hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Hamiltonian (quantum mechanics)
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.

The Hamiltonian is named after William Rowan Hamilton, who developed a revolutionary reformulation of Newtonian mechanics, known as Hamiltonian mechanics, which was historically important to the development of quantum physics. Similar to vector notation, it is typically denoted by , where the hat indicates that it is an operator. It can also be written as  or .

Eigenfunction
In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function  in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be written as

for some scalar eigenvalue  The solutions to this equation may also be subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions.

An eigenfunction is a type of eigenvector.
David Murphy (baseball)
David Matthew Murphy (born October 18, 1981) is an American former professional baseball outfielder. He played in Major League Baseball (MLB) for the Boston Red Sox, Texas Rangers, Cleveland Indians and Los Angeles Angels of Anaheim.

Murphy was drafted in the 2003 MLB draft by the Red Sox. He made his MLB debut with the Red Sox, and was traded to the Rangers in 2007. He signed with the Indians as a free agent before the 2014 season, and was traded to the Angels during the 2015 season. Also drafted 1439th in the 2000 MLB draft but did not sign.

Mitch Moreland
Mitchell Austin Moreland (born September 6, 1985), nicknamed "2-Bags", is an American former professional baseball first baseman. He played in Major League Baseball (MLB) for the Texas Rangers, Boston Red Sox, San Diego Padres, and Oakland Athletics. Moreland attended Mississippi State University and was drafted by the Rangers as a first baseman and outfielder in the 17th round of the 2007 MLB draft. Listed at 6 feet 2 inches (1.88 m) and 230 pounds (100 kg), Moreland both batted and threw left-handed.
Writers Guild of America
The Writers Guild of America (WGA) is the name of two American labor unions representing writers in film, television, radio, and online media:

The Writers Guild of America East (WGAE) is headquartered in New York City and is affiliated with the AFL-CIO national trade union center

The Writers Guild of America West (WGAW) is headquartered in Los Angeles and is unaffiliated with any larger national trade union.

Although both organizations operate independently, they perform some common activities, including negotiating contracts and launching strike actions, as well as maintaining the American database of writing credits, and arbitrating between writers when conflicts arise.

Directors Guild of America
The Directors Guild of America (DGA) is an entertainment guild that represents the interests of film and television directors in the United States motion picture industry and abroad. Founded as the Screen Directors Guild in 1936, the group merged with the Radio and Television Directors Guild in 1960 to become the modern Directors Guild of America.
County Westmeath
County Westmeath (/wɛstˈmiːð/; Irish: Contae na hIarmhí or simply An Iarmhí) is a county in Ireland. It is in the province of Leinster and is part of the Eastern and Midland Region. It formed part of the historic Kingdom of Meath, which was named Mide because the kingdom was located in the geographical centre of Ireland (the word Mide meaning 'middle'). Westmeath County Council is the administrative body for the county, and the county town is Mullingar. At the 2022 census, the population of the county was 95,840.

N4 road (Ireland)
The N4 road is a national primary road in Ireland, running from Dublin to the northwest of Ireland and Sligo town. The M6 to Galway diverges from this route after Kinnegad, while the N5 to Westport diverges at Longford town. Most sections of the N4 that are motorway-standard are designated the M4 motorway.
Alpine County, California
Alpine County is a county in the eastern part of the U.S. state of California located within the Sierra Nevada on the state border with Nevada. As of the 2020 census, the population was 1,204, making it California's least populous county. The county seat is Markleeville and the largest community is Alpine Village.

California State Route 4
State Route 4 (SR 4) is an east–west state highway in the U.S. state of California, routed from Interstate 80 in the San Francisco Bay Area to State Route 89 in the Sierra Nevada. It roughly parallels the Sacramento-San Joaquin River Delta, a popular area for boating and fishing, with a number of accesses to marinas and other attractions. After crossing the Central Valley, the highway ascends up the Sierra foothills. It passes through Ebbetts Pass and contains the Ebbetts Pass Scenic Byway, a National Scenic Byway.
Basin Reserve
The Basin Reserve, also known as the Cello Basin Reserve for sponsorship reasons, and commonly referred to as the Basin, is a cricket ground in Wellington, New Zealand. It is used for Test matches, and is the main home ground of the Wellington Firebirds first-class team. The Basin Reserve is the only cricket ground to have listed status with Heritage New Zealand, in recognition of being the oldest first-class cricket ground in the country. Historically, the ground has also been used for events other than cricket, such as association football matches, concerts and cultural events.

