This note gives an expository chamber-coordinate presentation of the odd perfect number problem. A positive integer $N$ is perfect if $\sigma(N)=2N$, where $\sigma$ is the sum-of-divisors function. Even perfect numbers are completely characterized by the Euclid-Euler theorem, while the existence of an odd perfect number remains open. If an odd perfect number exists, Euler's classical theorem forces the form \[ N=p^{\alpha}m^2, \qquad p\equiv \alpha\equiv 1 \pmod 4, \qquad \gcd(p,m)=1. \] In this note, this is organized as a two-component atlas: an Euler-prime component $p^{\alpha}$ and a square-body component $m^2$. The perfectness equation becomes the abundancy balance \[ I(p^{\alpha})I(m^2)=2, \qquad I(n)=\frac{\sigma(n)}{n}. \] The same equation also imposes cross-divisibility constraints \[ p^{\alpha}\mid \sigma(m^2), \qquad \frac{\sigma(p^{\alpha})}{2}\mid m^2. \] The mathematics assembled here is classical. The novelty claimed is only the atlas-style vocabulary and organization. No proof of existence or nonexistence of odd perfect numbers is claimed.