The breed eligible to race in the Habletonian Stake is the Standardbred.
Hambletonian 10 or Rysdyk's Hambletonian, (May 5, 2024 – 1876) was an American trotter and a founding sire of the Standardbred horse breed. The stallion was born in Sugar Loaf, NY on 5 May 1849.
The name "Standardbred" distinguishes the harness horse from the Thoroughbred running horse and came from the breeding goal of developing horses that trotted or paced in a standard time.
To be recognized as a Standardbred, a horse had to be capable of trotting or pacing a mile within the prescribed limits of a certain standard of time. This was known as The Standard of Admission to Registration.
The Hambletonian Society is a non-profit organization formed in 1924 to sponsor the race for which it was named, the Hambletonian Stake. The Society’s mission is to encourage and support the breeding of Standardbred horses through the development, administration and promotion of harness racing stakes, early-closing races and other special events.
For more info about Standardbred, see this link: http://www.horseshowcentral.com/breeds/standardbred.