scientific: establish Pareto candidate-K recovery acceptance evidence #500

Finding

PR #409 (pareto_candidate_k_v1) currently has deterministic unit/integration examples and selected-K RMSE arithmetic, but no profile-level scientific acceptance evidence showing recovery behavior across realistic data-generating conditions. Hand-built exact/two-point fixtures are useful contracts and are not sufficient scientific acceptance.

Owner boundary

model_selection continues to own Pareto selection and selected-K RMSE arithmetic. This issue owns the scientific validation design/evidence for the Analysis Run profile; it must not introduce an LLM numerical judge, a second Pareto implementation, or mutable external model authority.

Required evidence

Use a realistic Monte Carlo design with true K varied across an explicitly stated design, nontrivial topic separation/prevalence/document-count conditions, deterministic replay seeds, and an explicit attempted/recovered/failed denominator. Report at minimum true-K recovery/selection frequency, selected-K RMSE and bias with Monte Carlo uncertainty, failure/convergence rate, and stability across the stated design. Where temporal availability affects the buyer path, evaluation must be leakage-safe and rolling-origin/cutoff-aware rather than fitting future evidence into earlier runs.

Synthetic data is acceptable for estimator/unit verification only; any product scientific-acceptance claim must be tied to the repository's declared validation-evidence policy and should include a realistic corpus or an explicitly justified generative benchmark. Do not relax thresholds after observing results.

Acceptance boundary

Do not call #409 scientifically accepted or release-ready until this evidence is checked in, TRACEABILITY points to the exact test/study/artifact, and the surviving Analysis Run head has current required checks, coverage, review, and release evidence. This issue does not block fixing the temporal provenance/resource/API defects already identified in #409; it blocks scientific-acceptance claims.