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

<b>This paper presents a novel and detailed approach to reconstructing arithmetic from</b><b>the unit 1 and employing a two-dimensional (2D) framework for sieving prime num-</b><b>bers. Our method reorganizes numbers as fractions in a 2D grid, applies a logarithmic</b><b>transformation to group them into cells, and then projects the data to a canonical rep-</b><b>resentation to recover the prime numbers. Although the final asymptotic result for the</b><b>prime distribution remains the classical</b>