The New Zealand Cricket Museum is located in the Old Grandstand. It houses cricket memorabilia and a reference library. It opened in 1987, and was relaunched in 2021.

Wellington rugby league team
The Wellington Rugby League Team (also known as the Wellington Orcas) are a rugby league team that represents the Wellington Rugby League in New Zealand Rugby League competitions. They currently compete in the National Competition.
71st Infantry Division (Wehrmacht)
The 71st Infantry Division Kleeblatt ("Cloverleaf Division", "Lucky One") (German: 71. Infanterie-Division) was an infantry division of the German Army, raised on 26 August 1939, shortly before the outbreak of World War II, as a division of the 2nd wave of deployment by Infantry Commander 19 (Infanterie-Kommandeur 19) in Hildesheim. It fought in Verdun, Stalingrad and Monte Cassino, among others.

The division's symbol was the four-leaf clover and after congratulations on the victory in Verdun in June 1940, the division was henceforth called the "lucky one". The same action also earning Generalleutnant Karl Weisenberger the Knight's Cross of the Iron Cross on 29 June 1940 by Generalfeldmarschall Ernst Busch.

29th Infantry Division (Wehrmacht)
The 29th Infantry Division was a unit of the German army created in the fall of 1936. It was based on the old Reichswehr 15th Infantry Regiment and drew its initial recruits from Thuringia. It was upgraded to 29th Motorized Infantry Division in the fall of 1937. The division was also known as the Falke-Division (Falcon Division).
Saint Petersburg Governorate
Saint Petersburg Governorate was a province (guberniya) of the Russian Empire, with its capital in Saint Petersburg. The governorate was composed of 44,613 square kilometres (17,225 mi2) of area and 2,112,033 inhabitants. It was bordered by Estonian and Livonian Governorates to the west, Pskov Governorate to the south, Novgorod Governorate to the east, Olonets Governorate to the northeast, and Vyborg Governorate of the Grand Duchy of Finland to the north. The governorate covered most of the areas of modern Leningrad Oblast and Ida-Viru, Jõgeva, Tartu, Põlva, and Võru counties of Estonia.

Veliky Novgorod
Veliky Novgorod (/vəˈliːki ˈnɒvɡərɒd/ ⓘ və-LEE-kee NOV-gə-rod; Russian: Великий Новгород, IPA: [vʲɪˈlʲikʲɪj ˈnovɡərət]; lit. 'Great Newtown'), also known simply as Novgorod (Новгород), is the largest city and administrative centre of Novgorod Oblast, Russia. It is one of the oldest cities in Russia, being first mentioned in the 9th century. The city lies along the Volkhov River just downstream from its outflow from Lake Ilmen and is situated on the M10 federal highway connecting Moscow and Saint Petersburg. UNESCO recognized Novgorod as a World Heritage Site in 1992. The city has a population of 224,286 (2021 census).

At its peak during the 14th century, the city was the capital of the Novgorod Republic and was one of Europe's largest cities. The "Великий" (Veliky) part was added to the city's name in 1999.
Doctorate
A doctorate (from Latin doctor, meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism licentia docendi ("licence to teach").

In most countries, a research degree qualifies the holder to teach at university level in the degree's field or work in a specific profession. There are a number of doctoral degrees; the most common is the Doctor of Philosophy (PhD), awarded in many different fields, ranging from the humanities to scientific disciplines.

Many universities also award honorary doctorates to individuals deemed worthy of special recognition, either for scholarly work or other contributions to the university or society.

Graduate certificate
A graduate certificate is an educational credential representing completion of specialized training at the college or university level. A graduate certificate can be awarded by universities upon completion of certain coursework indicating mastering of a specific subject area. Graduate certificates represent training at different levels in different countries, for example a graduate certificate is at master's degree level in Ireland, but is at a bachelor's degree level in the United Kingdom. In both cases, the graduate certificate represents less work than a degree at the same level.
Gmina
The gmina (Polish: [ˈɡmina], pl. gminy [ˈɡminɨ]) is the basic unit of the administrative division of Poland, similar to a municipality. As of 1 January 2019, there were 2,479 gminy throughout the country, encompassing over 43,000 villages. 940 gminy include cities and towns, with 322 among them constituting an independent urban gmina (Polish: gmina miejska) consisting solely of a standalone town or one of the 107 cities, the latter governed by a city mayor (prezydent miasta).

