hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Graded poset
In mathematics, in the branch of combinatorics, a graded poset is a partially-ordered set (poset) P equipped with a rank function ρ from P to the set N of all natural numbers. ρ must satisfy the following two properties:

The rank function is compatible with the ordering, meaning that for all x and y in the order, if x < y then ρ(x) < ρ(y), and

The rank is consistent with the covering relation of the ordering, meaning that for all x and y, if y covers x then ρ(y) = ρ(x) + 1.

The value of the rank function for an element of the poset is called its rank. Sometimes a graded poset is called a ranked poset but that phrase has other meanings; see Ranked poset. A rank or  rank level of a graded poset is the subset of all the elements of the poset that have a given rank value.

Graded posets play an important role in  combinatorics and can be visualized by means of a Hasse diagram.

Partially ordered set
In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word partial is used to indicate that not every pair of elements needs to be comparable; that is, there may be pairs for which neither element precedes the other. Partial orders thus generalize total orders, in which every pair is comparable.

Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is an ordered pair  consisting of a set  (called the ground set of ) and a partial order  on . When the meaning is clear from context and there is no ambiguity about the partial order, the set  itself is sometimes called a poset.
Pure submodule
In mathematics, especially in the field of module theory, the concept of pure submodule provides a generalization of direct summand, a type of particularly well-behaved piece of a module.  Pure modules are complementary to flat modules and generalize Prüfer's notion of pure subgroups.  While flat modules are those modules which leave short exact sequences exact after tensoring, a pure submodule defines a short exact sequence (known as a pure exact sequence) that remains exact after tensoring with any module.  Similarly a flat module is a direct limit of projective modules, and a pure exact sequence is a direct limit of split exact sequences.

Module (mathematics)
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative) ring. The concept of a module also generalizes the notion of an abelian group, since the abelian groups are exactly the modules over the ring of integers.

Like a vector space, a module is an additive abelian group, and scalar multiplication is distributive over the operations of addition between elements of the ring or module and is compatible with the ring multiplication.

Modules are very closely related to the representation theory of groups. They are also one of the central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology.
Trevor Keelor
Wing Commander Trevor Keelor, VrC, VM (8 December 1934 – 27 April 2002) was an officer of Indian Air Force who participated in the Indo-Pakistani War of 1965. He was honoured with a number of medals including the Vir Chakra and the Vayu Sena Medal. He had an elder brother, Denzil, who was also honoured for his service in the Indian Air Force. Both brothers have a Vir Chakra for the same feat of shooting down Pakistan Air Force F-86 Sabre fighters. It was the first time two brothers have received Vir Chakras for the same reason.

Vayu Sena Medal
The Vayu Sena Medal (lit. 'Air Force Medal') is a military decoration, usually awarded in peacetime for a job well done in the Indian Air Force. However, it has been granted during times of conflict for acts of gallantry in the face of enemy, though not in the same numbers as the Vir Chakra.

Posthumous awards may be made and a bar is authorized for subsequent awards of the Vayu Sena Medal.

The VM was established on 17 June 1960 by the President of India and awards have been made from 1961 onwards. Awards over the past decade or more have been classified into two categories. One is Vayu Sena Medal (Gallantry) and the other for Vayu Sena Medal (Devotion to Duty).
Sundhnúkur
Sundhnúkur (Icelandic pronunciation: [ˈsʏntˌn̥uːkʏr̥]) is a volcanic hill,  within its associated Sundhnúksgígar crater row and volcanic fissures (Sundhnúksgígaröðin [ˈsʏntˌn̥uksˌciːɣaˌrœːðɪn]) in the Svartsengi volcanic system, part of the Reykjanes Peninsula rift zone of Iceland. It is the location of the 2023–2025 Sundhnúkur eruptions.

Fissure vent
A fissure vent, also known as a volcanic fissure, eruption fissure or simply a fissure, is a linear volcanic vent through which lava erupts, usually without any explosive activity. The vent is often a few metres wide and may be many kilometres long. Fissure vents can cause large flood basalts which run first in lava channels and later in lava tubes. After some time, the eruption tends to become focused at one or more spatter cones. Volcanic cones and their craters that are aligned along a fissure form a crater row. Small fissure vents may not be easily discernible from the air, but the crater rows (see Laki) or the canyons (see Eldgjá) built up by some of them are.

