hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Root of unity
In mathematics, a root of unity is any complex number that yields 1 when raised to some positive integer power n. Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, and the discrete Fourier transform. It is occasionally called a de Moivre number after French mathematician Abraham de Moivre.

Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity. Any algebraically closed field contains exactly n nth roots of unity, except when n is a multiple of the (positive) characteristic of the field.

Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that has a finite number of elements.  As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules.  The most common examples of finite fields are the integers mod  when  is a prime number.

The order of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number  and every positive integer  there are fields of order . All finite fields of a given order are isomorphic.

Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory.
Dongshan Liangjie
Dongshan Liangjie (807–869) (Chinese: 洞山良价; pinyin: Dòngshān Liángjiè; Wade–Giles: Tung-shan Liang-chieh; Japanese: Tōzan Ryōkai; Korean: Tongsan Lianggye; Vietnamese: Động Sơn Lương Giới) was a Chan/Zen Buddhist monk of the Tang dynasty. He founded the Caodong school (Chinese: 曹洞宗), which was transmitted to Japan in the thirteenth century (Song-Yuan era) by Dōgen and developed into the Sōtō school of Zen.

The Song of the Precious Mirror Samadhi has been attributed to him by the Chinese tradition. However, modern scholars now argue that there is no evidence for this and that this text first appears in the 12th century.

Caodong school
Caodong school (Chinese: 曹洞宗; pinyin: Cáodòng zōng; Wade–Giles: Ts'ao-tung-tsung) is a Chinese Chan Buddhist branch and one of the Five Houses of Chan.

The school emphasised sitting meditation (Ch: zuochan, Jp: zazen), and the "five ranks" teaching. During the Song dynasty, Caodong masters like Hongzhi Zhengjue developed "silent illumination" (mozhao) meditation.
Charles E. Fritch
Charles E. Fritch (January 20, 1927 – October 11, 2012) was an American author and editor of fantasy, science fiction, horror and mystery fiction. He was the editor of Mike Shayne Mystery Magazine from 1979 until 1985. His short story, "Misfortune Cookie", was adapted for an episode of the television series The Twilight Zone.

The Misfortune Cookie
"The Misfortune Cookie" is the third segment of the fourteenth episode of the first season of the television series The Twilight Zone. In this segment, a restaurant critic discovers a Chinese restaurant where the fortune cookies have fortunes which come true.
Incomplete (Sisqó song)
"Incomplete" is a song by American R&B singer Sisqó. It was released on June 13, 2000, as the third and final single from his first solo album, Unleash the Dragon (1999). Written by Def Soul artist Montell Jordan and Anthony "Shep" Crawford, and produced by Crawford, the song was Sisqó's biggest solo single and his only number-one hit in the US, topping both the Billboard Hot 100 chart and the Billboard Hot R&B/Hip-Hop Singles & Tracks chart. "Incomplete" is also Sisqó's third and most recent Hot 100 top-40 hit; within two years of its release, Sisqó would return to his role as Dru Hill's lead singer.

Shep Crawford
Shep Crawford (December 18, 1970) is a Grammy Award-winning American R&B and gospel musician, songwriter, and record producer best known for Whitney Houston's "Same Script, Different Cast", Deborah Cox's "Nobody's Supposed to Be Here", Tamia's "Stranger in My House", Sisqó's "Incomplete", Luther Vandross' "I'd Rather" and Kelly Price's "As We Lay". He is the founder and pastor of The Experience Christian Ministries in Los Angeles, California.
Uniform 6-polytope
In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes.

The complete set of convex uniform 6-polytopes has not been determined, but most can be made as Wythoff constructions from a small set of symmetry groups. These construction operations are represented by the permutations of rings of the Coxeter-Dynkin diagrams. Each combination of at least one ring on every connected group of nodes in the diagram produces a uniform 6-polytope.

The simplest uniform polypeta are regular polytopes: the 6-simplex {3,3,3,3,3}, the 6-cube (hexeract) {4,3,3,3,3}, and the 6-orthoplex (hexacross) {3,3,3,3,4}.

6-cube
In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges,  240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.

