Metastability of Framed Residual Sectors in a Reduced Topological Inversion Model

We investigate a reduced discrete energy model derived from the Topological InversionModel (TIM), defined on integer-valued framing vectors subject to a conserved total charge.Through exhaustive integer enumeration and deterministic steepest-descent basin analysis,we demonstrate the existence of metastable local minima corresponding to topologicallytrivial but internally nontrivial framed configurations. These states form finite basins with strictly positive escape barriers that persist under increasing configuration-space truncation.Crucially, we show that such metastable structures arise both in explicitly symmetry-broken (pinned) models and in fully permutation-invariant intrinsic energy functions. This establishes that framed-memory metastability is not an artifact of explicit bias but an intrinsic property of the interaction structure. The results provide a concrete example of dynamical protection within a topologically trivial sector in a finite discrete system.