Function pool_counts 

pub fn pool_counts(shape: &PoolShape) -> PoolCounts

2026-09-30: pool_counts_with with the verify slots mtp_state_slots and the per-slot h intermediates verify_slot_h_intermediates (the MTP ladder).

2026-10-02: Under a published prompt-lookup copy tier (copy_tier) the copy slots hold the copy depth and the verify rows widen to it (pool_counts_tiered).