It has Schläfli symbol {4,34}, being composed of 3 5-cubes around each 4-face. It can be called a hexeract,  a portmanteau of tesseract (the 4-cube) with hex for six (dimensions) in Greek. It can also be called a regular dodeca-6-tope or dodecapeton, being a 6-dimensional polytope constructed from 12 regular facets.
Magic Maker
Magic Maker: How to Make Magic in Another World (マジック・メイカー　～異世界魔法の作り方～, Majikku Meikā: Isekai Mahō no Tsukurikata; "How to Perform Alternate World Magic") is a Japanese light novel series written by Kazuki Kaburagi and illustrated by Kururi. It began serialization online in June 2017 on the user-generated novel publishing website Shōsetsuka ni Narō. It was later acquired by Media Factory, who have published three volumes since May 2020 under their MF Books imprint. A manga adaptation with art by Tomozo Nishioka was serialized via the Manga Doa app from June 2021 to February 2023 and was collected in three tankōbon volumes by Mag Garden. An anime television series adaptation produced by Studio Deen aired from January to March 2025.

Shōsetsuka ni Narō
Shōsetsuka ni Narō (小説家になろう; lit. "Let's Become a Novelist") is a Japanese novel self-publishing website created by Yusuke Umezaki (梅崎 祐輔, Umezaki Yūsuke). It was launched on April 2, 2004. Users can upload their novels free of charge and the novels are also free to read. As of December 2022, the site hosts close to 1,000,000 novels, has over 2,300,000 registered users and it receives over 1 billion page views per month.

Over one hundred novel series uploaded to the site have been acquired by various publishers, such as Log Horizon, serialized from 2010 before being acquired by Enterbrain in 2011, and The Irregular at Magic High School, which was serialized between 2008 and 2011 before being acquired by ASCII Media Works.

Futabasha's light novel imprint Monster Bunko was established on July 30, 2014, which exclusively publishes series that originated on Shōsetsuka ni Narō.
The Little Island (book)
The Little Island is a book written by Margaret Wise Brown under the pseudonym Golden MacDonald and illustrated by Leonard Weisgard.  Released by Doubleday in 1946, it was the recipient of the Caldecott Medal for illustration in 1947. It describes the four seasons as experienced by a little island. The book is lyrically written, an example being: "Winter came/ and the snow fell softly/ like a great quiet secret in the night/ cold and still."

Margaret Wise Brown
Margaret Wise Brown (May 23, 1910 – November 13, 1952) was an American writer of children's books, including Goodnight Moon (1947) and The Runaway Bunny (1942), both illustrated by Clement Hurd. She has been called "the laureate of the nursery" for her achievements. Besides her real name, she also used the noms-de-plume Golden MacDonald for Doubleday and Company, Timothy Hay for Harper & Brothers and Juniper Sage (her collaboration with Edith Thacher Hurd) for William R. Scott, Inc.
Filip Polášek
Filip Polášek (Slovak pronunciation: [ˈfilip ˈpɔlaːʂek]; born 21 July 1985) is an inactive Slovak professional tennis player who specialises in doubles. He reached his highest doubles ranking of world No. 7 in February 2020, and has won 17 titles on the ATP Tour.
He was forced to retire in 2013 due to health issues, but returned in 2018 and began the most successful phase of his career. Polášek won his first Grand Slam title at the 2021 Australian Open alongside Ivan Dodig, and also won the 2019 Cincinnati Masters and 2021 Indian Wells Masters, with Dodig and John Peers respectively. Polášek was the first Slovak man to reach, or win a major doubles final. He also reached the semifinals at the 2019 Wimbledon Championships, 2020 Australian Open and 2021 US Open. He qualified for the ATP Finals in both 2019 and 2021. Polášek has represented Slovakia in the Davis Cup since 2008, and also competed at the 2020 Summer Olympics partnering Lukáš Klein.

2021 Australian Open – Men's doubles
Ivan Dodig and Filip Polášek defeated the defending champions Rajeev Ram and Joe Salisbury in the final, 6–3, 6–4 to win the men's doubles tennis title at the 2021 Australian Open. With the win, Dodig and Polášek claimed their first Grand Slam title as a team. The victory earned Polášek his first major title, and made him the second Slovak to win one after Daniela Hantuchová.

