THEK Research Institute · Formula Genomics and Evolution Theory (FGET) Teoría Genómica y Evolutiva de las Fórmulas Overview The Formula Genomics and Evolution Theory (FGET) proposes that mathematical formulas are not static abstractions constructed by the human mind to describe a pre-existing reality. Within the FGET framework, formulas are primordial entities whose genomic evolution generates the patterns that constitute physical reality — matter, energy, and the observable laws of physics. FGET introduces the concept of the mathematical pattern as the constitutive nexus between abstract formulas and empirical phenomena: it is the pattern — not the formula per se — that holds matter in place, keeps the laws of physics in force, and organises energy into stable forms. Finding a formula is therefore not discovery in the classical sense: it is reverse engineering applied to an observable pattern, decomposing its constitutive layers until reaching the primordial functions from which it originated. "A formula with no connection to the pattern that originated it is a mathematical zombie: it predicts without understanding, it computes without existing." — Moncayo Theurer (2025) Core Theoretical Contributions Evolutionary Formula Space (EFS) A countably infinite space of all constructible mathematical structures, explored progressively through history. Mathematical genome Each formula possesses a genome Γ = [g₁, g₂, …, gₙ] of elementary operators subject to mutation, recombination, and selection. Genotype vs. phenotype Two formulas with distinct genomes may share the same phenotype — mathematical evolutionary convergence. Mathematical zombie A formula disconnected from its constitutive pattern: high parametric fitness but no causal genomic link to the real phenomenon. Evolutionary fitness φ(F,D) Formal measure of a formula's capacity to describe phenomena: accuracy, parsimony, interpretability, and transferability. Evolutionary Platonism FGET's philosophical stance: mathematical forms have objective existence, but that existence evolves — complementing rather than replacing Platonic ontology. Operational Implementation: The NFF The Nested Formula Framework (NFF) is the operational instrument of FGET. Its recursive coefficient-nesting principle implements genomic reverse engineering: each nesting level decomposes one layer of the observable pattern, generating a fully interpretable, traceable hierarchy of equations in which every coefficient has direct physical meaning. The NFF constitutes one of the first formal implementations of explainable AI (xAI) grounded in a genomic mathematical theory. Philosophical Position FGET establishes a formal analogy between biological and mathematical evolution — genome, phenotype, pattern, mutation, recombination, speciation, extinction, convergence, and co-evolution — and operationalises them through the NFF as a genomic microscope. Not as metaphor. As a proposed mechanism. Its philosophical stance — Evolutionary Platonism / Evolutionary Mathematical Realism — positions FGET as a post-Darwinian ontology of mathematics: objective existence of mathematical structures combined with a dynamic, evolving space of possibilities that grows with human and technological development. Keywords mathematical genomics formula evolution mathematical patterns NFF explainable AI xAI reverse engineering mathematical natural selection evolutionary platonism emergent reality complex systems symbolic regression M.Sc. (TUM) Marcelo Moncayo TheurerIISEE – BRI – University of Tokyo · Full Professor, University of GuayaquilTHEK Research Institute CC BY 4.0 DOI : 20780971 WEB: https://nff.hithek.com