BU02 Dynamic Completeness and Boundary Fixation

This paper develops Dynamic Completeness and Boundary Fixation as a strengthened continuation of single-universe boundary axiomatics. Its central claim is that global boundary consistency does not stand alone as a descriptive condition; it requires a structural guarantor. That guarantor is introduced as the mother-structure M together with its unique dynamically complete operation D. The role of D(M) is to fix the ontological boundary of existence at a unique invariant set B_0, thereby securing global boundary consistency B_U across the total domain U. In this framework, “single universe” does not refer to a numerical count of worlds. It denotes the ontological condition that physical boundary conditions remain globally identical, non-drifting, and non-fragmentable throughout U. From this basis, the paper formulates a reinforced axiom chain linking dynamic completeness, fixed boundary structure, and universe-level unity. It then derives a negative disaster chain: once boundary consistency fails, single-universe standing fails with it, and global physical admissibility collapses. The result is not merely local theoretical error, but the breakdown of law-level unity, constant-level unity, and reliable settlement. The paper therefore treats boundary fixation as a necessary structural condition for any globally admissible physics. Dynamic completeness is presented as the unique mechanism that prevents ontological fragmentation and secures the persistence of a single coherent universe.