hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Exterior derivative
On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The exterior derivative was first described in its current form by Élie Cartan in 1899. The resulting calculus, known as exterior calculus, allows for a natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus.

If a differential k-form is thought of as measuring the flux through an infinitesimal k-parallelotope at each point of the manifold, then its exterior derivative can be thought of as measuring the net flux through the boundary of a (k + 1)-parallelotope at each point.

Musical isomorphism
In mathematics—more specifically, in differential geometry—the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle  and the cotangent bundle  of a Riemannian or pseudo-Riemannian manifold induced by its metric tensor. There are similar isomorphisms on symplectic manifolds. These isomorphisms are global versions of the canonical isomorphism between an inner product space and its dual. The term musical refers to the use of the musical notation symbols  (flat) and  (sharp).

In the notation of Ricci calculus and mathematical physics, the idea is expressed as the raising and lowering of indices. Raising and lowering indices are a form of index manipulation in tensor expressions.

In certain specialized applications, such as on Poisson manifolds, the relationship may fail to be an isomorphism at singular points, and so, for these cases, is technically only a homomorphism.
2013 Cork Intermediate Hurling Championship
The 2013 Cork Intermediate Hurling Championship was the 104th staging of the Cork Intermediate Hurling Championship since its establishment by the Cork County Board in 1909. The draw for the opening round fixtures took place on 9 December 2012. The championship began on 1 June 2013 and ended on 3 November 2013.

On 3 November 2013, Kanturk won the championship following a 2-22 to 1-12 defeat of Éire Óg in the final at Páirc Uí Chaoimh. This was their first ever championship title.

Michel Walsh and Kevin Hallissey were the championship's joint top scorers.

1909 Cork Intermediate Hurling Championship
The 1909 Cork Intermediate Hurling Championship was the inaugural staging of the Cork Intermediate Hurling Championship since its establishment by the Cork County Board. The championship began on 1 August 1909 and ended on 31 October 1909.

On 31 October 1909, Carrigtwohill won the championship following a 3–15 to 2–00 defeat of Bandon in the final at the Cork Athletic Grounds.
La Milpa
La Milpa is an archaeological site and an ancient Maya city within the Three River region of Northwest Belize bordering Mexico and Guatemala. La Milpa is located between the sites of Rio Azul and Lamanai.  Currently, La Milpa lies within the nature preserve owned by the Programme for Belize, a non-profit organization. PfB acquired land for the preserve from the Coco-Cola Company, who purchased land in Belize in 1988 with the goals of tearing down the rainforest to create a citrus plantation, however donated the land to Conservation and Management Project in  1990 and 1992. Following Caracol and Lamanai, La Milpa is the third largest site in Belize with the Main Plaza alone covering 18,000 square meters, making it one of the largest in the entire Maya region.

Caracol
Caracol is a large ancient Maya archaeological site, located in what is now the Cayo District of Belize. It is situated approximately 40 kilometres (25 mi) south of Xunantunich, and the town of San Ignacio, and 15 km (9.3 mi) from the Macal River. It rests on the Vaca Plateau, at an elevation of 500 m (1,600 ft) above sea-level, in the foothills of the Maya Mountains. Long thought to be a tertiary center, it is now known that the site was one of the most important regional political centers of the Maya Lowlands during the Classic Period. Caracol covered approximately 200 square kilometres (77 sq mi), covering an area much larger than present-day Belize City, the largest metropolitan area in the country, and supported more than twice the modern city's population.
Salina Blue Jays
The Salina Blue Jays were a minor league baseball team based in Salina, Kansas. The Salina Blue Jays and their immediate predecessor, the Salina "Millers" played as members of the Southwestern League (1922–1926) and Western Association (1938–1941, 1946–1952), winning the 1926 league championship and two league pennants. The Salina Millers were a minor league affiliate of the Cleveland Indians in 1941 and the Blue Jays were a Philadelphia Phillies affiliate from 1946 to 1952. Salina hosted home minor league games at Oakdale Park from 1922 to 1926 and Kenwood Field from 1938 to 1952. The 1922 Salina Millers team was preceded by the 1914 Salina Coyotes of the Kansas State League.