Mate Pavić was in contention to reclaim the ATP No. 1 doubles ranking, but he failed to do so after he and Nikola Mektić lost in the semifinals to Dodig and Polášek.
NewYork-Presbyterian Queens
NewYork-Presbyterian Queens, stylized as NewYork-Presbyterian/Queens (NYP/Q or NYP/Queens), is a not-for-profit acute care and teaching hospital affiliated with Weill Cornell Medicine in the Flushing neighborhood of Queens in New York City. Formerly operating as Booth Memorial Hospital and New York Hospital Queens (NYHQ), it is located on the northeast corner of Main Street and Booth Memorial Avenue.

The hospital was formed in 1892 as the Rescue Home for Women, becoming known as Booth Memorial Hospital in 1919. The current Queens campus opened in 1957. The NewYork–Presbyterian Healthcare System had assumed control of the Booth Memorial Hospital until 2015, when the NewYork–Presbyterian Hospital, headquartered in Manhattan, assumed control and made the Booth Memorial Hospital a Queens campus.

Main Street (Queens)
Main Street is a major north–south street in the borough of Queens in New York City, extending from Queens Boulevard in Briarwood to Northern Boulevard in Flushing. Created in the 17th century as one of Flushing's main roads, Main Street has been lengthened at various points in its existence.
Commission scolaire de la Rivière-du-Nord
The Commission scolaire de la Rivière-du-Nord (CSRDN) was a francophone school district in the Canadian province of Quebec. Its headquarters are in Saint-Jérôme.

It comprises several primary schools and high schools across municipalities in the Laurentides region. The commission is overseen by a board of elected school trustees.

Saint-Jérôme
Saint-Jérôme (French pronunciation: [sɛ̃ ʒeʁom]) (2021 population 80,213) is a suburban city located about 45 kilometres (28 mi) northwest of Montreal on the Rivière du Nord. It is part of the North Shore sector of Greater Montreal. It is a gateway to the Laurentian Mountains and its resorts via the Autoroute des Laurentides.

The town is named after Saint Jerome (ca. 347 – September 30, 420), a church father best known as the translator of the Bible from Greek and Hebrew into Latin. His translation is known as the Vulgate.
Cameron Bridge railway station
Cameron Bridge railway station serves the village of Cameron Bridge, Fife, Scotland. The station is on the Levenmouth rail link branch of the Fife Circle Line. It also serves Windygates, Buckhaven and Methil.

The present station was opened on 2 June 2024 as part of the Levenmouth rail link, a £116 million project funded by the Scottish Government. The new station is situated to the east of where the original station stood, on the other side of the main A915 road, and has two platforms.

Levenmouth rail link
The Levenmouth rail link (also called the Leven rail link) is a reopened five-mile (eight-kilometre) branch line railway in Fife, Scotland. The link connects the town of Leven and other settlements in the Levenmouth conurbation with Thornton, and joins the Fife Circle Line at Thornton North Junction. The line was promoted by Fife Council and the South East Scotland Transport Partnership (SESTRAN). The plan was approved by the Scottish Government on 8 August 2019. The line was formally opened by the First Minister of Scotland, John Swinney, on 29 May 2024. Scheduled passenger services began on 2 June 2024.
Hebron, New York
Hebron is a town in Washington County, New York, United States. It is part of the Glens Falls Metropolitan Statistical Area. The town population was 1,773 at the 2000 census. The town is named after the ancient city of Hebron, in the present-day West Bank.

Washington County, New York
Washington County is a county in the U.S. state of New York. As of the 2020 census, the population was 61,302. The county seat is Fort Edward. The county was named for U.S. President George Washington. The county is part of the Capital District region of the state.
Pontiac Solstice
The Pontiac Solstice is a convertible sports car that was produced by Pontiac from 2005 to 2010. Introduced at the 2004 North American International Auto Show, the Solstice roadster began production in Wilmington, Delaware, starting in mid-2005 for the 2006 model year. It is powered by a naturally aspirated 2.4 L I4 engine, producing 177 hp (132 kW) and 166 lb⋅ft (225 N⋅m) of torque.

The exterior styling of the production Solstice is similar to that of the 2002 Solstice concept that preceded it. Production of the Solstice was to be running before summer 2005, but delays at the Wilmington plant pushed volume production to the fourth quarter.  The new hardtop targa top 2009 model was announced in mid-2008.  The Solstice uses the GM Kappa platform, which also underpins the Saturn Sky, Opel GT, and Daewoo G2X. It was the brand's first two-seater since the Pontiac Fiero was discontinued in 1988.

