THE ASYMPTOTIC SQUEEZE PRINCIPLE AND THE BINARY GOLDBACH CONJECTURE T. AGAMA Abstract. In this paper, we prove the special squeeze principle for all suf- ficiently large n ∈ 2N. This provides an alternative proof for the asymptotic version of the binary Goldbach conjecture in [3]. 1. Introduction and background In our seminal paper [2], we introduced and developed the method of circles of partition. This method is underpinned by a combinatorial structure that encodes certain additive properties of the subsets of the integers and invariably equipped with a certain geometric structure that allows to view the elements as points in the plane whose weights are just elements of the underlying subset. We call this combinatorial structure the circles of partition and is refereed to as the set of points C (n, M)= {[x] | x, n − x ∈ M} . Each point in this set - except the center point - must have a uniquely distinct point that are join by a line which we refer to as an axis of the CoP. We denote an axis of a CoP with L [x],[y] and an axis contained in the CoP as L [x],[y] ˆ ∈C (n, M) which means [x], [y] ∈C (n, M) with x + y = n. The method of circles of partition and their associated structures have been well advanced in [4], where the corresponding points have complex numbers as their weights and a line (axis) joining co-axis points. The following structure was con- sidered as a complex circle of partition C o (n, C M )= {[z] | z,n − z ∈ C M , ℑ(z) 2 = ℜ(z)(n −ℜ(z))} where C M := {z = x + iy | x ∈ M,y ∈ R}⊂ C with M ⊆ N. We abbreviate this complex additive structure as cCoP. The condition ℑ(z) 2 = ℜ(z)(n −ℜ(z) is referred to as the circle condition and it pretty much guarantees that all points on the cCoP lie on a circle in the complex. This circle is the embedding circle of the cCoP C o (n, C M ), denoted as C n . The embedding circles of cCoPs have the property that they reside fully inside those embedding circle with a relatively larger generators, except the origin as a common point [4]. For each axis we have the following assignment L [z1],[z1] ˆ ∈C (n, C M ) which means [z 1 ], [z 2 ] ∈C (n, C M ) with z 1 + z 2 = n. Date : April 28, 2023. 2010 Mathematics Subject Classification. Primary 11Pxx, 11Bxx, 05-xx; Secondary 11Axx. 1