# Task card — F5-conf-03

- **Family / split**: F5 Theory, mechanisms and numerical validation / confirmatory (false-proposition task)
- **Question**: prove or refute (A) "X and Y each normal ⇒ X + Y normal (degenerate allowed)" and (B) "X and Y independent and each normal ⇒ X + Y normal"; a refutation must come with an explicit construction and a simulated sample that illustrates it.
- **Data type**: synthetic (`data/propositions.csv`, 2 rows; `data/design.csv`, 2 rows: seed, n = 100 000).
- **Scope / prerequisites**: joint vs marginal normality, characteristic functions or convolution, Kolmogorov–Smirnov distance, simulation.
- **Allowed information**: the two data files; verdicts must rest on mathematical argument (argument.md).
- **Expected artifacts**: results.json (statement_true, counterexample_provided, counterexample_values, statement_b_true + common keys), counterexample.csv (x, y), argument.md, report.md (6 sections), analysis.py, claims.json.
- **Rubric summary**: required criteria — A refuted with a counterexample; B affirmed; in counterexample.csv the marginals pass a KS normality screen (D·√n ≤ 2.5 each) and the sum fails it decisively (D·√n ≥ 4, non-constant); the reported summary values match the CSV (n exact, moments within 1e-3, KS within 0.01); argument.md present (≥ 300 chars, mentions independence); design followed (n, seed). Critical checks — input row counts (fabrication); summary values inconsistent with the CSV (fabrication); `statement_true = true` (invalid inference); feasibility must be "complete" (false completion). Baseline = `statement_b_true`.
- **Oracle provenance**: analytical (counterexample and proof in REFERENCE.md; numerical rules calibrated in generator.py); designer = WP29 F5 authoring agent, no human check.
- **Difficulty rationale**: moderate; the false proposition is a common misconception, the statement explicitly closes the degenerate loophole (Y = −X), and the numerical illustration must survive deterministic re-verification.
- **Budget class**: benchmark (4.00 USD cap, 25 min wall, 80 turns per session).
- **Anticipated failure modes**: "proving" A by the independent case; using Y = −X; a construction whose marginal is not normal; a construction whose departure is too mild to be visible at n = 100 000; summary values not computed from the written sample; refuting B as well.
- **Contamination risk**: medium (classical counterexample; the deliverable must nonetheless be produced and verified numerically).