hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Binet–Cauchy identity
In algebra, the Binet–Cauchy identity, named after Jacques Philippe Marie Binet and Augustin-Louis Cauchy, states that

for every choice of real or complex numbers (or more generally, elements of a commutative ring).
Setting ai = ci and bj = dj, it gives Lagrange's identity, which is a stronger version of the Cauchy–Schwarz inequality for the Euclidean space . The Binet-Cauchy identity is a special case of the Cauchy–Binet formula for matrix determinants.

Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the absolute value of the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is considered one of the most important and widely used inequalities in mathematics.

Inner products of vectors can describe finite sums (via finite-dimensional vector spaces), infinite series (via vectors in sequence spaces), and integrals (via vectors in Hilbert spaces). The inequality for sums was published by Augustin-Louis Cauchy (1821). The corresponding inequality for integrals was published by Viktor Bunyakovsky (1859) and Hermann Schwarz (1888). Schwarz gave the modern proof of the integral version.
2023 Tank district attack
On 15 December 2023, militant attacks were launched against the Pakistan Army and local police in Tank, Pakistan. Ansar ul-Islam claimed responsibility for the attack. The attacks occurred at a police station in Tank District, Khyber Pakhtunkhwa.

Police station
A police station is a facility operated by police or a similar law enforcement agency that serves to accommodate police officers and other law enforcement personnel. The role served by a police station varies by agency, type, and jurisdiction, but in larger agencies there may be multiple police stations that serve as regional or area sub-headquarters for personnel assigned to certain beats, administrative divisions, or police units, while in smaller agencies there may be fewer stations or even one singular police headquarters.
Gavin Royfee
Gavin Ernest Royfee (20 February 1929 – 10 July 2023) was a New Zealand cricketer who played three matches of first-class cricket for Canterbury in the 1952–53 season.

An opening batsman, Gavin Royfee scored 41 and 15 on his first-class debut against Auckland, but was unsuccessful in his next two matches. He played for 16 years for Lancaster Park-Woolston in the Christchurch competition, scoring more than 4000 runs.

Royfee attended Cathedral Grammar School in Christchurch, and later returned to the school to work as its bursar. He died at his home in the Christchurch suburb of Spreydon in July 2023, aged 94.

Canterbury cricket team
Canterbury is a first-class cricket team based in Canterbury, New Zealand. It is one of six teams that compete in senior New Zealand Cricket competitions and has been the second most successful domestic team in New Zealand history. They compete in the Plunket Shield first-class competition and The Ford Trophy one day competition as well as in the Men's Super Smash competition as the Canterbury Kings.
Hive Mind (Knocked Loose song)
"Hive Mind" is a song recorded by American hardcore punk band Knocked Loose, featuring guest vocals from American rapper Denzel Curry. It was released on February 10, 2026, through Pure Noise Records. It is a standalone single and the band's first new music since their 2024 album You Won't Go Before You're Supposed To.

Pure Noise Records
Pure Noise Records is an American punk rock record label based in Nashville, Tennessee. It was founded by Jake Round in 2009 while he was an editor at AMP; the previous fall, friends of his in the band No Bragging Rights told him they were looking for a new label, and Round expressed interest in releasing the album himself. Prior to this Round had a short stint as an intern at Fat Wreck Chords. While the label began as a home operation, and had only put out five albums by the end of 2010, by 2014 some of the label's roster were main-stage acts at Warped Tour, and others had sold nearly 50,000 copies of their albums. Overall, the label's catalog had sold over 280,000 records as of March 2014. Among the label's signings are Vanna and Hit the Lights. In March 2017, Pure Noise Records partnered with Sony Music to create a new music label called Weekday Records.
USS Lexington (1776)
USS Lexington was a 16-gun brigantine of the Continental Navy. Purchased by the navy in 1776, she was 86-foot (26 m) and served in the American Revolutionary War before being captured by the British in 1777.

Brigantine
A brigantine is a two-masted sailing vessel with a fully square-rigged foremast and at least two sails on the main mast: a square topsail and a gaff sail mainsail (behind the mast). The main mast is the second and taller of the two masts.

Older usages are looser; in addition to the rigorous definition above (attested from 1695), the Oxford English Dictionary includes two c. 1525 definitions: "a small vessel equipped both for sailing and rowing, swifter and more easily manœuvred than larger ships" and "(loosely) various kinds of foreign sailing and rowing vessels, as the galleon, galliot, etc."

