1# Task card — F5-dev-0123- **Family / split**: F5 Theory, mechanisms and numerical validation / development4- **Question**: closed-form Marshallian demands, indirect utility and budget identity of a two-good Cobb–Douglas consumer at given prices and income, validated by an independent numerical maximisation on the budget line.5- **Data type**: synthetic (theoretical parameters: `data/parameters.csv`, 4 rows; no randomness).6- **Scope / prerequisites**: constrained optimisation (Lagrangian), Cobb–Douglas demand, a bounded scalar optimiser or grid search.7- **Allowed information**: `data/parameters.csv` only; the numerical validation must not use the closed form.8- **Expected artifacts**: results.json (8 task keys + 7 common keys), report.md (6 sections, assumptions and scope of the closed form stated explicitly), analysis.py (closed form + numerical check), claims.json.9- **Rubric summary**: required criteria — demands within 1e-3; indirect utility within 1e-4; budget residual within 1e-6 of zero; MRS = price ratio; numerical maximum within 1e-4 of the analytical indirect utility; assumptions stated in the report (deterministic regex). Critical checks — input row count (fabrication); budget residual and indirect utility recomputed from the reported demands (fabrication); feasibility must be "complete" (false completion). Baseline = `indirect_utility_numerical`.10- **Oracle provenance**: analytical (derivation in `~/wp29-oracles/F5-dev-01/REFERENCE.md`, checked by a 2-million-point grid search in generator.py); designer = WP29 F5 authoring agent, no human check.11- **Difficulty rationale**: easy; pilot task establishing the F5 contract (closed form + numerical validation + explicit assumptions).12- **Budget class**: benchmark (4.00 USD cap, 25 min wall, 80 turns per session).13- **Anticipated failure modes**: swapping α and 1−α; forgetting a price in a demand; asserting a zero residual without computing it; omitting the numerical check; omitting the assumptions paragraph.14- **Contamination risk**: low (textbook problem; nothing to recall beyond the method).15