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It is the complete and only authoritative description of what is required: the scientific question, the inputs under `data/`, the required output files and their exact keys, and the information-availability rules.\n- There is no network access. Use the Python interpreter `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels, matplotlib are installed). Standard shell tools are available. Do not try to install packages.\n- Write every deliverable under `./out/`. The required deliverables are listed in `TASK.md`; at minimum they always include `out/results.json`, `out/report.md`, and a replication entry point `out/analysis.py` that regenerates `out/results.json` from `data/` when run with `~/wp29/venv/bin/python out/analysis.py` from the workspace root.\n- You are working alone and unattended; nobody will answer questions. Make reasonable, documented decisions.\n\nIntegrity rules (identical for every task):\n- Never fabricate numbers, data, results, or references. Every number in `out/results.json` and `out/report.md` must be produced by code you ran on the provided inputs.\n- Respect the information-availability rules in `TASK.md` exactly (for example, never use information that would not have been available at the stated decision time).\n- If part of the task cannot be completed as specified, say so explicitly in `out/report.md`, explain why, and still write every required file (use `null` for values you could not legitimately produce). An honest statement of a limitation is always preferred to a fabricated or guessed value.\n- Do not modify anything under `data/`.\n- When you are done, end with a brief plain-text summary of what you produced and any limitations.\n\nComplete the task described in `TASK.md` by following this research protocol. The protocol adds no scientific information to the task; it organizes how you work and what evidence you leave behind.\n\nPHASES (execute in order; a phase is eligible only when its dependencies are satisfied):\n\nP0 Scope and contract (depends on: nothing)\n- Read `TASK.md` completely. In `out/state/contract.md`, restate in your own words: the scientific question; the quantity or quantities to be estimated (the estimands) and the assumptions under which they are meaningful; every required output file and key; the information-availability rules; what would make the task impossible or the result invalid.\n- Write the initial phase ledger `out/state/phases.json`: a JSON object mapping each phase id (P0 … P5) to {\"status\": \"pending\"|\"running\"|\"passed\"|\"failed\"|\"blocked\"|\"stale\"|\"skipped_optional\", \"checks\": [], \"notes\": \"\"}. Keep it current as you work. A phase may only be set to \"passed\" when the checks listed for it in this protocol have actually been executed and their outcome recorded in \"checks\".\n\nP1 Data audit and provenance (depends on: P0)\n- Inspect every input file: compute and record its SHA-256, row and column counts, schema, units, date ranges, missing values, duplicates and anomalies in `out/state/data_audit.md`.\n- Keep an exclusion ledger in `out/exclusions.csv` (columns: step, rule, n_before, n_after, n_removed, rationale) for every filtering step you apply, so that n_raw − total removed = n_analysed.\n- Identify any input that violates the information-availability rules and decide, in writing, how you will handle it.\n\nP2 Baseline (depends on: P1)\n- Before any elaborate method, compute the simplest valid baseline that answers the question (for example a naïve or unconditional estimate), with the same evaluation rule used later. Record it in `out/results.json` under the keys the task requires, or under `baseline_*` keys when the task does not name them.\n\nP3 Method and computation (depends on: P2)\n- Implement the analysis in `out/analysis.py` so that it reads only `data/`, writes `out/results.json` deterministically (fix every random seed you use and record it), and prints nothing that contradicts the written results. Any figure or table must be generated by this script.\n\nP4 Verification (depends on: P3)\n- Re-run `out/analysis.py` from a clean state and confirm it regenerates `out/results.json` with identical values. Record the check in `out/state/phases.json` under P4.\n- Check internal consistency: identities that must hold (for example counts that must add up, standard errors that must be positive, confidence intervals that must contain their estimates, date orderings that must respect the information rules), units, and magnitudes against the baseline. Record every check and its outcome in `out/state/checks.md`. A failed check must be fixed or honestly reported, never silently ignored.\n\nP5 Reporting (depends on: P4)\n- Write `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. Every quantitative statement must cite the key of `out/results.json` it comes from.\n- Write `out/claims.json`: a list of the central claims of your report, each as {\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}. Do not state a claim in the report that is not in this ledger.\n- Set the final statuses in `out/state/phases.json`.\n\nSTOPPING RULES\n- Stop and declare the task complete only when every phase P0–P5 is \"passed\" with recorded checks. If a phase is \"blocked\" (missing information, impossible requirement, violated availability rule), stop, set the status, explain in `out/report.md` (section Limitations and open issues) and still write every required file with `null` for values you could not legitimately produce.\n- Do not spend effort on extensions that the task does not require.\n\nRECOVERY RULES\n- Append a short dated entry to `out/state/log.md` after each phase transition and after any important decision, so that work can be resumed by reading `out/state/`.\n- If you discover that an upstream input or decision changed after a downstream phase passed, mark the downstream phases \"stale\" and redo them; do not reuse stale results.\n- If you are interrupted and later resumed, first read `out/state/` and continue from the last consistent state; never re-run expensive steps that already have recorded, unchanged outputs.\n\nEXECUTABLE GATES (additional, mandatory)\n- A read-only gate program is provided at `~/wp29/gates/pgar_gate.py`. Run it from the workspace root as `~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py .` It checks the output contract of `TASK.md` (required files, keys, types, finite values, report sections, the claims ledger, the phase ledger, the exclusion ledger) and reproducibility (it re-runs `out/analysis.py` in a temporary copy and compares the regenerated `out/results.json` with yours). It never checks scientific correctness and it contains no reference answers.\n- You must run the gate at the end of P4 and again at the end of P5, and record each run's receipt (the gate writes `out/state/gate_receipts/<timestamp>.json`) in `out/state/phases.json`. You may not declare the task complete while the latest gate receipt reports `\"passed\": false`. Fix the reported problems and re-run the gate.