Question: The Castle Dairy implies a connection to which medieval fortification to the east of the town of Kendal, Cumbria, in northern England?

Context articles: Ludlow Castle
Harlech Castle
Kendal Castle
Deddington Castle
Conisbrough Castle
Altes Schloss (Drügendorf)
Castle Rising (castle)
Hay Castle
The Castle Dairy
Kirkbie Kendal School

Ludlow Castle is a ruined medieval fortification in the town of the same name in the English county of Shropshire, standing on a promontory overlooking the River Teme.
 The castle was probably founded by Walter de Lacy after the Norman conquest and was one of the first stone castles to be built in England.
 During the civil war of the 12th century the castle changed hands several times between the de Lacy's and rival claimants, and was further fortified with a Great Tower and a large outer bailey.
 In the mid-13th century, Ludlow was passed on to Geoffrey de Geneville who rebuilt part of the inner bailey, and the castle played a part in the Second Barons' War.
 Roger Mortimer acquired the castle in 1301, further extending the internal complex of buildings, and the Mortimer family went on to hold Ludlow for over a century.
Harlech Castle (Welsh: "Castell Harlech" ), located in Harlech, Gwynedd, Wales, is a medieval fortification, constructed atop a spur of rock close to the Irish Sea.
 It was built by Edward I during his invasion of Wales between 1282 and 1289 at the substantial cost of £8,190.
 Over the next few centuries, the castle played an important part in several wars, withstanding the siege of Madog ap Llywelyn between 1294–95, but falling to Owain Glyndŵr in 1404.
 It then became Glyndŵr's residence and military headquarters for the remainder of the uprising until being recaptured by English forces in 1409.
 During the 15th century Wars of the Roses, Harlech was held by the Lancastrians for seven years, before Yorkist troops forced its surrender in 1468, a siege memorialised in the song "Men of Harlech".
 Following the outbreak of the English Civil War in 1642, the castle was held by forces loyal to Charles I, holding out until 1647 when it became the last fortification to surrender to the Parliamentary armies.
 In the 21st century the ruined castle is managed by Cadw, the Welsh Government's historic environment service, as a tourist attraction.
Kendal Castle is a medieval fortification to the east of the town of Kendal, Cumbria, in northern England.
 The castle, which is atop a glacial drumlin, was built in the 12th century as the  Caput baroniae for the Barony of Kendal.
 By the 15th century, the Parr family owned the castle.
 Queen Catherine Parr  was once thought to have been born at the castle; however, modern research has shown that it was in great disrepair by the 16th century and she was most likely born in Blackfriars, London.
Deddington Castle was a medieval fortification in the village of Deddington, Oxfordshire.
 It was built on a wealthy former Anglo-Saxon estate by Bishop Odo of Bayeux following the Norman conquest of England in 1066.
 Odo constructed a large castle with two earthwork baileys and a central motte, intending that the castle administer his property in the region and provide a substantial military base in the event of an Anglo-Saxon revolt.
 Odo's estates in England were seized following a failed rebellion against William II in 1088, and Deddington Castle was taken back into royal control.
 The Anglo-Norman lord William de Chesney acquired the castle in the 12th century and rebuilt it in stone, raising a stone curtain wall around a new inner bailey, complete with a defensive tower, gatehouse and domestic buildings.
Conisbrough Castle is a medieval fortification in Conisbrough, South Yorkshire, England.
 The castle was initially built in the 11th century by William de Warenne, the Earl of Surrey, after the Norman conquest of England in 1066.
 Hamelin Plantagenet, the illegitimate, "parvenu" son of Henry II, acquired the property by marriage in the late 12th century.
 Hamelin and his son William rebuilt the castle in stone, including its prominent 28 m -high keep.
 The castle remained in the family line into the 14th century, despite being seized several times by the Crown.
 The fortification was then given to Edmund of Langley, passing back into royal ownership in 1461.
The small ringwork of the Altes Schloss ("old castle") is all that remains of a, now levelled, early medieval fortification on one of the projecting hill spurs of the Mirsberg Heights ("Mirsberger Höhe") on the Lange Meile in the valley of the Eggerbach.
 The spur is called the "Schlossberg" ("castle hill").
 The old castle site lies at a height of  sea level (NN) around 935 metres south-southeast of the Roman Catholic parish church of St. Margareta of Drügendorf in the Upper Franconian municipality of Eggolsheim in Bavaria, Germany.
 No historical or archaeological information about this hillfort exists, and there have been no finds that might be able to be used to date the site.
 Based on the design of the fortification it has been tentatively dated to the Carolingian-Ottonian period.
 All that has survived is a ringwork with an outer ditch in places.
 The fortification is protected today as heritage site number D-4-6132-0125: "Early Medieval Ringwork" ("Frühmittelalterliche Ringwallanlage").
Castle Rising is a ruined medieval fortification in the village of Castle Rising, Norfolk, England.
 It was built soon after 1138 by William d'Aubigny II, who had risen through the ranks of the Anglo-Norman nobility to become the Earl of Arundel.
 With his new wealth, he constructed Castle Rising and its surrounding deer park, a combination of fortress and palatial hunting lodge.
 It was inherited by William's descendants before passing into the hands of the de Montalt family in 1243.
 The Montalts later sold the castle to Queen Isabella, who lived there after her fall from power in 1330.
 Isabella extended the castle buildings and enjoyed a regal lifestyle, entertaining her son, Edward III, on several occasions.
 After her death, it was granted to Edward, the Black Prince, to form part of the Duchy of Cornwall.
Hay Castle (Welsh: "Castell y Gelli" ) is a medieval fortification and 17th-century mansion house in the small town of Hay-on-Wye in Powys, Wales.
 Originally constructed as part of the Norman invasion of Wales, the castle was designed as a ringwork overlooking the town in either the late-11th or early-12th centuries.
 It was rebuilt in stone around 1200 by the de Braose family and then had a turbulent history, being attacked and burnt several times during the First and Second Barons' Wars, the wars with the Welsh princes, the rebellion of Owain Glyndŵr and the Wars of the Roses.
 In the 17th century a Jacobean mansion house was built alongside the medieval keep and the property became a private home.
 Serious fires in 1939 and 1977 gutted the castle and, despite repairs in the 1980s, by the 21st century much of the building was derelict and unstable.
 Since 2011 it has been owned by the Hay Castle Trust who plan to renovate the property to form an arts and education centre.
The Castle Dairy is a medieval building located in Kendal, Cumbria.
 The name implies a connection to Kendal Castle and it is possibly the town's oldest continuously inhabited structure.
Kirkbie Kendal School is an academy school and known as a "Business and Enterprise College" in Kendal, Cumbria, Northern England, and serves the area around the town and rural countryside.
 Kirkbie Kendal School operates as a Foundation school, and has been regularly oversubscribed, accepting students based on a designated hierarchy.
 The school has 880 pupils on roll, ages 11–18.