Question: Osbeorn Bulax's father governed on what king's behalf?

Context paragraphs:
Osbeorn Bulax: Osbeorn (died c. 1054), given the nickname Bulax, was the son of Siward, Earl of Northumbria (died 1055).  He is one of two known sons — probably the older — of Siward.  While it is normally assumed he was the son of Siward's Bamburgh wife Ælfflæd, it has been suggested by William Kapelle that Osbeorn's mother was not Ælfflæd.  The nickname "Bulax" probably represents the Old Norse term for "Poleaxe".

Jean de Carrouges: Sir Jean de Carrouges IV (c. 1330s – 25 September 1396) was a fourteenth-century French knight who governed estates in Normandy as a vassal of Count Pierre d'Alençon and served under Admiral Jean de Vienne in several campaigns against the English and the forces of the Ottoman Empire.  He became infamous in medieval France for fighting in the last judicial duel permitted by the French king and the Parlement of Paris.  The combat was decreed in 1386 to contest charges of rape Carrouges had brought against his neighbour and erstwhile friend Jacques Le Gris on behalf of his wife Marguerite.  It was attended by much of the highest French nobility of the time led by King Charles VI and his family, including a number of royal dukes.  It was also attended by thousands of ordinary Parisians and in the ensuing decades was chronicled by such notable medieval historians as Jean Froissart, Jean Juvénal des Ursins and Jehan de Waurin.

Béla IV of Hungary: Béla IV (29 November 1206 – 3 May 1270) was King of Hungary and Croatia between 1235 and 1270, and Duke of Styria from 1254 to 1258.  Being the oldest son of King Andrew II, he was crowned upon the initiative of a group of influential noblemen in his father's lifetime in 1214.  His father, who strongly opposed Béla's coronation, refused to give him a province to rule until 1220.  In this year, Béla was appointed Duke of Slavonia, also with jurisdiction in Croatia and Dalmatia.  Around the same time, Béla married Maria, a daughter of Theodore I Laskaris, Emperor of Nicaea.  From 1226, he governed Transylvania with the title Duke.  He supported Christian missions among the pagan Cumans who dwelled in the plains to the east of his province.  Some Cuman chieftains acknowledged his suzerainty and he adopted the title of King of Cumania in 1233.  King Andrew died on 21 September 1235 and Béla succeeded him.  He attempted to restore royal authority, which had diminished under his father.  For this purpose, he revised his predecessors' land grants and reclaimed former royal estates, causing discontent among the noblemen and the prelates.

Isabella Jagiellon: Isabella Jagiellon (Hungarian: "Izabella királyné" ; Polish: "Izabela Jagiellonka" ; 18 January 1519 – 15 September 1559) was the oldest child of Polish King Sigismund I the Old and his Italian wife Bona Sforza.  In 1539, she married John Zápolya, Voivode of Transylvania and King of Hungary, becoming Queen consort of Hungary.  At the time Hungary was contested between Archduke Ferdinand of Austria who wanted to add it to the Habsburg domains (see Royal Hungary), local nobles who wanted to keep Hungary independent (see Eastern Hungarian Kingdom), and Sultan Suleiman the Magnificent who saw it as a vassal state of the Ottoman Empire (see also Little War in Hungary).  While Isabella's marriage lasted only a year and a half, it did produce a male heir – John Sigismund Zápolya born just two weeks before his father's death in July 1540.  She spent the rest of her life embroiled in succession disputes on behalf of her son.  Her husband's death sparked renewed hostilities but Sultan Suleiman established her as a regent of the eastern regions of the medieval Kingdom of Hungary on behalf of her infant son.  The region developed as a semi-independent buffer state noted for its freedom of religion.  Ferdinand, however, never renounced his claims to reunite Hungary and conspired with Bishop George Martinuzzi who forced Isabella to abdicate in 1551.  She returned to her native Poland to live with her family.  Sultan Suleiman retaliated and threatened to invade Hungary in 1555–56 forcing nobles to invite Isabella back to Transylvania.  She returned in October 1556 and ruled as her son's regent until her death in September 1559.