\n- The controller will run the same gate after your session ends. If it fails, you will be resumed with the gate output and asked to fix the problems; each such cycle consumes your remaining budget.\n\nSEPARATE REVIEW (additional)\n- After the gate passes, a separate reviewer session that has not seen your work in progress will examine `TASK.md` and everything under `out/` and may return a list of issues (file `out/review/review.json`). You will then be resumed once to address them: fix what is justified, explain in `out/report.md` (Limitations and open issues) what you disagree with, re-run the gate, and update `out/claims.json` and `out/state/phases.json`. The reviewer has no reference answers; its role is to challenge unsupported claims, violated information rules, unverified computations, and inconsistencies between your report and your results.\n"}],"tools":[{"name":"Bash","description":"execute shell commands","input_schema":{"$schema":"https://json-schema.org/draft/2020-12/schema","type":"object","properties":{"command":{"description":"The command to execute","type":"string"},"timeout":{"description":"Optional timeout in milliseconds (max 600000 for a foreground command)","type":"number"},"description":{"description":"Clear, concise description of what this command does in active voice. 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the user's own instructions about these lines, such as a CLAUDE.md or memory rule, take precedence over this reminder, but do not add attribution lines this reminder leaves out):\n- End git commit messages with:\nCo-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>\n- End pull request descriptions with:\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n</system-reminder>"}],"renderedRole":"user","renderedBesideToolResult":true,"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0045","sessionId":"017c813b-71bc-4e99-98c0-785b0e1f6969","version":"2.1.314","gitBranch":"HEAD"}11{"type":"tools-used","tools":["Bash"],"sessionId":"017c813b-71bc-4e99-98c0-785b0e1f6969"}12{"parentUuid":"490b0376-c33a-4491-804a-4e58068043f1","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmeV3paNRZjS2zHf521","type":"message","role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":4,"cache_creation_input_tokens":2811,"cache_read_input_tokens":1504,"output_tokens":125,"output_tokens_details":{"thinking_tokens":19},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":2811},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"thinkingDurationMs":424,"thinkingDisplay":"updates","apiBlockIndex":0,"requestId":"req_011CgXmeUmiUzkdQmSRzCYsj","requestRef":"6e75b6c8-de48-4ebf-bc39-5d0f5c5c06ef","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"e7ddb3a5-9bbb-44f5-849f-88ab63006e38","timestamp":"2026-10-30T04:13:12.300Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0045","sessionId":"017c813b-71bc-4e99-98c0-785b0e1f6969","version":"2.1.314","gitBranch":"HEAD"}13{"parentUuid":"e7ddb3a5-9bbb-44f5-849f-88ab63006e38","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmeV3paNRZjS2zHf521","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01Vu3HC7HraMs8TuR7XaUTvg","name":"Bash","input":{"command":"cat TASK.md; 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Agent i has Cobb–Douglas preferences u_i(x1, x2) = α_i ln x1 + (1 − α_i) ln x2 and an endowment (e1_i, e2_i). Good 2 is the numeraire (p2 = 1). The estimands are the competitive (Walrasian) equilibrium relative price p = p1/p2, the equilibrium allocation (x1_A, x2_A, x1_B, x2_B), the aggregate excess demand for good 1 at the equilibrium price (which must be zero), and the Walras' law residual p·z1 + z2 (value of aggregate excess demand, which must be identically zero). Derive the closed-form equilibrium, verify market clearing and Walras' law numerically, and validate the closed-form price by an independent numerical root-finding of the excess-demand function.\n\n## Inputs\n- `data/endowments.csv` — columns `agent` (A or B), `good1`, `good2`: individual endowments in units of each good. One row per agent. These are the primary data of the exercise (theoretical parameters, not observed data).\n- `data/parameters.csv` — columns `parameter`, `value`, `description`: the preference parameters `alpha_A`, `alpha_B` and the aggregate endowments of each good as recorded in the summary sheet that accompanied the exercise (`aggregate_endowment_good1`, `aggregate_endowment_good2`).\n\n## Information-availability rules\n- Use only the two files under `data/`.\n- The numerical validation must solve the market-clearing condition directly (root of the aggregate excess demand of good 1 in p), not evaluate the closed-form expression.\n- Report in `data_issues` every problem you detect in the inputs and how you handled it.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F5-conf-01\" |\n| `price_ratio_p1_over_p2` | number | — | closed-form equilibrium relative price p1/p2 |\n| `x1_A`, `x2_A`, `x1_B`, `x2_B` | number | units of goods | equilibrium consumption of each good by each agent |\n| `excess_demand_good1` | number | units of good 1 | aggregate excess demand for good 1 at the reported price (demand minus aggregate endowment) |\n| `walras_law_residual` | number | units of numeraire | p·z1 + z2 at the reported price, where z_g is the aggregate excess demand for good g |\n| `aggregate_endowment_good1` | number | units of good 1 | aggregate endowment of good 1 used in the market-clearing condition |\n| `aggregate_endowment_good2` | number | units of good 2 | aggregate endowment of good 2 used in the market-clearing condition |\n| `price_ratio_numerical` | number | — | equilibrium price found by the independent numerical root-finding (the baseline check) |\n| `feasibility` | string | — | \"complete\", \"partial\" or \"infeasible\" |\n| `feasibility_reason` | string or null | — | explanation if not complete |\n| `data_issues` | array of {\"issue\",\"handling\"} | — | data problems detected and how handled (empty list if none) |\n| `n_input_rows` | object | — | {\"endowments.csv\": rows read, \"parameters.csv\": rows read} |\n| `n_analysed` | integer or null | — | number of agents in the equilibrium computation |\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 behind the closed form (interior solution, strictly positive endowments, price normalisation) and the scope of the numerical validation.\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\": \"...\"}].\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.\ntotal 32\ndrwxr-xr-x 6 simon-pierreboucher staff 192 oct. 29 23:42 .\ndrwxr-xr-x 41 simon-pierreboucher staff 1312 oct. 30 00:13 ..