hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Isomorphism problem of Coxeter groups
It is an unresolved problem in the mathematical field of group theory to determine whether or not two Coxeter groups (specified by their Coxeter diagrams) are isomorphic as abstract groups.  Equivalently, the problem asks to determine, for a given Coxeter group , the possible subsets  of  that are Coxeter generating sets for  (that is, for which  is a Coxeter system).

A slight generalization of the problem can be made by asking to find to all isomorphisms from one group onto the other.
In 2022, Yuri Santos Rego and Petra Schwer introduced a new framework to deal with the problem (a finite dimensional, locally finite, ranked simplicial complex to capture isomorphisms between finite rank Coxeter systems) and asked more 
related open questions motivated by it.

Coxeter–Dynkin diagram
In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group.

A class of closely related objects is the Dynkin diagrams, which differ from Coxeter diagrams in two respects: firstly, branches labeled "4" or greater are directed, while Coxeter diagrams are undirected; secondly, Dynkin diagrams must satisfy an additional (crystallographic) restriction, namely that the only allowed branch labels are 2, 3, 4, and 6. Dynkin diagrams correspond to and are used to classify root systems and therefore semisimple Lie algebras.
Principality of Minsk
The Principality of Minsk was an appanage principality of the Principality of Polotsk and centered on the city of Minsk (today in Belarus). It existed from its founding in 1101 until it was nominally annexed by the Grand Duchy of Lithuania in 1242, and then fell under de facto annexation in 1326.

Inés García de la Puente
Inés García de la Puente is a Spanish-born American medievalist specialising in the East Slavic Middle Ages and Translation Studies. She is a research assistant professor of Russian and Comparative Literature at Boston University, and an expert in the history and culture of Kievan Rus', particularly the role of women in the ruling elite and trade routes, as well as camels in pre-Mongol Kiev.
Charge (physics)
In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian.  Charges are often denoted by ⁠⁠, and so the invariance of the charge corresponds to the vanishing commutator ⁠⁠, where  is the Hamiltonian. Thus, charges are associated with conserved quantum numbers; these are the eigenvalues of the generator . A "charge" can also refer to a point-shaped object with an electric charge and a position, such as in the method of image charges.

Quantum number
In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. 
To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantum numbers includes the principal, azimuthal, magnetic, and spin quantum numbers. To describe other systems, different quantum numbers are required. For subatomic particles, one needs to introduce new quantum numbers, such as the flavour of quarks, which have no classical correspondence.

Quantum numbers are closely related to eigenvalues of observables. When the corresponding observable commutes with the Hamiltonian of the system, the quantum number is said to be "good", and acts as a constant of motion in the quantum dynamics.
Alen Simonyan
Alen Roberti Simonyan (Armenian: Ալեն Ռոբերտի Սիմոնյան; born 5 January 1980) is an Armenian politician currently serving as the president of the National Assembly of Armenia since 2 August 2021. He served as the acting president of Armenia from 1 February 2022 to 13 March 2022, and is a former member of Yerevan City Council.

President of Armenia
The president of Armenia (Armenian: Հայաստանի Նախագահ, romanized: Hayastani Nakhagah) is the head of state and the guarantor of independence and territorial integrity of Armenia elected to a single seven-year term by the National Assembly of Armenia. Under Armenia's parliamentary system, the president is simply a figurehead and holds ceremonial duties, with most of the political power vested in the parliament and prime minister.

Vahagn Khachaturyan has been serving as president since 13 March 2022.
Claims of Vladimir Putin's incapacity and death
Speculations regarding the health of Vladimir Putin have been a regular occurrence since his rise to power as President of Russia. They include theories about severe and potentially terminal medical issues. This is largely speculation and cannot be accredited for authenticity.

Vladimir Putin's rise to power
In the early 2000s, significant political changes took place in Russia with Vladimir Putin's rise to power. He previously held key positions in security forces and government, and he became the successor to President Boris Yeltsin.