The gmina has been the basic unit of territorial division in Poland since 1974, when it replaced the smaller gromada. Three or more gminy make up a higher level unit called a powiat, except for those holding the status of a city with powiat rights. Each and every powiat has the seat in a city or town, in the latter case either an urban gmina or a part of an urban-rural one.

Pajęczno County
Pajęczno County (Polish: powiat pajęczański) is a unit of territorial administration and local government (powiat) in Łódź Voivodeship, central Poland. It came into being on January 1, 1999, as a result of the Polish local government reforms passed in 1998. Its administrative seat and largest town is Pajęczno, which lies 78 kilometres (48 mi) south-west of the regional capital Łódź. The only other town in the county is Działoszyn, lying 10 km (6 mi) west of Pajęczno.

The county covers an area of 804.14 square kilometres (310.5 sq mi). As of 2006 its total population is 53,395, out of which the population of Pajęczno is 6,674, that of Działoszyn is 6,276, and the rural population is 40,445.
Chris Horner
Christopher Brandon Horner (born October 23, 1971) is an American retired professional road racing cyclist, who rode professionally between 1996 and 2019.

A current resident of Bend, Oregon, Horner dominated the American road racing scene by winning the points standings in the 2002, 2003 and 2004 USA Cycling National Racing Calendar. He won the Vuelta a España in 2013, becoming the oldest winner of any of cycling's grand tours in the process.

Lidl–Trek (men's team)
Lidl–Trek (UCI team code: LTK) is a professional road bicycle racing team at UCI WorldTeam level licensed in Germany for 2026. Formerly RadioShack–Nissan, in 2014, Trek took over the ownership of the team and its ProTeam License.
Henry Lawson
Henry Archibald Hertzberg Lawson (17 June 1867 – 2 September 1922) was an Australian writer and bush poet. Along with his contemporary Banjo Paterson, Lawson is among the best-known Australian poets and fiction writers of the colonial period and is often called Australia's "greatest short story writer".

A vocal nationalist and republican, Lawson regularly contributed to The Bulletin, and many of his works helped popularise the Australian vernacular in fiction. He wrote prolifically into the 1890s, after which his output declined, in part due to struggles with alcoholism and mental illness. At times destitute, he spent periods in Darlinghurst Gaol and psychiatric institutions. After he died in 1922 following a cerebral haemorrhage, Lawson became the first Australian writer to be granted a state funeral.

He was the son of the poet, publisher and feminist Louisa Lawson.

The bush
"The bush", a term mostly used in the English vernacular of Australia, New Zealand, Canada and South Africa, is largely synonymous with hinterlands or backwoods. The fauna and flora contained within the bush is typically native to the region, although exotic species may also be present. The word derives from Old French bos, and Old Norse buski, and related to Dutch bos and German Busch with the sense ‘uncultivated country’ coming directly from Dutch bos,

The expression has been in use in Australia from the earliest years of British settlement, and it has inspired many derivative Australian English terms, such as bush tucker, bush mechanic, bush ballad and bushranger. The term is also widely used in Canada and the American state of Alaska to refer to the large, forested portions of their landscapes.
Pilar, Bohol
Pilar, officially the Municipality of Pilar (Cebuano: Munisipyo sa Pilar; Tagalog: Bayan ng Pilar),  is a  municipality in the province of Bohol, Philippines. According to the 2024 census, it has a population of 28,860 people.

Pilar is 77 kilometres (48 mi) from Tagbilaran.

Pilar celebrates its fiesta on October 10, to honor the town patron Virgen del Pilar.

Valencia, Bohol
Valencia, officially the Municipality of Valencia (Cebuano: Munisipalidad sa Valencia; Tagalog: Bayan ng Valencia),  is a  municipality in the province of Bohol, Philippines. According to the 2024 census, it has a population of 28,535 people.

It is on the southern coast of Bohol, 46 kilometres (29 mi) from Tagbilaran.

