2026-10-07T03:57:59Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33915316 2026-09-17T22:14:44Z category_29809 category_29785 category_29845 item_type_2 month_year_09_2026

A Recursive Sifting Framework for the Goldbach Conjecture via Cross-Addition Density Walter Lamparter (25065721) Experimental mathematics Algebraic structures in mathematical physics Mathematical logic, set theory, lattices and universal algebra Goldbach (1742) for the Goldbach Conjecture. <p dir="ltr">This paper establishes a structural and deterministic proof of the Goldbach Conjecture by introducing a recursive sifting framework. By partitioning the number line into a computationally verified base (Zone 1) and an analytically bounded asymptotic domain (Zone 2) governed by advanced sieve-theoretic error bounds, this paper examines the cross- addition sumsets generated iteratively between a growing base set of primes and newly emerging sift primes within intervals dictated by Bertrand’s Postulate. This paper proves that the density of cross-addition prime pairs scales at a super-linear rate, and through explicit sieve remainder estimates, decadal modular closure, and structural sift-prime resolution, local residual voids are shown to be permanently eliminated for all p > N. Furthermore, the foundational mechanics of this framework are formally verified using the Lean 4 interactive theorem prover to eliminate circularity and post-hoc test critiques.</p> 2026-09-17T22:14:44Z Dataset Media 10.6084/m9.figshare.33915316.v1 https://figshare.com/articles/media/A_Recursive_Sifting_Framework_for_the_Goldbach_Conjecture_via_Cross-Addition_Density/33915316 CC BY 4.0