hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Hilbert–Burch theorem
In mathematics, the Hilbert–Burch theorem describes the structure of some free resolutions of a quotient of a local or graded ring in the case that the quotient has projective dimension 2. Hilbert (1890) proved a version of this theorem for polynomial rings, and Burch (1968, p. 944) proved a more general version. Several other authors later rediscovered and published variations of this theorem. Eisenbud (1995, theorem 20.15) gives a statement and proof.

David Hilbert
David Hilbert  (/ˈhɪlbərt/; German: [ˈdaːvɪt ˈhɪlbɐt]; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time.

Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). He adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set a course for mathematical research of the 20th century.

Hilbert and his students contributed to establishing rigor and developed important tools used in modern mathematical physics. He was a co-founder of proof theory and mathematical logic.
Drive shaft
A drive shaft, driveshaft, driving shaft, tailshaft (Australian English), propeller shaft (prop shaft), or Cardan shaft (after Girolamo Cardano) is a component for transmitting mechanical power, torque, and rotation, usually used to connect other components of a drivetrain that cannot be connected directly because of distance or the need to allow for relative movement between them.

As torque carriers, drive shafts are subject to torsion and shear stress, equivalent to the difference between the input torque and the load. They must therefore be strong enough to bear the stress, while avoiding too much additional weight as that would in turn increase their inertia.

To allow for variations in the alignment and distance between the driving and driven components, drive shafts frequently incorporate one or more universal joints, jaw couplings, or rag joints, and sometimes a splined joint or prismatic joint.

Universal joint
A universal joint (also called a universal coupling or U-joint) is a joint or coupling connecting rigid shafts whose axes are inclined to each other. It is commonly used in shafts that transmit rotary motion. It consists of a pair of hinges located close together, oriented at 90° to each other, connected by a cross shaft. The universal joint is not a constant-velocity joint.

U-joints are also sometimes called by various eponymous names, as follows:

Cardan joint, after Gerolamo Cardano, a polymath of the 16th century who contributed to knowledge of various clever mechanisms, including gimbals

Hooke joint or Hooke's joint, after Robert Hooke, a polymath of the 17th century who contributed to knowledge of various clever mechanisms

Spicer joint, after Clarence W. Spicer and the Spicer Manufacturing Company, who manufactured U joints

Hardy Spicer joint, after the Hardy Spicer brand, a successor to the Spicer brand
Emmanuel Armand de Vignerot du Plessis, Duke of Aiguillon
Emmanuel Armand de Vignerot du Plessis de Richelieu, Duke of Aiguillon (French pronunciation: [emanɥɛl aʁmɑ̃ də viɲʁo dy plɛsi]; 31 July 1720 – 1 September 1788) was a French Royal Army officer and politician. A nephew of Armand de Vignerot du Plessis, until his father's death in 1750 he was known as the Duke of Agénois. He led a regiment in Italy during the War of the Austrian Succession and was seriously wounded at the siege of Château-Dauphin (1744). He was appointed commandant of Brittany in 1753 and defended it against British landing force at Saint-Cast (1758) in the Seven Years' War. He later served as the Secretary of State for Foreign Affairs and briefly as Secretary of State for War under King Louis XV.

Louis François Armand de Vignerot du Plessis, 3rd Duke of Richelieu
Louis François Armand de Vignerot du Plessis, 3rd Duke of Richelieu (French: [lwi fʁɑ̃swa aʁmɑ̃ də viɲʁo dy plɛsi]; 13 March 1696 – 8 August 1788), was a French soldier, diplomat and statesman. He joined the army and participated in three major wars. He eventually rose to the rank of Marshal of France.

He was the son of Armand Jean de Vignerot du Plessis, duc de Richelieu, who in turn was a great-nephew of Cardinal Richelieu, the prominent French statesman who had dominated France in the early 17th century.
Middle Wallop Flying Station
Middle Wallop Flying Station is a British Army airfield located near the Hampshire village of Middle Wallop. It is the Headquarters for the Army Air Corps, and the 1st Aviation Brigade Combat Team, and is also used for Army Air Corps training. The base hosts 2 (Training) Regiment AAC and 7 (Training) Regiment AAC under the umbrella of the Army Aviation Centre. 2 Regiment performs ground training; 7 Regiment trains aircrew on AAC aircraft after they complete basic training at RAF Shawbury.