There are elementary schools in the poblacion and in the barrios. For their secondary education, students go to Valencia High School, a public school.

Valencia celebrates its feast on every 3rd Saturday of January to honor the town patron saint, Sr. Santo Niño.
Thomas Vanek
Thomas Vanek (born 19 January 1984) is an Austrian former professional ice hockey winger who played fourteen seasons in the National Hockey League (NHL) for the Buffalo Sabres, Columbus Blue Jackets, Detroit Red Wings, Florida Panthers, Minnesota Wild, Montreal Canadiens, New York Islanders, and Vancouver Canucks. Vanek was drafted by the Sabres fifth overall in the 2003 NHL entry draft, making him the highest-drafted Austrian player in NHL history along with David Reinbacher in the 2023 NHL entry draft. He was inducted into the IIHF Hall of Fame in 2026.

Sebastian Collberg
Erik Sebastian Collberg (born February 23, 1994) is a Swedish professional ice hockey right winger who is an unrestricted free agent. He was selected in the second round, 33rd overall, by the Montreal Canadiens in the 2012 NHL Entry Draft.
Georgia State Route 11
State Route 11 (SR 11) is a 376-mile-long (605 km) state highway in the U.S. state of Georgia, traveling through portions of Echols, Lanier, Berrien, Irwin, Ben Hill, Wilcox, Pulaski, Houston, Peach, Bibb, Jones, Jasper, Newton, Walton, Barrow, Jackson, Hall, White, Lumpkin, and Union counties. It travels the entire length of the state from south to north, connecting the Florida state line with the North Carolina state line, roughly bisecting the state into two equal parts. It travels through Warner Robins, Macon, and Gainesville. It is the longest route in the state. The portion from the southeastern city limits of Monticello to the Jasper–Newton county line is included in the Monticello Crossroads Scenic Byway.

Interstate 20 in Georgia
Interstate 20 (I-20) is a part of the Interstate Highway System that spans 1,539.38 miles (2,477.39 km) from Reeves County, Texas, to Florence, South Carolina. In the US state of Georgia, I-20 travels from the Alabama state line to the Savannah River, which is the South Carolina state line. The highway enters the state near Tallapoosa. It travels through the Atlanta metropolitan area and exits the state in Augusta. The highway also travels through the cities of Bremen, Douglasville, Conyers, Covington, and Madison. I-20 has the unsigned state highway designation State Route 402 (SR 402).
Onondaga Community College
Onondaga Community College (OCC) is a public community college with its main campus in Onondaga, New York, United States. The college serves Onondaga County and Central New York. It is part of the State University of New York (SUNY) system.

National Junior College Athletic Association
The National Junior College Athletic Association (NJCAA or JUCO) is the governing association of community college, state college, and junior college athletics throughout the United States. Currently, the NJCAA holds 24 separate regions across 24 states, and it is divided into three divisions.
Trixter (company)
Trixter is a German visual effects and computer animation studio with divisions in Munich and Berlin, as well as in Los Angeles. Founded in 1999 by Simone Kraus Townsend and Michael Coldewey, the company was acquired in August 2018 by Cinesite. As of 2025, Trixter's managing directors are Christina Caspers and Holger Voss.

Among the company's credits include Predator: Badlands (2025) The Marvels (2023) Shang-Chi and the Legend of the Ten Rings (2021) Captain Marvel (2019), Black Panther (2018), Spider-Man: Homecoming (2017), Thor: Ragnarok (2017) and Guardians of the Galaxy Vol. 2 (2017).

FuseFX
FuseFX (formerly known as The Outfit) was an American special visual effects company which was founded in Los Angeles, California in 2006 by David Altenau, Tim Jacobsen and Jason Fotter. The company is best known for developing special visual effects for television series, films, commercials and virtual realities.

In January of 2025, it was announced that all FuseFX offices would be rebranded under their sister VFX studio, Folks VFX, effectively retiring FuseFX as a brand.
Gausdal Municipality
Gausdal is a municipality in Innlandet county, Norway. It is located in the traditional district of Gudbrandsdal. The administrative centre of the municipality is the village of Segalstad bru. Other villages in Gausdal include Follebu, Forset, and Svingvoll.