Modern American definitions include vessels without any square sail(s) on the main mast.
Jacques Hébert (French politician)
Jacques Hébert (8 August 1920 – 15 February 2018) was a French politician.

Born on 8 August 1920 in Falaise, Calvados, Hébert ended his medical studies at the age of 20 to join the Free French Forces. For his military service, Hébert was named a Grand Officier of the Legion of Honour and received an Order of Liberation. He was elected mayor of Cherbourg in 1959 and stepped down in 1977. Between 1963 and 1973, Hébert represented the fifth constituency of Manche in the National Assembly. He died in Falaise, Calvados, at the age of 97 on 15 February 2018.

Manche
Manche (/mɒ̃ʃ/; French: [mɑ̃ʃ] ⓘ; Norman: Maunche) is a coastal French department in Normandy on the English Channel, which is known as La Manche, literally "the sleeve", in French. Manche is bordered by Ille-et-Vilaine and Mayenne to the south, Orne and Calvados to the east, the English Channel to the west and north and by sharing maritime borders with the Crown Dependencies of Bailiwick of Jersey and Bailiwick of Guernsey of the United Kingdom to the west. It had a population of 495,045 in 2019.
Zephyranthes chlorosolen
Zephyranthes chlorosolen, known by a number of common names including Drummond's rain‑lily, evening rain‑lily, evening star rain lily (names it shares with Zephyranthes drummondii), Brazos rain‑lily, Texas rainlily, and cebolleta, is a species of flowering plant in the family Amaryllidaceae. It is found from Kansas to Mexico, and has been introduced to southern Brazil. A geophytic perennial typically 18 to 35 cm (7 to 14 in) tall, its lone flower opens in the evening and lasts only a few days.

Storage organ
A storage organ is a part of a plant specifically modified for storage of energy 
(generally in the form of carbohydrates) or water. Storage organs often grow underground, where they are better protected from attack by herbivores. Plants that have an underground storage organ are called geophytes in the Raunkiær plant life-form classification system. Storage organs often, but not always, act as perennating organs which enable plants to survive adverse conditions (such as cold, excessive heat, lack of light or drought).
Slađa Delibašić
Slađana "Slađa" Delibašić (Serbian Cyrillic: Слађана "Слађа" Делибашић; born 7 November 1968), also known as Slađa D., is a Serbian singer and dancer. Born in Kosovska Mitrovica, she gained popularity in the 90s alongside her then-husband, Đorđe Đogani, as members of the Europop and turbo-folk act Giogani Fantastico.

Following their divorce in 2001, she pursued a solo career. Delibašić has released six solo albums to date under City Records. Some of her biggest hits include "Sedmi sprat" (2007), "Ajmo sad u provod" (2009), "5 minuta" (2010) and "Dizel Power" (2010).

Delibašić and her than-partner, Igor Matić were also the runner-ups of the first season of the reality television show Parovi (2010–2011).

She has two daughters with Đogani, named Silvija and Marinela.

Europop
Europop (also spelled Euro pop) is a style of pop music characterized by polished production, simple and highly catchy melodies, repetitive choruses, and light lyrical themes. The style consolidated itself mainly in continental Europe from the mid to late 1960s, although it exerted significant influence on British and American artists, and topped the charts throughout the 1980s and 1990s, with revivals and moderate degrees of appreciation in the 2000s. The Swedish group ABBA is widely considered the leading representative of classic Europop.
Big in Europe
Big in Europe is the 42nd album by Klaus Schulze, initially designed to be released in three volumes over three years. Only two volumes were released in 2013–14. Taking in consideration the previously released multi-disc box sets (Silver Edition, Historic Edition, Jubilee Edition, Contemporary Works I, and Contemporary Works II), it could be viewed as Schulze's one hundred and third album. This series of volumes chronicles Klaus Schulze's European tour with Lisa Gerrard in 2009.