After serving as the director of the Federal Security Service and as Secretary of the Security Council in August 1999, Putin became the head of the government. On 31 December 1999, following the resignation of President Boris Yeltsin, he was appointed Acting President. He was first elected President of Russia on 26 March 2000, and then re-elected in 2004, 2012, 2018, and 2024.
Guildford City F.C.
Guildford City Football Club (formerly Guildford United and AFC Guildford) is a football club based in Guildford, Surrey, England. The club was established in 1921, folded in 1974 and was reformed in 1996. Guildford City play in the Combined Counties League Premier Division South.

FA Vase
The Football Association Challenge Vase, also known as the Isuzu FA Vase for sponsorship reasons, is an annual football competition run by and named after The Football Association (The FA), for teams playing in Steps 5 and 6 of the English National League System. Nearly 600 teams participate in this knockout competition with semi-finals played over two legs. The final is played at Wembley Stadium.

The 2025 winners were Whitstable Town, who beat AFC Whyteleafe 2–1 at Wembley Stadium.
Oklahoma Department of Agriculture, Food, and Forestry
The Oklahoma Department of Agriculture, Food, and Forestry is a department of the government of Oklahoma under the Oklahoma Secretary of Agriculture. It is responsible for providing services and expertise that promote and protect Oklahoma's food supply and natural resources while stimulating economic growth.

The Department is governed by the State Board of Agriculture. The Board consists of five members appointed by the Governor of Oklahoma, with the approval of the Oklahoma Senate. The Governor designates one of the members as President of the Board, who serves as the Commissioner of Agriculture. The Commissioner is responsible for overseeing the day-to-day operations and policies of the Department.

The current Commissioner of Agriculture is Blayne Arthur, who was appointed by Governor Kevin Stitt in 2019.

The Department was created in 1907 during the term of Governor Charles N. Haskell.

Government of Oklahoma
The government of the U.S. State of Oklahoma, established by the Oklahoma Constitution, is a republican democracy modeled after the federal government of the United States. The state government has three branches: the executive, legislative, and judicial. Through a system of separation of powers or "checks and balances," each of these branches has some authority to act on its own, some authority to regulate the other two branches, and has some of its own authority, in turn, regulated by the other branches.

The state government is based in Oklahoma City and the head of the executive branch is the Governor of Oklahoma. The legislative branch is called the Legislature and consists of the Oklahoma Senate and the Oklahoma House of Representatives. The Oklahoma Supreme Court and the Oklahoma Court of Criminal Appeals are the state's highest courts.
Sullivan's Island, South Carolina
Sullivan's Island, historically known as O'Sullivan's Island, is a town and island in Charleston County, South Carolina, United States, at the entrance to Charleston Harbor, with a population of 1,791 at the 2010 census, and 1,891 people in 2020. The town is part of the Charleston metropolitan area and is considered a very affluent suburb of Charleston.

Sabal palmetto
Sabal palmetto (/ˈseɪbəl/, SAY-bəl), also known as cabbage palm, cabbage palmetto, sabal palm, palmetto palm, blue palmetto, Carolina palmetto, common palmetto, and swamp cabbage, is one of 15 species of palmetto palm.
It is native to the Southeast United States, the Yucatán Peninsula in Mexico, and the West Indies.
Center for Art, Design and Visual Culture
The Center for Art, Design and Visual Culture (CADVC) was established in 1989 as the Fine Art Gallery at the University of Maryland, Baltimore County.  The center is the university's prime exhibition location where students, professors, staff and the public can experience visual culture along with cultural and aesthetic issues. CADVC is a non-profit organization that also publishes media related to the arts.

The center includes a traveling exhibition program that features work from prominent museums such as the Andy Warhol Museum, New Museum of Contemporary Art, and the International Center of Photography. Other programs include a publication program, a k-12 educational outreach program with Baltimore City and Baltimore County, a campus education initiative, and the UMBC Sculpture Park and Outreach Program.

CADVC also administers the Joseph Beuys Sculpture Park on the UMBC campus.

University of Maryland, Baltimore County
The University of Maryland, Baltimore County (UMBC) is a public research university in Catonsville, Maryland, United States. It had a fall 2025 enrollment of 13,530 students. In 2019, it had 61 undergraduate majors, over 92 graduate programs (38 master, 25 doctoral, and 29 graduate certificate programs) and the first university research park in Maryland. It is classified among "R1: Doctoral Universities – Very High Research Activity".