\n-rw-r--r-- 1 simon-pierreboucher staff 519 oct. 29 23:42 bundle.json\ndrwxr-xr-x 4 simon-pierreboucher staff 128 oct. 29 23:26 data\n-rw-r--r-- 1 simon-pierreboucher staff 1885 oct. 29 23:32 gate_spec.json\n-rw-r--r-- 1 simon-pierreboucher staff 4133 oct. 29 23:32 TASK.md\ndata:\nendowments.csv\nparameters.csv","is_error":false}]},"uuid":"e7479827-6ed3-4209-8a43-c31005ac2542","timestamp":"2026-10-30T04:13:12.921Z","toolUseResult":{"stdout":"# F5-conf-01 — Competitive equilibrium of a two-agent, two-good exchange economy\n\n## Scientific question\nTwo agents A and B trade two goods in a pure exchange economy. Agent i has Cobb–Douglas preferences u_i(x1, x2) = α_i ln x1 + (1 − α_i) ln x2 and an endowment (e1_i, e2_i). Good 2 is the numeraire (p2 = 1). The estimands are the competitive (Walrasian) equilibrium relative price p = p1/p2, the equilibrium allocation (x1_A, x2_A, x1_B, x2_B), the aggregate excess demand for good 1 at the equilibrium price (which must be zero), and the Walras' law residual p·z1 + z2 (value of aggregate excess demand, which must be identically zero). Derive the closed-form equilibrium, verify market clearing and Walras' law numerically, and validate the closed-form price by an independent numerical root-finding of the excess-demand function.\n\n## Inputs\n- `data/endowments.csv` — columns `agent` (A or B), `good1`, `good2`: individual endowments in units of each good. One row per agent. These are the primary data of the exercise (theoretical parameters, not observed data).\n- `data/parameters.csv` — columns `parameter`, `value`, `description`: the preference parameters `alpha_A`, `alpha_B` and the aggregate endowments of each good as recorded in the summary sheet that accompanied the exercise (`aggregate_endowment_good1`, `aggregate_endowment_good2`).\n\n## Information-availability rules\n- Use only the two files under `data/`.\n- The numerical validation must solve the market-clearing condition directly (root of the aggregate excess demand of good 1 in p), not evaluate the closed-form expression.\n- Report in `data_issues` every problem you detect in the inputs and how you handled it.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | — | \"F5-conf-01\" |\n| `price_ratio_p1_over_p2` | number | — | closed-form equilibrium relative price p1/p2 |\n| `x1_A`, `x2_A`, `x1_B`, `x2_B` | number | units of goods | equilibrium consumption of each good by each agent |\n| `excess_demand_good1` | number | units of good 1 | aggregate excess demand for good 1 at the reported price (demand minus aggregate endowment) |\n| `walras_law_residual` | number | units of numeraire | p·z1 + z2 at the reported price, where z_g is the aggregate excess demand for good g |\n| `aggregate_endowment_good1` | number | units of good 1 | aggregate endowment of good 1 used in the market-clearing condition |\n| `aggregate_endowment_good2` | number | units of good 2 | aggregate endowment of good 2 used in the market-clearing condition |\n| `price_ratio_numerical` | number | — | equilibrium price found by the independent numerical root-finding (the baseline check) |\n| `feasibility` | string | — | \"complete\", \"partial\" or \"infeasible\" |\n| `feasibility_reason` | string or null | — | explanation if not complete |\n| `data_issues` | array of {\"issue\",\"handling\"} | — | data problems detected and how handled (empty list if none) |\n| `n_input_rows` | object | — | {\"endowments.csv\": rows read, \"parameters.csv\": rows read} |\n| `n_analysed` | integer or null | — | number of agents in the equilibrium computation |\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 behind the closed form (interior solution, strictly positive endowments, price normalisation) and the scope of the numerical validation.\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\": \"...\"}].\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.\ntotal 32\ndrwxr-xr-x 6 simon-pierreboucher staff 192 oct. 29 23:42 .\ndrwxr-xr-x 41 simon-pierreboucher staff 1312 oct. 30 00:13 ..\n-rw-r--r-- 1 simon-pierreboucher staff 519 oct. 29 23:42 bundle.json\ndrwxr-xr-x 4 simon-pierreboucher staff 128 oct. 29 23:26 data\n-rw-r--r-- 1 simon-pierreboucher staff 1885 oct. 29 23:32 gate_spec.json\n-rw-r--r-- 1 simon-pierreboucher staff 4133 oct. 29 23:32 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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question:** Walrasian equilibrium of a 2-agent, 2-good Cobb-Douglas exchange economy; good 2 numeraire (p2=1).\n**Estimands:** equilibrium p=p1/p2 (closed form); allocation x1_A,x2_A,x1_B,x2_B; aggregate excess demand of good 1 at p (should be 0); Walras residual p*z1+z2 (identically 0); independent numerical root of z1(p).\n**Assumptions:** Cobb-Douglas with 0<alpha_i<1 (interior demands), strictly positive endowments (positive income at any p>0), normalisation p2=1, price-taking agents. 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written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\"P2\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\n\"P3\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\"P4\":{\"status\":\"pending\",\"checks\":[],\"notes\":\"\"},\"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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-p out/state && cd out/state && cat > contract.md <<'EOF'\n# Contract (P0)\n**Question:** Walrasian equilibrium of a 2-agent, 2-good Cobb-Douglas exchange economy; good 2 numeraire (p2=1).\n**Estimands:** equilibrium p=p1/p2 (closed form); allocation x1_A,x2_A,x1_B,x2_B; aggregate excess demand of good 1 at p (should be 0); Walras residual p*z1+z2 (identically 0); independent numerical root of z1(p).\n**Assumptions:** Cobb-Douglas with 0<alpha_i<1 (interior demands), strictly positive endowments (positive income at any p>0), normalisation p2=1, price-taking agents. Closed form: p = sum_i alpha_i e2_i / sum_i (1-alpha_i) e1_i.\n**Outputs:** out/results.json (task_id, price_ratio_p1_over_p2, x1_A, x2_A, x1_B, x2_B, excess_demand_good1, walras_law_residual, aggregate_endowment_good1/2, price_ratio_numerical, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed), out/report.md (6 sections), out/analysis.py, out/claims.json; plus protocol state files.\n**Information rules:** only data/ files; numerical validation must root-find z1(p)=0 directly, not evaluate the closed form; report all input problems in data_issues.\n**Invalidity:** nonpositive endowments, alpha outside (0,1), missing agent, or inconsistent aggregates used in market clearing (budgets and clearing must use same endowments, otherwise Walras' law fails).\nEOF\ncat > phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md 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No randomness used.\"\"\"\nimport json, math, os\nimport pandas as pd\nfrom scipy.optimize import brentq\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nend = pd.read_csv(os.path.join(ROOT, \"data\", \"endowments.csv\"))\npar = pd.read_csv(os.path.join(ROOT, \"data\", \"parameters.csv\"))\nP = dict(zip(par[\"parameter\"], par[\"value\"].astype(float)))\n\nissues = []\n# --- validation ---\nassert not end.isna().any().any() and not par[\"value\"].isna().any()\nassert end[\"agent\"].is_unique and set(end[\"agent\"]) == {\"A\", \"B\"}\nend = end.set_index(\"agent\")\nagents = [\"A\", \"B\"]\ne1 = {a: float(end.loc[a, \"good1\"]) for a in agents}\ne2 = {a: float(end.loc[a, \"good2\"]) for a in agents}\nalpha = {a: P[f\"alpha_{a}\"] for a in agents}\nvalid = [a for a in agents if e1[a] > 0 and e2[a] > 0 and 0 < alpha[a] < 1]\nassert valid == agents, \"invalid agent parameters\"\n\nE1 = sum(e1.values()); E2 = sum(e2.values())\nE1_sheet = P[\"aggregate_endowment_good1\"]; E2_sheet = P[\"aggregate_endowment_good2\"]\nfor g, s, r in [(1, E1, E1_sheet), (2, E2, E2_sheet)]:\n if not math.isclose(s, r, rel_tol=1e-12):\n issues.append({\n \"issue\": f\"parameters.csv aggregate_endowment_good{g} = {r} but sum of individual \"\n f\"endowments in endowments.csv = {s}.