Determining the absolute oldest katana in the world is challenging due to the passage of time, the scarcity of well-preserved ancient swords, and the complex nature of sword history. The oldest surviving katana swords typically date back to the Kamakura period (1185-1333) or later.

While specific dating of individual swords is difficult, there are a few notable katana swords that are considered among the oldest and highly prized:

1. "Dojigiri Yasutsuna": This katana is attributed to the legendary swordsmith Yasutsuna and is considered one of the oldest extant katana swords. It is believed to have been crafted in the late Heian period (late 12th century). The sword is designated as a National Treasure of Japan and is currently held at the Tokyo National Museum.
2. "Sanjo Munechika": Sanjo Munechika is a renowned swordsmith from the Heian period. Swords attributed to Munechika, such as the "Sanjo Munechika," are considered among the earliest surviving katana swords. The exact age and origins of these swords can vary, but they are highly regarded for their historical significance and craftsmanship.

It's important to note that the specific age and origins of ancient swords can be difficult to ascertain definitively. The rarity and historical significance of certain katana swords can make them highly sought after by collectors and enthusiasts. As new archaeological discoveries and research emerge, our understanding of the oldest katana swords may evolve.