Collatz Conjecture: A Geometric Construction from Euler's Formula to Fourier Isolation of +1 (V2)

Starting from the single line e^(iπ) = −1, this paper builds a complete geometric argument for the Collatz conjecture. Euler's formula gives cos(πn) = (−1)^n — an exact odd-even switch. The +1 in the Collatz operation, modulated by this switch, falls uniquely into the frequency-1/2 pure wave C₃ = (1−cos πz)/4, orthogonally isolated from the ÷2 and 3n channels. With +1 isolated, each odd step has frequency factor 3/2^k. The k=1 growth chain has length exactly v₂(n+1)−1 — finite for all positive integers. An infinite chain requires n = −1 (2-adic), not in Z⁺. Finite growth plus infinite shrinkage forces descent to 1. The same framework proves 5n+1 divergence and the uniqueness of p = 3. Bilingual: Chinese and English PDFs included.