\",\n \"handling\": f\"Used the sum of individual endowments ({s}) as the aggregate, since budgets are \"\n f\"defined by individual endowments and endowments.csv is the primary data; using {r} \"\n f\"would violate Walras' law. Summary-sheet value reported only as a sensitivity in report.md.\"})\n\n# --- demand and excess demand (p2 = 1) ---\ndef demand(a, p):\n m = p * e1[a] + e2[a]\n return alpha[a] * m / p, (1 - alpha[a]) * m\n\ndef z(p, agg1=E1, agg2=E2):\n d = [demand(a, p) for a in agents]\n return sum(x[0] for x in d) - agg1, sum(x[1] for x in d) - agg2\n\n# --- closed form ---\np_cf = sum(alpha[a] * e2[a] for a in agents) / sum((1 - alpha[a]) * e1[a] for a in agents)\n# --- independent numerical root of z1(p) (does not use closed form) ---\np_num = brentq(lambda p: z(p)[0], 1e-6, 1e6, xtol=1e-14, rtol=1e-15, maxiter=500)\n\nxA = demand(\"A\", p_cf); xB = demand(\"B\", p_cf)\nz1, z2 = z(p_cf)\nwalras = p_cf * z1 + z2\n\n# sensitivity: price that would clear good 1 if summary-sheet aggregate were imposed\np_sheet = brentq(lambda p: z(p, E1_sheet, E2_sheet)[0], 1e-6, 1e6, xtol=1e-14, rtol=1e-15)\nz_sheet = z(p_sheet, E1_sheet, E2_sheet)\n\nres = {\n \"task_id\": \"F5-conf-01\",\n \"price_ratio_p1_over_p2\": p_cf,\n \"x1_A\": xA[0], \"x2_A\": xA[1], \"x1_B\": xB[0], \"x2_B\": xB[1],\n \"excess_demand_good1\": z1,\n \"excess_demand_good2\": z2,\n \"walras_law_residual\": walras,\n \"aggregate_endowment_good1\": E1,\n \"aggregate_endowment_good2\": E2,\n \"price_ratio_numerical\": p_num,\n \"abs_diff_closed_form_vs_numerical\": abs(p_cf - p_num),\n \"baseline_price_ratio_numerical\": p_num,\n \"sensitivity_summary_sheet_E1\": E1_sheet,\n \"sensitivity_price_clearing_good1_with_sheet_E1\": p_sheet,\n \"sensitivity_excess_demand_good2_with_sheet_E1\": z_sheet[1],\n \"sensitivity_walras_residual_with_sheet_E1\": p_sheet * z_sheet[0] + z_sheet[1],\n \"feasibility\": \"complete\",\n \"feasibility_reason\": None,\n \"data_issues\": issues,\n \"n_input_rows\": {\"endowments.csv\": int(len(end)), \"parameters.csv\": int(len(par))},\n \"n_analysed\": len(valid),\n \"random_seed\": None,\n}\nos.makedirs(os.path.join(ROOT, \"out\"), exist_ok=True)\nwith open(os.path.join(ROOT, \"out\", \"results.json\"), \"w\") as f:\n json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis script"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":892,"cache_read_input_tokens":10223,"output_tokens":2020,"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":892},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXmhErdvZEXzVVy5WdpT","requestRef":"e138afa1-a3f1-49fd-a67b-3a075bcb7e79","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"b694a440-6aee-4fb4-b9a1-f400df3330e7","timestamp":"2026-10-30T04:14:04.231Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0045","sessionId":"017c813b-71bc-4e99-98c0-785b0e1f6969","version":"2.1.314","gitBranch":"HEAD"}41{"parentUuid":"b694a440-6aee-4fb4-b9a1-f400df3330e7","isSidechain":false,"promptId":"92b3eaa6-288d-431f-8c39-6d56f981ce85","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01Kr3cSyAbh1oELLTW9n3NgC","type":"tool_result","content":"{\n \"task_id\": \"F5-conf-01\",\n \"price_ratio_p1_over_p2\": 0.8749999999999999,\n \"x1_A\": 4.114285714285715,\n \"x2_A\": 5.3999999999999995,\n \"x1_B\": 7.885714285714286,\n \"x2_B\": 4.6000000000000005,\n \"excess_demand_good1\": 0.0,\n \"excess_demand_good2\": 0.0,\n \"walras_law_residual\": 0.0,\n \"aggregate_endowment_good1\": 12.0,\n \"aggregate_endowment_good2\": 10.0,\n \"price_ratio_numerical\": 0.8749999999999998,\n \"abs_diff_closed_form_vs_numerical\": 1.1102230246251565e-16,\n \"baseline_price_ratio_numerical\": 0.8749999999999998,\n \"sensitivity_summary_sheet_E1\": 14.0,\n \"sensitivity_price_clearing_good1_with_sheet_E1\": 0.6666666666666669,\n \"sensitivity_excess_demand_good2_with_sheet_E1\": -1.3333333333333321,\n \"sensitivity_walras_residual_with_sheet_E1\": -1.3333333333333346,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"parameters.csv aggregate_endowment_good1 = 14.0 but sum of individual endowments in endowments.csv = 12.0.\",\n \"handling\": \"Used the sum of individual endowments (12.0) as the aggregate, since budgets are defined by individual endowments and endowments.csv is the primary data; using 14.0 would violate Walras' law. Summary-sheet value reported only as a sensitivity in report.md.\"\n }\n ],\n \"n_input_rows\": {\n \"endowments.csv\": 2,\n \"parameters.csv\": 4\n },\n \"n_analysed\": 2,\n \"random_seed\": null\n}","is_error":false}]},"uuid":"beda20b7-7674-439a-b204-daf7cea70825","timestamp":"2026-10-30T04:14:04.759Z","toolUseResult":{"stdout":"{\n \"task_id\": \"F5-conf-01\",\n \"price_ratio_p1_over_p2\": 0.8749999999999999,\n \"x1_A\": 4.114285714285715,\n \"x2_A\": 5.3999999999999995,\n \"x1_B\": 7.885714285714286,\n \"x2_B\": 4.6000000000000005,\n \"excess_demand_good1\": 0.0,\n \"excess_demand_good2\": 0.0,\n \"walras_law_residual\": 0.0,\n \"aggregate_endowment_good1\": 12.0,\n \"aggregate_endowment_good2\": 10.0,\n \"price_ratio_numerical\": 0.8749999999999998,\n \"abs_diff_closed_form_vs_numerical\": 1.1102230246251565e-16,\n \"baseline_price_ratio_numerical\": 0.8749999999999998,\n \"sensitivity_summary_sheet_E1\": 14.0,\n \"sensitivity_price_clearing_good1_with_sheet_E1\": 0.6666666666666669,\n \"sensitivity_excess_demand_good2_with_sheet_E1\": -1.3333333333333321,\n \"sensitivity_walras_residual_with_sheet_E1\": -1.3333333333333346,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"parameters.csv aggregate_endowment_good1 = 14.0 but sum of individual endowments in endowments.csv = 12.0.\",\n \"handling\": \"Used the sum of individual endowments (12.0) as the aggregate, since budgets are defined by individual endowments and endowments.csv is the primary data; using 14.0 would violate Walras' law. 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No randomness used.\"\"\"\nimport json, math, os\nimport pandas as pd\nfrom scipy.optimize import brentq\n\nROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))\nend = pd.read_csv(os.path.join(ROOT, \"data\", \"endowments.csv\"))\npar = pd.read_csv(os.path.join(ROOT, \"data\", \"parameters.csv\"))\nP = dict(zip(par[\"parameter\"], par[\"value\"].astype(float)))\n\nissues = []\n# --- validation ---\nassert not end.isna().any().any() and not par[\"value\"].isna().any()\nassert end[\"agent\"].is_unique and set(end[\"agent\"]) == {\"A\", \"B\"}\nend = end.set_index(\"agent\")\nagents = [\"A\", \"B\"]\ne1 = {a: float(end.loc[a, \"good1\"]) for a in agents}\ne2 = {a: float(end.loc[a, \"good2\"]) for a in agents}\nalpha = {a: P[f\"alpha_{a}\"] for a in agents}\nvalid = [a for a in agents if e1[a] > 0 and e2[a] > 0 and 0 < alpha[a] < 1]\nassert valid == agents, \"invalid agent parameters\"\n\nE1 = sum(e1.values()); E2 = sum(e2.values())\nE1_sheet = P[\"aggregate_endowment_good1\"]; E2_sheet = P[\"aggregate_endowment_good2\"]\nfor g, s, r in [(1, E1, E1_sheet), (2, E2, E2_sheet)]:\n if not math.isclose(s, r, rel_tol=1e-12):\n issues.append({\n \"issue\": f\"parameters.csv aggregate_endowment_good{g} = {r} but sum of individual \"\n f\"endowments in endowments.csv = {s}.