Muskogee Reds
Muskogee Reds refers to three baseball teams based in Muskogee, Oklahoma, United States. The first team played in the Missouri Valley League in 1905. The next played in the Western Association in 1917, and the third played in the Western Association from 1937 to 1942, and from 1946 to 1950. They were affiliated with the Cincinnati Reds from 1937 to 1939, the Chicago Cubs in 1941, the Detroit Tigers in 1946 and the St. Louis Cardinals from 1947 to 1949.
Miss Colombia 2017
Miss Colombia 2017 was the 64th edition of the Miss Colombia pageant. It was held on March 20, 2017 in Cartagena, Colombia.

At the end of the event, Andrea Tovar of Chocó crowned Laura González of Cartagena D.T. and C as Miss Colombia 2017. She represented Colombia in Miss Universe 2017 and placed 1st Runner-Up.

Miss Colombia
Miss Colombia (Formally Concurso Nacional de Belleza de Colombia, English: "National Beauty Contest of Colombia") is the national beauty pageant organization in Colombia.

The current Miss Colombia is María Antonia Mosquera of Valle del Cauca, who was crowned on 17 November 2025.
Rand Grange
Rand Grange is a civil parish in the county of North Yorkshire, England.  It is a very small parish, consisting of a single farmhouse and surrounding fields and woodland, less than a mile north of the town of Bedale.  Its total area is 359 acres (145 ha), and the population was estimated at 10 in 2015.

From 1974 to 2023 it was part of the district of Hambleton, it is now administered by the unitary North Yorkshire Council.

The farmhouse is a Grade II listed building, dating from the early 19th century.

Bedale
Bedale (/ˈbiːdeɪl/ BEE-dayl), is a market town and civil parish in North Yorkshire, England. Bedale Beck is a tributary of the River Swale, which forms one of the Yorkshire Dales. The dale has a predominant agriculture sector and its related small traditional trades, although tourism is increasingly important. Northallerton is 7 miles (11 km) north-east, Middlesbrough 26 miles (42 km) north-east and York is 31 miles (50 km) south-south-east.

Historically part of the North Riding of Yorkshire, the town was listed in  Domesday Book under what became the honour of Richmond. The honour had several wapentakes and Bedale was part of Hang (named after Hang Bank in Finghall or alternatively named after Catterick) and later Hang East.
2012 Texas Tennis Open
The 2012 Texas Tennis Open was a tennis tournament played on outdoor hard courts. It was the second edition of the tournament. It was classified as one of the WTA International tournaments of the 2012 WTA Tour. It took place in Dallas, United States from 17 to 24 August 2012.

Texas Tennis Open
The Texas Tennis Open was a professional tennis tournament for women. After some contradictory statements, the Women's Tennis Association (WTA) made it a late addition to the 2011 WTA Tour. It was played at the Hilton Lakes Tennis & Sports Club in Grapevine (near Dallas), Texas in the United States. It was an International level event in August during the same week (the week before the US Open) as the New Haven Open at Yale. In 2013, the event was cancelled from the WTA calendar due to economic reasons.
Adobe eLearning Suite
Adobe eLearning Suite was a collection of applications made by Adobe Systems for learning professionals, instructional designers, training managers, content developers, and educators.

The suite allowed users to author, manage, and publish interactive instructional information including screencast demonstrations, simulations, and other interactive content.

The Adobe Flash and Dreamweaver applications included in this Suite were special versions that contained additional features to improve the workflow and integration between the applications. These versions were available only as part of the suite and can not be purchased separately.

Adobe eLearning Suite was the only way to legally get Adobe Creative Suite 6 applications (other than getting a boxed copy of Adobe Creative Suite 6) without Creative Cloud.

Adobe Flash
Adobe Flash (formerly Macromedia Flash and FutureSplash) is a mostly discontinued multimedia software platform used for production of animations, rich internet applications, desktop applications, mobile apps, mobile games, and embedded web browser video players.
Agreement on 5% NATO defence spending by 2035
At the 2025 The Hague NATO summit, member states pledged to increase defence spending to five percent of GDP in what is called The Hague Investment Plan.

The Agreement on 5% Defence Spending by 2035 was the principal outcome of the 2025 NATO Summit, held in The Hague, Netherlands, on 24–25 June 2025. Under this declaration, all 32 NATO member states except Spain, which received an exemption, committed to raising their annual defence and security-related expenditures to 5% of gross domestic product (GDP) by 2035, with progress to be reviewed in 2029.

