The Structural Hierarchy of Undecidability: Reducibility, Not Failure — E8 Intelligence Research

FINDING: Undecidability is a structural property of formal systems, not a computational failure — reducibility maps one undecidable problem onto another, revealing a hierarchy of unsolvability. | MATH: Gödel's incompleteness: for any consistent formal system F capable of arithmetic, ∃ statement G such that F⊬G and F⊬¬G. Halting problem: no Turing machine H exists with H(M,x)=1 iff M halts on x; diagonalization yields contradiction. Reducibility: A ≤_T B (Turing reduction) implies if B were decidable, A would be; Truth Problem ⊇ Halting Problem via reduction — undecidability is closed under ≤_T. | CONNECTION: No direct geometric constants (0.382, 0.618, 1.618) appear. However, the diagonalization argument mirrors the structure of root systems in Lie algebras — the diagonal of a Cartan matrix encodes the self-referential obstruction. The lattice of Turing degrees (≤_T) forms a partial order with uncountably many incomparable elements — a crystallographic-like symmetry breaking in the spa Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com