Complete balanced four-gap chamber
Abstract
Balanced actual-source certificates
For every s>=2 and every offset pattern, the polynomial bounds are transported to the actual physical masses, negative increments and capacities. The labelled partition, negative permutation and explicit ear slot form a PacketNormalForm certificate. The accepted equivalence reconstructs one old physical permutation and one literal ear cut, proving every natural prefix bound and both zero totals. The old and new orders share the same old-label permutation.