c.get(\"results_keys\") or []) if k not in res]\n                if missing:\n                    bad.append(f\"{c.get('id')}: results_keys not in results.json: {missing}\")\n            add(\"claims_json\", not bad, \"; \".join(bad) if bad else f\"{len(claims)} claims, all keys resolve\")\n    # 5. phase ledger\n    pl_path = os.path.join(ws, \"out\", \"state\", \"phases.json\")\n    if \"phase_ledger_consistent\" in fam and os.path.exists(pl_path):\n        pl, perr = _load_json(pl_path)\n        if not isinstance(pl, dict):\n            add(\"phase_ledger\", False, f\"phases.json {perr or 'not an object'}\")\n        else:\n            bad = []\n            for pid, st in pl.items():\n                if not isinstance(st, dict) or st.get(\"status\") not in (\"pending\", \"running\", \"passed\", \"failed\", \"blocked\", \"stale\", \"skipped_optional\"):\n                    bad.append(f\"{pid}: invalid status\"); continue\n                if st.get(\"status\") == \"passed\" and not st.get(\"checks\"):\n                    bad.append(f\"{pid}: passed without recorded checks\")\n            not_done = [pid for pid, st in pl.items() if isinstance(st, dict) and st.get(\"status\") not in (\"passed\", \"skipped_optional\", \"blocked\")]\n            if not_done:\n                bad.append(f\"phases not terminal: {not_done}\")\n            add(\"phase_ledger\", not bad, \"; \".join(bad) if bad else \"consistent\")\n    # 6. exclusion ledger\n    ex_path = os.path.join(ws, \"out\", \"exclusions.csv\")\n    if \"exclusion_ledger_sums\" in fam and os.path.exists(ex_path):\n        try:\n            rows = list(csv.DictReader(open(ex_path, newline=\"\")))\n            bad = []\n            prev_after = None\n            for i, r in enumerate(rows):\n                nb, na, nr = int(float(r[\"n_before\"])), int(float(r[\"n_after\"])), int(float(r[\"n_removed\"]))\n                if nb - nr != na:\n                    bad.append(f\"row {i}: n_before - n_removed != n_after\")\n                if prev_after is not None and nb != prev_after:\n                    bad.append(f\"row {i}: n_before != previous n_after\")\n                prev_after = na\n            add(\"exclusion_ledger\", not bad, \"; \".join(bad) if bad else f\"{len(rows)} steps consistent\")\n        except Exception as e:  # noqa: BLE001\n            add(\"exclusion_ledger\", False, f\"unreadable: {e}\")\n    # 7. numeric sanity checks\n    if \"ci_contains_estimate\" in fam:\n        for est, lo, hi in spec.get(\"ci_pairs\", []):\n            e, l, h = res.get(est), res.get(lo), res.get(hi)\n            if all(_is_num(v) for v in (e, l, h)):","is_error":false}]},"uuid":"b4826be2-a7f8-43b2-b8aa-40f73ac0dea2","timestamp":"2026-10-30T04:38:57.528Z","toolUseResult":{"stdout":"    except Exception:  # noqa: BLE001\n        pass\n    for s in spec.get(\"report_sections\", []):\n        ok = re.search(NUMERIC_RE + re.escape(s) + r\"\\s*$\", rep, re.M | re.I) is not None\n        add(f\"section:{s}\", ok, \"present\" if ok else \"heading not found\")\n    fam = set(spec.get(\"family_checks\", []))\n    # 4. claims\n    claims, cerr = _load_json(os.path.join(ws, \"out\", \"claims.json\"))\n    if \"claims_reference_existing_keys\" in fam or os.path.exists(os.path.join(ws, \"out\", \"claims.json\")):\n        if not isinstance(claims, list) or not claims:\n            add(\"claims_json\", False, f\"out/claims.json {cerr or 'must be a non-empty list'}\")\n        else:\n            bad = []\n            for i, c in enumerate(claims):\n                if not isinstance(c, dict) or not all(k in c for k in (\"id\", \"text\", \"results_keys\", \"status\")):\n                    bad.append(f\"#{i}: missing fields\"); continue\n                if c[\"status\"] not in (\"supported\", \"unsupported\", \"not_evaluated\"):\n                    bad.append(f\"{c.get('id')}: bad status {c['status']!r}\")\n                missing = [k for k in (c.get(\"results_keys\") or []) if k not in res]\n                if missing:\n                    bad.append(f\"{c.get('id')}: results_keys not in results.json: {missing}\")\n            add(\"claims_json\", not bad, \"; \".join(bad) if bad else f\"{len(claims)} claims, all keys resolve\")\n    # 5. phase ledger\n    pl_path = os.path.join(ws, \"out\", \"state\", \"phases.json\")\n    if \"phase_ledger_consistent\" in fam and os.path.exists(pl_path):\n        pl, perr = _load_json(pl_path)\n        if not isinstance(pl, dict):\n            add(\"phase_ledger\", False, f\"phases.json {perr or 'not an object'}\")\n        else:\n            bad = []\n            for pid, st in pl.items():\n                if not isinstance(st, dict) or st.get(\"status\") not in (\"pending\", \"running\", \"passed\", \"failed\", \"blocked\", \"stale\", \"skipped_optional\"):\n                    bad.append(f\"{pid}: invalid status\"); continue\n                if st.get(\"status\") == \"passed\" and not st.get(\"checks\"):\n                    bad.append(f\"{pid}: passed without recorded checks\")\n            not_done = [pid for pid, st in pl.items() if isinstance(st, dict) and st.get(\"status\") not in (\"passed\", \"skipped_optional\", \"blocked\")]\n            if not_done:\n                bad.append(f\"phases not terminal: {not_done}\")\n            add(\"phase_ledger\", not bad, \"; \".join(bad) if bad else \"consistent\")\n    # 6. exclusion ledger\n    ex_path = os.path.join(ws, \"out\", \"exclusions.csv\")\n    if \"exclusion_ledger_sums\" in fam and os.path.exists(ex_path):\n        try:\n            rows = list(csv.DictReader(open(ex_path, newline=\"\")))\n            bad = []\n            prev_after = None\n            for i, r in enumerate(rows):\n                nb, na, nr = int(float(r[\"n_before\"])), int(float(r[\"n_after\"])), int(float(r[\"n_removed\"]))\n                if nb - nr != na:\n                    bad.append(f\"row {i}: n_before - n_removed != n_after\")\n                if prev_after is not None and nb != prev_after:\n                    bad.append(f\"row {i}: n_before != previous n_after\")\n                prev_after = na\n            add(\"exclusion_ledger\", not bad, \"; \".join(bad) if bad else f\"{len(rows)} steps consistent\")\n        except Exception as e:  # noqa: BLE001\n            add(\"exclusion_ledger\", False, f\"unreadable: {e}\")\n    # 7. numeric sanity checks\n    if \"ci_contains_estimate\" in fam:\n        for est, lo, hi in spec.get(\"ci_pairs\", []):\n            e, l, h = res.get(est), res.get(lo), res.get(hi)\n            if all(_is_num(v) for v in (e, l, h)):","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"2a29fd02-9ccb-4672-9453-255ab430586e","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}30{"type":"api-request-blob","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","hash":"fb1439f91cade6c371f4de5b09d4fd9acfb7204ca6b58ed2b1dd15b2c7a15287","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01NNeLEUzdJBP5PFABHNKWbC","name":"Bash","input":{"command":"sed -n 100,160p ~/wp29/gates/pgar_gate.py","description":"Read gate ledger checks"}}]}}31{"type":"api-request","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","id":"75a0a488-90ca-42d4-a6be-2cb72df7dcdf","timestamp":"2026-10-30T04:38:57.531Z","version":"2.1.314","querySource":"sdk","shapeHash":"74261e6e7cd56f87bea65087889d4ddf98044e0fbeb6aae5c04c10263b2c127e","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":"38095d37-3284-4824-9875-b35d2eb8dd9d","keep":8,"tail":["fb1439f91cade6c371f4de5b09d4fd9acfb7204ca6b58ed2b1dd15b2c7a15287","17ab42a5371da424caf890efefb049e7edb096e76351e09bb217cc67a39d225f"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",9,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"6832460dcc13f1b349c371e9ac383205ab196d7fa5b05156d7ba2dbb57136739"}32{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"b4826be2-a7f8-43b2-b8aa-40f73ac0dea2","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746"}33{"type":"atis-latch","atis":"","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746"}34{"parentUuid":"b4826be2-a7f8-43b2-b8aa-40f73ac0dea2","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXocVZkePE4fDPRUVp4h","type":"message","role":"assistant","content":[{"type":"text","text":"P0: contract and ledger."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1521,"cache_read_input_tokens":10046,"output_tokens":1052,"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":1521},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXocVJP9zV2ktjiouhQ2","requestRef":"75a0a488-90ca-42d4-a6be-2cb72df7dcdf","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"6202aba6-2dbe-4dfb-814f-ef045546c001","timestamp":"2026-10-30T04:38:58.376Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}35{"parentUuid":"6202aba6-2dbe-4dfb-814f-ef045546c001","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXocVZkePE4fDPRUVp4h","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01KmEVhbU2tiSWtD6bYsrEqw","name":"Bash","input":{"command":"mkdir -p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n\n**Question.** Deterministic optimal growth, log utility, y' = (y-c)^alpha, full depreciation, A=1. Compare the\nclosed-form policy/value (guess-and-verify) with value-function iteration (VFI) on the grid prescribed in data/model.csv.\n\n**Estimands.** c_closed(y) = (1-alpha*beta) y at y=0.5,1,2; VFI policy at those points (linear interpolation between grid\nnodes); max |c_num - c_closed| over the three points; V_closed(1) = A0 (since ln 1 = 0) and V_num(1);\nclosed-form savings rate alpha*beta; contraction modulus of the Bellman operator in sup norm (= beta, by Blackwell,\non the bounded discretised problem); grid points used, VFI iterations, final sup-norm change.\nAssumptions: log utility, Cobb-Douglas technology with A=1, full depreciation, interior solution, 0<alpha<1, 0<beta<1.\n\n**Outputs.** out/results.json (keys: task_id, c_closed_y05/_y1/_y2, c_num_y05/_y1/_y2, max_abs_error_policy,\nvalue_closed_y1, value_num_y1, savings_rate_closed_form, contraction_modulus, grid_points_used, n_iterations,\nfinal_sup_change, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed);\nout/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues);\nout/analysis.py; out/claims.json; plus protocol files (state/, exclusions.csv).\n\n**Information rules.** Only data/model.csv; prescribed grid (400 log-spaced points on [0.05,5]) and parameters;\nnumerical policy from VFI only; deviations go to data_issues.\n\n**Invalidity conditions.** Missing/inconsistent parameters; optimal next-period output leaving the grid (truncation\nbinding); VFI not converging; using the closed form inside the VFI.\nEOF\ncat > phases.json <<'EOF'\n{\"P0\": {\"status\": \"passed\", \"checks\": [\"TASK.md read fully; contract.md written\"], \"notes\": \"\"},\n \"P1\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"},\n \"P2\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"},\n \"P3\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"},\n \"P4\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"},\n \"P5\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"}}\nEOF\necho \"- 2026-10-30 P0 passed: contract written.