Both directions use the same physical partition
Abstract
Physical packet canonicalization
A legal word is split at its negative physical labels. Its packets have no repetitions because the whole word is a physical permutation. Passing to finite sets preserves each mass and the complete multiset partition. Conversely the partition reconstructs every label exactly once. The two coordinate endpoint checks are invariant under arbitrary internal positive-packet permutations. Ear right-normalization preserves the old word and selects one of its four negative slots. These are the structural steps consumed by the actual all-parameter endpoint equivalence.