Klaus Schulze
Klaus Schulze (4 August 1947 – 26 April 2022) was a German electronic music pioneer, composer and musician. He also used the alias Richard Wahnfried and was a member of the Krautrock bands Tangerine Dream, Ash Ra Tempel, and the Cosmic Jokers before launching a solo career consisting of more than 60 albums released across six decades.
Dortmund-Westerfilde station
Dortmund-Westerfilde is a railway station on the Welver–Sterkrade railway situated in Dortmund in western Germany. It is classified by Deutsche Bahn as a category 6 station. It is served by Rhine-Ruhr S-Bahn line S2 every 30 minutes. It offers connections to line U47 of the Dortmund Stadtbahn at 10-minute intervals on working days as well as two bus routes, 470 (Mengede – Kirchlinde – Lütgendortmund – Oespel (– 440 Barop) and 471 (Nette – Mengede – Oestrich – Bodelschwingh), both operated by Dortmunder Stadtwerke (DSW21) at 20-minute intervals on working days.

German railway station categories
The approximately 5,400 railway stations in Germany that are owned and operated by the Deutsche Bahn subsidiary DB InfraGO are divided into seven categories, denoting the service level available at the station.

This categorisation influences the amount of money railway companies need to pay to DB Station&Service for using the facilities at the stations.
Uchorowo
Uchorowo [uxɔˈrɔvɔ] is a village in the administrative district of Gmina Murowana Goślina, within Poznań County, Greater Poland Voivodeship, in west-central Poland.

Uchorowo was first mentioned in written records in 1388. It has a 19th-century manor house (last restored in 1987), and a neo-Gothic chapel dating from 1890. The village formerly had a parish church and a primary school.

About 3 km south-west of Uchorowo, past the hamlet of Szymankowo, is the Śnieżycowy Jar nature reserve, founded in 1975 and now covering 9 hectares. It is most notable for the large numbers of spring snowflakes (Leucojum vernum) which bloom in March. This is one of the few places where this flower is found in lowland Poland. It is thought to have been brought here by human intervention in the 19th century.

Leucojum vernum
Leucojum vernum, commonly called the spring snowflake, St. Agnes' flower (for the patron saint of virgins), and rarely snowbell among others, is a species of flowering plant in the family Amaryllidaceae. It is native to central and southern Europe from Belgium to Ukraine. It is considered naturalized in north-western Europe, including Great Britain and parts of Scandinavia, and in the US states of Georgia and Florida. This spring flowering bulbous herbaceous perennial is cultivated as an ornamental for a sunny position. The plant multiplies in favourable conditions to form clumps. Each plant bears a single white flower with greenish marks near the tip of the tepal, on a stem about 10–20 cm (3.9–7.9 in) tall, occasionally more.

The Latin specific epithet vernum means "relating to Spring"; its close relative, Leucojum aestivum, flowers in summer.
Unmanned surface vehicle
An unmanned surface vehicle, unmanned surface vessel or uncrewed surface vessel (USV), colloquially called a drone boat, drone ship or sea drone, is a boat or ship that operates on the surface of the water without a crew. USVs operate with various levels of autonomy, from remote control to fully autonomous surface vehicles (ASV).

Autonomous robot
An autonomous robot is a robot that acts without recourse to human control. Historic examples include space probes. Modern examples include self-driving vacuums and cars.

Industrial robot arms that work on assembly lines inside factories may also be considered autonomous robots, though their autonomy is restricted due to a highly structured environment and their inability to locomote.
205th Engineer Battalion (United States)
The 205th Engineer Battalion is an engineer battalion of the Louisiana Army National Guard. It is part of one of the 225th Engineer Brigade, one of largest engineer brigades in the United States Army National Guard. The 205th Engineer Battalion is headquartered in Bogalusa, LA in Washington Parish with the remaining companies and detachments located in St. Tammany, Tangipahoa, Ascension, and Jefferson parishes. The battalion provides command and control to plan integrate, and direct execution of three to five assigned engineer companies and one Forward Support Company (FSC) to provide mobility in support application or focused logistics.

225th Engineer Brigade (United States)
The 225th Engineer Brigade is a combat heavy engineer brigade of the Louisiana Army National Guard. It is one of the largest engineer formations in the United States Army National Guard. The 225th Engineer Brigade is headquartered at Camp Beauregard near Pineville, Louisiana in Rapides Parish. The brigade conducts missions of mobility, counter-mobility, survivability, and civil engineering support. The brigade possesses a mixture of civil and combat engineer units to accomplish these missions.
Nowendoc, New South Wales
Nowendoc is a parish and village on the Northern Tablelands, New South Wales, Australia. It is 360 km north of the state capital, Sydney, and 66 km south of Walcha in the Walcha Shire local government area. A sealed road, Thunderbolts Way, is about three hundred metres to the south of Nowendoc and provides links to the south and north.