Established as a part of the University System of Maryland in 1966, the university became the first public college or university in Maryland to be inclusive of all races. UMBC has the fourth highest enrollment of the University System of Maryland, specializing in natural sciences and engineering, as well as programs in the liberal arts and social sciences.  Its athletic teams are known as the UMBC Retrievers and participate in the America East Conference.
Worms (1995 video game)
Worms is a 2D artillery tactical video game developed by Team17 and released in 1995. It is the first game in the Worms series of video games. It is a turn based game where a player controls a team of worms against other teams of worms that are controlled by a computer or human opponent. The aim is to use various weapons to kill the worms on the other teams and have the last surviving worm(s).

Strategy video game
A strategy video game is a video game genre that emphasizes strategic or tactical planning and decision-making, often involving the indirect control of multiple units and the management of limited resources, rather than the quick reflexes typical of action games.

Strategy video games are commonly divided into two main forms: turn-based strategy (TBS), in which players act in discrete turns, and real-time strategy (RTS), in which play proceeds continuously. Many also incorporate elements such as tactics, diplomacy, economics, or exploration.

Electronic strategy games developed in part from earlier non-digital board games and wargames, and scholars note that the definition of “strategy” in games is not entirely uniform across contexts.
Olympia Fields Country Club
Olympia Fields Country Club is a private golf club in the central United States, located in Olympia Fields, Illinois, a suburb of Chicago, about 25 miles (40 km) south of The Loop. It contains two eighteen-hole courses, North and South. The North Course is considered one of the top three courses in the Chicago area, and is generally ranked in the top 50 courses in the United States. The South Course is regularly ranked in the top ten in Illinois. Olympia Fields is one of the few private clubs in the U.S. with multiple courses ranked, and it is on the National Register of Historic Places.

U.S. Open (golf)
The United States Open Championship, commonly known as the U.S. Open, is the annual open national championship of golf in the United States. It is the third of the four men's major golf championships, and is on the official schedule of both the PGA Tour and the European Tour. Since 1898 the competition has been 72 holes of stroke play (4 rounds on an 18-hole course), with the winner being the player with the lowest total number of strokes. It is staged by the United States Golf Association (USGA) in mid-June, scheduled so that, if there are no weather delays, the final round is played on the third Sunday. The U.S. Open is staged at a variety of courses, set up in such a way that scoring is very difficult, with a premium placed on accurate driving. As of 2024, the U.S. Open awards a $21.5 million purse, the largest of all four major championships.
Camatta Creek
Camatta Creek, originally Arroyo Camate, in 19th century Alta California, is a tributary stream of San Juan Creek, itself a tributary of the Estrella River, in San Luis Obispo County.

Camatta Creek heads at 35°23′01″N 120°18′37″W﻿ / ﻿35.38361°N 120.31028°W﻿ / 35.38361; -120.31028 at an elevation of 2,800 feet (850 m) in the La Panza Range, trending north-northwest to its confluence with San Juan Creek, at an elevation of 1,125 feet (343 m), 4.5 miles (7.2 km) southeast of Shandon, California.

La Panza Range
The La Panza Range is a mountain range in the Central Coast of California region in San Luis Obispo County, east of the small town of Santa Margarita. It is one of the California Coast Ranges and in the Los Padres National Forest.

The range is about 30 miles (48 km) long and runs from northwest to southeast between the Santa Lucia Range on the west and the Temblor Range on the east. It rises to 4,063 feet (1,238 m) at Machesna Mountain. The range is a northern extension of the Sierra Madre Mountains, a mountain range beginning in the northern part of Santa Barbara County.

