Structural Isomorphism Between Undecidability and NP-Completeness via Self-Reference — E8 Intelligence Research

FINDING: Formal analogy between Gödel sentences and NP-complete problems suggests a structural isomorphism between undecidability and computational intractability, rooted in self-reference and reduction. MATH: - Gödel sentence G: ¬∃x Proof(x, ⌜G⌝) — self-referential unprovability. - NP-complete problem: L ∈ NPC iff ∀L' ∈ NP, L' ≤ₚ L (polynomial-time reduction). - Key constant: no explicit numeric constant; structural constant is the polynomial-time reduction ≤ₚ, analogous to the arithmetization mapping in Gödel numbering. - No equations with numeric constants (0.382, 0.618, etc.) appear in the findings. CONNECTION: - No direct geometric harmony (ratios, base-60, crystallographic symmetry) is present. - However, the reduction structure in NP-completeness forms a partial order with a maximal element (the NP-complete set), analogous to a lattice. This is a weak connection to lattice theory, not to specific geometric ratios. - The self-reference in Gödel sentences mirrors f Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com