Arithmetic Reconstructed from 1:A Two-Dimensional Sieve for Prime Numbers

This paper presents a novel and detailed approach to reconstructing arithmetic from

the unit 1 and employing a two-dimensional (2D) framework for sieving prime num-bers. Our method reorganizes numbers as fractions in a 2D grid, applies a logarithmictransformation to group them into cells, and then projects the data to a canonical rep-resentation to recover the prime numbers. Although the final asymptotic result for theprime distribution remains the classical