Innovation-Consolidation Cycle in Finite Ring Continuum: Packets, Invariants, and Shell Transfer

The Finite Ring Continuum (FRC) models structure through finite arithmetic shells. At symmetry-complete prime checkpoints, a quadratic extension introduces a second involution alongside spatial reversal, and the coexistence of these symmetries generates a finite shell-transfer problem. This paper studies that problem in terms of existential admissibility: the question is which structural updates are internally allowed, not how an external agent might operate on the shells. We prove that every nondegenerate admissible innovation decomposes into four-element Klein packets, so primitive shell updates occur in multiples of four and have plus four as their elementary admissible increment. We then define orbit-level invariant extraction and show that every finite invariant family admits an explicit code in the elementary receiving shell with a minimal symbol count, namely the least number of receiving-shell symbols needed to encode the invariant alphabet. In addition, every finite extractor admits an exact fiber decomposition that records how many primitive states consolidate to each invariant value. A fully explicit example at prime 13 exhibits a four-element innovation packet, a one-symbol recoding into the receiving shell of order 17, and the norm profile with one singleton fiber and twelve fibers of size fourteen. In this paper the norm is used only as an exact algebraic packet-invariant; any identification of such invariants with specific physical observables is deferred to follow-up work. The result reframes innovation-consolidation in FRC as a finite problem of packet formation, invariant extraction, consolidation profile, and shell coding, with larger updates understood as coarse-grained bundles of the same primitive admissible step.