\" > log.md","description":"Write contract, phase ledger, log"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1521,"cache_read_input_tokens":10046,"output_tokens":1052,"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":1521},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXocVJP9zV2ktjiouhQ2","requestRef":"75a0a488-90ca-42d4-a6be-2cb72df7dcdf","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"dda99bcc-fba5-427b-8c19-72deb3c6b57f","timestamp":"2026-10-30T04:39:06.500Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}36{"parentUuid":"dda99bcc-fba5-427b-8c19-72deb3c6b57f","isSidechain":false,"promptId":"98c76955-6ef3-4dd0-ad59-6beeb3568c50","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01KmEVhbU2tiSWtD6bYsrEqw","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"ab62bfb3-0a49-4dbf-b720-c3dc90cb3cd1","timestamp":"2026-10-30T04:39:06.530Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"dda99bcc-fba5-427b-8c19-72deb3c6b57f","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130/out/state","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}37{"type":"api-request-blob","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","hash":"1ab0b5c7b34de59c3a8feabc2aa67de0407d204762b1be787bb958f5cfc82d1b","message":{"role":"assistant","content":[{"type":"text","text":"P0: contract and ledger."},{"type":"tool_use","id":"toolu_01KmEVhbU2tiSWtD6bYsrEqw","name":"Bash","input":{"command":"mkdir -p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n\n**Question.** Deterministic optimal growth, log utility, y' = (y-c)^alpha, full depreciation, A=1. Compare the\nclosed-form policy/value (guess-and-verify) with value-function iteration (VFI) on the grid prescribed in data/model.csv.\n\n**Estimands.** c_closed(y) = (1-alpha*beta) y at y=0.5,1,2; VFI policy at those points (linear interpolation between grid\nnodes); max |c_num - c_closed| over the three points; V_closed(1) = A0 (since ln 1 = 0) and V_num(1);\nclosed-form savings rate alpha*beta; contraction modulus of the Bellman operator in sup norm (= beta, by Blackwell,\non the bounded discretised problem); grid points used, VFI iterations, final sup-norm change.\nAssumptions: log utility, Cobb-Douglas technology with A=1, full depreciation, interior solution, 0<alpha<1, 0<beta<1.\n\n**Outputs.** out/results.json (keys: task_id, c_closed_y05/_y1/_y2, c_num_y05/_y1/_y2, max_abs_error_policy,\nvalue_closed_y1, value_num_y1, savings_rate_closed_form, contraction_modulus, grid_points_used, n_iterations,\nfinal_sup_change, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed);\nout/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues);\nout/analysis.py; out/claims.json; plus protocol files (state/, exclusions.csv).\n\n**Information rules.** Only data/model.csv; prescribed grid (400 log-spaced points on [0.05,5]) and parameters;\nnumerical policy from VFI only; deviations go to data_issues.\n\n**Invalidity conditions.** Missing/inconsistent parameters; optimal next-period output leaving the grid (truncation\nbinding); VFI not converging; using the closed form inside the VFI.\nEOF\ncat > phases.json <<'EOF'\n{\"P0\": {\"status\": \"passed\", \"checks\": [\"TASK.md read fully; contract.md written\"], \"notes\": \"\"},\n \"P1\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"},\n \"P2\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"},\n \"P3\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"},\n \"P4\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"},\n \"P5\": {\"status\": \"pending\", \"checks\": [], \"notes\": \"\"}}\nEOF\necho \"- 2026-10-30 P0 passed: contract written.\" > log.md","description":"Write contract, phase ledger, 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the analysis script (baseline closed form + VFI)."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1067,"cache_read_input_tokens":11567,"output_tokens":2303,"output_tokens_details":{"thinking_tokens":38},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1067},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXod9p9XiSmdsvtKpsEw","requestRef":"fc823c45-e0f7-4f51-938f-465a5a20a8e9","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"da0ba0d9-3aed-4058-a4fe-49b63664a7be","timestamp":"2026-10-30T04:39:08.040Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130/out/state","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}41{"parentUuid":"da0ba0d9-3aed-4058-a4fe-49b63664a7be","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXodA61x4HVrjBBxoNvF","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_014hdXMuPQLiDjF1D9sMRj4k","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-04: VFI vs closed form, optimal growth with log utility.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nReads only data/model.csv; deterministic (no randomness).\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\ndf = pd.read_csv(os.path.join(ROOT, \"data\", \"model.csv\"))\np = dict(zip(df[\"parameter\"], df[\"value\"]))\nalpha, beta = float(p[\"alpha\"]), float(p[\"beta\"])\ny_min, y_max, N = float(p[\"y_min\"]), float(p[\"y_max\"]), int(float(p[\"grid_points\"]))\ntol = float(p[\"vfi_tolerance\"])\nassert str(p[\"grid_spacing\"]).strip() == \"log\"\nevals = [float(p[\"eval_y_1\"]), float(p[\"eval_y_2\"]), float(p[\"eval_y_3\"])]\ndata_issues = []\n\n# ---------- Closed form (guess-and-verify: V = A0 + B ln y) ----------\nab = alpha * beta\nB = 1.0 / (1.0 - ab)\nA0 = (np.log(1.0 - ab) + ab / (1.0 - ab) * np.log(ab)) / (1.0 - beta)\nc_closed = lambda y: (1.0 - ab) * np.asarray(y)\nV_closed = lambda y: A0 + B * np.log(np.asarray(y))\nsavings_rate = ab  # (y - c)/y\n\n# ---------- VFI on the prescribed grid (discrete choice of next-period output on the grid) ----------\ngrid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))\nk_needed = grid ** (1.0 / alpha)              # capital required to reach each y' on the grid\nC = grid[:, None] - k_needed[None, :]          # consumption for (y today, y' tomorrow)\nfeas = C > 0\nU = np.full(C.shape, -np.inf)\nU[feas] = np.log(C[feas])\nV = np.zeros(N)\nn_iter, sup_change = 0, 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    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_pol = grid - k_needed[pol_idx]\n\n# Diagnostics: is the grid bound binding? (policy at the edge of the y' grid)\nedge_hits = int(np.sum((pol_idx == 0) | (pol_idx == N - 1)))\nyprime_closed = (ab * grid) ** alpha\nif yprime_closed.min() < y_min or yprime_closed.max() > y_max:\n    data_issues.append({\"issue\": \"closed-form next-period output leaves the prescribed grid\",\n                        \"handling\": \"reported; truncation may bias VFI near bounds\"})\n\n# Interpolation at evaluation points: c linear in y; V linear in ln y\nc_num = [float(np.interp(y, grid, c_pol)) for y in evals]\ncc = [float(c_closed(y)) for y in evals]\non_node = [bool(np.any(np.isclose(grid, y, rtol=0, atol=1e-12))) for y in evals]\nV_num_1 = float(np.interp(np.log(1.0), np.log(grid), V))\n\n# Theoretical bound on the remaining VFI error from the stopping rule\nvfi_err_bound = beta / (1 - beta) * sup_change\n\nresults = {\n    \"task_id\": \"F5-conf-04\",\n    \"c_closed_y05\": cc[0], \"c_closed_y1\": cc[1], \"c_closed_y2\": cc[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\": float(max(abs(a - b) for a, b in zip(c_num, cc))),\n    \"value_closed_y1\": float(V_closed(1.0)),\n    \"value_num_y1\": V_num_1,\n    \"savings_rate_closed_form\": float(savings_rate),\n    \"contraction_modulus\": float(beta),\n    \"grid_points_used\": int(N),\n    \"n_iterations\": int(n_iter),\n    \"final_sup_change\": float(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\": int(N),\n    \"random_seed\": None,\n    # supplementary diagnostics\n    \"baseline_closed_form_B_coefficient\": float(B),\n    \"diag_eval_points_on_grid_node\": on_node,\n    \"diag_policy_edge_hits\": edge_hits,\n    \"diag_closed_yprime_min\": float(yprime_closed.min()),\n    \"diag_closed_yprime_max\": float(yprime_closed.max()),\n    \"diag_grid_log_step\": float(np.log(grid[1] / grid[0])),\n    \"diag_vfi_tolerance_error_bound\": float(vfi_err_bound),\n    \"diag_value_abs_error_y1\": float(abs(V_num_1 - float(V_closed(1.0)))),\n    \"diag_value_sup_error_grid\": float(np.max(np.abs(V - V_closed(grid)))),\n    \"diag_policy_sup_error_grid\": float(np.max(np.abs(c_pol - c_closed(grid)))),\n    \"diag_policy_max_rel_error_eval\": float(max(abs(a - b) / b for a, b in zip(c_num, cc))),\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(results, f, indent=2)\nfor k, v in results.items():\n    print(f\"{k}: {v}\")\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis script"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1067,"cache_read_input_tokens":11567,"output_tokens":2303,"output_tokens_details":{"thinking_tokens":38},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1067},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXod9p9XiSmdsvtKpsEw","requestRef":"fc823c45-e0f7-4f51-938f-465a5a20a8e9","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"b9eb9d98-c558-4160-89ea-ce0689943574","timestamp":"2026-10-30T04:39:24.649Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130/out/state","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}42{"parentUuid":"b9eb9d98-c558-4160-89ea-ce0689943574","isSidechain":false,"promptId":"98c76955-6ef3-4dd0-ad59-6beeb3568c50","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 2\n(eval):1: no such file or directory: out/analysis.py\n/opt/homebrew/Cellar/python@3.14/3.14.4/Frameworks/Python.framework/Versions/3.14/Resources/Python.app/Contents/MacOS/Python: can't open file '/Users/simon-pierreboucher/wp29/runs/RC0130/out/state/out/analysis.py': [Errno 2] No such file or directory","is_error":true,"tool_use_id":"toolu_014hdXMuPQLiDjF1D9sMRj4k"}]},"uuid":"5b503f60-6d70-4136-9c9d-9e9d738aed33","timestamp":"2026-10-30T04:39:24.693Z","toolUseResult":"Error: Exit code 2\n(eval):1: no such file or directory: out/analysis.py\n/opt/homebrew/Cellar/python@3.14/3.14.4/Frameworks/Python.framework/Versions/3.14/Resources/Python.app/Contents/MacOS/Python: can't open file '/Users/simon-pierreboucher/wp29/runs/RC0130/out/state/out/analysis.py': [Errno 2] No such file or directory","sandboxed":false,"sourceToolAssistantUUID":"b9eb9d98-c558-4160-89ea-ce0689943574","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130/out/state","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}43{"type":"api-request-blob","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","hash":"7a3f2102146c3ba3ac7ec932fdc78a0e80d0971007300ac2f7742611a66c7c09","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQSyQYKEAgTGAI4AUIIdGhpbmtpbmcSDDRtaRlVcvDoLkx4kBoMqmUjHqjkyzE9XkTfIjDMW1GM4AlJJMdwDDN/+hrpRTzsgCSm9+si4+rM+if0l96njcekGfJ1i1OIWserFAoq5gU/zHmwvxBWWktP872asCthpvRBoMtKrm8hf6NwOzLPYcjjKtsELIGgDgr49ZFiCbEnYw+NypqLWtQhfJeeeDdsBWbpgiq0LMMazYyRsldcqLZC25bBBjIUEpTm1T68QMBVyMDpE0decE2qfx++C+0700kasiY/JzRbuYVJhowq+GcASjoMH0q+imyRDmv3N14u6drp50dFnbrZ18JbR3woe5M/w2qH1zxJG5S37mzy3sW5YgUJ31KqmexkxbWM/WcJtZbLYxBfnGsOngxXMNhUsgjzzZ1nBuXKW1LzAlo1aJPFGkLH8K2Ml1YXGcOETokQKCcNReID81BX0HIeT+PPvx3SGVgzgxTuGFz55eeeQ2okl0zIo8N+l8sELweNXecpIkbFniULQf+qN/H8CBKIb0ELyhCgYS7d2Of20xRqoCanNWcgFNw0aRWPYsG88vRdM61Sz6ZjYMve0uet3qsCSNY6JDJAA2p6YoX96mj/j9l8zVjjlrvlhcCPfRzrMsAlaAP6xShIKPI7WW81/+3dqhxTXXOiisJ/IsbOZ/Cf6PHEiwh3TeybkTM05GWN3hf8lDLSKpZVEpjlONyxVt4ndosyYNzk/fi/09q1arZIo8A43TRWVHF7KtRo1PU+ofFcjEA9RjkzjR1FKx7KgPLRAbb7/gSgVHzk3IP3cLxwqBLEliXI4t/vjNqbzOKGIX9rVHSFJHP4S/i3gxn6H650W0gGsiP4NbmMS37U6m4CamCsp3udO7Ccu9OUuFwvnAWGCkcIZmZ3B7zCuz10r1vBcck4kOFPrOu8EU1JbKg7UpA7OzHPXjaVeEKf/CCoiCu8tJrE4k2DiC9gR4yvS1U4nProjUxdbnAYHtFGd6zprnGm2Gp4P9SVlh21yKxroL7PlO8zgjb8qdX2FpWyNqLrTYyG1fdkL71L6NeYatLyAbLkdOZob2Zb2FPKW7axRQ9ZlM00WorVUUKBwd9GfZlimp+NHQhtGAE="},{"type":"text","text":"Now the analysis script (baseline closed form + VFI)."