Ayocuan Cuetzpaltzin: Ayocuan, the son of Cuetzpaltzin the Elder, was from the city of Puebla according to Historia Tolteca-Chichimeca.  His father governed the towns of Cohuayocan and Cuauhtepec during the 15th century.  He lost his domain in 1441 when he suffered a joint attack by the people of Coatlinchan, Cholula, Huexotzinco, and Tlaxcala.  Ayocuan was educated in the town of Quimixtlan.

Jayanta: In Hindu mythology, Jayanta (Sanskrit: जयन्त , "victorious"), also spelled as Jayanta, is the son of Indra, the king of the gods (Immortals) and his consort Indrani.  He resides in Svarga, the Hindu heaven, governed by Indra.  He has a sister called Jayanti.  He appears in various Hindu scriptures as fighting wars on behalf of the gods and his father.  Jayanta also appears in the epic "Ramayana" and other lore, in which he disguises himself as a crow.

Washington's National Park Fund: Washington’s National Park Fund is a 501(c)(3) non-profit organization that serves as the official fund raising partner for Mount Rainier National Park, North Cascades National Park, and Olympic National Park in Washington state, United States.  The Fund is governed by a voluntary board of directors.  The Fund both solicits and accepts charitable contributions on behalf of the parks and distributes them under guidelines agreed to by both the park superintendents and the board of directors for the Fund.  This relationship is governed by partnership agreements.

Monarchy in the Irish Free State: From its foundation on 6 December 1922 until 11 December 1936, the Irish Free State was in accordance with its constitution, governed formally under a form of constitutional monarchy.  The monarch exercised a number of important duties, including appointing the cabinet, dissolving the legislature and promulgating laws.  Nonetheless, by convention the monarch's role was largely ceremonial and exercised on his behalf by his official representative, the governor-general.  The monarch's role and duties under the constitution were ended under a constitutional amendment adopted in 1936.  From that point, the monarch no longer played any role in appointing the cabinet, dissolving the legislature or promulgating laws.  Nor was the monarch mentioned anywhere in the constitution.  Under separate legislation also adopted in 1936 it was provided that Irish diplomatic representatives would be appointed on the authority of the cabinet alone and international agreements would be concluded with the authority of the cabinet alone.  At the same time, that legislation also created a new role for the king in his capacity as the "symbol of [the] co-operation" of Australia, Canada, Great Britain, New Zealand, and South Africa for so long as the Irish Free State was associated with those states.  The new role of the king in that capacity alone was to act on behalf of the Irish government with respect to the appointment of diplomatic and consular representatives and the conclusion of international agreements when advised by the cabinet so to do.  The role of the king in acting on behalf of the Irish government with respect to appointing diplomats was not ended until 1949 and under United Kingdom law the king is regarded as having been the sovereign until that time but not under Irish law.

Executive Council of the Irish Free State: The Executive Council (Irish: "Ard-Chomhairle" ) was the cabinet and "de facto" executive branch of government of the 1922–1937 Irish Free State.  Formally, executive power was vested in the Governor-General on behalf of the King.  In practice, however, it was the Council that governed, since the Governor-General was (with few exceptions) bound to act on its advice.  The Executive Council included a prime minister called the President of the Executive Council and a deputy prime minister called the Vice-President.  A member of the Council was called an executive minister, as distinct from an extern minister who had charge of a department without being in the Council.

Siward, Earl of Northumbria: Siward or Sigurd ( or more recently ; Old English: "Sigeweard") was an important earl of 11th-century northern England.  The Old Norse nickname "Digri" and its Latin translation "Grossus" ("the stout") are given to him by near-contemporary texts.  Siward was probably of Scandinavian origin, perhaps a relative of Earl Ulf, and emerged as a powerful regional strongman in England during the reign of Cnut ("Canute the Great", 1016–1035).  Cnut was a Scandinavian ruler who conquered England in the 1010s, and Siward was one of the many Scandinavians who came to England in the aftermath of that conquest.  Siward subsequently rose to become sub-ruler of most of northern England.  From 1033 at the latest Siward was in control of southern Northumbria, that is, present-day Yorkshire, governing as earl on Cnut's behalf.

Supporting paragraphs: Osbeorn Bulax Siward, Earl of Northumbria
Answer: Cnut