The dikes that feed fissures reach the surface from depths of a few kilometers and connect them to deeper magma reservoirs, often under volcanic centers. Fissures are usually found in or along rifts and rift zones, such as Iceland and the East African Rift. Fissure vents are often part of the structure of shield volcanoes.
Frogger 2 (2008 video game)
Frogger 2 is a 2008 action video game developed by Voltex and published by Konami as a sequel to the 1981 arcade game Frogger. It was released on Xbox Live Arcade for the Xbox 360 on June 11, 2008, and is the third game to be called Frogger 2, the others being Frogger II: ThreeeDeep! (1984) and Frogger 2: Swampy's Revenge (2000).

Frogger
Frogger is a 1981 action video game developed by Konami and published by Sega for arcades. It was released in North America by Sega/Gremlin. The object of the game is to direct five frogs to their homes by dodging traffic on a busy road, then crossing a river by jumping on floating logs, turtles, and alligators.

Frogger was positively received by critics upon its release, and is considered one of the greatest video games ever made. It was followed by numerous clones and several home-only sequels in the Frogger series. By 2005, 20 million copies of its various home video game incarnations had been sold worldwide.
Temple and Cemetery of Confucius and the Kong Family Mansion in Qufu
Temple and Cemetery of Confucius and the Kong Family Mansion in Qufu, Shandong Province of China, include Temple of Confucius, Cemetery of Confucius and the Kong Family Mansion.

Since 1994, the Temple of Confucius (Chinese: 孔庙; pinyin: Kǒng Miào) has been  part of the UNESCO World Heritage Site "Temple and Cemetery of Confucius and the Kong Family Mansion in Qufu". The two other parts of the site are the nearby Kong Family Mansion (Chinese: 孔府; pinyin: Kǒng Fǔ), where the main-line descendants of Confucius lived, and the Cemetery of Confucius (Chinese: 孔林; pinyin: Kǒng Lín) a couple kilometers to the north, where Confucius and many of his descendants have been buried. Those three sites are collectively known in Qufu as San Kong (三孔), i.e. "The Three Confucian [sites]".

Cemetery of Confucius
The Cemetery of Confucius (Chinese: 孔林; pinyin: Kǒng lín; lit. 'Kong Forest [of gravestones]') is a cemetery of the Kong clan (the descendants of Confucius) in Confucius' hometown Qufu in eastern Shandong province. Confucius himself and some of his disciples are buried there, as well as many thousands of his descendants.

Since 1994, the Cemetery of Confucius has been part of the UNESCO World Heritage Site "Temple and Cemetery of Confucius and the Kong Family Mansion in Qufu". The two other components of the site are the Temple of Confucius dedicated to the memory of the statesman and philosopher and the Kong Family Mansion, where his descendants lived. The three sites are collectively known in Qufu as San Kong (三孔), i.e. "The Three Confucian [sites]".
Youth philanthropy
Youth philanthropy is the donation of time, energy or resources, including money, by children and youth towards philanthropic causes. According to one study, "youth philanthropy is, at the broadest level, youth giving of their time, talents and treasure." It is seen as an effective means in which youth develop knowledge of and participate in philanthropic projects such as volunteering, grant writing, and community service.

Youth
Youth is the time of life when one is young. The word, youth, can also mean the time between childhood and adulthood (maturity), but it can also refer to one's peak, in terms of health or the period of life known as being a young adult. Youth is also defined as "the appearance, freshness, vigor, spirit, etc., characteristic of one, who is young". Its definitions of a specific age range varies, as youth is not defined chronologically as a stage that can be tied to specific age ranges; nor can its end point be linked to specific activities, such as taking unpaid work, or having sexual relations.

Youth is an experience that may shape an individual's level of dependency, which can be marked in various ways according to different cultural perspectives. Personal experience is marked by an individual's cultural norms or traditions, while a youth's level of dependency means the extent to which they still rely on their family emotionally and economically.
Arena Livyi Bereh
Arena Livyi Bereh (Ukrainian: Арена Лівий берег) is a football stadium in Kyiv Oblast, Ukraine. It is the home stadium of FC Livyi Bereh. The football stadium was opened on October 15, 2022. The arena has a natural grass field with heating, stands for 4,700 seats and a lighting system of 1,600 lux.