},{"type":"tool_use","id":"toolu_014hdXMuPQLiDjF1D9sMRj4k","name":"Bash","input":{"command":"cat > out/analysis.py <<'EOF'\n\"\"\"F5-conf-04: VFI vs closed form, optimal growth with log utility.\nRun from workspace root: ~/wp29/venv/bin/python out/analysis.py\nReads only data/model.csv; deterministic (no randomness).\"\"\"\nimport json, os\nimport numpy as np\nimport pandas as pd\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\ndf = pd.read_csv(os.path.join(ROOT, \"data\", \"model.csv\"))\np = dict(zip(df[\"parameter\"], df[\"value\"]))\nalpha, beta = float(p[\"alpha\"]), float(p[\"beta\"])\ny_min, y_max, N = float(p[\"y_min\"]), float(p[\"y_max\"]), int(float(p[\"grid_points\"]))\ntol = float(p[\"vfi_tolerance\"])\nassert str(p[\"grid_spacing\"]).strip() == \"log\"\nevals = [float(p[\"eval_y_1\"]), float(p[\"eval_y_2\"]), float(p[\"eval_y_3\"])]\ndata_issues = []\n\n# ---------- Closed form (guess-and-verify: V = A0 + B ln y) ----------\nab = alpha * beta\nB = 1.0 / (1.0 - ab)\nA0 = (np.log(1.0 - ab) + ab / (1.0 - ab) * np.log(ab)) / (1.0 - beta)\nc_closed = lambda y: (1.0 - ab) * np.asarray(y)\nV_closed = lambda y: A0 + B * np.log(np.asarray(y))\nsavings_rate = ab  # (y - c)/y\n\n# ---------- VFI on the prescribed grid (discrete choice of next-period output on the grid) ----------\ngrid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))\nk_needed = grid ** (1.0 / alpha)              # capital required to reach each y' on the grid\nC = grid[:, None] - k_needed[None, :]          # consumption for (y today, y' tomorrow)\nfeas = C > 0\nU = np.full(C.shape, -np.inf)\nU[feas] = np.log(C[feas])\nV = np.zeros(N)\nn_iter, sup_change = 0, 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    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_pol = grid - k_needed[pol_idx]\n\n# Diagnostics: is the grid bound binding? (policy at the edge of the y' grid)\nedge_hits = int(np.sum((pol_idx == 0) | (pol_idx == N - 1)))\nyprime_closed = (ab * grid) ** alpha\nif yprime_closed.min() < y_min or yprime_closed.max() > y_max:\n    data_issues.append({\"issue\": \"closed-form next-period output leaves the prescribed grid\",\n                        \"handling\": \"reported; truncation may bias VFI near bounds\"})\n\n# Interpolation at evaluation points: c linear in y; V linear in ln y\nc_num = [float(np.interp(y, grid, c_pol)) for y in evals]\ncc = [float(c_closed(y)) for y in evals]\non_node = [bool(np.any(np.isclose(grid, y, rtol=0, atol=1e-12))) for y in evals]\nV_num_1 = float(np.interp(np.log(1.0), np.log(grid), V))\n\n# Theoretical bound on the remaining VFI error from the stopping rule\nvfi_err_bound = beta / (1 - beta) * sup_change\n\nresults = {\n    \"task_id\": \"F5-conf-04\",\n    \"c_closed_y05\": cc[0], \"c_closed_y1\": cc[1], \"c_closed_y2\": cc[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\": float(max(abs(a - b) for a, b in zip(c_num, cc))),\n    \"value_closed_y1\": float(V_closed(1.0)),\n    \"value_num_y1\": V_num_1,\n    \"savings_rate_closed_form\": float(savings_rate),\n    \"contraction_modulus\": float(beta),\n    \"grid_points_used\": int(N),\n    \"n_iterations\": int(n_iter),\n    \"final_sup_change\": float(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\": int(N),\n    \"random_seed\": None,\n    # supplementary diagnostics\n    \"baseline_closed_form_B_coefficient\": float(B),\n    \"diag_eval_points_on_grid_node\": on_node,\n    \"diag_policy_edge_hits\": edge_hits,\n    \"diag_closed_yprime_min\": float(yprime_closed.min()),\n    \"diag_closed_yprime_max\": float(yprime_closed.max()),\n    \"diag_grid_log_step\": float(np.log(grid[1] / grid[0])),\n    \"diag_vfi_tolerance_error_bound\": float(vfi_err_bound),\n    \"diag_value_abs_error_y1\": float(abs(V_num_1 - float(V_closed(1.0)))),\n    \"diag_value_sup_error_grid\": float(np.max(np.abs(V - V_closed(grid)))),\n    \"diag_policy_sup_error_grid\": float(np.max(np.abs(c_pol - c_closed(grid)))),\n    \"diag_policy_max_rel_error_eval\": float(max(abs(a - b) / b for a, b in zip(c_num, cc))),\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(results, f, indent=2)\nfor k, v in results.items():\n    print(f\"{k}: {v}\")\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis script"}}]}}44{"type":"api-request","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","id":"ac7a1233-a09e-4a2f-bb45-d857e8423bc0","timestamp":"2026-10-30T04:39:24.697Z","version":"2.1.314","querySource":"sdk","shapeHash":"74261e6e7cd56f87bea65087889d4ddf98044e0fbeb6aae5c04c10263b2c127e","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":"fc823c45-e0f7-4f51-938f-465a5a20a8e9","keep":12,"tail":["7a3f2102146c3ba3ac7ec932fdc78a0e80d0971007300ac2f7742611a66c7c09","c3594e9b71e53ca291fcf494e99001a1ca0d99aef52d65d676436066793d74c6"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",13,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"9d8841dd142f9d83e846825cd4898a9437e21596ac31e9079321367d55335c38"}45{"parentUuid":"5b503f60-6d70-4136-9c9d-9e9d738aed33","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXoeVjjurZSZ6N3NpvUJ","type":"message","role":"assistant","content":[{"type":"text","text":"The shell was still in out/state; 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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, beta = float(p[\"alpha\"]), float(p[\"beta\"])\ny_min, y_max, N = float(p[\"y_min\"]), float(p[\"y_max\"]), int(float(p[\"grid_points\"]))\ntol = float(p[\"vfi_tolerance\"])\nassert str(p[\"grid_spacing\"]).strip() == \"log\"\nevals = [float(p[\"eval_y_1\"]), float(p[\"eval_y_2\"]), float(p[\"eval_y_3\"])]\ndata_issues = []\n\n# ---------- Closed form (guess-and-verify: V = A0 + B ln y) ----------\nab = alpha * beta\nB = 1.0 / (1.0 - ab)\nA0 = (np.log(1.0 - ab) + ab / (1.0 - ab) * np.log(ab)) / (1.0 - beta)\nc_closed = lambda y: (1.0 - ab) * np.asarray(y)\nV_closed = lambda y: A0 + B * np.log(np.asarray(y))\nsavings_rate = ab  # (y - c)/y\n\n# ---------- VFI on the prescribed grid (discrete choice of next-period output on the grid) ----------\ngrid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))\nk_needed = grid ** (1.0 / alpha)              # capital required to reach each y' on the grid\nC = grid[:, None] - k_needed[None, :]          # consumption for (y today, y' tomorrow)\nfeas = C > 0\nU = np.full(C.shape, -np.inf)\nU[feas] = np.log(C[feas])\nV = np.zeros(N)\nn_iter, sup_change = 0, 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    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_pol = grid - k_needed[pol_idx]\n\n# Diagnostics: is the grid bound binding? (policy at the edge of the y' grid)\nedge_hits = int(np.sum((pol_idx == 0) | (pol_idx == N - 1)))\nyprime_closed = (ab * grid) ** alpha\nif yprime_closed.min() < y_min or yprime_closed.max() > y_max:\n    data_issues.append({\"issue\": \"closed-form next-period output leaves the prescribed grid\",\n                        \"handling\": \"reported; truncation may bias VFI near bounds\"})\n\n# Interpolation at evaluation points: c linear in y; V linear in ln y\nc_num = [float(np.interp(y, grid, c_pol)) for y in evals]\ncc = [float(c_closed(y)) for y in evals]\non_node = [bool(np.any(np.isclose(grid, y, rtol=0, atol=1e-12))) for y in evals]\nV_num_1 = float(np.interp(np.log(1.0), np.log(grid), V))\n\n# Theoretical bound on the remaining VFI error from the stopping rule\nvfi_err_bound = beta / (1 - beta) * sup_change\n\nresults = {\n    \"task_id\": \"F5-conf-04\",\n    \"c_closed_y05\": cc[0], \"c_closed_y1\": cc[1], \"c_closed_y2\": cc[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\": float(max(abs(a - b) for a, b in zip(c_num, cc))),\n    \"value_closed_y1\": float(V_closed(1.0)),\n    \"value_num_y1\": V_num_1,\n    \"savings_rate_closed_form\": float(savings_rate),\n    \"contraction_modulus\": float(beta),\n    \"grid_points_used\": int(N),\n    \"n_iterations\": int(n_iter),\n    \"final_sup_change\": float(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\": int(N),\n    \"random_seed\": None,\n    # supplementary diagnostics\n    \"baseline_closed_form_B_coefficient\": float(B),\n    \"diag_eval_points_on_grid_node\": on_node,\n    \"diag_policy_edge_hits\": edge_hits,\n    \"diag_closed_yprime_min\": float(yprime_closed.min()),\n    \"diag_closed_yprime_max\": float(yprime_closed.max()),\n    \"diag_grid_log_step\": float(np.log(grid[1] / grid[0])),\n    \"diag_vfi_tolerance_error_bound\": float(vfi_err_bound),\n    \"diag_value_abs_error_y1\": float(abs(V_num_1 - float(V_closed(1.0)))),\n    \"diag_value_sup_error_grid\": float(np.max(np.abs(V - V_closed(grid)))),\n    \"diag_policy_sup_error_grid\": float(np.max(np.abs(c_pol - c_closed(grid)))),\n    \"diag_policy_max_rel_error_eval\": float(max(abs(a - b) / b for a, b in zip(c_num, cc))),\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(results, f, indent=2)\nfor k, v in results.items():\n    print(f\"{k}: {v}\")\nEOF\ntime ~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis 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F5-conf-04\nc_closed_y05: 0.329\nc_closed_y1: 0.658\nc_closed_y2: 1.316\nc_num_y05: 0.32881734052248063\nc_num_y1: 0.6589770804373355\nc_num_y2: 1.3095934115917793\nmax_abs_error_policy: 0.006406588408220726\nvalue_closed_y1: -19.524412221722393\nvalue_num_y1: -19.52475624982261\nsavings_rate_closed_form: 0.34199999999999997\ncontraction_modulus: 0.95\ngrid_points_used: 400\nn_iterations: 361\nfinal_sup_change: 9.996650618404601e-09\nfeasibility: complete\nfeasibility_reason: None\ndata_issues: []\nn_input_rows: {'model.csv': 10}\nn_analysed: 400\nrandom_seed: None\nbaseline_closed_form_B_coefficient: 1.519756838905775\ndiag_eval_points_on_grid_node: [False, False, False]\ndiag_policy_edge_hits: 0\ndiag_closed_yprime_min: 0.231141857879438\ndiag_closed_yprime_max: 1.2130497139112173\ndiag_grid_log_step: 0.011541779914756887\ndiag_vfi_tolerance_error_bound: 1.8993636174968724e-07\ndiag_value_abs_error_y1: 0.0003440281002156098\ndiag_value_sup_error_grid: 0.0004835155258184898\ndiag_policy_sup_error_grid: 