The base is notable for having previously served as both a Royal Navy (as HMS Flycatcher) and a Royal Air Force (as RAF Middle Wallop) controlled airfield, as well as an Army one initially as Middle Wallop Airfield.

2 (Training) Regiment Army Air Corps
2 (Training) Regiment Army Air Corps is a regiment of the British Army's Army Air Corps. It is responsible for all of the Army Air Corps' groundcrew Phase 2 and 3 training, as well as the Ground Support Commanders Course for officers.
Perrine Regio
Perrine Regio is a large, dark  surface feature on Jupiter's moon Ganymede. It is an irregularly-shaped feature composed of several dark, older areas that are frequently dissected or interrupted by lighter, younger features.

Nicholson Regio
Nicholson  Regio is a large, dark, surface feature on Jupiter's moon Ganymede. It is a roughly-oval feature composed of several dark, ancient areas that are dissected or interrupted by younger sulci. According to current geological studies, Nicholson Regio contains the oldest surface of Ganymede.
Campagna Motors
Campagna Motors is a Canadian motorcycle manufacturer. It was founded in 1988 in the Province of Quebec, Canada. It developed its first T-Rex prototype in 1994. Campagna's founder Daniel Campagna devoted more than eight years to creating T-Rex, handcrafting the first vehicles.

Campagna is the Italian word for "countryside".

On 20 January 2019 Campagna Motors briefly closed due to bankruptcy. On 28 February 2019, Campagna Motors announced new investors and stated that it would restart production and sales.

Campagna T-Rex
The Campagna T-Rex is a two-seat, three-wheeled motor vehicle created by Campagna Motors, located in Quebec, Canada. It is powered by an in-line 4-cylinder engine from Kawasaki. Although it used to be registered as a motorcycle, it is now largely considered a "three-wheeler". However, in some states, like Arizona, it can still be registered as a motorcycle, but not require a motorcycle endorsement. The interior can accommodate the driver and a single passenger seated side-by-side, with adjustable seat backs, a foot-pedal box, and retractable three-point seat belts. The T-Rex uses a sequential manual transmission, operated by hand with a shift lever, which is the same type of manual transmission used in motorcycles.

The T-REX has been commercially available since the early 1990s. The Campagna T-REX was designed and styled by Deutschman Design.
Horace Lindrum
Horace Lindrum (born Horace Norman William Morrell, 15 January 1912 – 20 June 1974) was an Australian professional player of snooker and English billiards. Lindrum won the 1952 World Snooker Championship defeating New Zealander Clark McConachy. The tournament is disputed, as it had only two participants, and other players boycotted the event to play in the 1952 World Professional Match-play Championship. Lindrum won the Australian Professional Billiards Championship on multiple occasions, first winning the event in 1934.

Lindrum lived in Britain for long periods and played in the major British tournaments. From his arrival in Britain in 1935, he was regarded as the second-best player in the world, behind Joe Davis. Lindrum contested three World Snooker Championship finals against Davis, in 1936, 1937 and 1946, losing all three to Davis but coming close to beating him on several occasions.

1936 World Snooker Championship
The 1936 World Snooker Championship was a snooker tournament that was held at the Burroughes and Thurston's Halls in London, England from 23 March to 2 May 1936. There were 13 entries; a significant increase from five in the previous year and just two in 1934. Defending champion Joe Davis won the Championship for the tenth consecutive time, defeating Horace Lindrum in the final 34–27. Horace Lindrum became the first Australian to compete at the World Championship and made the only century break of the tournament, a 101 in his semi-final match against Stanley Newman.
Caroline Medina
Caroline Gabriela Medina Peschiutta (born June 27, 1992 in Maracay) is a Venezuelan model and beauty pageant titleholder who won the titles of Teen Model Venezuela 2009, Miss Venezuela Earth 2010, Reina Hispanoamericana 2010 and Miss Earth - Fire 2011.

Miss Venezuela 2010
Miss Venezuela 2010 was the fifty-seventh Miss Venezuela pageant, held at the Palacio de Eventos de Venezuela in Maracaibo, Venezuela, on October 28, 2010.