The stadium is located just outside of the city of Kyiv, next to the Kyivan neighborhood Osokorky. It is part of the Zolochivska rural hromada and its Mlynovo residential neighborhood.

In the 2023/24 season, in addition to the matches of the Livyi Bereh team, the arena hosted the home games of the Ukrainian Premier League teams Metalist 1925 Kharkiv and Zorya Luhansk. In the 2024/25 season the stadium will host matches of FC Livyi Bereh and Shakhtar Donetsk.

FC Livyi Bereh Kyiv
Football Club Livyi Bereh Kyiv (Ukrainian: Футбольний клуб «Лівий берег» Київ) is a Ukrainian professional football club from Kyiv Oblast. The club is based at the Kyiv's Osokorky neighborhood located at the left-bank of Dnipro. It hosts its games in the Kyiv's suburb of Hnidyn (Zolochivska rural hromada), just outside of the city limits. In June 2021, the club was admitted to the Second League. In the 2025–26 season, the team played in the Ukrainian First League after relegation from Premier League.
Baglan railway station
Baglan railway station is a minor station in the village of Baglan in Neath Port Talbot county borough, south Wales. It is 204 miles 53 chains (329.4 km) from the zero point at London Paddington, measured via Stroud. It is a stop on the South Wales Main Line, served by Transport for Wales Swanline regional trains between Swansea and Cardiff.

It is a relatively new station, opened in 1996. The station is located at street level but passenger access is from the Seaway Parade flyover. It is close to Neath Port Talbot Hospital.

Swansea railway station
Swansea railway station serves the city of Swansea, Wales. It is sited 216 miles 7 chains (348 km) from London Paddington, via Stroud, on the National Rail network, although most services use a shorter route via Bristol Parkway. In 2023/24, it was the third-busiest station in Wales, after Cardiff Central and Newport.
Drayton, Norfolk
Drayton is a suburban village and civil parish in the English county of Norfolk. It is located in the district of Broadland, 4.3 miles (6.9 km) north-west of Norwich and 8.3 miles (13.4 km) south of Aylsham. Today, Drayton is largely dominated by the Thorpe Marriott housing estate built in the late twentieth century.

Aylsham
Aylsham is a historic market town and civil parish on the River Bure in north Norfolk, England, nearly 9 mi (14 km) north of Norwich. The town is close to Blickling, Felbrigg, Mannington and Wolterton, which are important tourist attractions.

The civil parish has an area of 4,329 acres (17.52 km2) and in the 2001 census had a population of 5,504 increasing to a population of 6,016 at the 2011 census. For the purposes of local government, the parish falls within the district of Broadland.
Firebird (Marvel Comics)
Firebird (Bonita Juarez) is a superhero character appearing in American comic books published by Marvel Comics. Created by writer Bill Mantlo and artist Sal Buscema, she first appeared in Incredible Hulk vol. 2 #265 (August 1981). At various points in her history, she has adopted the aliases of Pajaro Del Fuego, Firemaiden, and La Espirita. Firebird has associated with high-profile superheroes like Hank Pym and Hawkeye and been a member of the Rangers, the Avengers West Coast, and the Secret Avengers.

Firebird has been described by critics and commentators as one of Marvel's most notable and powerful female heroes, and a prominent Latina character.

Hawkeye (Clint Barton)
Hawkeye (Clinton Francis "Clint" Barton) is a character appearing in American comic books published by Marvel Comics. Created by writer Stan Lee and artist Don Heck, the character first appeared as a supervillain in Tales of Suspense #57 (September 1964) and later joined the Avengers as a superhero in The Avengers #16 (May 1965). He has since been a prominent member of several Avengers teams, founding the West Coast Avengers, briefly marrying and subsequently divorcing Bobbi Morse / Mockingbird, adopting the Ronin alias after his death and resurrection before mentoring Kate Bishop as his successor as Hawkeye. He was also ranked at #44 on IGN's Top 100 Comic Book Heroes list.

Jeremy Renner plays the character in the Marvel Cinematic Universe films Thor (2011), The Avengers (2012), Avengers: Age of Ultron (2015), Captain America: Civil War (2016), and Avengers: Endgame (2019), the animated series What If...? (2021), and the television miniseries Hawkeye (2021).
Same-sex marriage in Yukon
Same-sex marriage has been legal in Yukon since July 14, 2004, immediately following a ruling from the Supreme Court of Yukon. This made the territory the fourth jurisdiction in Canada, and the seventh in the world after the Netherlands, Belgium, Ontario, British Columbia, Quebec and Massachusetts, to legalise same-sex marriage. Yukon was the first of Canada's three territories to legalise same-sex marriage, and the only one to do so before the federal legalisation of same-sex marriage in July 2005 by the Parliament of Canada.

