There are many reasons why people visit Japan, and different areas like to encourage tourists to visit in any way they can. Unique food, events and sights are utilized or created to attract both domestic and international travelers. This explains nicely why Kansai's smallest mountain is found in Osaka, and why it's just over four and a half meters tall.
Also called Mount Tenpo in English, it's actually an artificial mountain created in the 1800s as an orientation point for ships. Originally around 20 meters, the summit is now 4.53 meters above sea level and significantly lower than other parts of Tenpozan Park. The park is a few minutes' walk from Osakako Station (on the Chuo Subway Line); it's almost directly at the foot of Tenpozan Ferris Wheel, next to Osaka Aquarium Kaiyukan.
It's such an insignificant spot that it needs a sign to point out where it actually is, but it is officially considered a mountain. If it's included on a map published by the Geographical Survey Institute of Japan, then it counts. It actually used to be Japan's lowest mountain, but it was recently replaced by Hiyoriyama in the northeastern region of Tohoku. Both have interesting tales behind them, and visiting it will make another for you to tell when you return from your travels. While you're there you can visit the aquarium and Ferris wheel; you can even get proof of your ascent from the Mt. Tenpo Expedition Society.
The Society's website still states that they are based in a small cafe, but this appears to have closed. You can ask at the shop which is at the same location, but there may not be anyone available. However, the Society still has a mailbox at the same location, south of Osakako Station. Their website shows the location - near Exit 4, just past a Family Mart convenience store. When you find it, there should be paper and a pencil on a string. Just write the date, your name, address in Japan and how many people made the ascent, then wrap ¥100 plus ¥10 per person inside the paper and post it in the mailbox. They only mail certificates within Japan, but it seems they're quick in sending them, so if you're in Japan for a while, you could have it sent to your hotel or hostel.
The certificate is a cheerful, yellow piece of paper written in Japanese and formally stamped. It congratulates you for reaching the summit, and for possessing the ability to take a joke. It's a pretty unique souvenir which shows the more informal side of Japanese culture.