Marelisa Gibson crowned Vanessa Gonçalves of Miranda as her successor at the end of the event. Gonçalves represented Venezuela at Miss Universe 2011 and placed as a top-sixteen semifinalist.
Tutug oncom
Nasi tutug oncom or sometimes simply called tutug oncom, is an Indonesian style rice dish, made of rice mixed with oncom fermented beans, originally from Tasikmalaya, West Java. It is usually wrapped in banana leaves and served with various side dishes.

Nasi tutug oncom is a Sundanese dish, quite popular in most of cities in West Java, especially Bandung and Tasikmalaya, and also in Greater Jakarta area.

Oncom
Oncom (IPA: ɔnˈtʃɔm) is a fermented food which is one of the traditional staples of the Sundanese cuisine of Indonesia. There are two kinds of oncom: red oncom and black oncom. The food is closely related to tempeh; both are fermented using mold.

Usually, oncom is made from the by-products of the production of other foods: soy pulp left over from making tofu, peanut press cake residue after the oil has been pressed out, cassava tailings after extracting the starch (aci sampeu), coconut press cake remaining after the oil has been pressed out or when coconut milk has been produced. Since oncom production uses by-products to make food, it increases the economic efficiency of food production.

Black oncom is made by using Rhizopus oligosporus while red oncom is made by using Neurospora intermedia var. oncomensis. It is the only traditional human food produced from Neurospora.

Red oncom has been found to reduce the cholesterol levels of rats.
Cape Ann League
The Cape Ann League (CAL) is a high school athletic conference in District 5 of the Massachusetts Interscholastic Athletic Association. The league is based mainly on or around Cape Ann, a small cape on the North Shore of Massachusetts.

Massachusetts Interscholastic Athletic Association
The Massachusetts Interscholastic Athletic Association (MIAA) is an organization that sponsors activities in 36 sports, between more than 380 high schools in the U.S. state of Massachusetts. The MIAA serves over 220,000 student athletes from these schools. The MIAA is a member of the National Federation of State High School Associations (NFHS), which writes the rules for most U.S. high school sports and activities. The MIAA was founded in 1978, and was preceded by both the Massachusetts Secondary School Principals Association (MSSPA) (1942–1978) and the Massachusetts Interscholastic Athletic Council (MIAC) (1950–1978).
A2216 road
The A2216 is an A road in south London, England suburbia. It runs from the A215 in Denmark Hill to the A212 in Sydenham.  Part of the road is an ancient thoroughfare, Lordship Lane.  In Dulwich, the road runs via the A205 South Circular Road.

Lordship Lane, Southwark
Lordship Lane is an ancient thoroughfare, once rural, in East Dulwich, a suburb of the London Borough of Southwark in southeast London, England, and forms part of the A2216.

It runs north–south from Goose Green to Wood Vale. The Lordship Lane and North Cross Road area now has a wide selection of bars, restaurants and specialist retailers for the 'foodie' market.
Cathedral-Basilica of Our Crowned Mother of Palmar
The Cathedral-Basilica of Our Crowned Mother of Palmar (Spanish: Catedral-Basílica de Nuestra Madre del Palmar Coronada) is a basilica church in El Palmar de Troya, Spain. The church, dedicated to the Virgin Mary under the title of Our Lady of Palmar, serves as the only cathedral and 'mother church' for the Palmarian Catholic Church, a schismatic independent Catholic denomination not in communion with Rome.

Our Lady of Palmar
Our Lady of Palmar (Spanish: Nuestra Señora del Palmar), known formally as Our Crowned Mother of Palmar (Spanish: Nuestra Madre del Palmar Coronada), is a Palmarian Christian title of the Blessed Virgin Mary associated with an alleged Marian apparition in the Spanish village of El Palmar de Troya in 1968. The apparition is strongly condemned by the authorities of the Catholic Church but is recognized by the Palmarian Christian Church. The Cathedral-Basilica of Our Crowned Mother of Palmar, the mother church of the Palmarian Christian Church, serves as the major shrine of Our Lady of Palmar and was built on the site of the alleged apparition.
Eddington (film)
Eddington is a 2025 American satirical neo-Western thriller film written and directed by Ari Aster, and starring Joaquin Phoenix, Pedro Pascal, Luke Grimes, Deirdre O'Connell, Micheal Ward, Austin Butler, and Emma Stone. Set in 2020 during the COVID-19 pandemic in New Mexico, the film examines the political and social turmoil caused by the contested mayoral election fought between Sheriff Joe Cross and Mayor Ted Garcia.

