This paper provides an algebraic reconstruction of Einstein's own argument for the incompleteness quantum mechanics -- one that he thought did not make it into EPR in order to clarify assumptions underlie understanding Einstein completeness as categoricity, sense which is a type descriptive completeness, and some various ways has been more often misconstrued.

in this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $s_b$-metric spaces satisfying a contrctive type condition. we furnish an example to support our main theorem. we also give a corollary for junck type maps.

7.2 Let M = {(x, y) ∈ {0, 1}2n : x = y}. Note that d(z,M) = 1 2n |{i ∈ [n] : zi 6= zn+i}|, so let’s have our local tester pick a uniformly random j ∼ [n] and accept iff zj = zn+j . The completeness of this test is obviously 1, and in general we see that z is accepted with probability equal to 1 − 1 n |{i ∈ [n] : zi 6= zn+i}| = 1 − 2d(z,M), so the rejection rate is actually 2. 7.3 We’ll still wa...