This upload collects the final residual, kernel, and extreme boundary representations of the KFX family. The included documents formalize the residual extension (KFX-R), minimal residual compression (ε-KFX), the extreme decidability shell, and the core logical kernel statements of the family. These texts do not introduce new systems or assumptions. Instead, they characterize irreducible representational boundaries of the KFX family under fixed invariants, including decidability, uniqueness, and responsibility preservation. All documents are frozen and define minimal, non-compressible forms at their respective representational layers. No physical, probabilistic, empirical, or semantic interpretation is assumed.Other family members:https://doi.org/10.5281/zenodo.18469061https://doi.org/10.5281/zenodo.18481284