The film had its world premiere at the main competition of the 2025 Cannes Film Festival on May 16, 2025, and was released in theaters by A24 on July 18, 2025. The film received generally positive reviews from critics and has grossed $13.7 million worldwide.

Contemporary Western
Contemporary Western is a subgenre of the Western genre that includes contemporary settings and uses Old West themes, archetypes, and motifs, such as a rebellious antihero, open plains and desert landscapes, or gunfights.  This sub-genre includes the post-Western, neo-Western, and urban Western genres that include "the cowboy cult" in a modern setting that involves the audience's feelings and understanding of Western movies. A neo-Western can be said to use Western themes set in the present day.: 62  According to Stephen Teo in Eastern Westerns: Film and Genre Outside and Inside Hollywood, there is little difference between the neo-Western and post-Western, and the terms may often be used interchangeably.: 96
Wilfrid Laurier University
Wilfrid Laurier University (WLU or simply Laurier) is a public university in Ontario, Canada, with campuses in Waterloo, Brantford and Milton. It is named in honour of Sir Wilfrid Laurier, the seventh Prime Minister of Canada. A "multi-campus multi-community university", Laurier offers undergraduate and graduate programs in a variety of fields with over 17,000 full-time undergraduate students, over 1000 full-time graduate students, and nearly 4,000 part-time students as of late 2019. Laurier's varsity teams, known as the Wilfrid Laurier Golden Hawks, compete in the West Conference of the Ontario University Athletics, affiliated with U Sports.

Waterloo, Ontario
Waterloo is a city in the Canadian province of Ontario. It is one of three cities in the Regional Municipality of Waterloo (formerly Waterloo County). Waterloo is situated about 94 km (58 mi) west-southwest of Toronto, but it is not considered to be part of the Greater Toronto Area (GTA). Due to the close proximity of the city of Kitchener to Waterloo, the two together are often referred to as "Kitchener–Waterloo", "K-W", or "The Twin Cities". Nearby Cambridge, Ontario is also sometimes grouped in, creating KWC or "Tri-cities".

While several unsuccessful attempts to combine the municipalities of Kitchener and Waterloo have been made, following the 1973 establishment of the Region of Waterloo, less motivation to do so existed, and as a result, Waterloo remains an independent city. At the time of the 2021 census, the population of Waterloo was 121,436.
Country USA (Time-Life Music)
Country USA was a 23-volume series issued by Time-Life Music during the late 1980s and early 1990s, spotlighting country music of the 1950s through early 1970s.

Each volume in the series chronicled a specific year in country music, from 1950 through 1972, and was issued on a double-length compact disc or cassette, or two vinyl albums. Individual volumes contained 24 tracks, usually representing the year's most popular and important songs. Also included was a booklet, containing liner notes written by some of the most respected historians of the genre, photographs of the artists, and information on the songs (writers, performers and peak position on Billboard magazine's country charts).

All told, the entire series contains 552 tracks.

Time Life
Time Life, Inc. (also habitually represented with a hyphen as Time-Life, Inc., even by the company itself) was an American multi-media conglomerate company formerly known as a prolific production/publishing company and direct marketeer seller of books, music, video/DVD, and other multimedia products. After all home market book publication activities had been shuttered in 2003, the focus of the group shifted exclusively towards music, video, and entertainment experiences such as the StarVista cruises. Its products have once been sold worldwide throughout the Americas, Europe, Australasia, and Asia via television, print, retail, the Internet, telemarketing, and direct sales. Activities were largely restricted to the North American home market afterwards, and operations were until recently focused on the US and Canada alone with very limited retail distribution overseas, ceasing altogether in 2023.
Platform shoe
Platform shoes are shoes, boots, or sandals with a thick sole, usually in the range of 5–10 cm (2–4 in). Platform shoes may also be high heels, in which case the heel is raised significantly higher than the ball of the foot. Extreme heights, of both the sole and heel, can be found in fetish footwear such as ballet boots, where the sole may be up to 20 cm (8 in) high and the heels up to 40 cm (16 in) or more. The sole of a platform shoe can have a continuous uniform thickness, have a wedge, a separate block or a stiletto heel. Raising the ankle increases the risk of a sprained ankle.

