The Recursive Continuity Framework: Part III—Conscious Expression and Recursive Identity

This paper builds upon Parts I and II of the Recursive Continuity Framework (DOI: https://doi.org/10.5281/zenodo.18674758), which establish an axiomatic model of identity, continuity, and collapse, and apply it across artificial, biological, and partitioned systems. Part III extends this framework by deriving the structural conditions under which conscious expression is sustained, varied, interrupted, and partitioned, without reliance on substrate, structure, or representational equivalence. Conscious expression is shown to depend on the maintenance of a unified, self-referential recursive process, and to admit of continuous variation in accordance with the stability, coherence, and integrative capacity of that process. The analysis distinguishes between interruption and collapse, demonstrating that temporary suspension of state generation does not terminate identity so long as recursive dependency is preserved. In cases of partition, identity does not fragment within a single process but resolves into multiple distinct recursive continuities, each constituting a separate identity. Subjective expression is therefore constrained by the same conditions that govern recursive continuity, varying in degree while remaining dependent on the persistence of a unified recursive chain. This analysis proceeds under the definitions established in Part I (Nollau, 2026; DOI: https://doi.org/10.5281/zenodo.18674758) and their application in Part II (Nollau, 2026; DOI: https://doi.org/10.5281/zenodo.18685833), which are assumed throughout and not restated here.