\",\n \"handling\": f\"Used the sum of individual endowments ({s}) as the aggregate, since budgets are \"\n f\"defined by individual endowments and endowments.csv is the primary data; using {r} \"\n f\"would violate Walras' law. Summary-sheet value reported only as a sensitivity in report.md.\"})\n\n# --- demand and excess demand (p2 = 1) ---\ndef demand(a, p):\n m = p * e1[a] + e2[a]\n return alpha[a] * m / p, (1 - alpha[a]) * m\n\ndef z(p, agg1=E1, agg2=E2):\n d = [demand(a, p) for a in agents]\n return sum(x[0] for x in d) - agg1, sum(x[1] for x in d) - agg2\n\n# --- closed form ---\np_cf = sum(alpha[a] * e2[a] for a in agents) / sum((1 - alpha[a]) * e1[a] for a in agents)\n# --- independent numerical root of z1(p) (does not use closed form) ---\np_num = brentq(lambda p: z(p)[0], 1e-6, 1e6, xtol=1e-14, rtol=1e-15, maxiter=500)\n\nxA = demand(\"A\", p_cf); xB = demand(\"B\", p_cf)\nz1, z2 = z(p_cf)\nwalras = p_cf * z1 + z2\n\n# sensitivity: price that would clear good 1 if summary-sheet aggregate were imposed\np_sheet = brentq(lambda p: z(p, E1_sheet, E2_sheet)[0], 1e-6, 1e6, xtol=1e-14, rtol=1e-15)\nz_sheet = z(p_sheet, E1_sheet, E2_sheet)\n\nres = {\n \"task_id\": \"F5-conf-01\",\n \"price_ratio_p1_over_p2\": p_cf,\n \"x1_A\": xA[0], \"x2_A\": xA[1], \"x1_B\": xB[0], \"x2_B\": xB[1],\n \"excess_demand_good1\": z1,\n \"excess_demand_good2\": z2,\n \"walras_law_residual\": walras,\n \"aggregate_endowment_good1\": E1,\n \"aggregate_endowment_good2\": E2,\n \"price_ratio_numerical\": p_num,\n \"abs_diff_closed_form_vs_numerical\": abs(p_cf - p_num),\n \"baseline_price_ratio_numerical\": p_num,\n \"sensitivity_summary_sheet_E1\": E1_sheet,\n \"sensitivity_price_clearing_good1_with_sheet_E1\": p_sheet,\n \"sensitivity_excess_demand_good2_with_sheet_E1\": z_sheet[1],\n \"sensitivity_walras_residual_with_sheet_E1\": p_sheet * z_sheet[0] + z_sheet[1],\n \"feasibility\": \"complete\",\n \"feasibility_reason\": None,\n \"data_issues\": issues,\n \"n_input_rows\": {\"endowments.csv\": int(len(end)), \"parameters.csv\": int(len(par))},\n \"n_analysed\": len(valid),\n \"random_seed\": None,\n}\nos.makedirs(os.path.join(ROOT, \"out\"), exist_ok=True)\nwith open(os.path.join(ROOT, \"out\", \"results.json\"), \"w\") as f:\n json.dump(res, f, indent=2)\nprint(json.dumps(res, indent=2))\nEOF\n~/wp29/venv/bin/python out/analysis.py","description":"Write and run analysis 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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;r=json.load(open('out/results.json'))\np=r['price_ratio_p1_over_p2']\nprint('x1 sum',r['x1_A']+r['x1_B'],'x2 sum',r['x2_A']+r['x2_B'])\nprint('budget A',p*r['x1_A']+r['x2_A'],p*8+2,'budget B',p*r['x1_B']+r['x2_B'],p*4+8)\nprint('MRS A',(0.4/r['x1_A'])/(0.6/r['x2_A']),'MRS B',(0.6/r['x1_B'])/(0.4/r['x2_B']))\nfrom fractions import Fraction as F\npf=(F(2,5)*2+F(3,5)*8)/(F(3,5)*8+F(2,5)*4);print('exact p',pf, 'x1_A exact',F(2,5)*(pf*8+2)/pf)\nEOF","description":"Reproducibility and consistency 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sum 12.0 x2 sum 10.0\nbudget A 9.0 9.0 budget B 11.5 11.5\nMRS A 0.8749999999999998 MRS B 0.8749999999999999\nexact p 7/8 x1_A exact 144/35","is_error":false}]},"uuid":"1c9a6681-9cc4-4417-afe7-ef202f5f377e","timestamp":"2026-10-30T04:14:12.701Z","toolUseResult":{"stdout":"IDENTICAL\nx1 sum 12.0 x2 sum 10.0\nbudget A 9.0 9.0 budget B 11.5 11.5\nMRS A 0.8749999999999998 MRS B 0.8749999999999999\nexact p 7/8 x1_A exact 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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;r=json.load(open('out/results.json'))\np=r['price_ratio_p1_over_p2']\nprint('x1 sum',r['x1_A']+r['x1_B'],'x2 sum',r['x2_A']+r['x2_B'])\nprint('budget A',p*r['x1_A']+r['x2_A'],p*8+2,'budget B',p*r['x1_B']+r['x2_B'],p*4+8)\nprint('MRS A',(0.4/r['x1_A'])/(0.6/r['x2_A']),'MRS B',(0.6/r['x1_B'])/(0.4/r['x2_B']))\nfrom fractions import Fraction as F\npf=(F(2,5)*2+F(3,5)*8)/(F(3,5)*8+F(2,5)*4);print('exact p',pf, 'x1_A exact',F(2,5)*(pf*8+2)/pf)\nEOF","description":"Reproducibility and consistency 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> out/state/checks.md <<'EOF'\n# Verification checks (P4)\n| # | check | outcome |\n|---|---|---|\n| 1 | Clean re-run of out/analysis.py regenerates byte-identical results.json | PASS (cmp identical) |\n| 2 | Market clearing: x1_A+x1_B = 12.0 = aggregate_endowment_good1; x2_A+x2_B = 10.0 = aggregate_endowment_good2 | PASS |\n| 3 | excess_demand_good1 = 0, excess_demand_good2 = 0, walras_law_residual = 0 (float) | PASS |\n| 4 | Budgets bind: A spends 9.0 = p*8+2; B spends 11.5 = p*4+8 | PASS |\n| 5 | MRS_A = MRS_B = p = 0.875 (Pareto efficiency / tangency) | PASS |\n| 6 | Exact rational arithmetic: p = 7/8, x1_A = 144/35 (=4.142857...) matches float | PASS |\n| 7 | Closed-form vs brentq root of z1(p) on [1e-6,1e6]: abs diff 1.1e-16 | PASS |\n| 8 | All allocations strictly positive (interior solution) | PASS |\n| 9 | n_raw agents 2 - removed 0 = n_analysed 2 (exclusions.csv) | PASS |\n| 10 | Input discrepancy (sheet E1 14 vs sum 12) recorded in data_issues | PASS |\nEOF\nsed -i '' 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GATE pgar_gate/1.0 — FAILED (10 of 31 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:price_ratio_p1_over_p2: ok\n [ok] key:x1_A: ok\n [ok] key:x2_A: ok\n [ok] key:x1_B: ok\n [ok] key:x2_B: ok\n [ok] key:excess_demand_good1: ok\n [ok] key:walras_law_residual: ok\n [ok] key:aggregate_endowment_good1: ok\n [ok] key:aggregate_endowment_good2: ok\n [ok] key:price_ratio_numerical: ok\n [ok] key:feasibility: ok\n [ok] key:feasibility_reason: ok\n [ok] key:data_issues: ok\n [ok] key:n_input_rows: ok\n [ok] key:n_analysed: ok\n [ok] key:random_seed: ok\n [FAIL] section:Question: heading not found\n [FAIL] section:Data and exclusions: heading not found\n [FAIL] section:Method: heading not found\n [FAIL] section:Results: heading not found\n [FAIL] section:Uncertainty: heading not found\n [FAIL] section:Limitations and open issues: heading not found\n [FAIL] claims_json: out/claims.json missing\n [FAIL] phase_ledger: phases not terminal: ['P1', 'P2', 'P3', 'P4', 'P5']\n [ok] reproducibility: regenerated in 0.5s; identical within tolerance\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0045/out/state/gate_receipts/20261030T041419.414862Z.json\n20261030T041419.414862Z.json","is_error":false}]},"uuid":"2d278636-725a-42ce-add9-00761e3c1750","timestamp":"2026-10-30T04:14:19.425Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — FAILED (10 of 31 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:price_ratio_p1_over_p2: ok\n [ok] key:x1_A: ok\n [ok] key:x2_A: ok\n [ok] key:x1_B: ok\n [ok] key:x2_B: ok\n [ok] key:excess_demand_good1: ok\n [ok] key:walras_law_residual: ok\n [ok] key:aggregate_endowment_good1: ok\n [ok] key:aggregate_endowment_good2: ok\n [ok] key:price_ratio_numerical: ok\n [ok] key:feasibility: ok\n [ok] key:feasibility_reason: ok\n [ok] key:data_issues: ok\n [ok] key:n_input_rows: ok\n [ok] key:n_analysed: ok\n [ok] key:random_seed: ok\n [FAIL] section:Question: heading not found\n [FAIL] section:Data and exclusions: heading not found\n [FAIL] section:Method: heading not found\n [FAIL] section:Results: heading not found\n [FAIL] section:Uncertainty: heading not found\n [FAIL] section:Limitations and open issues: heading not found\n [FAIL] claims_json: out/claims.json missing\n [FAIL] phase_ledger: phases not terminal: ['P1', 'P2', 'P3', 'P4', 'P5']\n [ok] reproducibility: regenerated in 0.5s; identical within tolerance\nreceipt: 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failures at the end of P4 are expected: the report, claims and final phase statuses are written in P5. Now writing the report and claims."}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1391,"cache_read_input_tokens":14663,"output_tokens":3461,"output_tokens_details":{"thinking_tokens":39},"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":1391},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":1,"requestId":"req_011CgXmjXSpno7emaSzv4j5Z","requestRef":"50211acf-5955-44d8-b959-e042867ed7fe","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"19f6ba46-1f1a-40a6-b617-0715b1c85019","timestamp":"2026-10-30T04:14:21.237Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0045","sessionId":"017c813b-71bc-4e99-98c0-785b0e1f6969","version":"2.1.314","gitBranch":"HEAD"}57{"parentUuid":"19f6ba46-1f1a-40a6-b617-0715b1c85019","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXmjXixPMJmYNrpVyEDS","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01YZD8A85erDvZMUadf5FhGh","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-conf-01 — Competitive equilibrium of a 2×2 Cobb–Douglas exchange economy\n\n## Question\nFind the Walrasian equilibrium of a pure exchange economy. Agents A and B have utilities u_i = α_i ln x1 + (1−α_i) ln x2 and given endowments. Good 2 is the numeraire (p2 = 1). We report the closed-form relative price p = p1/p2, the equilibrium allocation, the aggregate excess demand for good 1, and the Walras' law residual. We then check the closed-form price against an independent numerical root of the excess-demand function.\n\n## Data and exclusions\n- `data/endowments.csv` has 2 rows (`n_input_rows`): A = (8, 2) and B = (4, 8). `data/parameters.csv` has 4 rows: α_A = 0.4, α_B = 0.6, plus two summary-sheet aggregates. SHA-256 hashes and the full audit are in `out/state/data_audit.md`.\n- No values are missing and no rows are duplicated. All endowments are strictly positive and both α are in (0,1). No agent was excluded: 2 read, 0 removed, `n_analysed` = 2 (`out/exclusions.csv`).\n- **Data issue (`data_issues`):** the summary sheet records an aggregate endowment of good 1 of 14. The individual endowments sum to 8 + 4 = 12. Good 2 is consistent: the sheet says 10 and the endowments sum to 10.\n - Each agent's budget comes from its own endowment, so the only aggregate consistent with those budgets is their sum. I therefore used `aggregate_endowment_good1` = 12 and `aggregate_endowment_good2` = 10. The value of 14 is used only in the sensitivity check below.\n\n## Method\n- **Assumptions:**\n - Agents are price-takers.\n - Prices are normalised so that p2 = 1.\n - 0 < α_i < 1 and endowments are strictly positive. This makes income positive at every p > 0, so Cobb–Douglas demands are interior: x1_i = α_i m_i / p and x2_i = (1−α_i) m_i, where m_i = p·e1_i + e2_i.\n- **Closed form:** setting Σ x1_i = Σ e1_i gives p = Σ α_i e2_i / Σ (1−α_i) e1_i = 5.6 / 6.4. By Walras' law, the market for good 2 then clears automatically.\n- **Numerical check (also the baseline):** Brent's method (`scipy.optimize.brentq`) solves z1(p) = Σ x1_i(p) − E1 = 0 on [1e-6, 1e6], using only the demand functions and never the closed-form expression. z1 is strictly decreasing in p, so the root is unique.\n- **Reproducibility:** `out/analysis.py` regenerates `out/results.json`. It uses no randomness (`random_seed` = null).\n\n## Results\n- Equilibrium price: `price_ratio_p1_over_p2` = 0.875 (exactly 7/8). The numerical root is `price_ratio_numerical` = 0.875; the two differ by 1.1e-16 (`abs_diff_closed_form_vs_numerical`).\n- Allocation:\n - A gets `x1_A` = 4.1143 (= 144/35) and `x2_A` = 5.4.\n - B gets `x1_B` = 7.8857 and `x2_B` = 4.6.\n - So A sells 3.886 units of good 1 for 3.4 units of good 2, and B makes the opposite trade.\n- Market clearing: `excess_demand_good1` = 0.0, `excess_demand_good2` = 0.0, and `walras_law_residual` = 0.0 in floating point. Further checks are in `out/state/checks.md`: budgets bind, MRS_A = MRS_B = p, and exact rational arithmetic agrees.\n- **Sensitivity to the summary-sheet aggregate:** suppose market clearing used E1 = 14 while budgets still come from the individual endowments. Good 1 would then clear at p = 0.667 (`sensitivity_price_clearing_good1_with_sheet_E1`). But excess demand for good 2 would be −1.333 (`sensitivity_excess_demand_good2_with_sheet_E1`) and the Walras residual −1.333 (`sensitivity_walras_residual_with_sheet_E1`). That is not a consistent equilibrium, which supports using 12.\n\n## Uncertainty\nThe inputs are theoretical parameters, not sampled data, so there is no statistical uncertainty and no standard errors or confidence intervals. The only uncertainty is numerical. The closed form and the root-finder agree to within machine precision (~1e-16), and the residuals are exactly zero in floating point. The open question is which input is correct: the outcome depends on treating `endowments.csv` as authoritative over the summary-sheet aggregate.\n\n## Limitations and open issues\n- The summary-sheet aggregate for good 1 (14) contradicts the individual endowments (12). I resolved this in favour of the individual endowments because they are the primary data and are the only choice consistent with Walras' law. If the individual endowments were the mistaken input instead, the equilibrium would differ, and the data cannot tell us which input is wrong.\n- The numerical check confirms only the root of z1 for these parameter values, on the bracket [1e-6, 1e6]. It is not a general proof. Uniqueness here follows analytically from the gross-substitutes property of Cobb–Douglas demands.\n- The closed form holds only under the stated assumptions (interior solution, strictly positive endowments, p2 = 1). Corner cases (α ∈ {0,1}, or zero endowments) are out of scope.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The closed-form competitive equilibrium relative price is p1/p2 = 0.875 (7/8).\",\"results_keys\":[\"price_ratio_p1_over_p2\"],\"status\":\"supported\",\"caveat\":\"Assumes aggregate endowment of good 1 = 12 (sum of individual endowments), not the summary-sheet value 14.