2014 Wales NATO summit
The 2014 Wales Summit of the North Atlantic Treaty Organization (NATO) was the summit of the heads of state and heads of government of the NATO countries, held in Newport, Wales on 4 and 5 September 2014. Such summits are sporadically held and allow leaders and officials from NATO Allies to discuss current issues of mutual concern and to plan strategic activities. The 2014 summit has been described by US Navy Admiral James G. Stavridis as the most important since the fall of the Berlin Wall.
Miss Universe 1991
Miss Universe 1991, the 40th anniversary of the Miss Universe pageant, was held at the Aladdin Theatre for the Performing Arts in Las Vegas, Nevada, United States, on May 17, 1991.

At the end of the event, Lupita Jones of Mexico was crowned as Miss Universe 1991 by Mona Grudt of Norway. Seventy-three contestants competed in the pageant.

Miss Universe 1992
Miss Universe 1992 was the 41st Miss Universe pageant, held at the Queen Sirikit National Convention Center in Bangkok, Thailand, on 9 May 1992.

Michelle McLean of Namibia was crowned by Lupita Jones of Mexico at the conclusion of the event. Seventy-eight contestants competed in the pageant. This is the first and thus far, the only Namibian to have won the pageant.
Software bug
A software bug is a defect (bug) in computer software. A computer program with many or serious bugs may be described as buggy.

The effects of a software bug range from minor (such as a misspelled word in the user interface) to severe (such as frequent crashing).

In 2002, a study commissioned by the US Department of Commerce's National Institute of Standards and Technology concluded that "software bugs, or errors, are so prevalent and so detrimental that they cost the US economy an estimated $59 billion annually, or about 0.6 percent of the gross domestic product".

Since the 1950s, some computer systems have been designed to detect or auto-correct various software errors during operations.

Relational operator
In computer science, a relational operator is a  programming language construct or operator that defines syntactically a relationship between two entities. These include numerical equality (e.g., 5 = 5) and inequalities (e.g., 4 ≥ 3).

In programming languages that include a distinct boolean data type in their type system, like Pascal, Ada, Python or Java, these operators usually evaluate to true or false, depending on if the conditional relationship between the two operands holds or not.

In languages such as C, relational operators return the integers 0 or 1, where 0 stands for false and any non-zero value stands for true.

An expression created using a relational operator forms what is termed a relational expression or a condition. Relational operators can be seen as special cases of logical predicates.
Porta Westfalica
Porta Westfalica (German: [ˈpɔʁta vɛstˈfaːlɪka] ⓘ) is a town in the district of Minden-Lübbecke, in North Rhine-Westphalia, Germany.

The name "Porta Westfalica" is Latin and means "gate to Westphalia". Coming from the north, the gorge is the entry to the region of Westphalia. The name was coined by scholars of the 19th century.

Minden-Lübbecke
52°23′57″N 8°43′04″E﻿ / ﻿52.39917°N 8.71778°E﻿ / 52.39917; 8.71778

Minden-Lübbecke is a Kreis (district) in the northeastern part of North Rhine-Westphalia, Germany. Neighboring districts are Diepholz, Nienburg, Schaumburg, Lippe, Herford, Osnabrück.
Bea (Dennis the Menace)
Beatrice "Bea" Menace is a fictional character from the British comic magazine The Beano. She was born in issue 2931 (introduced by David Parkins) and is the baby sister of Dennis the Menace. She appears frequently in her brother's comic strip, but would receive comic strips of her own to star in, including a crossover comic strip with Ivy the Terrible.

She is very flatulent and often farts. She uses her farts as a way of menacing.

Dennis the Menace and Gnasher (2009 TV series)
Dennis the Menace and Gnasher (originally known as Dennis and Gnasher in its first series) is an animated television series which was aired on CBBC. Based on the original comic strips from The Beano, it features the adventures of the rebellious schoolboy Dennis the Menace and his dog Gnasher. and commenced on 7 September 2009 and ended on 26 February 2010 after 52 episodes. A second series was started on 8 July 2013 on the CBBC Channel. It was preceded by Dennis and Gnasher which aired between 1996 and 1998.
2008 Chicago Bears season
The 2008 season was the Chicago Bears' 89th season in the National Football League (NFL), and the fifth under head coach Lovie Smith. They finished the 2008 season with a 9–7 record, improving upon their 7–9 record from the 2007 season. The Bears failed to qualify for the playoffs for the second consecutive season.