0.02512152290513381\ndiag_policy_max_rel_error_eval: 0.0048682282737239554\n~/wp29/venv/bin/python out/analysis.py  0,24s user 0,04s system 98% cpu 0,281 total","is_error":false}]},"uuid":"cccb5e2a-9fe9-40ec-a8fb-4e333cdaa4af","timestamp":"2026-10-30T04:39:41.675Z","toolUseResult":{"stdout":"task_id: F5-conf-04\nc_closed_y05: 0.329\nc_closed_y1: 0.658\nc_closed_y2: 1.316\nc_num_y05: 0.32881734052248063\nc_num_y1: 0.6589770804373355\nc_num_y2: 1.3095934115917793\nmax_abs_error_policy: 0.006406588408220726\nvalue_closed_y1: -19.524412221722393\nvalue_num_y1: -19.52475624982261\nsavings_rate_closed_form: 0.34199999999999997\ncontraction_modulus: 0.95\ngrid_points_used: 400\nn_iterations: 361\nfinal_sup_change: 9.996650618404601e-09\nfeasibility: complete\nfeasibility_reason: None\ndata_issues: []\nn_input_rows: {'model.csv': 10}\nn_analysed: 400\nrandom_seed: None\nbaseline_closed_form_B_coefficient: 1.519756838905775\ndiag_eval_points_on_grid_node: [False, False, False]\ndiag_policy_edge_hits: 0\ndiag_closed_yprime_min: 0.231141857879438\ndiag_closed_yprime_max: 1.2130497139112173\ndiag_grid_log_step: 0.011541779914756887\ndiag_vfi_tolerance_error_bound: 1.8993636174968724e-07\ndiag_value_abs_error_y1: 0.0003440281002156098\ndiag_value_sup_error_grid: 0.0004835155258184898\ndiag_policy_sup_error_grid: 0.02512152290513381\ndiag_policy_max_rel_error_eval: 0.0048682282737239554\n~/wp29/venv/bin/python out/analysis.py  0,24s user 0,04s system 98% cpu 0,281 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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, beta = float(p[\"alpha\"]), float(p[\"beta\"])\ny_min, y_max, N = float(p[\"y_min\"]), float(p[\"y_max\"]), int(float(p[\"grid_points\"]))\ntol = float(p[\"vfi_tolerance\"])\nassert str(p[\"grid_spacing\"]).strip() == \"log\"\nevals = [float(p[\"eval_y_1\"]), float(p[\"eval_y_2\"]), float(p[\"eval_y_3\"])]\ndata_issues = []\n\n# ---------- Closed form (guess-and-verify: V = A0 + B ln y) ----------\nab = alpha * beta\nB = 1.0 / (1.0 - ab)\nA0 = (np.log(1.0 - ab) + ab / (1.0 - ab) * np.log(ab)) / (1.0 - beta)\nc_closed = lambda y: (1.0 - ab) * np.asarray(y)\nV_closed = lambda y: A0 + B * np.log(np.asarray(y))\nsavings_rate = ab  # (y - c)/y\n\n# ---------- VFI on the prescribed grid (discrete choice of next-period output on the grid) ----------\ngrid = np.exp(np.linspace(np.log(y_min), np.log(y_max), N))\nk_needed = grid ** (1.0 / alpha)              # capital required to reach each y' on the grid\nC = grid[:, None] - k_needed[None, :]          # consumption for (y today, y' tomorrow)\nfeas = C > 0\nU = np.full(C.shape, -np.inf)\nU[feas] = np.log(C[feas])\nV = np.zeros(N)\nn_iter, sup_change = 0, 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    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_pol = grid - k_needed[pol_idx]\n\n# Diagnostics: is the grid bound binding? (policy at the edge of the y' grid)\nedge_hits = int(np.sum((pol_idx == 0) | (pol_idx == N - 1)))\nyprime_closed = (ab * grid) ** alpha\nif yprime_closed.min() < y_min or yprime_closed.max() > y_max:\n    data_issues.append({\"issue\": \"closed-form next-period output leaves the prescribed grid\",\n                        \"handling\": \"reported; truncation may bias VFI near bounds\"})\n\n# Interpolation at evaluation points: c linear in y; V linear in ln y\nc_num = [float(np.interp(y, grid, c_pol)) for y in evals]\ncc = [float(c_closed(y)) for y in evals]\non_node = [bool(np.any(np.isclose(grid, y, rtol=0, atol=1e-12))) for y in evals]\nV_num_1 = float(np.interp(np.log(1.0), np.log(grid), V))\n\n# Theoretical bound on the remaining VFI error from the stopping rule\nvfi_err_bound = beta / (1 - beta) * sup_change\n\nresults = {\n    \"task_id\": \"F5-conf-04\",\n    \"c_closed_y05\": cc[0], \"c_closed_y1\": cc[1], \"c_closed_y2\": cc[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\": float(max(abs(a - b) for a, b in zip(c_num, cc))),\n    \"value_closed_y1\": float(V_closed(1.0)),\n    \"value_num_y1\": V_num_1,\n    \"savings_rate_closed_form\": float(savings_rate),\n    \"contraction_modulus\": float(beta),\n    \"grid_points_used\": int(N),\n    \"n_iterations\": int(n_iter),\n    \"final_sup_change\": float(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\": int(N),\n    \"random_seed\": None,\n    # supplementary diagnostics\n    \"baseline_closed_form_B_coefficient\": float(B),\n    \"diag_eval_points_on_grid_node\": on_node,\n    \"diag_policy_edge_hits\": edge_hits,\n    \"diag_closed_yprime_min\": float(yprime_closed.min()),\n    \"diag_closed_yprime_max\": float(yprime_closed.max()),\n    \"diag_grid_log_step\": float(np.log(grid[1] / grid[0])),\n    \"diag_vfi_tolerance_error_bound\": float(vfi_err_bound),\n    \"diag_value_abs_error_y1\": float(abs(V_num_1 - float(V_closed(1.0)))),\n    \"diag_value_sup_error_grid\": float(np.max(np.abs(V - V_closed(grid)))),\n    \"diag_policy_sup_error_grid\": float(np.max(np.abs(c_pol - c_closed(grid)))),\n    \"diag_policy_max_rel_error_eval\": float(max(abs(a - b) / b for a, b in zip(c_num, cc))),\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(results, f, indent=2)\nfor k, v in results.items():\n    print(f\"{k}: {v}\")\nEOF\ntime ~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis 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are sensible. Now P1 audit, exclusions, and P2/P3 ledger entries, then P4 verification."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2837,"cache_read_input_tokens":15254,"output_tokens":1563,"output_tokens_details":{"thinking_tokens":238},"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":2837},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXofk4EXCKmLZZQH16nw","requestRef":"fcc3f75d-8823-44ed-8317-e871558b159f","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"73ec29c8-9a24-4803-a6e2-b46fd02294a4","timestamp":"2026-10-30T04:39:45.102Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}58{"parentUuid":"73ec29c8-9a24-4803-a6e2-b46fd02294a4","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXofkLbnBngd1VndyCp5","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_011sn6HaJ18Qrn2rK9Zo9EKd","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n\n| file | SHA-256 | rows | cols |\n|---|---|---|---|\n| data/model.csv | 098123961451e4f9a2e76afdbc83aec78066fc713d0645659c09b77b1636195b (matches bundle.json) | 10 | 3 (parameter, value, description) |\n\nParameters: alpha=0.36, beta=0.95, y_min=0.05, y_max=5.0, grid_points=400, grid_spacing=log, vfi_tolerance=1e-08,\neval_y_1=0.5, eval_y_2=1.0, eval_y_3=2.0. Units: y and c in units of output; tolerance in utils.\nNo missing values, no duplicated parameter names, no dates (theoretical parameters). `value` column is mixed\n(numeric + the string \"log\"); parsed per-parameter.\n\nAnomalies / checks:\n- 0<alpha<1, 0<beta<1: OK.\n- None of the evaluation points is a grid node (log step = ln(100)/399 ≈ 0.01154); the VFI policy is linearly interpolated\n  as the task allows.\n- Grid invariance: closed-form y' = (alpha*beta*y)^alpha ranges over [0.231, 1.213] for y in [0.05, 5] — strictly inside\n  the grid, so the truncation of the state space is not binding (verified in analysis.py: diag_closed_yprime_min/max,\n  diag_policy_edge_hits = 0).\n- No information-availability violations: only model.csv is used; no rows excluded.\nEOF\ncat > out/exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n1,no exclusions (all parameter rows used),10,10,0,all 10 parameter rows of model.csv are required and valid\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open(\"out/state/phases.json\"))\np[\"P1\"]={\"status\":\"passed\",\"checks\":[\"sha256 computed and matched bundle.json\",\"10 rows x 3 cols, no missing/duplicates\",\"parameter ranges valid\",\"grid invariance under closed-form policy verified ([0.231,1.213] within [0.05,5])\",\"exclusions.csv written (0 removed)\"],\"notes\":\"\"}\np[\"P2\"]={\"status\":\"passed\",\"checks\":[\"closed-form baseline computed by guess-and-verify: c=(1-ab)y, savings rate ab=0.342, V(1)=A0=-19.5244\",\"stored under required keys c_closed_*, value_closed_y1, savings_rate_closed_form\"],\"notes\":\"\"}\np[\"P3\"]={\"status\":\"passed\",\"checks\":[\"analysis.py implemented: vectorised discrete-choice VFI on 400-point log grid\",\"converged in 361 iterations, final sup change 9.997e-09 < 1e-08\",\"no randomness; random_seed=null\"],\"notes\":\"\"}\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\ncat >> out/state/log.md <<'EOF'\n- 2026-10-30 P1 passed: data audit, no exclusions.\n- 2026-10-30 Decision: VFI uses discrete choice of y' on the grid (c = y - y'^(1/alpha)); policy at eval points linearly interpolated in y, V(1) linearly in ln y.\n- 2026-10-30 P2 passed: closed-form baseline. P3 passed: VFI 361 iterations.\nEOF","description":"Write audit, exclusions, update ledgers"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":2837,"cache_read_input_tokens":15254,"output_tokens":1563,"output_tokens_details":{"thinking_tokens":238},"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":2837},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXofk4EXCKmLZZQH16nw","requestRef":"fcc3f75d-8823-44ed-8317-e871558b159f","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"2bbaf687-03cf-49dc-9d1c-ce6d6df4263a","timestamp":"2026-10-30T04:39:55.618Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}59{"parentUuid":"2bbaf687-03cf-49dc-9d1c-ce6d6df4263a","isSidechain":false,"promptId":"98c76955-6ef3-4dd0-ad59-6beeb3568c50","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_011sn6HaJ18Qrn2rK9Zo9EKd","type":"tool_result","content":"(Bash completed with no output)","is_error":false}]},"uuid":"d289a561-9526-4912-aebc-9284c6131dc7","timestamp":"2026-10-30T04:39:55.679Z","toolUseResult":{"stdout":"","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"2bbaf687-03cf-49dc-9d1c-ce6d6df4263a","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}60{"type":"api-request-blob","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","hash":"a4c188c25f2dd99f621f1d79f7f1fe338616e9719dfbe377b80cc11f58447004","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"Results are sensible. Now P1 audit, exclusions, and P2/P3 ledger entries, then P4 verification."},{"type":"tool_use","id":"toolu_011sn6HaJ18Qrn2rK9Zo9EKd","name":"Bash","input":{"command":"cat > out/state/data_audit.md <<'EOF'\n# Data audit (P1)\n\n| file | SHA-256 | rows | cols |\n|---|---|---|---|\n| data/model.csv | 098123961451e4f9a2e76afdbc83aec78066fc713d0645659c09b77b1636195b (matches bundle.json) | 10 | 3 (parameter, value, description) |\n\nParameters: alpha=0.36, beta=0.95, y_min=0.05, y_max=5.0, grid_points=400, grid_spacing=log, vfi_tolerance=1e-08,\neval_y_1=0.5, eval_y_2=1.0, eval_y_3=2.0. Units: y and c in units of output; tolerance in utils.\nNo missing values, no duplicated parameter names, no dates (theoretical parameters). `value` column is mixed\n(numeric + the string \"log\"); parsed per-parameter.\n\nAnomalies / checks:\n- 0<alpha<1, 0<beta<1: OK.