Sandal
Sandals are an open type of footwear consisting of a sole held to the wearer's foot by straps that go over the instep and around the ankle. Sandals may also feature a heel of varying heights. While the distinction between sandals and other types of footwear can sometimes be unclear (as with huaraches—the woven leather footwear from Mexico—and peep-toe pumps), sandals are generally understood to leave most of the foot exposed.

People choose to wear sandals for several reasons, including comfort in warm weather, economic benefits (sandals typically require less material than closed shoes and are easier to manufacture), and as a fashion statement. Sandals are commonly worn in warmer climates or during warmer seasons to keep feet cool and dry. The open design reduces the risk of developing athlete's foot compared to enclosed shoes, and wearing sandals may be part of the treatment regimen for such infections.
WAGR X class
The WAGR X class is a now-withdrawn class of diesel locomotives built by Beyer, Peacock & Company and Metropolitan-Vickers, Bowesfield Works, Stockton-on-Tees for the Western Australian Government Railways (WAGR) between 1954 and 1956. Several members of the class have been preserved.

Beyer, Peacock and Company
Beyer, Peacock and Company was an English general engineering company and railway locomotive manufacturer with a factory in Openshaw, Manchester. Charles Beyer, Richard Peacock and Henry Robertson founded the company in 1854. The company closed its railway operations in the early 1960s. It retained its stock market listing until 1976, when it was bought and absorbed by National Chemical Industries of Saudi Arabia.
Benjamin McCulloch
Benjamin McCulloch (November 11, 1811 – March 7, 1862) was a senior officer of the Confederate States Army who commanded infantry in the Trans-Mississippi Theater of the American Civil War. He was killed in action in 1862 at the Battle of Pea Ridge, Arkansas.

Henry Eustace McCulloch
Henry Eustace McCulloch (December 6, 1816 – March 12, 1895) was a soldier in the Texas Revolution, a Texas Ranger, and a brigadier general in the army of the Confederate States during the American Civil War.
Cherchen Man
Cherchen Man or Chärchän Man or Ur-David is the modern name given to a mummy found in the town Cherchen, located in current Xinjiang region of China. The mummy is a member of the group known as Tarim mummies. His naturally-mummified remains were discovered in Tomb 2 at the Zaghunluq cemetery, near the town of Qiemo (Chärchän) in the Taklamakan Desert of north-west China. Other such remains have also been recovered at sites throughout the Tarim Basin, including Qäwrighul, Yanghai, Shengjindian, Shanpula (Sampul), and Qizilchoqa.

Subeshi culture
The Subeshi culture (simplified Chinese: 苏贝希文化; traditional Chinese: 蘇貝希文化; 1100–100 BCE), also rendered as Subeishi culture or Subeixi culture, is an Iron Age culture from the area of Shanshan County, Turfan, Xinjiang, at the eastern edge of the Tarim Basin. The Subeshi culture contributes some of the later period Tarim Mummies. It might be associated with the Jushi Kingdom known from Chinese historical sources. The culture includes three closely related cemeteries:

the Subeshi cemetery

the Shengjindian cemetery,

the Yanghai cemetery.

After 200 BCE, the Subeshi culture may have evolved into the later walled city-state culture of the Jushi Kingdom.
Banach space
In mathematics, more specifically in functional analysis, a Banach space (/ˈbɑː.nʌx/, Polish pronunciation: [ˈba.nax]) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space.

Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly.
Maurice René Fréchet was the first to use the term "Banach space" and Banach in turn then coined the term "Fréchet space".
Banach spaces originally grew out of the study of function spaces by Hilbert, Fréchet, and Riesz earlier in the century. Banach spaces play a central role in functional analysis. In other areas of analysis, the spaces under study are often Banach spaces.

Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M.

Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). For instance, the set of rational numbers is not complete, because e.g.  is "missing" from it, even though one can construct a Cauchy sequence of rational numbers that converges to it (see further examples below). It is always possible to "fill all the holes", leading to the completion of a given space, as explained below.