Lovie Smith
Lovie Lee Smith (born May 8, 1958) is an American professional football coach. He has served as the head coach of the Chicago Bears, Tampa Bay Buccaneers, and Houston Texans of the National Football League (NFL) and the Illinois Fighting Illini. Smith has been to the Super Bowl twice, as the defensive coordinator for the St. Louis Rams in 2001 and head coach for the Bears in 2006.
Run-O-Waters
Run-O-Waters is a locality in the Goulburn Mulwaree Council, New South Wales, Australia. It is a rural residential area located on the western outskirts of Goulburn, generally to the north of the Hume Highway and Run-O-Waters creek. At the 2016 census, it had a population of 471.

Goulburn
Goulburn (/ɡoʊlbərn/ GOHL-bərn) is a regional city in the Southern Tablelands of New South Wales, Australia, approximately 195 kilometres (121 mi) south-west of Sydney and 90 kilometres (56 mi) north-east of Canberra. It was proclaimed as Australia's first inland city through letters patent by Queen Victoria in 1863. Goulburn had a population of 24,565 as of the 2021 census. Goulburn is the seat of Goulburn Mulwaree Council.

Goulburn is a railhead on the Main Southern line, and regional health & government services centre, supporting the surrounding pastoral industry as well as being a stopover for travellers on the Hume Highway. It has a central historic park and many historic and listed buildings. It is also home to the monument the Big Merino, a sculpture that is the world's largest concrete sheep.
History of Poznań
Poznań, today Poland's fifth largest city, is also one of the country's oldest cities, and was an important political and religious center in the early Polish state of the 10th century. Poznań Cathedral is the oldest church in the country, containing the tombs of the first Polish rulers, Duke Mieszko I and King Bolesław I Chrobry.

Although the centre of national political power moved to Kraków in the 11th century, and later to Warsaw, Poznań remained an important regional center, being the chief city of the Greater Poland (Wielkopolska) region. It came under Prussian (later German) rule for most of the period from 1793 to 1918, during which it expanded significantly, and was also heavily fortified. The city resumed its role as a Polish voivodeship capital in the Second Polish Republic, and later, following the 1939–1945 Nazi German occupation, in the communist Polish People's Republic. Since 1999 Poznań has been the capital of Greater Poland Voivodeship.

Poznań International Fair
The Poznań International Fair (PIF, Polish: Międzynarodowe Targi Poznańskie, MTP) is the biggest industrial fair in Poland. It is held on the Poznań fairground in Poland. Poznań International Fair is located in the centre of the city opposite the main railway station – Poznań Główny, in the centre of Poland and in the centre of Europe.

Typically, there are about 13,200 exhibitors including about 3,000 foreign companies from 70 countries of the world participating in 80 trade fair events organized on the grounds of the Poznań fair.

The Poznań-based fair owns the largest exhibition and conference infrastructure in Poland, including 16 high standard air-conditioned halls with a large exhibition area (over 110,000 square metres (1,200,000 sq ft) in exhibition halls and almost 35,000 square metres (380,000 sq ft) on open grounds) and 81 modern conference rooms.
Hatia–Rourkela line
The Hatia–Rourkela line is an Indian railway line connecting Hatia on the Netaji S.C.Bose Gomoh–Hatia line in Jharkhand with Rourkela on the Tatanagar–Bilaspur section in Odisha. This 165-kilometre (103 mi) track is under the jurisdiction of South Eastern Railway.

Rourkela Junction railway station
Rourkela Junction railway station (station code:- ROU) is a railway junction located in the north-western part of the Indian state of Odisha and serves Rourkela in Sundergarh district. Rourkela is the third-largest urban agglomeration in Odisha.
Joscelin II, Count of Edessa
Joscelin II, sometimes known as Joscelin the Younger (1113–1159) was the fourth and last ruling count of Edessa.  He was son of his predecessor, Joscelin I, and Beatrice, daughter of Constantine I of Armenia. Under his reign the county was absorbed by the Zengids.

Leo I, Prince of Armenia
Leo I (Armenian: Լևոն Ա), also Levon I or Leon I, (unknown – Constantinople, February 14, 1140) was the fifth lord of Armenian Cilicia (1129/1130–1137).