Same-sex marriage in Quebec
Same-sex marriage has been legal in Quebec since March 19, 2004, following a ruling by the Quebec Court of Appeal that the heterosexual definition of marriage violated the Canadian Charter of Rights and Freedoms. Quebec was the third Canadian province after Ontario and British Columbia and the fifth jurisdiction in the world to open marriage to same-sex couples.

Quebec has also recognised civil unions offering most of the rights and benefits of marriage since 24 June 2002.
Prolochus
Prolochus is a possible genus of tropical spiders. As of September 2018, the World Spider Catalog does not accept the genus and treats it as a synonym of Dolichognatha, a genus in the family Tetragnathidae. In 2014, it was suggested that the genus be restored, and a newly discovered species was named as Prolochus junlitjri. Prolochus is said to have four main traits that distinguishes it from Dolichognatha: the total absence of posterior median eyes, a dorsal abdomen without dorsal humps, a distinct shape of abdomen and the palpal organ of the male.

Dolichognatha junlitjri
Dolichognatha junlitjri is a species of orb-weaver spiders found in the Philippines. The species was discovered in Molawin Creek at Mount Makiling, and was described, illustrated and named by Aimee Lynn Barrion-Dupo and Alberto T. Barrion who published their discovery in 2014. They considered that the genus Prolochus, treated a synonym of Dolichognatha by sources such as the World Spider Catalog as of January 2021, should be revived. It would include Dolichognatha longiceps as Prolochus longiceps, and Prolochus junlitjri. However, a molecular phylogenetic study in 2018 did not support this, and placed the species in Dolichognatha, the placement accepted by the World Spider Catalog.
Kahl (river)
The Kahl (German pronunciation: [kaːl] ⓘ) is a river in the northern Spessart in Bavaria and Hesse, Germany. It is a right tributary of the Main and is 35.6 km (22.1 mi) long. The name Kahl comes from the Old High German word kaldaha, which means cool and clear. The Kahl rises from two sources left and right of the road at the foot of the Spessart hills, near Kleinkahl. These springs produce 50–60 litres per second. The Kahl flows into the Main in Kahl am Main near the old Kahl Nuclear Power Plant. The largest tributaries are Westerbach, Sommerkahl, Reichenbach and Geiselbach.

Main (river)
The Main (German pronunciation: [ˈmaɪn] ⓘ) is the longest tributary of the Rhine, one of the major European rivers. It rises as the White Main in the Fichtel Mountains of northeastern Bavaria and flows west through central Germany for 525 kilometres (326 mi) to meet the Rhine below Rüsselsheim, Hesse. The cities of Mainz and Wiesbaden are close to the confluence.

The largest cities on the Main are Frankfurt am Main, Offenbach am Main and Würzburg. It is the longest river lying entirely in Germany (if the Weser-Werra are considered separate).
Union Street station (BMT Fourth Avenue Line)
The Union Street station is a local station on the BMT Fourth Avenue Line of the New York City Subway. It is located at the corner of Fourth Avenue and Union Street in Brooklyn, New York City, serving the communities of Park Slope, Gowanus and Carroll Gardens. It is served by the R train at all times. The D and N trains also stop here during late nights, and some rush-hour W trains stop here in the peak direction.

The Union Street station was constructed as part of the Fourth Avenue Line, which was approved in 1905. Construction on the segment of the line that includes Union Street started on December 20, 1909, and was completed in September 1912. The station opened on June 22, 1915, as part of the initial portion of the BMT Fourth Avenue Line to 59th Street. The station's platforms were lengthened in 1926–1927, and again during a renovation in 1968–1970. The station was also renovated in 1970 and in the mid-1990s.

59th Street station (BMT Fourth Avenue Line)
The 59th Street station is an express station on the BMT Fourth Avenue Line of the New York City Subway. Located at 59th Street and Fourth Avenue in Sunset Park, Brooklyn, it is served by the N and R trains at all times. During rush hours, several W trains also serve the station.