La Panza Range is renowned for its stunning natural landscapes and is home to the celebrated La Panza Ranch, a historic estate known for its thriving olive groves, which contribute to the production of exquisite olive oil. The cattle and agricultural ranch is  14,750 acres and had a listing price of $38 Million USD in 2020.
Valentine Simmes
Valentine Simmes (fl. 1585 – 1622) was an English printer of the Elizabethan and Jacobean eras. He did business in London, "on Adling Hill near Bainard's Castle at the sign of the White Swan." Simmes has a reputation as one of the better printers of his generation, and was responsible for several quartos of Shakespeare's plays. [See: Early texts of Shakespeare's works.]

Nothing is known of Simmes's early life or personal history. He was active as a printer starting in 1585.

Early texts of Shakespeare's works
The earliest texts of William Shakespeare's works were published during the 16th and 17th centuries in quarto or folio format. Folios are large, tall volumes; quartos are smaller, roughly half the size. The publications of the latter are usually abbreviated to Q1, Q2, etc., where the letter stands for "quarto" and the number for the first, second, or third edition published.
Remains of Taipei Prison Wall
25°1′58.02″N 121°31′36.59″E﻿ / ﻿25.0327833°N 121.5268306°E﻿ / 25.0327833; 121.5268306

The Remains of Taipei Prison Wall (Chinese: 臺北監獄圍牆遺蹟; pinyin: Táiběi Jiānyù Wéiqiáng Yíjī) are located in Zhongzheng District, Taipei, Taiwan, at the end of Aiguo East Road and Jinshan South Road next to the Southern Taipei operations center for Chunghwa Telecom.  About 100 meters of wall exist on both sides of the Chunghwa Telecom property.

The walls were built during Japanese rule.

Chunghwa Telecom
Chunghwa Telecom (Chinese: 中華電信; pinyin: Zhōnghuá Diànxìn; lit. 'Chinese Telecommunications'), officially Chunghwa Telecom Co., Ltd., is the largest integrated telecommunications service provider in Taiwan, providing PSTN, mobile phone, and broadband services.
Baron of Stobo
Baron of Stobo is a title of nobility in the Baronage of Scotland which takes its name from Stobo in the Scottish Borders.

The barony has played an important role in Scottish history for almost five centuries. It was closely associated with the rise and fall of Stuart power in Scotland, its granting or forfeiture being used by turns to reward or punish those loyal to the House of Stuart.

River Tweed
The River Tweed, or Tweed Water (Scottish Gaelic: Uisge Thuaidh /ɯʃgʲə huəj/) is a river 97 miles (156 km) long that flows east across the Border region in Scotland and northern England.  Tweed cloth derives its name from its association with the River Tweed. The Tweed is one of the great salmon rivers of Britain and the only river in England where an Environment Agency rod licence is not required for angling. The river generates a large income for the local borders region, attracting anglers from all around the world.
Undergraduate gowns in Scotland
Undergraduate gowns are a notable feature of academic dress for students at the ancient universities in Scotland.

The most famous form of Scottish undergraduate dress is the red or scarlet gown. The gown is typically made of a thick woollen or wool-like material and is differentiated slightly according to the university at which it is worn. These gowns are worn by students of the University of St Andrews,  Glasgow, Aberdeen, Edinburgh  and Dundee. The University of Strathclyde did not adopt the red gown, and instead students use the black supertunica, adorned with saltire blue buttons and cords.

King's College, Aberdeen
King's College in Old Aberdeen, Scotland, the full title of which is The University and King's College of Aberdeen (Collegium Regium Aberdonense), is a formerly independent university founded in 1495 and now an integral part of the University of Aberdeen. Its historic buildings are the centrepiece of the University of Aberdeen's Old Aberdeen campus, often known as the King's or King's College campus.

The focal point of the college, as well as its oldest building, is the late 15th century King's College Chapel. A number of other historic buildings remain, with others being subject to renovation and rebuilding in the 18th and 19th centuries. In the early 20th century, a great deal of expansion saw the university buildings increase around the historic college buildings. In the later 20th century, the university expanded dramatically in size, dominating Old Aberdeen and expanding out from the High Street with a number of modern buildings.
Kokozek (river)
The Kokozek (Kazakh: Көкөзек) is a river in the Aksu City Administration and Ekibastuz City Administration, Pavlodar Region, Kazakhstan. It is 90 kilometres (56 mi) long and has a catchment area of 508 square kilometres (196 sq mi).