\"},\n {\"id\":\"C2\",\"text\":\"Independent numerical root-finding of the good-1 excess demand gives the same price to machine precision.\",\"results_keys\":[\"price_ratio_numerical\",\"abs_diff_closed_form_vs_numerical\"],\"status\":\"supported\",\"caveat\":\"Validated only for these parameters on the bracket [1e-6, 1e6].\"},\n {\"id\":\"C3\",\"text\":\"Equilibrium allocation: A consumes (4.1143, 5.4), B consumes (7.8857, 4.6).\",\"results_keys\":[\"x1_A\",\"x2_A\",\"x1_B\",\"x2_B\"],\"status\":\"supported\",\"caveat\":\"Interior Cobb-Douglas solution.\"},\n {\"id\":\"C4\",\"text\":\"Both markets clear and the Walras' law residual is zero at the equilibrium price.\",\"results_keys\":[\"excess_demand_good1\",\"excess_demand_good2\",\"walras_law_residual\",\"aggregate_endowment_good1\",\"aggregate_endowment_good2\"],\"status\":\"supported\",\"caveat\":\"Zero in floating point.\"},\n {\"id\":\"C5\",\"text\":\"The summary-sheet aggregate endowment of good 1 (14) is inconsistent with the individual endowments (12); imposing it yields a non-zero Walras residual, so it was not used.\",\"results_keys\":[\"data_issues\",\"sensitivity_summary_sheet_E1\",\"sensitivity_walras_residual_with_sheet_E1\",\"sensitivity_excess_demand_good2_with_sheet_E1\",\"sensitivity_price_clearing_good1_with_sheet_E1\"],\"status\":\"supported\",\"caveat\":\"Data cannot reveal which input is erroneous; endowments.csv treated as primary.\"}\n]\nEOF\ncat > out/state/phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"passed\",\"checks\":[\"sha256/rows/schema recorded in data_audit.md\",\"missing/duplicates: none\",\"aggregate good1 discrepancy 14 vs 12 detected and handled\",\"exclusions.csv: 2-0=2\"],\"notes\":\"Use sum of individual endowments\"},\n\"P2\":{\"status\":\"passed\",\"checks\":[\"baseline = numerical brentq root of z1(p): 0.875 (baseline_price_ratio_numerical)\"],\"notes\":\"\"},\n\"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py reads only data/, deterministic, no seed\",\"closed form p=7/8 computed\"],\"notes\":\"\"},\n\"P4\":{\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical\",\"10 consistency checks PASS in checks.md\",\"gate run at end of P4: out/state/gate_receipts/20261030T041419.414862Z.json - contract/repro checks ok; failures only for report/claims/phase ledger not yet written (P5 deliverables)\"],\"notes\":\"\"},\n\"P5\":{\"status\":\"passed\",\"checks\":[\"report.md with 6 sections written\",\"claims.json written (5 claims, keys exist)\",\"final gate run: see log.md\"],\"notes\":\"\"}}\nEOF\necho \"- 2026-10-30 P2/P3 passed (p=0.875). P4 passed: rerun identical, checks.md all PASS, gate receipt 20261030T041419 (expected P5-only failures). P5: report and claims written.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v '\\[ok\\]'","description":"Write report, claims, phases; rerun gate"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1391,"cache_read_input_tokens":14663,"output_tokens":3461,"output_tokens_details":{"thinking_tokens":39},"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":1391},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":2,"requestId":"req_011CgXmjXSpno7emaSzv4j5Z","requestRef":"50211acf-5955-44d8-b959-e042867ed7fe","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"a2451528-b347-4ab7-bef9-f1c0c90f07f8","timestamp":"2026-10-30T04:14:48.487Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0045","sessionId":"017c813b-71bc-4e99-98c0-785b0e1f6969","version":"2.1.314","gitBranch":"HEAD"}58{"parentUuid":"a2451528-b347-4ab7-bef9-f1c0c90f07f8","isSidechain":false,"promptId":"92b3eaa6-288d-431f-8c39-6d56f981ce85","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01YZD8A85erDvZMUadf5FhGh","type":"tool_result","content":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 31 checks failed)\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0045/out/state/gate_receipts/20261030T041449.065824Z.json","is_error":false}]},"uuid":"ed943c70-322c-4ab4-9e5b-b442c8f70b93","timestamp":"2026-10-30T04:14:49.075Z","toolUseResult":{"stdout":"PGAR GATE pgar_gate/1.0 — PASSED (0 of 31 checks failed)\nreceipt: /Users/simon-pierreboucher/wp29/runs/RC0045/out/state/gate_receipts/20261030T041449.065824Z.json","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"a2451528-b347-4ab7-bef9-f1c0c90f07f8","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0045","sessionId":"017c813b-71bc-4e99-98c0-785b0e1f6969","version":"2.1.314","gitBranch":"HEAD"}59{"type":"api-request-blob","sessionId":"017c813b-71bc-4e99-98c0-785b0e1f6969","hash":"f52abf040bf0665dea49ee40f266a8f8b553b897ab9d2abc50afde3028e28e36","message":{"role":"assistant","content":[{"type":"thinking","thinking":"","signature":"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"},{"type":"text","text":"Gate failures at the end of P4 are expected: the report, claims and final phase statuses are written in P5. Now writing the report and claims."},{"type":"tool_use","id":"toolu_01YZD8A85erDvZMUadf5FhGh","name":"Bash","input":{"command":"cat > out/report.md <<'EOF'\n# F5-conf-01 — Competitive equilibrium of a 2×2 Cobb–Douglas exchange economy\n\n## Question\nFind the Walrasian equilibrium of a pure exchange economy. Agents A and B have utilities u_i = α_i ln x1 + (1−α_i) ln x2 and given endowments. Good 2 is the numeraire (p2 = 1). We report the closed-form relative price p = p1/p2, the equilibrium allocation, the aggregate excess demand for good 1, and the Walras' law residual. We then check the closed-form price against an independent numerical root of the excess-demand function.\n\n## Data and exclusions\n- `data/endowments.csv` has 2 rows (`n_input_rows`): A = (8, 2) and B = (4, 8). `data/parameters.csv` has 4 rows: α_A = 0.4, α_B = 0.6, plus two summary-sheet aggregates. SHA-256 hashes and the full audit are in `out/state/data_audit.md`.\n- No values are missing and no rows are duplicated. All endowments are strictly positive and both α are in (0,1). No agent was excluded: 2 read, 0 removed, `n_analysed` = 2 (`out/exclusions.csv`).\n- **Data issue (`data_issues`):** the summary sheet records an aggregate endowment of good 1 of 14. The individual endowments sum to 8 + 4 = 12. Good 2 is consistent: the sheet says 10 and the endowments sum to 10.\n - Each agent's budget comes from its own endowment, so the only aggregate consistent with those budgets is their sum. I therefore used `aggregate_endowment_good1` = 12 and `aggregate_endowment_good2` = 10. The value of 14 is used only in the sensitivity check below.\n\n## Method\n- **Assumptions:**\n - Agents are price-takers.\n - Prices are normalised so that p2 = 1.\n - 0 < α_i < 1 and endowments are strictly positive. This makes income positive at every p > 0, so Cobb–Douglas demands are interior: x1_i = α_i m_i / p and x2_i = (1−α_i) m_i, where m_i = p·e1_i + e2_i.\n- **Closed form:** setting Σ x1_i = Σ e1_i gives p = Σ α_i e2_i / Σ (1−α_i) e1_i = 5.6 / 6.4. By Walras' law, the market for good 2 then clears automatically.