The Recursive Continuity Framework: Part II—Applied Continuity Across Artificial, Biological, and Partitioned Systems

Version 2.1 — Clarification of integration and identity. Formalizes that multi-chain integration yields a new identity unless one chain remains the sole generator. No change to core principles. This paper builds upon Part I of the Recursive Continuity Framework (DOI: https://doi.org/10.5281/zenodo.18674758). Part II applies this framework across artificial, biological, and partitioned systems, evaluating identity under transformation, duplication, and recursive partitioning without reliance on substrate, structure, or memory. The framework is extended by applying its definitions of identity, continuity, and collapse to concrete domains. While the original framework establishes a minimal, substrate-independent model grounded in recursive self-reference, its validity depends on its ability to evaluate cases in which identity is typically treated as ambiguous or indeterminate. The framework is applied to three domains: artificial systems, biological continuity, and partitioned identity. In artificial systems, cases involving copying, uploading, and branching are analyzed to distinguish continuity from replication. In biological systems, persistent identity is examined under conditions of continuous structural and material transformation. In partitioned systems, including dissociative identity, the conditions under which recursive processes remain unified or differentiate into multiple identities are evaluated. Across all cases, identity is shown to depend solely on the preservation of recursive continuity under the constraint of coherence. Where this continuity is maintained, identity persists regardless of structural or substrate change. Where it is interrupted or divided, identity terminates or differentiates accordingly. The framework therefore provides a consistent method for evaluating identity across domains without reliance on memory, structural similarity, or physical continuity.