The 59th Street station was constructed as part of the Fourth Avenue Line, which was approved in 1905. Construction on the segment of the line that includes 59th Street started on March 15, 1913, and was completed in 1915. The station opened on June 22, 1915, as the southernmost station of the initial portion of the BMT Fourth Avenue Line. The station's platforms were lengthened in 1926–1927, and again during the 1960s. Elevator access was added in late 2020, in tandem with a station renovation between 2018 and 2020 to make the station compliant with the Americans with Disabilities Act of 1990.
Pandiagonal magic cube
In recreational mathematics, a pandiagonal magic cube is a magic cube with the additional property that all broken diagonals (parallel to exactly two of the three coordinate axes) have the same sum as each other. Pandiagonal magic cubes are extensions of diagonal magic cubes (in which only the unbroken diagonals need to have the same sum as the rows of the cube) and generalize pandiagonal magic squares to three dimensions.

In a pandiagonal magic cube, all 3m planar arrays must be panmagic squares. The 6 oblique squares are always magic. Several of them may be panmagic squares.
A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main space diagonals summing correctly (no broken space diagonals have the correct sum.)

The smallest pandiagonal magic cube has order 7.

Pandiagonal magic square
A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant.

A pandiagonal magic square remains pandiagonally magic not only under rotation or reflection, but also if a row or column is moved from one side of the square to the opposite side.  As such, an  pandiagonal magic square can be regarded as having  orientations.
ARV Super2
The ARV Super2 (Air Recreational Vehicle) is a British two-seat light aircraft with strut-braced shoulder wings and tricycle landing gear.  Designed by Bruce Giddings, the Super2 was available either factory-built or as a kit. It was intended to be both a cost-effective trainer and an affordable aircraft for private owners. Later called the "Opus", it gained US FAA Light-Sport Aircraft approval in February 2008.

About 35 aircraft were produced in the 1980s before the Isle of Wight-based company went into liquidation.  Subsequently, there have been a number of attempts to  restart production, all unsuccessful, of which the most recent was by Opus Aircraft. In November 2013,  Opus Aircraft announced that its assets had been auctioned off successfully, adding: "We hope to see our plans continued and to see the all-aluminum plane flying by 2015." Since 2015, little has been heard of the ARV and no resumption of production has occurred.

Light-sport aircraft
A light-sport aircraft (LSA), or light sport aircraft, is a category of small, lightweight aircraft that are simple to fly. LSAs tend to be heavier and more sophisticated than ultralight (aka "microlight") aircraft, but LSA restrictions on weight and performance separates the category from established GA aircraft. There is no standard worldwide description of an LSA.
Ulan-Ude railway station
Ulan-Ude railway station is the primary passenger railway station for the city of Ulan-Ude in the Republic of Buryatia in Russia, and an important stop along the Trans-Siberian Railway and Trans-Mongolian Railway.

Ulan-Ude
Ulan-Ude (/ʊˈlɑːnʊˈdɛ/; Russian: Улан-Удэ, Russian pronunciation: [ʊˈlan ʊˈdɛ]; Buryat: Улаан-Үдэ, romanized: Ulaan-Üde, IPA: [ʊˌlaːɴ‿ˈʉdə]) is the capital city of Buryatia, Russia, located about 100 kilometers (62 mi) southeast of Lake Baikal on the Uda River at its confluence with the Selenga. According to the 2021 Census, 437,565 people lived in Ulan-Ude; up from 404,426 recorded in the 2010 Census, making the city the third-largest in the Russian Far East by population.
Sir Thomas Hare, 5th Baronet
Sir Thomas Hare, 5th Baronet (27 July 1930 – 25 January 1993) was an English first-class cricketer. Hare played first-class cricket for Cambridge University and the Free Foresters in 1953–54.  He succeeded his father as the 5th Baronet of the Stow Hall Baronetcy in 1976, before being succeeded by his cousin upon his death in 1993.

Hare baronets
There have been three baronetcies created for persons with the surname Hare, one in the Baronetage of England and two in the Baronetage of the United Kingdom. One creation is extant as of 2026.

Hare baronets of Stow Bardolph (1641)

Hare baronets of Stow Hall (1818)

Hare baronets of Stow Hall (1905): see Sir Thomas Leigh Hare, 1st Baronet (1859–1941)