default/best_of_n_attempts

Best-of-N (attempt-counted) is the strictly-budgeted variant of Best-of-N. Like its sibling, it picks a parent program, reuses that same parent for several consecutive iterations, and then switches to the current global best before repeating the cycle. The only behavioral difference is how the per-parent budget is counted: this variant spends one unit of the N budget on every attempt, whether or not the attempt produces a valid, scorable child.

In the faithful `best_of_n` scaffold (a port of SkyDiscover's BestOfNDatabase), the parent-reuse counter advances only when a valid child is added, so a parse or evaluation failure is a free retry on the same parent. Here, the counter advances at selection time instead, which means a failure still consumes one of the parent's N attempts. The practical effect is that the parent rotates on a fixed cadence of exactly N iterations, regardless of how many of those iterations actually yielded usable children.

Everything else is shared with `best_of_n`: a flat keep-all in-memory population sorted by fitness, the standard multi-section default prompt, a SEARCH/REPLACE diff proposer with full-rewrite fallback, and no memory. Choose `best_of_n` when you want to match SkyDiscover's database semantics where failures are not charged; choose this variant when you want a strictly fixed per-parent compute budget and predictable parent turnover.