He expanded his rule over the Cilician plains and even to the Mediterranean shores. In his time, relations between the Armenians and the Franks (the Crusaders), two former allies, were not always as courteous as before: a major cause of dissension between them was the ownership of the strongholds of the southern Amanus, and on the neighboring coasts of the Gulf of Alexandretta.

Leo was captured after being invited to a meeting by the Byzantine Emperor John II Comnenus, who had sworn a false promise of peace.
4,4'-Dinitro-3,3'-diazenofuroxan
4,4’-Dinitro-3,3’-diazenofuroxan (DDF) is a powerful experimental high explosive, with performance comparable to that of other high-density high-explosives such as octanitrocubane and TKX-50. It is synthesised by oxidative coupling of 4-amino-3-(azidocarbonyl)furoxan followed by Curtius rearrangement and further oxidation.

TKX-50
TKX-50 is the chemical compound with the formula C2H8N10O4; it is a hydroxylammonium salt of 5,5′-bistetrazolyl-1,1′-diolate that forms colorless crystals, and it is a high-performing explosive with performance superior to RDX and HMX while being safer with regard to mechanical stimuli.  It is also considered an environmentally-friendly replacement for several conventional explosives.  As of 2014, the US Army was preparing it in 20 kg batches in order to evaluate it as an explosive.  It was invented by Niko Fischer, Dennis Fischer, Davin G. Piercey, Thomas M. Klapötke and Jörg Stierstorfer in the research group of Thomas M. Klapötke at LMU Munich. Its development was funded by LMU Munich, the U.S. Army Research Laboratory (ARL), the Armament Research, Development and Engineering Center (ARDEC), the Strategic Environmental Research and Development Program (SERDP) and the Office of Naval Research (ONR).
Tang Jiaxuan
Tang Jiaxuan (Chinese: 唐家璇; pinyin: Táng Jiāxuán; born January 17, 1938) is a Chinese diplomat and politician who was foreign minister of the People's Republic of China from 1998–2003.

After various diplomatic postings in Japan, he became Assistant to the Minister of Foreign Affairs in 1991, Vice Minister of Foreign Affairs in 1993 and Minister of Foreign Affairs from 1998 to 2003. He continued to serve on the State Council until 2008.

Minister of Foreign Affairs (China)
The minister of foreign affairs of the People's Republic of China is the head of the Ministry of Foreign Affairs of the People's Republic of China and one of the country's top and most important State Council posts. Officially, the minister is nominated by the premier of the State Council, who is then approved by the National People's Congress or its Standing Committee and appointed by the president.

The minister usually is also a member of the Central Committee of the Chinese Communist Party and a state councillor. The Minister is the second-highest ranking diplomat in China after the director of the Office of the Central Foreign Affairs Commission. The current minister is Wang Yi, who concurrently serves as the director of the Office of the Central Foreign Affairs Commission.
Architecture of Fez
The architecture of Fez, Morocco, reflects the wider trends of Moroccan architecture dating from the city's foundation in the late 8th century and up to modern times. The old city (medina) of Fes, consisting of Fes el-Bali and Fes el-Jdid, is notable for being an exceptionally well-preserved medieval North African city and is classified as a UNESCO World Heritage Site. A large number of historic monuments from different periods still exist in it today, including mosques, madrasas, synagogues, hammams (bathhouses), souqs (markets), funduqs (caravanserais), defensive walls, city gates, historic houses, and palaces.

Dar Batha
Dar Batḥa (Arabic: دار البطحاء, pronounced Bat-ḥaa), or Qasr al-Batḥa (Arabic: قصر البطحاء), is a former royal palace and present-day museum in Fez, Morocco. The palace was commissioned by the Alawi sultan Hassan I in the late 19th century and finished under his successor Abdelaziz. It was converted into a museum of historical arts and crafts in 1915 with a collection that now comprises over 6,500 objects. Since a renovation completed in 2025, it is officially known as the Al Batha Museum of Islamic Arts.

The palace is located near Bab Bou Jeloud at the western edge of Fes el-Bali, the old medina quarter of the city, and close to Fes el-Jdid, the new medina quarter. It is adjacent to the Dar el-Beida palace located to its southeast, which was originally part of the same complex.