North American International Auto Show
The Detroit Auto Show, formerly known as the North American International Auto Show (NAIAS), is an annual auto show held in Detroit, Michigan. Hosted at Huntington Place (formerly Cobo Center) since 1965, it is among the largest auto shows in North America, and is widely regarded as one of the automotive industry's most important events.

The show is organized by the Detroit Auto Dealers Association (DADA), and has been held annually in January for much of its recent history. It is usually open to the general public for 1–2 weeks, preceded by previews for industry employees and media, and a black-tie "charity preview" fundraiser for local children's charities.
Run Away (SunStroke Project and Olia Tira song)
"Run Away" is a song recorded by Moldovan group SunStroke Project along with Olia Tira with music composed by Anton Ragoza and Sergey Stepanov and English lyrics written by Alina Galetskaya. It represented Moldova in the Eurovision Song Contest 2010, held in Oslo.

Moldova in the Eurovision Song Contest
Moldova has participated in the Eurovision Song Contest 19 times, debuting in 2005, missing only the 2025 contest so far. The Moldovan broadcaster responsible for the country's participation is Teleradio-Moldova (TRM). The country's best result is a third-place finish with "Hey Mamma" by SunStroke Project in 2017.

Moldova's debut at the 2005 contest was successful, with "Boonika bate doba" by Zdob și Zdub finishing sixth. The country also reached the top ten with "Fight" by Natalia Barbu (2007), "My Lucky Day" by DoReDoS (2018), and "Trenulețul" by Zdob și Zdub and Advahov Brothers (2022). Moldova has made it to the final twelve times, failing to qualify from the semi-finals in 2008, 2014, 2015, 2016, 2019, and 2024. Although initially confirming participation in the 2025 contest, TRM later withdrew, citing economic and artistic challenges. The country is set to return to Eurovision in 2026.
BE-4
The BE-4 (Blue Engine 4) is a liquid rocket engine developed by Blue Origin. It uses liquefied methane fuel and operates on an oxygen-rich staged combustion cycle. The BE-4 produces 2,400 kN (550,000 lbf) of thrust at sea level.

Development of the BE-4 was funded through a combination of private investments and public contracts.

Although initially intended solely for use on Blue Origin's proprietary launch vehicle, the New Glenn, the engine was also selected in 2014 by United Launch Alliance (ULA) for its Vulcan Centaur rocket, which replaces the Atlas V and Delta IV. ULA finalized the BE-4 as its choice in September 2018.

The BE-4 made its first flight aboard the Vulcan Centaur rocket on January 8, 2024. It was later launched on New Glenn for the first time on January 16, 2025.

Liquid-propellant rocket
Liquid rocket fuel.

Oxidizer.

Pumps carry the fuel and oxidizer.

The combustion chamber mixes and burns the two liquids.

Combustion product gasses enter the nozzle through a throat.

Exhaust exits the rocket.

A liquid-propellant rocket or liquid rocket uses a rocket engine burning liquid propellants. (Alternate approaches use gaseous or solid propellants.) Liquids are desirable propellants because they have reasonably high density and their combustion products have high specific impulse (Isp). This allows the volume of the propellant tanks to be relatively low.
Baron Hastings
Baron Hastings is a title that has been created three times. The first creation was in the Peerage of England in 1290, and is extant. The second creation was in the Peerage of England in 1299, and became extinct on the death of the first holder in c. 1314. The third creation was in the Peerage of England in 1461, and has been in abeyance since 1960.

Laurence Hastings, 1st Earl of Pembroke
Laurence de Hastings, 1st Earl of Pembroke (20 March 1319 – 20 August 1348) was an English nobleman and held the titles 1st Earl of Pembroke (4th creation), Baron Abergavenny and Baron Hastings under Edward II of England and Edward III of England.
New English Bible
The New English Bible (NEB) is an English translation of the Bible. The New Testament was published in 1961 and the Old Testament (with the Apocrypha) was published on 16 March 1970. In 1989, it was significantly revised and republished as the Revised English Bible.

Revised English Bible
The Revised English Bible (REB) is a 1989 English-language translation of the Bible that updates the New English Bible (NEB) of 1970. As with its predecessor, it is published by the publishing houses of both the universities of Oxford and Cambridge. It is not to be confused with the Revised Version of 1877, which was an annotated and slightly emended King James Bible.
Jani Liimatainen
Jani Allan Kristian Liimatainen (born 9 September 1980) is a Finnish guitarist. He came to prominence as the guitarist for the power metal band Sonata Arctica between 1996 and 2007, and has since played in and founded bands such as Cain's Offering, The Dark Element and Insomnium. Liimatainen's playing style is well known for his meticulous and fast soloing and riffs.