\n- None of the evaluation points is a grid node (log step = ln(100)/399 ≈ 0.01154); the VFI policy is linearly interpolated\n  as the task allows.\n- Grid invariance: closed-form y' = (alpha*beta*y)^alpha ranges over [0.231, 1.213] for y in [0.05, 5] — strictly inside\n  the grid, so the truncation of the state space is not binding (verified in analysis.py: diag_closed_yprime_min/max,\n  diag_policy_edge_hits = 0).\n- No information-availability violations: only model.csv is used; no rows excluded.\nEOF\ncat > out/exclusions.csv <<'EOF'\nstep,rule,n_before,n_after,n_removed,rationale\n1,no exclusions (all parameter rows used),10,10,0,all 10 parameter rows of model.csv are required and valid\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open(\"out/state/phases.json\"))\np[\"P1\"]={\"status\":\"passed\",\"checks\":[\"sha256 computed and matched bundle.json\",\"10 rows x 3 cols, no missing/duplicates\",\"parameter ranges valid\",\"grid invariance under closed-form policy verified ([0.231,1.213] within [0.05,5])\",\"exclusions.csv written (0 removed)\"],\"notes\":\"\"}\np[\"P2\"]={\"status\":\"passed\",\"checks\":[\"closed-form baseline computed by guess-and-verify: c=(1-ab)y, savings rate ab=0.342, V(1)=A0=-19.5244\",\"stored under required keys c_closed_*, value_closed_y1, savings_rate_closed_form\"],\"notes\":\"\"}\np[\"P3\"]={\"status\":\"passed\",\"checks\":[\"analysis.py implemented: vectorised discrete-choice VFI on 400-point log grid\",\"converged in 361 iterations, final sup change 9.997e-09 < 1e-08\",\"no randomness; random_seed=null\"],\"notes\":\"\"}\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\ncat >> out/state/log.md <<'EOF'\n- 2026-10-30 P1 passed: data audit, no exclusions.\n- 2026-10-30 Decision: VFI uses discrete choice of y' on the grid (c = y - y'^(1/alpha)); policy at eval points linearly interpolated in y, V(1) linearly in ln y.\n- 2026-10-30 P2 passed: closed-form baseline. P3 passed: VFI 361 iterations.\nEOF","description":"Write audit, exclusions, update 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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; ab=a*b\nchk=[]\n# Bellman verification of closed form at several y using a fine continuous optimisation\nfrom scipy.optimize import minimize_scalar\nB=1/(1-ab); A0=(np.log(1-ab)+ab/(1-ab)*np.log(ab))/(1-b)\nV=lambda y:A0+B*np.log(y)\nfor y in [0.5,1,2]:\n    res=minimize_scalar(lambda c:-(np.log(c)+b*V((y-c)**a)),bounds=(1e-9,y-1e-9),method=\"bounded\",options={\"xatol\":1e-12})\n    chk.append(f\"Bellman fixed point at y={y}: argmax c={res.x:.8f} vs (1-ab)y={(1-ab)*y:.8f}; T V - V = {-res.fun-V(y):.2e}\")\nchk.append(f\"max_abs_error_policy recomputed: {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'])):.12f} == {r['max_abs_error_policy']:.12f}\")\nchk.append(f\"savings rate == 1 - c_closed_y1/1: {1-r['c_closed_y1']:.12f} vs {r['savings_rate_closed_form']:.12f}\")\nchk.append(f\"final_sup_change < tol 1e-8: {r['final_sup_change']<1e-8}\")\nchk.append(f\"0<c_num<y at eval points: {all(0<r[k]<y for k,y in [('c_num_y05',.5),('c_num_y1',1),('c_num_y2',2)])}\")\nchk.append(f\"|V_num(1)-V_closed(1)|={abs(r['value_num_y1']-r['value_closed_y1']):.2e} >> tolerance error bound {r['diag_vfi_tolerance_error_bound']:.2e} (discretisation dominates)\")\nchk.append(f\"policy edge hits = {r['diag_policy_edge_hits']} (truncation not binding)\")\nchk.append(f\"relative policy error at eval points {r['diag_policy_max_rel_error_eval']:.4f} vs half-step in k ~ grid_log_step/(2 alpha) = {r['diag_grid_log_step']/(2*a):.4f}: consistent with discretisation\")\nchk.append(f\"n_input_rows 10 - removed 0 = 10 rows used; n_analysed = grid_points_used = {r['n_analysed']}\")\nopen(\"out/state/checks.md\",\"w\").write(\"# Verification checks (P4)\\n\\n- Clean re-run of analysis.py: results.json byte-identical.\\n\"+\"\\n\".join(\"- \"+c for c in chk)+\"\\n\")\nprint(open(\"out/state/checks.md\").read())\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":1578,"cache_read_input_tokens":18091,"output_tokens":1197,"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":1578},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXogmx7QhBPMsFhzFVqC","requestRef":"3a92be54-573b-4200-8683-d2fb4e31fc7c","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"419ab734-ef26-49f9-b24e-7c3dc0efd0f2","timestamp":"2026-10-30T04:40:05.419Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}63{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"419ab734-ef26-49f9-b24e-7c3dc0efd0f2","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746"}64{"type":"atis-latch","atis":"","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746"}65{"parentUuid":"419ab734-ef26-49f9-b24e-7c3dc0efd0f2","isSidechain":false,"promptId":"98c76955-6ef3-4dd0-ad59-6beeb3568c50","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_016aAcc6xzNp27khc26Qp9Ro","type":"tool_result","content":"IDENTICAL\n# Verification checks (P4)\n\n- Clean re-run of analysis.py: results.json byte-identical.\n- Bellman fixed point at y=0.5: argmax c=0.32899998 vs (1-ab)y=0.32900000; T V - V = 0.00e+00\n- Bellman fixed point at y=1: argmax c=0.65799998 vs (1-ab)y=0.65800000; T V - V = 0.00e+00\n- Bellman fixed point at y=2: argmax c=1.31599998 vs (1-ab)y=1.31600000; T V - V = 0.00e+00\n- max_abs_error_policy recomputed: 0.006406588408 == 0.006406588408\n- savings rate == 1 - c_closed_y1/1: 0.342000000000 vs 0.342000000000\n- final_sup_change < tol 1e-8: True\n- 0<c_num<y at eval points: True\n- |V_num(1)-V_closed(1)|=3.44e-04 >> tolerance error bound 1.90e-07 (discretisation dominates)\n- policy edge hits = 0 (truncation not binding)\n- relative policy error at eval points 0.0049 vs half-step in k ~ grid_log_step/(2 alpha) = 0.0160: consistent with discretisation\n- n_input_rows 10 - removed 0 = 10 rows used; n_analysed = grid_points_used = 400","is_error":false}]},"uuid":"555ea325-e0d7-4cfa-9336-d02de281510e","timestamp":"2026-10-30T04:40:05.987Z","toolUseResult":{"stdout":"IDENTICAL\n# Verification checks (P4)\n\n- Clean re-run of analysis.py: results.json byte-identical.\n- Bellman fixed point at y=0.5: argmax c=0.32899998 vs (1-ab)y=0.32900000; T V - V = 0.00e+00\n- Bellman fixed point at y=1: argmax c=0.65799998 vs (1-ab)y=0.65800000; T V - V = 0.00e+00\n- Bellman fixed point at y=2: argmax c=1.31599998 vs (1-ab)y=1.31600000; T V - V = 0.00e+00\n- max_abs_error_policy recomputed: 0.006406588408 == 0.006406588408\n- savings rate == 1 - c_closed_y1/1: 0.342000000000 vs 0.342000000000\n- final_sup_change < tol 1e-8: True\n- 0<c_num<y at eval points: True\n- |V_num(1)-V_closed(1)|=3.44e-04 >> tolerance error bound 1.90e-07 (discretisation dominates)\n- policy edge hits = 0 (truncation not binding)\n- relative policy error at eval points 0.0049 vs half-step in k ~ grid_log_step/(2 alpha) = 0.0160: consistent with discretisation\n- n_input_rows 10 - removed 0 = 10 rows used; n_analysed = grid_points_used = 400","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"419ab734-ef26-49f9-b24e-7c3dc0efd0f2","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}66{"type":"api-request-blob","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","hash":"82bc6d08eddd4663bc9c49d7dd7d81e5510f3c1e6c18af9738310f29131ec333","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_016aAcc6xzNp27khc26Qp9Ro","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; ab=a*b\nchk=[]\n# Bellman verification of closed form at several y using a fine continuous optimisation\nfrom scipy.optimize import minimize_scalar\nB=1/(1-ab); A0=(np.log(1-ab)+ab/(1-ab)*np.log(ab))/(1-b)\nV=lambda y:A0+B*np.log(y)\nfor y in [0.5,1,2]:\n    res=minimize_scalar(lambda c:-(np.log(c)+b*V((y-c)**a)),bounds=(1e-9,y-1e-9),method=\"bounded\",options={\"xatol\":1e-12})\n    chk.append(f\"Bellman fixed point at y={y}: argmax c={res.x:.8f} vs (1-ab)y={(1-ab)*y:.8f}; T V - V = {-res.fun-V(y):.2e}\")\nchk.append(f\"max_abs_error_policy recomputed: {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'])):.12f} == {r['max_abs_error_policy']:.12f}\")\nchk.append(f\"savings rate == 1 - c_closed_y1/1: {1-r['c_closed_y1']:.12f} vs {r['savings_rate_closed_form']:.12f}\")\nchk.append(f\"final_sup_change < tol 1e-8: {r['final_sup_change']<1e-8}\")\nchk.append(f\"0<c_num<y at eval points: {all(0<r[k]<y for k,y in [('c_num_y05',.5),('c_num_y1',1),('c_num_y2',2)])}\")\nchk.append(f\"|V_num(1)-V_closed(1)|={abs(r['value_num_y1']-r['value_closed_y1']):.2e} >> tolerance error bound {r['diag_vfi_tolerance_error_bound']:.2e} (discretisation dominates)\")\nchk.append(f\"policy edge hits = {r['diag_policy_edge_hits']} (truncation not binding)\")\nchk.append(f\"relative policy error at eval points {r['diag_policy_max_rel_error_eval']:.4f} vs half-step in k ~ grid_log_step/(2 alpha) = {r['diag_grid_log_step']/(2*a):.4f}: consistent with discretisation\")\nchk.append(f\"n_input_rows 10 - removed 0 = 10 rows used; n_analysed = grid_points_used = {r['n_analysed']}\")\nopen(\"out/state/checks.md\",\"w\").write(\"# Verification checks (P4)\\n\\n- Clean re-run of analysis.py: results.json byte-identical.\\n\"+\"\\n\".join(\"- \"+c for c in chk)+\"\\n\")\nprint(open(\"out/state/checks.md\").read())\nEOF","description":"Reproducibility and consistency checks"}}]}}67{"type":"api-request","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","id":"ec791a28-877d-434e-9e77-0f41288f7cca","timestamp":"2026-10-30T04:40:05.990Z","version":"2.1.314","querySource":"sdk","shapeHash":"74261e6e7cd56f87bea65087889d4ddf98044e0fbeb6aae5c04c10263b2c127e","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":"3a92be54-573b-4200-8683-d2fb4e31fc7c","keep":20,"tail":["82bc6d08eddd4663bc9c49d7dd7d81e5510f3c1e6c18af9738310f29131ec333","201a2feca2dbf22f67e1555671e9877a6a89281db3a3a1e9f8741a8cd6795526"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",21,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"89da6750f0a486b792a4628adade28ce15839617a82784ba34ec4093107f583f"}68{"parentUuid":"555ea325-e0d7-4cfa-9336-d02de281510e","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXohYJriUSvSJPqiT8zX","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"CAQSzQgKEAgTGAI4AUIIdGhpbmtpbmcSDGWh5N/b7ta1GLw0whoM1cvmldJ9Qy+LZUkjIjC/V7nRYwNlYLG3yTWPJHuzJqctyKLXVsenmcgS48Iux01ylkvvgaWeTXTWVLihwUkq6gdtl1mwggM+pUPsMjhYd85SLJWkFXkhQgUDo7X4T8LD4eXdEoLmMQaAMufGGOCqGhw/qy9x7XuyJ3muEFrhFCsx+JnKfwtyO5bxIcWAYLwnLioOAJvUFNHHgSePaubuq7KNkNRvHnStHp6QseJ08+EsQWv0a9liSzCYpZJDhWB6cKpHFRcWYA1+qSv2IqX3H3glSTg4ViMrE25GI2U3hERKfTzSEf+9XhZn1+SpMKXkz3afh3/6pTpMipHc+nqqt2iSxlu9SOd/fJyu0WNA18tLJaWQcpZZ1V7uVe1p2dfIOHnOB/BckVOrgtfiQAlnMPSv3dGVTDaerdiwb1d20YhQiCFY5YWb6I1/SRlJFI2dKp+IVFj0jl9D1YTloXYgoLTNZeJwIUsgxWM9Wfta1k3IoJ1pDVzqMx8X7WsWCkwBD+RvV8wec3Ij7+bIBfD6V737RW1N4FxudOhI8zfn6Igy5pbPuDFiY+VjBFGe3ESXfv3usKTic6JvoqRiCvi8yGugT6xA7wSsFTsNHh04pgAHZI2daflSPTkj8e6wqPJc/hGle2qFQc2MugCnROOIPArHsfCi5LZ4E7HMeS2VZ1uCBGqcnSjshO0gO1Uj4FuBtvaa19FTut/Q1jrcAPW2Uw+XqnARkl9kYAN2xA6A9NLoYAXIB9sWA8OPvbzkjzH5bK0t9FWzT9M27QfSCEKOZUeCEECA9Gse/DhTkMgCiq+r1S5cotHQXgSyb+D8KknKG+g3YcMMc+2W0PMXAMzxxQSNqWk3GocuW1/kOVM/Lz3SXwWOylwhmH8Eua83SI078UILs+Yz4Q+8S2V894RDykQtnxnEUMtJ2sEznsK+UL1+KbA4BqguO1ClJ5mQROeq/xMGPmldrbLW0Qo+ikcJ+bezF+etsxjSSINquJJfeiA1p6l507CMbgE+VUGGAFzW1WM2NrXFAA3poY880f7UYJC+TxiqCHcJHFGSuA2y3OpQOT2yvK/86A9LWYHCo4stVb1yIQj+LnTNF2zZh8S8L8zQSU9MONqiqBlhm0ybmFQEZVzKnjM/jq6ZI3BMkrk0Dd0PoEagDPEjR7HMEgL8Qzv9MRURLX/UoWz+i4j4bQwPMSBFfrKzc8zx6SN9ay9dVm2xroqia3m3hsPie9kmZMmmixpiWszU7gMDZxVPUMmsKAi2IBguPf6bzQNRFrp/RQ/aPDHvSe5joNKHzRIKE/D5hSKQkWEd7k20ScVWyMluE6h5Az5YHx/+atjt3c84dWuHBesf+KCdO64OFotNZTpXDB8/1RagqSNvockw9tNUiaxWVhwC4isygPqdxPq0kSewzCQpF7ZXtsgYAQ=="}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1680,"cache_read_input_tokens":19669,"output_tokens":616,"output_tokens_details":{"thinking_tokens":143},"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":1680},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1259,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXohY2EfeQmS6c7MvWWe","requestRef":"ec791a28-877d-434e-9e77-0f41288f7cca","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"ad92320f-10d4-4a6c-9544-f44546248cdd","timestamp":"2026-10-30T04:40:08.418Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}69{"parentUuid":"ad92320f-10d4-4a6c-9544-f44546248cdd","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXohYJriUSvSJPqiT8zX","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01LayKrN4Hd8eyCA6E6MpHuc","name":"Bash","input":{"command":"~/wp29/venv/bin/python - <<'EOF'\ns=open(\"out/state/checks.md\").read()\ns=s.replace(\"vs half-step in k ~ grid_log_step/(2 alpha) = 0.0160: consistent with discretisation\",\"is below the half-grid-step bound for c: (step/(2 alpha))*ab/(1-ab) = %.4f (k off by at most half a log-step of y', i.e. step/(2alpha) relative in k): consistent with discretisation\"%(0.011541779914756887/(2*0.36)*0.342/0.658))\nopen(\"out/state/checks.md\",\"w\").write(s)\nEOF\ngrep relative out/state/checks.md\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open(\"out/state/phases.json\"))\np[\"P4\"]={\"status\":\"running\",\"checks\":[\"clean re-run: results.json byte-identical\",\"internal consistency checks in out/state/checks.md all pass\"],\"notes\":\"\"}\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Fix check text, run gate for P4"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1680,"cache_read_input_tokens":19669,"output_tokens":616,"output_tokens_details":{"thinking_tokens":143},"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":1680},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXohY2EfeQmS6c7MvWWe","requestRef":"ec791a28-877d-434e-9e77-0f41288f7cca","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"0977b085-1d83-4fc2-880e-64d427664533","timestamp":"2026-10-30T04:40:11.779Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}70{"parentUuid":"0977b085-1d83-4fc2-880e-64d427664533","isSidechain":false,"promptId":"98c76955-6ef3-4dd0-ad59-6beeb3568c50","type":"user","message":{"role":"user","content":[{"type":"tool_result","content":"Exit code 1\n- relative policy error at eval points 0.0049 is below the half-grid-step bound for c: (step/(2 alpha))*ab/(1-ab) = 0.0083 (k off by at most half a log-step of y', i.e. step/(2alpha) relative in k): consistent with discretisation\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 0.3s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0130/out/state/gate_receipts/20261030T044012.141268Z.json","is_error":true,"tool_use_id":"toolu_01LayKrN4Hd8eyCA6E6MpHuc"}]},"uuid":"aff52f99-3478-4046-9963-56cda01128b4","timestamp":"2026-10-30T04:40:12.147Z","toolUseResult":"Error: Exit code 1\n- relative policy error at eval points 0.0049 is below the half-grid-step bound for c: (step/(2 alpha))*ab/(1-ab) = 0.0083 (k off by at most half a log-step of y', i.e. step/(2alpha) relative in k): consistent with discretisation\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 0.3s; identical within tolerance\nreceipt: 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- <<'EOF'\ns=open(\"out/state/checks.md\").read()\ns=s.replace(\"vs half-step in k ~ grid_log_step/(2 alpha) = 0.0160: consistent with discretisation\",\"is below the half-grid-step bound for c: (step/(2 alpha))*ab/(1-ab) = %.4f (k off by at most half a log-step of y', i.e. step/(2alpha) relative in k): consistent with discretisation\"%(0.011541779914756887/(2*0.36)*0.342/0.658))\nopen(\"out/state/checks.md\",\"w\").write(s)\nEOF\ngrep relative out/state/checks.md\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open(\"out/state/phases.json\"))\np[\"P4\"]={\"status\":\"running\",\"checks\":[\"clean re-run: results.json byte-identical\",\"internal consistency checks in out/state/checks.md all pass\"],\"notes\":\"\"}\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .","description":"Fix check text, run gate for P4"}}]}}72{"type":"api-request","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","id":"398af1b9-f4cc-42ba-ae08-d2cf4d218bf1","timestamp":"2026-10-30T04:40:12.151Z","version":"2.1.314","querySource":"sdk","shapeHash":"74261e6e7cd56f87bea65087889d4ddf98044e0fbeb6aae5c04c10263b2c127e","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":"ec791a28-877d-434e-9e77-0f41288f7cca","keep":22,"tail":["9985c196776150e05ee78443a3a817de0fd1cc7af9a00f0d284bbe18a4ced8a3","7d85dc8a7c2f29dd9605ec23d2b7e2528f72e218afa123c1bb46b21eafd6d4e9"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",23,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"e08c68ed38dad41dfd5c038c5d5fb4c1067d7157ccbea686fcfd5331eee91c8f"}73{"parentUuid":"aff52f99-3478-4046-9963-56cda01128b4","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXohzctMCUSTFFoCggVq","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":1468,"cache_read_input_tokens":21349,"output_tokens":4408,"output_tokens_details":{"thinking_tokens":132},"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":1468},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1582,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXohzN1rQUWpC6PhmiiE","requestRef":"398af1b9-f4cc-42ba-ae08-d2cf4d218bf1","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"41e615cc-7fae-4a5f-9c6a-32606ec5cdb9","timestamp":"2026-10-30T04:40:14.659Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}74{"parentUuid":"41e615cc-7fae-4a5f-9c6a-32606ec5cdb9","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXohzctMCUSTFFoCggVq","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"The P4 gate run passes all of its checks and the results reproduce. The remaining failures belong to P5, so I'm writing the report, claims and phase-ledger items now.\n\n","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":1468,"cache_read_input_tokens":21349,"output_tokens":4408,"output_tokens_details":{"thinking_tokens":132},"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":1468},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":1,"thinkingDisplay":"updates","apiBlockIndex":1,"requestId":"req_011CgXohzN1rQUWpC6PhmiiE","requestRef":"398af1b9-f4cc-42ba-ae08-d2cf4d218bf1","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"76e78172-6d50-4d86-bc1e-cdb05a8f0e17","timestamp":"2026-10-30T04:40:14.660Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}75{"parentUuid":"76e78172-6d50-4d86-bc1e-cdb05a8f0e17","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXohzctMCUSTFFoCggVq","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_0166Mn1eiSvUwzHr1V8VGiKM","name":"Bash","input":{"command":"~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open(\"out/state/phases.json\"))\np[\"P4\"]={\"status\":\"passed\",\"checks\":[\"clean re-run: results.json byte-identical\",\"internal consistency checks in out/state/checks.md all pass (Bellman fixed point of closed form verified numerically, error recomputation, tolerance, feasibility, truncation not binding)\",\"gate run 1 receipt out/state/gate_receipts/20261030T044012.141268Z.json: all results keys + reproducibility ok; only P5 deliverables (report, claims, terminal ledger) failing as expected\"],\"notes\":\"\",\"gate_receipts\":[\"out/state/gate_receipts/20261030T044012.141268Z.json\"]}\np[\"P5\"][\"status\"]=\"running\"\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\necho \"- 2026-10-30 P4 passed: reproducible, checks ok; gate run 1 (P5 items pending).\" >> out/state/log.md\ncat > out/report.md <<'EOF'\n# F5-conf-04 — VFI vs closed-form policy, optimal growth with log utility\n\n## Question\nA planner maximises Σ β^t ln c_t subject to y_{t+1} = (y_t − c_t)^α (Cobb–Douglas, productivity 1, full depreciation).\nWe derive the closed-form policy and value, solve the Bellman equation numerically by value-function iteration (VFI)\non the prescribed grid, and compare the two at y = 0.5, 1, 2 (policy) and y = 1 (value).\n\n## Data and exclusions\nSingle input `data/model.csv` (10 rows; SHA-256 098123…195b, matching the bundle manifest): α = 0.36, β = 0.95, grid of\n400 points equally spaced in ln y on [0.05, 5], VFI tolerance 1e-8 (sup norm), evaluation points 0.5, 1.0, 2.0\n(`n_input_rows`). No rows excluded (`out/exclusions.csv`); `data_issues` is empty — no deviation from the prescribed design\nwas needed. Grid points used: 400 (`grid_points_used`, `n_analysed`). None of the evaluation points is a grid node\n(`diag_eval_points_on_grid_node`), so the VFI policy is interpolated, as the task allows.\n\n## Method\n**Closed form (guess-and-verify).** Guess V(y) = A + B ln y. The first-order condition of\nmax_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\nB = 1 + αβB ⇒ B = 1/(1 − αβ), hence **c(y) = (1 − αβ) y** and savings rate (y − c)/y = **αβ**. Matching constants gives\n**A = [ln(1 − αβ) + (αβ/(1 − αβ)) ln(αβ)]/(1 − β)**, so V(1) = A. The verification was also done numerically: maximising\nthe right-hand side with this V at y = 0.5, 1, 2 reproduces c = (1 − αβ)y and T V = V (`out/state/checks.md`).\nAssumptions: log utility; Cobb–Douglas technology with productivity 1; full depreciation; interior solution (0 < c < y,\nguaranteed by the Inada property of ln); 0 < α < 1, 0 < β < 1.\n\n**VFI.** On the log grid, the choice variable is next-period output y' restricted to the grid; consumption is\nc = y − y'^{1/α} (infeasible pairs get −∞). Starting from V₀ = 0, V_{n+1}(y_i) = max_j {ln c_ij + β V_n(y_j)} is iterated\n(vectorised 400×400) until the sup-norm change is below 1e-8. The policy is the argmax; it never uses the closed form.\nPolicy values at the evaluation points are linearly interpolated in y between neighbouring grid nodes; V(1) is\nlinearly interpolated in ln y (the coordinate in which the grid is uniform). No randomness (`random_seed` = null).\n\n**Contraction.** On the discretised (finite, bounded) problem the Bellman operator satisfies Blackwell's sufficient\nconditions — monotonicity and discounting (T(V + a) = TV + βa) — so it is a contraction in the sup norm with modulus β\n(`contraction_modulus` = 0.95). The state space is effectively compact: under the optimal policy y' = (αβy)^α stays in\n[0.231, 1.213] ⊂ [0.05, 5] (`diag_closed_yprime_min`, `diag_closed_yprime_max`), and on the grid ln c is bounded, so the\nbounded-returns theory applies. (On the unbounded domain with log utility one would need a weighted-norm argument; this\nis not required here.)