SparseMin.argmin(l,r): nonempty half-open range; leftmost minimum index; invalid range raises IndexError.
LCA(parents): unique root -1, valid nonempty rooted tree; invalid structure raises ValueError. query(u,v) returns LCA, invalid node raises IndexError.
Deterministic worst-case word-model bounds: O(n log(n+1)) preprocessing/space, O(1) query. Python integer comparison costs are additional.
Run evidence remains pending; no prohibited check was retried.