This work develops a non-idempotent reflection theory in the context of ∞-topoi.Unlike classical reflective localization, the reflection functor is not assumed to stabilize under iteration, leading to orbit-valued structures rather than fixed points. We introduce the notion of orbit ∞-topoi, where objects are replaced by non-stabilizing sequences generated by repeated application of a reflection functor. Standard descent theory is reformulated as a non-stable descent condition, where cocycle compatibility is weakened to a dynamic coherence relation. Furthermore, we construct a model category structure on the category of orbit diagrams, in which weak equivalences are defined via orbit equivalence rather than pointwise equivalence. This framework replaces classical notions of localization and idempotence with a dynamical homotopical structure. The resulting theory provides a homotopy-theoretic setting in which reflection is interpreted as an iterative deformation process rather than a stabilization mechanism.
Hidaka et al. (Thu,) studied this question.