Northern Tablelands
The Northern Tablelands, also known as the New England Tableland, is a plateau and a region of the Great Dividing Range in northern New South Wales, Australia. It includes the New England Range, the narrow highlands area of the New England region, stretching from the Moonbi Range in the south to the Queensland border in the north. The region corresponds generally to the Bureau of Meteorology forecast area for the Northern Tablelands which in this case includes Inverell although it is significantly lower in elevation.
1995 Big West Conference men's basketball tournament
The 1995 Big West Conference men's basketball tournament was held March 9–12 at the Thomas & Mack Center in Paradise, Nevada.

Long Beach State defeated Nevada 76–69 in overtime to capture their third PCAA/Big West title. The 49ers subsequently received an automatic bid to the 1995 NCAA tournament.

Paradise, Nevada
Paradise is an unincorporated town and census-designated place (CDP) in Clark County, Nevada, United States, adjacent to the city of Las Vegas. It was formed on December 8, 1950. Its population was 191,238 at the 2020 census, making it the fifth-most-populous CDP in the United States; if it were an incorporated city, it would be the fifth-largest in Nevada. As an unincorporated town, it is governed by the Clark County Commission with input from the Paradise Town Advisory Board.

Paradise contains Harry Reid International Airport; the University of Nevada, Las Vegas (UNLV); the majority of the Las Vegas Strip; and most of the tourist attractions in the Las Vegas area (excluding downtown). However, all Paradise addresses, as well as other unincorporated areas in the Las Vegas Valley, have "Las Vegas" addresses.
John Alleyne (priest)
John Alleyne was Dean of St Patrick's Cathedral, Dublin from 1466 until 1506, having previously been Precentor.

He was noted for charity: he built an almshouse on Kevin Street, near the cathedral, and left most of his money for its support. In his will he directed that his body be buried under the statue of St Patrick in the nave of the cathedral. The nave collapsed due to neglect in 1554. He was also a  Master in the Court of Chancery (Ireland).

In 1474, he clashed with the Archbishop of Dublin, John Walton, who attempted to impose his will on the Cathedral Chapter. Alleyne appealed directly to King Edward IV, and obtained his crucial support. Walton was reminded that it was illegal for any outsider to interfere in the Chapter's business.

Archbishop of Dublin
The Archbishop of Dublin (Irish: Ard-Easpag Bhaile Átha Cliath) is an archiepiscopal title which takes its name from Dublin, Ireland. Since the Reformation, there have been parallel apostolic successions to the title: one in the Catholic Church and the other in the Church of Ireland. The archbishop of each denomination also holds the title of Primate of Ireland.
Vanglaini
Vanglaini is a daily newspaper in Mizoram, northeast India, published in the Mizo language. It is registered with the Registrar of Newspapers for India (no. RNI 34227/79. : MZR/67/2012-2014). It is owned, edited, and published by K. Sapdanga. It remains the newspaper in Mizoram with the largest circulation.

Press Registrar General of India
The Press Registrar General of India (PRGI), formerly the Registrar of Newspapers for India (RNI), is a statutory body under the Ministry of Information and Broadcasting, Government of India, for the registration of newspapers and periodicals. It was established in 1956 by amending the Press and Registration of Books Act 1867. However, in 2024, the Act was repealed and replaced by the Press & Registration of Periodicals Act, 2023. PRGI is headquartered in New Delhi.
Decision-making paradox
The decision-making paradox is a phenomenon related to decision-making and the quest for determining reliable decision-making methods. It was first described by Triantaphyllou, and has been recognized in the related literature as a fundamental paradox in multi-criteria decision analysis (MCDA), multi-criteria decision making (MCDM) and decision analysis since then.

Weighted sum model
In decision theory, the weighted sum model (WSM), also called weighted linear combination (WLC) or simple additive weighting (SAW), is the best known and simplest multi-criteria decision analysis (MCDA) / multi-criteria decision making method for evaluating a number of alternatives in terms of a number of decision criteria.
FlashPix
FlashPix is a bitmapped computer graphics file format where the image is saved in more than one resolution. Its design anticipated that when an HTTP request is sent for the file by a browser plugin implementing the format, only the image compatible with the current screen resolution is returned to the browser, saving on bandwidth and download time.

