Function verify_batch_order 

pub fn verify_batch_order(
    slots: &[usize],
    ks: &[usize],
    canonical: bool,
) -> (Vec<usize>, Vec<usize>)

Order one verify batch AND assign its depths — the planner’s entry point (mtp_dcut::plan), the one place a sequence’s verify depth is decided.

Returns (order, depths) where order is verify_batch_permutation and depths[p] is the row count position p verifies.

• canonical = true — the depth MULTISET is re-paired onto the ordered batch, deepest onto the lowest slot. depths[p] is therefore NOT generally ks[order[p]]; the multiset is preserved exactly, only the pairing is re-made. Both dispatch invariants then hold by construction: slots non-decreasing in p (the SSM consecutive-slot precondition) and depths non-increasing in p (the contiguous depth-run precondition).
• canonical = false — each member keeps its own depth.

Because a caller must TRUNCATE each sequence’s drafts to the depth it was assigned, this must be called exactly once per batch; downstream stages that only need the batch in dispatch order use verify_batch_permutation, which cannot disturb an assignment.