\n\n## Results\n| quantity | closed form | VFI |\n|---|---|---|\n| c(0.5) | 0.329 (`c_closed_y05`) | 0.32882 (`c_num_y05`) |\n| c(1.0) | 0.658 (`c_closed_y1`) | 0.65898 (`c_num_y1`) |\n| c(2.0) | 1.316 (`c_closed_y2`) | 1.30959 (`c_num_y2`) |\n| V(1) | −19.52441 (`value_closed_y1`) | −19.52476 (`value_num_y1`) |\n\n- Maximum absolute policy discrepancy over the three points: 0.00641 units of output (`max_abs_error_policy`), attained\n  at y = 2; the largest relative discrepancy is 0.49 % (`diag_policy_max_rel_error_eval`).\n- Value at y = 1 differs by 3.4e-4 utils (`diag_value_abs_error_y1`); the sup-norm value error over the grid is 4.8e-4\n  (`diag_value_sup_error_grid`).\n- Closed-form savings rate αβ = 0.342 (`savings_rate_closed_form`).\n- VFI converged in 361 iterations (`n_iterations`) with final sup-norm change 9.997e-9 (`final_sup_change`) < 1e-8.\n- Contraction modulus β = 0.95 (`contraction_modulus`).\n- The VFI policy never hits the edge of the grid (`diag_policy_edge_hits` = 0).\n\n## Uncertainty\nThe problem is deterministic; there is no sampling uncertainty and no confidence interval is meaningful. Numerical error\nhas two sources:\n1. *Stopping rule.* By the contraction property, ‖V_n − V*_grid‖ ≤ β/(1 − β)·‖V_n − V_{n−1}‖ ≈ 1.9e-7 utils\n   (`diag_vfi_tolerance_error_bound`) — negligible.\n2. *Discretisation*, which dominates: the choice of y' is restricted to grid nodes with log-step 0.01154\n   (`diag_grid_log_step`), so capital k = y'^{1/α} can be off by up to about step/(2α) ≈ 1.6 % in relative terms, i.e. an\n   error in c of up to about 0.83 % of c; the observed relative errors (≤ 0.49 %) are within that bound. Linear interpolation\n   between nodes adds a smaller component. The error grows in absolute terms with y because c and k scale with y\n   (sup over the grid: 0.025 at y = 5, `diag_policy_sup_error_grid`), and shrinks proportionally with the grid step\n   (more points or a narrower range); it also depends on α (through 1/α) and on β only through the tolerance bound.\n\n## Limitations and open issues\n- The validation covers only the prescribed parameter point (α = 0.36, β = 0.95) and grid (400 log-spaced points on\n  [0.05, 5]); no other grids or parameters were tested, as the task does not require it.\n- The closed form relies on log utility, Cobb–Douglas technology, full depreciation and an interior solution; with\n  partial depreciation or CRRA ≠ 1 no closed form of this kind exists and the comparison would not apply.\n- The policy discrepancy (`max_abs_error_policy`) reflects the discrete-choice VFI on this grid; it is not an error in the\n  closed form. A continuous-choice VFI with interpolated V would reduce it but is outside the prescribed design.\n- The contraction statement with modulus β is for the bounded, discretised problem; the unbounded continuous problem with\n  log utility requires a weighted sup-norm or a direct verification argument, which we do not develop here.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"Guess-and-verify gives the closed-form policy c(y) = (1 - alpha*beta) y, i.e. 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\":\"Valid under log utility, Cobb-Douglas technology with unit productivity, full depreciation, interior solution.\"},\n {\"id\":\"C2\",\"text\":\"The closed-form value at y = 1 is V(1) = A = -19.5244 utils.\",\"results_keys\":[\"value_closed_y1\"],\"status\":\"supported\",\"caveat\":\"Closed form also verified numerically as a Bellman fixed point at three points (checks.md).\"},\n {\"id\":\"C3\",\"text\":\"VFI on the prescribed 400-point log grid converged in 361 iterations with final sup-norm change below 1e-8.\",\"results_keys\":[\"n_iterations\",\"final_sup_change\",\"grid_points_used\"],\"status\":\"supported\",\"caveat\":\"Starting value V0 = 0.\"},\n {\"id\":\"C4\",\"text\":\"The VFI policy matches the closed form to within 0.0064 units of output (at most 0.49% relative) at the three evaluation points.\",\"results_keys\":[\"c_num_y05\",\"c_num_y1\",\"c_num_y2\",\"max_abs_error_policy\",\"diag_policy_max_rel_error_eval\"],\"status\":\"supported\",\"caveat\":\"Discrepancy is discretisation error of the discrete-choice grid plus linear interpolation; specific to this grid and parameter point.\"},\n {\"id\":\"C5\",\"text\":\"The VFI value at y = 1 is -19.5248, within 3.4e-4 utils of the closed form.\",\"results_keys\":[\"value_num_y1\",\"value_closed_y1\",\"diag_value_abs_error_y1\"],\"status\":\"supported\",\"caveat\":\"Interpolated linearly in ln y; y = 1 is not a grid node.\"},\n {\"id\":\"C6\",\"text\":\"The Bellman operator (on the bounded discretised problem) is a sup-norm contraction with modulus beta = 0.95, so the stopping-rule error is at most about 1.9e-7 utils, and discretisation dominates the numerical error.\",\"results_keys\":[\"contraction_modulus\",\"diag_vfi_tolerance_error_bound\",\"diag_value_abs_error_y1\"],\"status\":\"supported\",\"caveat\":\"Blackwell conditions on the bounded discretised problem; unbounded log-utility case needs a weighted-norm argument not developed here.\"},\n {\"id\":\"C7\",\"text\":\"The grid truncation is not binding: under the closed-form policy next-period output stays in [0.231, 1.213] and the VFI policy never selects a grid edge.\",\"results_keys\":[\"diag_closed_yprime_min\",\"diag_closed_yprime_max\",\"diag_policy_edge_hits\"],\"status\":\"supported\",\"caveat\":\"\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open(\"out/state/phases.json\"))\np[\"P5\"]={\"status\":\"passed\",\"checks\":[\"report.md written with all 6 sections, quantitative statements cite results keys\",\"claims.json written (7 claims, all supported, keys resolve)\",\"gate run at end of P5 (see gate_receipts)\"],\"notes\":\"\"}\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v \"\\[ok\\]\"","description":"Write report, claims, run final gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1468,"cache_read_input_tokens":21349,"output_tokens":4408,"output_tokens_details":{"thinking_tokens":132},"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":1468},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXohzN1rQUWpC6PhmiiE","requestRef":"398af1b9-f4cc-42ba-ae08-d2cf4d218bf1","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"59c431fe-0dbe-4e56-827b-4a0a626e1ebe","timestamp":"2026-10-30T04:40:48.884Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}76{"type":"last-prompt","lastPrompt":"Begin","leafUuid":"59c431fe-0dbe-4e56-827b-4a0a626e1ebe","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746"}77{"type":"atis-latch","atis":"","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746"}78{"parentUuid":"59c431fe-0dbe-4e56-827b-4a0a626e1ebe","isSidechain":false,"promptId":"98c76955-6ef3-4dd0-ad59-6beeb3568c50","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_0166Mn1eiSvUwzHr1V8VGiKM","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 35 checks failed)\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0130/out/state/gate_receipts/20261030T044049.257087Z.json","is_error":false}]},"uuid":"fcd963be-3ea8-4bfd-bf6a-18a7f21592f0","timestamp":"2026-10-30T04:40:49.266Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 35 checks failed)\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0130/out/state/gate_receipts/20261030T044049.257087Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"59c431fe-0dbe-4e56-827b-4a0a626e1ebe","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0130","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","version":"2.1.314","gitBranch":"HEAD"}79{"type":"api-request-blob","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","hash":"e5af73fedb62e66f47cea9698faf5670c3a0472433224e43ff9de6a9939e84fb","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"thinking","thinking":"The P4 gate run passes all of its checks and the results reproduce. The remaining failures belong to P5, so I'm writing the report, claims and phase-ledger items now.\n\n","signature":"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"},{"type":"tool_use","id":"toolu_0166Mn1eiSvUwzHr1V8VGiKM","name":"Bash","input":{"command":"~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open(\"out/state/phases.json\"))\np[\"P4\"]={\"status\":\"passed\",\"checks\":[\"clean re-run: results.json byte-identical\",\"internal consistency checks in out/state/checks.md all pass (Bellman fixed point of closed form verified numerically, error recomputation, tolerance, feasibility, truncation not binding)\",\"gate run 1 receipt out/state/gate_receipts/20261030T044012.141268Z.json: all results keys + reproducibility ok; only P5 deliverables (report, claims, terminal ledger) failing as expected\"],\"notes\":\"\",\"gate_receipts\":[\"out/state/gate_receipts/20261030T044012.141268Z.json\"]}\np[\"P5\"][\"status\"]=\"running\"\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\necho \"- 2026-10-30 P4 passed: reproducible, checks ok; gate run 1 (P5 items pending).\" >> out/state/log.md\ncat > out/report.md <<'EOF'\n# F5-conf-04 — VFI vs closed-form policy, optimal growth with log utility\n\n## Question\nA planner maximises Σ β^t ln c_t subject to y_{t+1} = (y_t − c_t)^α (Cobb–Douglas, productivity 1, full depreciation).\nWe derive the closed-form policy and value, solve the Bellman equation numerically by value-function iteration (VFI)\non the prescribed grid, and compare the two at y = 0.5, 1, 2 (policy) and y = 1 (value).\n\n## Data and exclusions\nSingle input `data/model.csv` (10 rows; SHA-256 098123…195b, matching the bundle manifest): α = 0.36, β = 0.95, grid of\n400 points equally spaced in ln y on [0.05, 5], VFI tolerance 1e-8 (sup norm), evaluation points 0.5, 1.0, 2.0\n(`n_input_rows`). No rows excluded (`out/exclusions.csv`); `data_issues` is empty — no deviation from the prescribed design\nwas needed. Grid points used: 400 (`grid_points_used`, `n_analysed`). None of the evaluation points is a grid node\n(`diag_eval_points_on_grid_node`), so the VFI policy is interpolated, as the task allows.\n\n## Method\n**Closed form (guess-and-verify).** Guess V(y) = A + B ln y. The first-order condition of\nmax_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\nB = 1 + αβB ⇒ B = 1/(1 − αβ), hence **c(y) = (1 − αβ) y** and savings rate (y − c)/y = **αβ**. Matching constants gives\n**A = [ln(1 − αβ) + (αβ/(1 − αβ)) ln(αβ)]/(1 − β)**, so V(1) = A. The verification was also done numerically: maximising\nthe right-hand side with this V at y = 0.5, 1, 2 reproduces c = (1 − αβ)y and T V = V (`out/state/checks.md`).\nAssumptions: log utility; Cobb–Douglas technology with productivity 1; full depreciation; interior solution (0 < c < y,\nguaranteed by the Inada property of ln); 0 < α < 1, 0 < β < 1.\n\n**VFI.