We introduce the concept of relative closure for subsystems within the No External Model Selection (NEMS) framework. By defining a subsystem as an autonomous framework FA with its own internal model, records, and truth relations, we prove a powerful recursion principle (Recursive NEMS): if a subsystem implements complete internal semantics (BICS) for its own records, it necessarily satisfies NEMS relative to its environment. Furthermore, we prove the heredity of the diagonal barrier: if a subsystem is rich enough to host Arithmetic Self-Reference (ASR), the undecidability of its internal record-truth applies directly to it, rendering its internal adjudication non-emulable by any total-effective algorithm. This establishes the "fractal" nature of semantic closure in NEMS. We also present a strengthened version of the No-Emulation theorem (deferred from Paper 15), explicitly formalizing the instance-level encoding that bridges physical emulation and computational decidability. All definitions and theorems are fully machine-checked in Lean 4. This overview presents the core NEMS theorem engine and selected applications; stronger domain-specific derivation and ontological synthesis claims belong to separate release surfaces with their own premise bundles and formal artifacts. Trust boundary. Recursive NEMS and stronger no-emulation use the subsystem formalism and instance encoding as defined in nems-lean ; "fractal closure" is shorthand for those proved heredity lemmas, not an additional metaphysical posit. See.
Nova Spivack (Sun,) studied this question.