scientific(selection): bind candidate K to fitted topic dimension #676

Finding

model_selection::statistical_candidate_from_fit(input, candidate_k, model) accepts the candidate label separately from the fitted model. The function computes a finite Schwarz-style score and free-parameter count from model, but it never verifies that candidate_k equals the fitted topic dimension.

That means a dimensionally valid 2-topic ReferenceTopicModel can be scored and emitted as ModelCandidate::statistical(3, ...). select_candidate_k(...) then treats the mislabeled K as statistical authority, so the model-selection decision can attribute one fit's diagnostic to a different topic count.

The ordinary select_fitted_candidate_k(...) loop currently passes matching values, but the public scoring API itself is not fail closed and can manufacture a scientifically false K/diagnostic association.

Required RED

At the public statistical_candidate_from_fit boundary:

• a valid model scored with its actual topic count remains accepted;
• the same model passed with a different candidate_k returns ModelSelectionError::InvalidDiagnostic before creating ModelCandidate;
• the repair does not alter likelihood arithmetic, free-parameter counting, candidate Pareto logic, fitted estimator arithmetic, or LLM refusal rules.

A small synthetic unit/integration fixture is sufficient because this is an API identity invariant, not scientific acceptance evidence.

Minimal causal direction

Derive the fitted topic count from the model's document-topic coordinate width, validate that it is representable as u32, and require exact equality with candidate_k before calculating or emitting the candidate score. Keep existing dimensional validation in free_parameter_count as defense in depth.

Boundary

This issue closes only K/fit label integrity. It does not solve the separate detached input/model substitution path in statistical_candidate_from_fit, Evidence provenance (#527/#658/#671/#675), fitted-topic semantic identity (#663), or release projection (#664).

Refs #638 #639 #668 #670.