  We demonstrate a compact iodine-stabilized laser operating at 531 nm using a
coin-sized light source consisting of a 1062-nm distributed-feedback diode
laser and a frequency-doubling element. A hyperfine transition of molecular
iodine is observed using the light source with saturated absorption
spectroscopy. The light source is frequency stabilized to the observed iodine
transition and achieves frequency stability at the 10$^{-12}$ level. The
absolute frequency of the compact laser stabilized to the $a_{1}$ hyperfine
component of the $R(36)32-0$ transition is determined as
$564\,074\,632\,419(8)$ kHz with a relative uncertainty of $1.4\times10^{-11}$.
The iodine-stabilized laser can be used for various applications including
interferometric measurements.
