Regime Equivalence and Refinement: Transport, Normal Forms, and the Boundary of Declared Change

Abstract

Abstract This second-edition layer develops the retirement calculus implicit in Regime Equivalence and Refinement v1.0. Holding the frozen regime and carrier fixed, retirement removes declared demands and therefore moves in the direction opposite refinement: fewer demands induce coarser contextual equivalence and canonical quotient maps toward smaller cores. A retirement is conservative exactly when this coarsening leaves the governing congruence unchanged. The central result prices retirement through the frozen antitone Galois connection between demand families and congruences. A demand is conservatively withdrawable exactly when the remainder still definably makes it. More generally, a set of demands is jointly retireable if and only if every retired demand belongs to the Galois closure generated by the final remainder. This makes retirement certificates remainder-relative: individually valid certificates need not compose when they were issued against different remainders, while final-remainder certification gives an exact, order-independent criterion. The paper also establishes the forced-floor retirement bound. Although the empty demand mathematically collapses each inhabited sort to a single equivalence class, admissible retirement within a fixed problem class cannot generally proceed that far. Every admissible retirement remains above the owner-proved forced obligation floor. Consequently, the operational ceiling on lawful forgetting is the core induced by that floor, not the zero-demand collapse. Crossing the floor yields an under-declared, inadmissible specification over the same problem class and regime; it is not thereby a change of either. All results are additions to the frozen v1.0 theory. The layer alters no frozen claim and records its hostile-audit repairs, finite witnesses, and machine corroboration explicitly.