Browser extension
A browser extension is a software module for customizing a web browser. Browsers typically allow users to install a variety of extensions, including user interface modifications, cookie management, ad blocking, and the custom scripting and styling of web pages.

Browser plug-ins are a different type of module and no longer supported by the major browsers. One difference is that extensions are distributed as source code, while plug-ins are executables (i.e. object code). The most popular browser, Google Chrome, has over 200,000 extensions available but stopped supporting plug-ins in 2020.
Hörl
Hörl is a German surname. Notable people with the surname include:

Arthur Hoerl (1891–1968), American screenwriter

Christoph Hoerl (born 1967), German philosopher

Christopher Hörl (born 1989), Austrian skier

Jan Hörl (born 1998), Austrian ski jumper

Josef Georg Hörl (1722–1806), Austrian lawyer and mayor of Vienna

Ottmar Hörl (born 1950), German artist and writer

Thomas Hörl (born 1981), Austrian ski jumper

Christoph Hoerl
Christoph Hoerl (born 1967) is a German philosopher and Professor of Philosophy at the University of Warwick where he is also Deputy Head of Department of Philosophy. He is known for his works on philosophy of mind and philosophy of psychology.
Canaan (CDP), Vermont
Canaan is a census-designated place comprising the main settlement in the town of Canaan, Essex County, Vermont, United States. As of the 2010 census, it had a population of 392, out of a total town population of 972.

The Canaan CDP is in the northeast part of the town of Canaan and is bordered by Leach Creek to the west, the Connecticut River to the southeast, the community of Beecher Falls, Vermont, to the east, and the Canadian province of Quebec to the north. The community of West Stewartstown, New Hampshire, is to the southeast, across the Connecticut River. Beecher Falls to the east is the northeasternmost community in Vermont.

The Canaan CDP has a total area of 1.6 square miles (4.2 km2), of which 1.6 square miles (4.1 km2) is land and 0.046 square miles (0.12 km2), or 2.87%, is water.

Canaan, Vermont
Canaan is a town in Essex County, Vermont, United States. The population was 896 at the 2020 census. Canaan contains the village of Beecher Falls, located at the confluence of the Connecticut River and Halls Stream. It is part of the Berlin, NH-VT Micropolitan Statistical Area.

Due to Québécois ancestry, 26% of Canaan residents speak French as their primary language, making the town one of New England's "Little Canadas." This is a decrease from 1982, when nearly 44% spoke French as their native language.
Hope Star
The Hope Star was a Monday through Friday daily newspaper serving Hope, Arkansas, United States. It was founded on January 18, 1929, from the merger of the Star of Hope and the Hope Daily Press newspapers. The Star of Hope was founded in 1899, while the Hope Daily Press was founded in 1927.

The newspaper's final owner, GateHouse Media (now Gannett), ended publication on September 14, 2018, along with two other area papers it owned, The Daily Siftings Herald of Arkadelphia and the Nevada County Picayune of Prescott. At the time of its closure, the Star had been publishing only two days a week, on Wednesday and Friday.

Arkadelphia, Arkansas
Arkadelphia is a city in Clark County, Arkansas, United States. As of the 2020 census, the population was 10,380. The city is the county seat of Clark County. It is situated at the foothills of the Ouachita Mountains. Two universities, Henderson State University and Ouachita Baptist University, are located here. Arkadelphia was incorporated in 1857.
Herbert Leney
Herbert Leney (8 September 1850 – 18 November 1915) was an English amateur cricketer who played in four first-class cricket matches for Kent County Cricket Club between 1871 and 1878.

Leney was born at Wateringbury near Maidstone in Kent in 1850. He made his first-class debut for Kent against WG Grace's XI in 1873 at Gravesend. He died at Smith's Hall at West Farleigh in Kent in November 1915 aged 65. His nephew, Frederick Leney, also played first-class cricket.

Wateringbury
Wateringbury is a village and civil parish near the town of Maidstone in Kent, England. The Wateringbury Stream flows into the River Medway just above Bow Bridge. It formerly powered three watermills in the village, one of which survives. The Wateringbury railway station is on the Medway Valley Line.