Proof of `Exact-pin peeling for the actual raw frame law`
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
The reference pin cap is the checked all-rank raw image cap. Substituting it in bounded peeling gives a disjoint partition, preserves all initial images, and bounds the total dimension by the initial rank plus K. The normalized leaves retain the quantitative joint density and image bounds.