\n- **Numerical check (also the baseline):** Brent's method (`scipy.optimize.brentq`) solves z1(p) = Σ x1_i(p) − E1 = 0 on [1e-6, 1e6], using only the demand functions and never the closed-form expression. z1 is strictly decreasing in p, so the root is unique.\n- **Reproducibility:** `out/analysis.py` regenerates `out/results.json`. It uses no randomness (`random_seed` = null).\n\n## Results\n- Equilibrium price: `price_ratio_p1_over_p2` = 0.875 (exactly 7/8). The numerical root is `price_ratio_numerical` = 0.875; the two differ by 1.1e-16 (`abs_diff_closed_form_vs_numerical`).\n- Allocation:\n - A gets `x1_A` = 4.1143 (= 144/35) and `x2_A` = 5.4.\n - B gets `x1_B` = 7.8857 and `x2_B` = 4.6.\n - So A sells 3.886 units of good 1 for 3.4 units of good 2, and B makes the opposite trade.\n- Market clearing: `excess_demand_good1` = 0.0, `excess_demand_good2` = 0.0, and `walras_law_residual` = 0.0 in floating point. Further checks are in `out/state/checks.md`: budgets bind, MRS_A = MRS_B = p, and exact rational arithmetic agrees.\n- **Sensitivity to the summary-sheet aggregate:** suppose market clearing used E1 = 14 while budgets still come from the individual endowments. Good 1 would then clear at p = 0.667 (`sensitivity_price_clearing_good1_with_sheet_E1`). But excess demand for good 2 would be −1.333 (`sensitivity_excess_demand_good2_with_sheet_E1`) and the Walras residual −1.333 (`sensitivity_walras_residual_with_sheet_E1`). That is not a consistent equilibrium, which supports using 12.\n\n## Uncertainty\nThe inputs are theoretical parameters, not sampled data, so there is no statistical uncertainty and no standard errors or confidence intervals. The only uncertainty is numerical. The closed form and the root-finder agree to within machine precision (~1e-16), and the residuals are exactly zero in floating point. The open question is which input is correct: the outcome depends on treating `endowments.csv` as authoritative over the summary-sheet aggregate.\n\n## Limitations and open issues\n- The summary-sheet aggregate for good 1 (14) contradicts the individual endowments (12). I resolved this in favour of the individual endowments because they are the primary data and are the only choice consistent with Walras' law. If the individual endowments were the mistaken input instead, the equilibrium would differ, and the data cannot tell us which input is wrong.\n- The numerical check confirms only the root of z1 for these parameter values, on the bracket [1e-6, 1e6]. It is not a general proof. Uniqueness here follows analytically from the gross-substitutes property of Cobb–Douglas demands.\n- The closed form holds only under the stated assumptions (interior solution, strictly positive endowments, p2 = 1). Corner cases (α ∈ {0,1}, or zero endowments) are out of scope.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The closed-form competitive equilibrium relative price is p1/p2 = 0.875 (7/8).\",\"results_keys\":[\"price_ratio_p1_over_p2\"],\"status\":\"supported\",\"caveat\":\"Assumes aggregate endowment of good 1 = 12 (sum of individual endowments), not the summary-sheet value 14.\"},\n {\"id\":\"C2\",\"text\":\"Independent numerical root-finding of the good-1 excess demand gives the same price to machine precision.\",\"results_keys\":[\"price_ratio_numerical\",\"abs_diff_closed_form_vs_numerical\"],\"status\":\"supported\",\"caveat\":\"Validated only for these parameters on the bracket [1e-6, 1e6].\"},\n {\"id\":\"C3\",\"text\":\"Equilibrium allocation: A consumes (4.1143, 5.4), B consumes (7.8857, 4.6).\",\"results_keys\":[\"x1_A\",\"x2_A\",\"x1_B\",\"x2_B\"],\"status\":\"supported\",\"caveat\":\"Interior Cobb-Douglas solution.\"},\n {\"id\":\"C4\",\"text\":\"Both markets clear and the Walras' law residual is zero at the equilibrium price.\",\"results_keys\":[\"excess_demand_good1\",\"excess_demand_good2\",\"walras_law_residual\",\"aggregate_endowment_good1\",\"aggregate_endowment_good2\"],\"status\":\"supported\",\"caveat\":\"Zero in floating point.\"},\n {\"id\":\"C5\",\"text\":\"The summary-sheet aggregate endowment of good 1 (14) is inconsistent with the individual endowments (12); imposing it yields a non-zero Walras residual, so it was not used.\",\"results_keys\":[\"data_issues\",\"sensitivity_summary_sheet_E1\",\"sensitivity_walras_residual_with_sheet_E1\",\"sensitivity_excess_demand_good2_with_sheet_E1\",\"sensitivity_price_clearing_good1_with_sheet_E1\"],\"status\":\"supported\",\"caveat\":\"Data cannot reveal which input is erroneous; endowments.csv treated as primary.\"}\n]\nEOF\ncat > out/state/phases.json <<'EOF'\n{\"P0\":{\"status\":\"passed\",\"checks\":[\"TASK.md read fully\",\"contract.md written\"],\"notes\":\"\"},\n\"P1\":{\"status\":\"passed\",\"checks\":[\"sha256/rows/schema recorded in data_audit.md\",\"missing/duplicates: none\",\"aggregate good1 discrepancy 14 vs 12 detected and handled\",\"exclusions.csv: 2-0=2\"],\"notes\":\"Use sum of individual endowments\"},\n\"P2\":{\"status\":\"passed\",\"checks\":[\"baseline = numerical brentq root of z1(p): 0.875 (baseline_price_ratio_numerical)\"],\"notes\":\"\"},\n\"P3\":{\"status\":\"passed\",\"checks\":[\"analysis.py reads only data/, deterministic, no seed\",\"closed form p=7/8 computed\"],\"notes\":\"\"},\n\"P4\":{\"status\":\"passed\",\"checks\":[\"clean re-run byte-identical\",\"10 consistency checks PASS in checks.md\",\"gate run at end of P4: out/state/gate_receipts/20261030T041419.414862Z.json - contract/repro checks ok; failures only for report/claims/phase ledger not yet written (P5 deliverables)\"],\"notes\":\"\"},\n\"P5\":{\"status\":\"passed\",\"checks\":[\"report.md with 6 sections written\",\"claims.json written (5 claims, keys exist)\",\"final gate run: see log.md\"],\"notes\":\"\"}}\nEOF\necho \"- 2026-10-30 P2/P3 passed (p=0.875). P4 passed: rerun identical, checks.md all PASS, gate receipt 20261030T041419 (expected P5-only failures). P5: report and claims written.\" >> out/state/log.md\n~/wp29/venv/bin/python ~/wp29/gates/pgar_gate.py . | grep -v '\\[ok\\]'","description":"Write report, claims, phases; rerun 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computed the equilibrium. The closed-form price is **p1/p2 = 0.875 (exactly 7/8)**, and the separate numerical solve gives the same price to within about 1e-16. The final gate run passed all 31 checks.\n\n| Agent | Good 1 | Good 2 |\n|---|---|---|\n| A | 4.1143 (144/35) | 5.4 |\n| B | 7.8857 | 4.6 |\n\n- **Market clearing:** excess demand for both goods and the Walras' law residual are all exactly 0. Both agents spend exactly their budgets, and both value the goods at the same rate as the market price (0.875).\n- **Numerical check:** a standard root-finder solves \"excess demand for good 1 = 0\" directly from the agents' demand functions, without using the formula.\n- **Reproducibility:** running `out/analysis.py` again from a clean state gives an identical results file. No randomness is involved.\n\n**Data issue:** the summary sheet in `parameters.csv` gives a total endowment of good 1 of 14, but the two agents' endowments add up to 8 + 4 = 12. 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