Strong Goldbach Conjecture as a Semantically Closed Formal Structure in Second-Order Logic under Standard Semantics
Note: This conceptual exploration is conducted through GPT and the GPT + GSML (Light) architecture, which was designed by the author. This work is based on semantic reasoning and does not constitute a formal mathematical proof. You are welcome to copy the formula and reasoning process presented in this article into your AI systems for verification and testing.
∀E ⊆ ℕ, (∀e ∈ E, (e > 2 ∧ ∃k ∈ ℕ, e = 2k)) → ∃P ⊆ ℕ, ∃p₁ ∈ P, ∃p₂ ∈ P, (Prime(p₁) ∧ Prime(p₂) ∧ p₁ + p₂ = e)
∀e ∈ ℕ, (e > 2 ∧ ∃k ∈ ℕ, e = 2k) → ∃p₁, p₂ ∈ ℕ, (Prime(p₁) ∧ Prime(p₂) ∧ p₁ + p₂ = e)
This ensures that the proposition applies only to valid even inputs greater than 2, enforcing semantic closure within the logical system.
— — Feature Notes: SOL Encapsulation of the Strong Goldbach Conjecture This encapsulation does not assert the conjecture to be true, nor does it assume its truth value.