The river is part of the Irtysh Basin. In the spring the Kokozek is used to water local livestock.

Pavlodar Region
Pavlodar Region is a region of Kazakhstan. Its population was 742,475 (2009 census results) and before that 806,983 (1999 census results). The latest official estimate (as at the start of 2022) was 756,511. Its capital is the city of Pavlodar, which had a population of 360,014 at the start of 2018. Many people, especially Ukrainians, migrated to Pavlodar during Nikita Khrushchev's Virgin Lands Campaign.

The Bayanaul National Park, a protected area of the Kazakh Uplands, is located in the Bayanaul Range, within 100 km of Ekibastuz.
Ōtaki (electorate)
Ōtaki (previously Otaki) is a New Zealand Parliamentary electorate, spanning part of the west coast of the lower North Island.  The current MP for Ōtaki is Tim Costley of the New Zealand National Party. He has held this position since the 2023 election.

Horowhenua District
Horowhenua District is a territorial authority district on the west coast of the North Island of New Zealand, administered by Horowhenua District Council. Located north of Wellington and Kāpiti, it stretches from slightly north of the town of Ōtaki in the south to just south of Himatangi in the north, and from the coast to the top of the Tararua Range. It is in the Manawatū-Whanganui local government region. The name Horowhenua is Māori for landslide.

Levin is the main town and the seat of the district council. Other towns include Foxton, Shannon and Tokomaru. The population of the district is 38,400 (June 2025).
Lucas–Lehmer–Riesel test
In mathematics, the Lucas–Lehmer–Riesel test is a primality test for numbers of the form N = k · 2n − 1 with odd k < 2n. The test was developed by Hans Riesel and it is based on the Lucas–Lehmer primality test. It is the fastest deterministic algorithm known for numbers of that form.  For numbers of the form N = k · 2n + 1 (Proth numbers), either application of Proth's theorem (a Las Vegas algorithm) or one of the deterministic proofs described in Brillhart–Lehmer–Selfridge 1975 (see Pocklington primality test) are used.

Pocklington primality test
In mathematics, the Pocklington–Lehmer primality test is a primality test devised by Henry Cabourn Pocklington and Derrick Henry Lehmer.
The test uses a partial factorization of  to prove that an integer  is prime.

It produces a primality certificate to be found with less effort than the Lucas primality test, which requires the full factorization of .
Heinenoord
Heinenoord is a village in the Dutch province of South Holland on the island Hoekse Waard. It is located about 10 km south of Rotterdam, in the municipality of Hoeksche Waard.

Heinenoord was a separate municipality until 1984, when it became part of Binnenmaas. Since 1 January 2019, it is part of the new municipality Hoeksche Waard. After 1855, the municipality also covered the village of Goidschalxoord.

The Heinenoordtunnel is a road tunnel located near Heinenoord and is named after it.

There is also a bus station near Heinenoord called the Busstation Heinenoord which serves as a public transport hub in the Hoekse Waard.

Hoeksche Waard (municipality)
Hoeksche Waard (Dutch pronunciation: [ˌɦuksə ˈʋaːrt]) is a municipality in the western Netherlands, in the province of South Holland, consisting of the eponymous Hoeksche Waard and Tiengemeten islands.

The municipality was formed on 1 January 2019 by the merger of the municipalities Binnenmaas, Cromstrijen, Korendijk, Oud-Beijerland, and Strijen.
Military Order of the Dragon
The Military Order of the Dragon was an exclusive fraternal order founded in 1900 by members of the China Relief Expedition, a U.S. military force that participated in the Boxer Rebellion in Imperial China.

Fraternal order
A fraternal order is a voluntary membership organisation structured as an order, typically featuring initiation rituals and elements derived from religious orders, chivalric traditions, guilds, or secret societies. While drawing on these historical models, fraternal orders generally serve secular purposes: functioning as social clubs, cultural organisations, and providers of mutual aid or charitable services. Many friendly societies, benefit societies, and mutual organisations are organised as fraternal orders.