Total Biomedical INVAR: A Lean 4 Formalization of Genome-Driven Multi-Organ Cell Induction and Healthy Attractor Invariance

This work presents a formally verified mathematical framework for genome-driven multi-organ cell induction and systemic healthy-attractor dynamics, implemented in Lean 4 with Mathlib. The model encodes eight somatic cell types, nineteen master transcription factors, genomic induction protocols, and a rational-valued whole-body state. Its central result is a machine-checked, sorry-free theorem proving the invariance of the healthy attractor under the defined transition dynamics. A nephron-induction example demonstrates an exact three-step transition from a severe pathological initial state to the healthy attractor, which remains invariant through subsequent iterations. Developed within the F-Theory framework, this work provides a compact formal-methods foundation for exploring genome-driven cellular repair, systemic state transitions, and multi-organ mathematical modeling. It is a theoretical and computational formalization, not an experimentally validated physiological model or a clinical therapeutic proposal. Implementation: Lean 4 / MathlibLicense: Apache-2.0 (Lean source code); CC BY 4.0 (paper)