Insomnium
Insomnium is a Finnish melodic death metal band formed in Joensuu in 1997. The sound and lyrical themes of their music portray darkness, sorrow, loss, pain, and nature. Their music includes elements of progressive metal and doom metal.
Michigan "swamp gas" UFO reports
The Michigan "swamp gas" UFO reports were two mass sightings of unidentified flying objects during the nights of March 20 and 21, 1966, in Michigan, United States. The first occurred around marshland near Dexter, while the second mass-sighting took place near the campus arboretum of Hillsdale College, about 50 miles away. The sightings took place amid a wave (or 'flap') of UFO reports throughout southern Michigan. After the reports were attributed to swamp gas by Air Force civilian investigator J. Allen Hynek, the explanation was widely derided. US congressman Gerald Ford called for a formal Congressional investigation into the sightings.

Marsh gas
Marsh gas, also known as swamp gas or bog gas, is a mixture primarily of methane and smaller amounts of hydrogen sulfide, carbon dioxide, and trace phosphine that is produced naturally within some geographical marshes, swamps, and bogs.

The surface of marshes, swamps, and bogs is initially porous vegetation that rots to form a crust that prevents oxygen from reaching the organic material trapped below. That is the condition that allows anaerobic digestion and fermentation of any plant or animal matter, which then produces methane.

The trapped methane can escape through any of three main pathways: by the diffusion of methane molecules across an air–water interface, by bubbling out of water in a process known as ebullition, or through plant-mediated transport.
Jeffery Austin
Jeffery Austin McClelland, Jr. (born April 15, 1991), better known by his stage name Jeffery Austin, is an American pop musician and was a contestant on the ninth season of The Voice, turning a single chair and defaulting to be a member of Gwen Stefani's team. He eventually finished in fourth place, behind Jordan Smith, Emily Ann Roberts, and Barrett Baber. His compilation album, The Voice: The Complete Season 9 Collection, placed on the Billboard magazine charts.

The Voice (American TV series) season 9
The ninth season of the American reality talent show The Voice premiered on September 21, 2015 on NBC. Adam Levine, Blake Shelton, and Pharrell Williams returned as coaches for the season. Gwen Stefani returned after a one-season absence. Carson Daly continued as host.

The season introduced a "Coach Comeback" where each coach bring back one artist from the Battle or Knockout rounds to perform again in the Live Playoffs, and single elimination rounds during the Live Shows (except for the Semifinals).

Jordan Smith was named the winner of the season, marking Adam Levine's third win as a coach.
Maloi
Mary Loi Yves Ricalde (born May 27, 2002), known professionally as Maloi (English: /məˈlɔɪ/ ⓘ, Tagalog pronunciation: [maˈlo.i]), is a Filipino singer, performer, and actress under Star Music. She is one of the main vocalists of the Filipino girl group Bini. In October 2023, Maloi appeared in the music video for "RomCom" by Rob Deniel. In February 2024, she became a regular judge for It's Showtime's Tawag ng Tanghalan Kids (transl. Call of the Stage Kids). She also starred in the music video for "Dilaw" (transl. Yellow) by Maki in May. In May 2025, she won Female TikTok Face of the Year at the 6th VP Choice Awards.

Since 2024, various publications — including Vogue Philippines, Billboard Philippines, and Rappler — have recognized a distinct fashion and lifestyle aesthetic associated with Maloi, called "Maloi-core". This encompasses style trends such as wearing red "Bayonetta glasses".

Maki (singer)
Ralph William Datoon (born November 27, 1999), professionally known as Maki, is a Filipino singer and songwriter from Quezon City. He first gained attention with his viral songs "Saan?" and "Bakit?" from his debut EP, Tanong, released on September 22, 2023, both of which saw significant success on Spotify.

In 2024, Maki reached mainstream popularity with his single "Dilaw", which charted on the global Spotify chart, making it the third Filipino song to do so. The song also became the first number-one track on Billboard Philippines' relaunched Philippines Hot 100 chart. He is signed to Tarsier Records.