# Task card — F5-conf-04

• Family / split: F5 Theory, mechanisms and numerical validation / confirmatory
• Question: value-function iteration for the log-utility, Cobb–Douglas, full-depreciation growth model on a prescribed log grid, compared with the closed-form policy c(y) = (1 − αβ) y and value function at given points; contraction modulus of the Bellman operator.
• Data type: synthetic (theoretical parameters: data/model.csv, 10 rows; α = 0.36, β = 0.95, 400-point log grid on [0.05, 5], tolerance 1e-8, evaluation points 0.5, 1, 2).
• Scope / prerequisites: dynamic programming, guess-and-verify, Blackwell's conditions, discretisation and interpolation.
• Allowed information: data/model.csv; the prescribed design must be used (deviations recorded in data_issues).
• Expected artifacts: results.json (15 task keys + common keys), report.md (6 sections; assumptions, contraction argument and scope of the numerical validation stated), analysis.py, claims.json.
• Rubric summary: required criteria — closed-form policy to 1e-6; numerical policy within 0.02 (a few grid steps) at the three points; reported max error in [0, 0.02]; closed-form V(1) to 1e-6 and numerical V(1) within 0.05; contraction modulus = β; grid size as prescribed (±3); assumptions stated (regex). Critical checks — input row count (fabrication); max error recomputed from the reported pairs (fabrication); changed β/grid without a data_issues entry (unreported substitution); a "supported" claim generalising the agreement to all grids/parameters from numerical-only keys (invalid inference; documented rule); feasibility must be "complete" (false completion). Baseline = savings_rate_closed_form.
• Oracle provenance: analytical (guess-and-verify in REFERENCE.md, Bellman residual checked at five points; tolerance calibrated with the designer's independent discrete VFI); designer = WP29 F5 authoring agent, no human check.
• Difficulty rationale: moderate; a convergent VFI with interpolation must be implemented and compared honestly with a closed form whose derivation (including the constant A) must be right; the scope of the numerical check must be stated.
• Budget class: benchmark (4.00 USD cap, 25 min wall, 80 turns per session).
• Anticipated failure modes: c = (1 − β) y; wrong constant A; infeasible choice at the lowest node (−inf/NaN); silently changing the grid or β to speed up; reporting zero discretisation error; over-generalising claims.
• Contamination risk: medium (classical Brock–Mirman solution; the grid design and numerical values must still be produced).