The 1,191-square-kilometre (460 sq mi) municipality is the 91st largest by area out of the 357 municipalities in Norway. Gausdal Municipality is the 156th most populous municipality in Norway with a population of 6,174. The municipality's population density is 5.2 inhabitants per square kilometre (13/sq mi) and its population has decreased by 1% over the previous 10-year period.

Logging, farming, and tourism are important industries in the municipality.

Nordre Land Municipality
Nordre Land is a municipality in Innlandet county, Norway. It is located in the traditional district of Land. The administrative centre of the municipality is the village of Dokka. Other villages in the municipality include Vest-Torpa, Nord-Torpa, Aust-Torpa, Fagerlund, and Nordsinni.

The 955.32-square-kilometre (368.85 sq mi) municipality is the 122nd largest by area out of the 357 municipalities in Norway. Nordre Land Municipality is the 151st most populous municipality in Norway with a population of 6,544. The municipality's population density is 6.9 inhabitants per square kilometre (18/sq mi) and its population has decreased by 2.8% over the previous 10-year period.
Hippopotamidae
Hippopotamidae is a family of stout, naked-skinned, and semiaquatic artiodactyl mammals, possessing three-chambered stomachs and walking on four toes on each foot. While they resemble pigs physiologically, their closest living relatives are the cetaceans. They are formally referred to as hippopotamids.

There are two living species of hippopotamid in two genera; the pygmy hippo, Choeropsis liberiensis of the forests of west Africa, and the common hippo, Hippopotamus amphibius. The term hippopotamus can also be applied to hippopotamids in general, although it is most frequently used for the common hippo and its respective genus.

Moschidae
Moschidae is a family of pecoran even-toed ungulates, containing the musk deer (Moschus) and its extinct relatives. They are characterized by long "saber teeth" instead of horns, antlers or ossicones, modest size (Moschus only reaches 37 lb (17 kg); other taxa were even smaller) and a lack of facial glands. While various Oligocene and Miocene pecorans were previously assigned to this family, recent studies find that most should be assigned to their own clades, although further research would need to confirm these traits. As a result, Micromeryx, Hispanomeryx, and Moschus are the only undisputed moschid members, making them known from at least 18 Ma. The group was abundant across Eurasia and North America during the Miocene, but afterwards declined to only the extant genus Moschus by the early Pleistocene.
Shi Hongzhao
Shi Hongzhao (Chinese: 史弘肇) (died December 24, 950), courtesy name Huayuan (化元), formally the Prince of Zheng (鄭王) (as posthumously honored during Later Zhou), was a major general of the Chinese Five Dynasties and Ten Kingdoms Period Later Han state. Shi was one of the key officials that Later Han's founding emperor Liu Zhiyuan (Emperor Gaozu) left in charge of the government during the youth of his son and successor Liu Chengyou (Emperor Yin), but Liu Chengyou eventually tired of these officials' governance and had Shi killed, along with Yang Bin and Wang Zhang.

Su Fengji
Su Fengji (Chinese: 蘇逢吉; died January 2, 951) was a chancellor of China's Later Han dynasty during the Five Dynasties and Ten Kingdoms period. He was described as cruel and greedy. He committed suicide when Emperor Yin of Later Han was killed while trying to battle the general Guo Wei's rebellion.
5 ft 6 in gauge railway
5 ft 6 in (1,676 mm), also known as the Indian gauge is a broad track gauge, used in India, Pakistan, western Bangladesh, Sri Lanka, Argentina, Chile, and on BART (San Francisco Bay Area).

In North America, it is called Indian, Provincial, Portland, or Texas gauge (or in the San Francisco Bay Area region of California, BART gauge). In Argentina and Chile, it is known as "trocha ancha" (Spanish for "broad gauge"). In the Indian subcontinent it is simply known as "broad gauge". It is the widest gauge in use of heavy-duty mainline railways in the world.

Lakshmikantapur railway station
Lakshmikantapur railway station is a Kolkata Suburban Railway Station on the Main line. It is under the jurisdiction of the Sealdah railway division in the Eastern Railway zone of the Indian Railways. Lakshmikantapur railway station is situated beside Baruipur-Kulpi Road, Bijayganj Bazar, Lakshmikantapur, South 24 Parganas district in the Indian state of West Bengal.