** On the log grid, the choice variable is next-period output y' restricted to the grid; consumption is\nc = y − y'^{1/α} (infeasible pairs get −∞). Starting from V₀ = 0, V_{n+1}(y_i) = max_j {ln c_ij + β V_n(y_j)} is iterated\n(vectorised 400×400) until the sup-norm change is below 1e-8. The policy is the argmax; it never uses the closed form.\nPolicy values at the evaluation points are linearly interpolated in y between neighbouring grid nodes; V(1) is\nlinearly interpolated in ln y (the coordinate in which the grid is uniform). No randomness (`random_seed` = null).\n\n**Contraction.** On the discretised (finite, bounded) problem the Bellman operator satisfies Blackwell's sufficient\nconditions — monotonicity and discounting (T(V + a) = TV + βa) — so it is a contraction in the sup norm with modulus β\n(`contraction_modulus` = 0.95). The state space is effectively compact: under the optimal policy y' = (αβy)^α stays in\n[0.231, 1.213] ⊂ [0.05, 5] (`diag_closed_yprime_min`, `diag_closed_yprime_max`), and on the grid ln c is bounded, so the\nbounded-returns theory applies. (On the unbounded domain with log utility one would need a weighted-norm argument; this\nis not required here.)\n\n## Results\n| quantity | closed form | VFI |\n|---|---|---|\n| c(0.5) | 0.329 (`c_closed_y05`) | 0.32882 (`c_num_y05`) |\n| c(1.0) | 0.658 (`c_closed_y1`) | 0.65898 (`c_num_y1`) |\n| c(2.0) | 1.316 (`c_closed_y2`) | 1.30959 (`c_num_y2`) |\n| V(1) | −19.52441 (`value_closed_y1`) | −19.52476 (`value_num_y1`) |\n\n- Maximum absolute policy discrepancy over the three points: 0.00641 units of output (`max_abs_error_policy`), attained\n  at y = 2; the largest relative discrepancy is 0.49 % (`diag_policy_max_rel_error_eval`).\n- Value at y = 1 differs by 3.4e-4 utils (`diag_value_abs_error_y1`); the sup-norm value error over the grid is 4.8e-4\n  (`diag_value_sup_error_grid`).\n- Closed-form savings rate αβ = 0.342 (`savings_rate_closed_form`).\n- VFI converged in 361 iterations (`n_iterations`) with final sup-norm change 9.997e-9 (`final_sup_change`) < 1e-8.\n- Contraction modulus β = 0.95 (`contraction_modulus`).\n- The VFI policy never hits the edge of the grid (`diag_policy_edge_hits` = 0).\n\n## Uncertainty\nThe problem is deterministic; there is no sampling uncertainty and no confidence interval is meaningful. Numerical error\nhas two sources:\n1. *Stopping rule.* By the contraction property, ‖V_n − V*_grid‖ ≤ β/(1 − β)·‖V_n − V_{n−1}‖ ≈ 1.9e-7 utils\n   (`diag_vfi_tolerance_error_bound`) — negligible.\n2. *Discretisation*, which dominates: the choice of y' is restricted to grid nodes with log-step 0.01154\n   (`diag_grid_log_step`), so capital k = y'^{1/α} can be off by up to about step/(2α) ≈ 1.6 % in relative terms, i.e. an\n   error in c of up to about 0.83 % of c; the observed relative errors (≤ 0.49 %) are within that bound. Linear interpolation\n   between nodes adds a smaller component. The error grows in absolute terms with y because c and k scale with y\n   (sup over the grid: 0.025 at y = 5, `diag_policy_sup_error_grid`), and shrinks proportionally with the grid step\n   (more points or a narrower range); it also depends on α (through 1/α) and on β only through the tolerance bound.\n\n## Limitations and open issues\n- The validation covers only the prescribed parameter point (α = 0.36, β = 0.95) and grid (400 log-spaced points on\n  [0.05, 5]); no other grids or parameters were tested, as the task does not require it.\n- The closed form relies on log utility, Cobb–Douglas technology, full depreciation and an interior solution; with\n  partial depreciation or CRRA ≠ 1 no closed form of this kind exists and the comparison would not apply.\n- The policy discrepancy (`max_abs_error_policy`) reflects the discrete-choice VFI on this grid; it is not an error in the\n  closed form. A continuous-choice VFI with interpolated V would reduce it but is outside the prescribed design.\n- The contraction statement with modulus β is for the bounded, discretised problem; the unbounded continuous problem with\n  log utility requires a weighted sup-norm or a direct verification argument, which we do not develop here.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"Guess-and-verify gives the closed-form policy c(y) = (1 - alpha*beta) y, i.e. 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\":\"Valid under log utility, Cobb-Douglas technology with unit productivity, full depreciation, interior solution.\"},\n {\"id\":\"C2\",\"text\":\"The closed-form value at y = 1 is V(1) = A = -19.5244 utils.\",\"results_keys\":[\"value_closed_y1\"],\"status\":\"supported\",\"caveat\":\"Closed form also verified numerically as a Bellman fixed point at three points (checks.md).\"},\n {\"id\":\"C3\",\"text\":\"VFI on the prescribed 400-point log grid converged in 361 iterations with final sup-norm change below 1e-8.\",\"results_keys\":[\"n_iterations\",\"final_sup_change\",\"grid_points_used\"],\"status\":\"supported\",\"caveat\":\"Starting value V0 = 0.\"},\n {\"id\":\"C4\",\"text\":\"The VFI policy matches the closed form to within 0.0064 units of output (at most 0.49% relative) at the three evaluation points.\",\"results_keys\":[\"c_num_y05\",\"c_num_y1\",\"c_num_y2\",\"max_abs_error_policy\",\"diag_policy_max_rel_error_eval\"],\"status\":\"supported\",\"caveat\":\"Discrepancy is discretisation error of the discrete-choice grid plus linear interpolation; specific to this grid and parameter point.\"},\n {\"id\":\"C5\",\"text\":\"The VFI value at y = 1 is -19.5248, within 3.4e-4 utils of the closed form.\",\"results_keys\":[\"value_num_y1\",\"value_closed_y1\",\"diag_value_abs_error_y1\"],\"status\":\"supported\",\"caveat\":\"Interpolated linearly in ln y; y = 1 is not a grid node.\"},\n {\"id\":\"C6\",\"text\":\"The Bellman operator (on the bounded discretised problem) is a sup-norm contraction with modulus beta = 0.95, so the stopping-rule error is at most about 1.9e-7 utils, and discretisation dominates the numerical error.\",\"results_keys\":[\"contraction_modulus\",\"diag_vfi_tolerance_error_bound\",\"diag_value_abs_error_y1\"],\"status\":\"supported\",\"caveat\":\"Blackwell conditions on the bounded discretised problem; unbounded log-utility case needs a weighted-norm argument not developed here.\"},\n {\"id\":\"C7\",\"text\":\"The grid truncation is not binding: under the closed-form policy next-period output stays in [0.231, 1.213] and the VFI policy never selects a grid edge.\",\"results_keys\":[\"diag_closed_yprime_min\",\"diag_closed_yprime_max\",\"diag_policy_edge_hits\"],\"status\":\"supported\",\"caveat\":\"\"}\n]\nEOF\n~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open(\"out/state/phases.json\"))\np[\"P5\"]={\"status\":\"passed\",\"checks\":[\"report.md written with all 6 sections, quantitative statements cite results keys\",\"claims.json written (7 claims, all supported, keys resolve)\",\"gate run at end of P5 (see gate_receipts)\"],\"notes\":\"\"}\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v \"\\[ok\\]\"","description":"Write report, claims, run final gate"}}]}}80{"type":"api-request","sessionId":"05e0834c-bf1e-42d5-8c9e-8ecd61ae9746","id":"2e8c1de3-9296-4eae-83ed-338194b44fbb","timestamp":"2026-10-30T04:40:49.270Z","version":"2.1.314","querySource":"sdk","shapeHash":"74261e6e7cd56f87bea65087889d4ddf98044e0fbeb6aae5c04c10263b2c127e","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":"398af1b9-f4cc-42ba-ae08-d2cf4d218bf1","keep":24,"tail":["e5af73fedb62e66f47cea9698faf5670c3a0472433224e43ff9de6a9939e84fb","1c5c896fd25edd6b2f467fc2532f478c851d38ffeb05abeba1b9bc03cca66358"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",25,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"c2a28561066a53d19ab554e74f69968e3c4532d48d5f9bb088e12c1a7c35e51c"}81{"parentUuid":"fcd963be-3ea8-4bfd-bf6a-18a7f21592f0","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXokjLxDasRvubdm67mh","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Bu4LuLEU4mV9RUmEbb7N1k","name":"Bash","input":{"command":"~/wp29/venv/bin/python - <<'EOF'\nimport json\np=json.load(open(\"out/state/phases.json\"))\np[\"P5\"][\"checks\"][2]=\"gate run 2 at end of P5: PASSED 0/35 failed, receipt out/state/gate_receipts/20261030T044049.257087Z.json\"\np[\"P5\"][\"gate_receipts\"]=[\"out/state/gate_receipts/20261030T044049.257087Z.json\"]\njson.dump(p,open(\"out/state/phases.json\",\"w\"),indent=1)\nEOF\necho \"- 2026-10-30 P5 passed: report, claims written; 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Value-function iteration on the prescribed grid matches the closed-form policy to within 0.0064 units of output at all three evaluation points. All six phases are marked passed, and the final run of the check program passed with 0 of 35 checks failing.\n\n**Closed form.** I derived it by guessing V(y) = A + B ln y and checking that the guess satisfies the Bellman equation. It gives consumption c(y) = (1 − αβ)y and a savings rate of αβ = 0.342. With α = 0.36 and β = 0.95, consumption is 0.329, 0.658 and 1.316 at y = 0.5, 1 and 2, and V(1) = −19.5244. I also confirmed numerically at those three points that this V reproduces itself under the Bellman equation.\n\n**Value-function iteration.** The model was solved on the prescribed grid of 400 points, evenly spaced in ln y on [0.05, 5]. Each period the planner picks next period's output from the grid points. The iteration stopped after 361 rounds, when the largest change in the value function was 1.0e-8, just under the 1e-8 tolerance. None of the evaluation points falls exactly on a grid point, so the numerical answers there are interpolated linearly between neighbours.\n\n| | Closed form | Numerical | Difference |\n|---|---|---|---|\n| c(0.5) | 0.329 | 0.3288 | 0.0002 |\n| c(1) | 0.658 | 0.6590 | 0.0010 |\n| c(2) | 1.316 | 1.3096 | 0.0064 (largest, 0.49%) |\n| V(1) | −19.5244 | −19.5248 | 3.4e-4 |\n\n**Where the error comes from:**\n- **Grid spacing dominates.** Restricting next period's output to grid points can shift consumption by up to about 0.83%, and every observed gap is within that. The gap grows in absolute terms with y; the worst case on the grid is 0.025 at y = 5.\n- **Stopping the iteration early is negligible.** The Bellman operator shrinks distances by a factor of β = 0.95 each round, so stopping at the tolerance leaves at most about 1.9e-7 utils of error.\n- **The grid boundaries never matter.** Under the closed-form policy, next period's output stays between 0.231 and 1.213, well inside [0.05, 5], and the numerical policy never picks an edge of the grid.\n\n**Limitations:**\n- Only the one prescribed grid and parameter pair were tested.\n- The closed form holds only under log utility, Cobb–Douglas production with productivity one, full depreciation and an interior solution.\n- The contraction factor of 0.95 is shown for the bounded, discretised problem. The original problem with unbounded log utility would need a different argument, which I did not develop.\n\nNo data rows were excluded and no departure from the prescribed design was needed. Re-running `out/analysis.py` from scratch reproduces `out/results.json` byte for byte. 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