Question: At the center of Rothesay, Bute, is what ruined castle that is described as one of the most remarkable in Scotland, and dates back to the beginning of the 13th century?

Context paragraphs:
Kildrummy Castle: Kildrummy Castle is a ruined castle near Kildrummy, in Aberdeenshire, Scotland.  Though ruined, it is one of the most extensive castles dating from the 13th century to survive in eastern Scotland, and was the seat of the Earls of Mar.  It is owned today by Historic Scotland and is open to the public as a scheduled ancient monument.

Braal Castle: Braal Castle is located by the River Thurso north of the village of Halkirk, in Caithness, northern Scotland.  The ruined castle, which dates back to the mid-14th century, was originally known as the Castle of Brathwell.

Chiesa Matrice, Erice: The Chiesa Matrice is a church in Erice, Sicily, southern Italy.  It dates back the beginning of the 15th century (an original fresco dates back to 1420) and is built in the shape of a Latin cross with two entrances.  The church is enriched by numerous Baroque altars and paintings from the 17th century.  A silver statue of St Anthony of Padua dates back 17th century and is an example of Neapolitan silver-craft.

Duart Castle: Duart Castle or Caisteal Dhubhairt in Scottish Gaelic is a castle on the Isle of Mull, off the west coast of Scotland, within the council area of Argyll and Bute.  The castle dates back to the 13th century and is the seat of Clan MacLean.

Rothesay Castle: Rothesay Castle is a ruined castle in Rothesay, the principal town on the Isle of Bute, in western Scotland.  Located at [ NS086646] , the castle has been described as "one of the most remarkable in Scotland", for its long history dating back to the beginning of the 13th century, and its unusual circular plan.

Castlelost Castle: Castlelost Castle (Irish: "Caisleán Loiste") is a ruined castle located just north of Rochfortbridge in County Westmeath, Ireland.  The castle itself dates back to the Norman invasion of Ireland.  The only visible features still on the site are the ruined tower house as well as a small mote.

History of Lithuania: The history of Lithuania dates back to settlements founded many thousands of years ago , but the first written record of the name for the country dates back to 1009 AD.  Lithuanians, one of the Baltic peoples, later conquered neighboring lands and established the Grand Duchy of Lithuania in the 13th century (and also a short-lived Kingdom of Lithuania).  The Grand Duchy was a successful and lasting warrior state.  It remained fiercely independent and was one of the last areas of Europe to adopt Christianity (beginning in the 14th century).  A formidable power, it became the largest state in Europe in the 15th century through the conquest of large groups of East Slavs who resided in Ruthenia.  In 1385, the Grand Duchy formed a dynastic union with Poland through the Union of Krewo.  Later, the Union of Lublin (1569) created the Polish–Lithuanian Commonwealth that lasted until 1795, when the last of the Partitions of Poland erased both Lithuania and Poland from the political map.  Afterward, the Lithuanians lived under the rule of the Russian Empire until the 20th century.

Clun Castle: Clun Castle is a ruined castle in the small town of Clun, Shropshire.  Clun Castle was established by the Norman lord Robert de Say after the Norman invasion of England and went on to become an important Marcher lord castle in the 12th century, with an extensive castle-guard system.  Owned for many years by the Fitzalan family, Clun played a key part in protecting the region from Welsh attack until it was gradually abandoned as a property in favour of the more luxurious Arundel Castle.  The Fitzalans converted Clun Castle into a hunting lodge in the 14th century, complete with pleasure gardens, but by the 16th century the castle was largely ruined.  Slighted in 1646 after the English Civil War Clun remained in poor condition until renovation work in the 1890s.

Rothesay, Bute: The City of Rothesay (Scottish Gaelic: "Baile Bhòid" ) is the principal town on the Isle of Bute, in the council area of Argyll and Bute, Scotland.  It can be reached by ferry from Wemyss Bay which offers an onward rail link to Glasgow.  At the centre of the town is Rothesay Castle, a ruined castle which dates back to the 13th century, and which is unique in Scotland for its circular plan.  Rothesay lies along the coast of the Firth of Clyde.

Caerlaverock Castle: Caerlaverock Castle (from "caer laverock", "lark castle") is a moated triangular castle first built in the 13th century.  It is located on the southern coast of Scotland, 11 km south of Dumfries, on the edge of the Caerlaverock National Nature Reserve.  Caerlaverock was a stronghold of the Maxwell family from the 13th century until the 17th century when the castle was abandoned.  It was besieged by the English during the Wars of Scottish Independence, and underwent several partial demolitions and reconstructions over the 14th and 15th centuries.  In the 17th century, the Maxwells were created Earls of Nithsdale, and built a new lodging within the walls, described as among "the most ambitious early classical domestic architecture in Scotland".  In 1640 the castle was besieged for the last time and was subsequently abandoned.  Although demolished and rebuilt several times, the castle retains the distinctive triangular plan first laid out in the 13th century.  Caerlaverock Castle was built to control trade in early times.

Supporting paragraphs: Rothesay, Bute Rothesay Castle
Answer: Rothesay Castle