hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Kleene fixed-point theorem
In the mathematical areas of order and lattice theory, the Kleene fixed-point theorem, named after American mathematician Stephen Cole Kleene, states the following:

Kleene Fixed-Point Theorem. Suppose  is a directed-complete partial order (dcpo) with a least element, and let  be a Scott-continuous (and therefore monotone) function. Then  has a least fixed point, which is the supremum of the ascending Kleene chain of

The ascending Kleene chain of f is the chain

obtained by iterating f on the least element ⊥ of L. Expressed in a formula, the theorem states that

where  denotes the least fixed point.

Although Tarski's fixed point theorem 
does not consider how fixed points can be computed by iterating f from some seed  (also, it pertains to monotone functions on complete lattices), this result is often attributed to Alfred Tarski who proves it for additive functions. Moreover, the Kleene fixed-point theorem can be extended to monotone functions using transfinite iterations.

Least fixed point
In order theory, a branch of mathematics, the least fixed point (lfp or LFP, sometimes also smallest fixed point) of a function from a partially ordered set ("poset" for short) to itself is the fixed point which is less than each other fixed point, according to the order of the poset. A function need not have a least fixed point, but if it does, then the least fixed point is unique.
Lumding–Dibrugarh section
The Lumding–Dibrugarh section is a broad-gauge railway line connecting Lumding and Dibrugarh. The 380-kilometre (240 mi) long railway line is functional in the Indian state of Assam. It is under the jurisdiction of Northeast Frontier Railway. Dibrugarh is a newly made Junction station to connect Pasighat. The old Dibrugarh Town station is 5-kilometre (3.1 mi) away from Dibrugarh.

Northeast Frontier Railway zone
The Northeast Frontier Railway (abbreviated NFR) is one of the 19 railway zones of the Indian Railways. It is headquartered in Maligaon, Guwahati in the state of Assam, and responsible for operation and expansion of rail network all across Northeastern states and some districts of eastern Bihar and northern West Bengal.
Peter Sterling (rugby league)
Peter Maxwell John Sterling OAM (born 16 June 1960), nicknamed Sterlo, is an Australian former rugby league commentator, television personality and player.  He was one of the all-time great halfbacks and a major contributor to Parramatta Eels' dominance of the New South Wales Rugby League premiership in the 1980s. Sterling played eighteen Tests for the Australian national team between 1982 and 1988. He also played in thirteen State of Origins for New South Wales, winning man of the match on four occasions (one of them being the 1987 exhibition match played in the USA). Sterling played in four premiership-winning sides with Parramatta in 1981–1983 and 1986 and has been inducted into the Australian Rugby League Hall of Fame. His time spent playing for English club Hull F.C. also earned him membership in their hall of fame.

Rugby League Week
Rugby League Week (frequently abbreviated to RLW) was the highest selling Australian rugby league magazine, ahead of major competitor Big League. It was published weekly (on Wednesdays) during the Australian rugby league season, which runs from March to late September (roughly corresponding to the southern hemisphere autumn and winter). The magazine was headquartered in Sydney.
Ptolemy of Aloros
Ptolemy of Aloros (Ancient Greek: Πτολεμαῖος), was sent by King Amyntas III of Macedon as an envoy to Athens c. 375–373 BC. After Amyntas' death, he began a liaison with his widow, Eurydice. In 368 BC, he assassinated her son, Alexander II, in order to gain control of the throne. His actions were not well-regarded by the leading families of Macedon, who called in the Theban general, Pelopidas, to re-establish peace.  As part of the peace settlement, Philip, Alexander II's younger brother, was taken as a hostage back to Thebes.  As Alexander II's younger brother, Perdiccas III, was under-age when Alexander II was killed, Ptolemy of Aloros ruled as regent.

Ptolemy ruled as a regent for Perdiccas III until Perdiccas killed him in 365 BC.

It is suggested that Ptolemy was descended from Amyntas II's brother, Menelaus, son of Alexander I.

Amyntas III of Macedon
Amyntas III (Ancient Greek: Ἀμύντας) was king of the ancient Greek kingdom of Macedonia from 393/2 to 388/7 BC and again from 387/6 to 370 BC. He was a member of the Argead dynasty through his father Arrhidaeus, a son of Amyntas, one of the sons of Alexander I. His most famous son is Philip II, father of Alexander the Great.
Proth prime
A Proth number is a natural number N of the form  where k and n are positive integers, k is odd and . A Proth prime is a Proth number that is prime. They are named after the French mathematician François Proth. The first few Proth primes are

3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857 (OEIS: A080076).

It is still an open question whether an infinite number of Proth primes exist. It was shown in 2022 that the reciprocal sum of Proth primes converges to a real number near 0.747392479, substantially less than the value of 1.093322456 for the reciprocal sum of Proth numbers.

The primality of Proth numbers can be tested more easily than many other numbers of similar magnitude.

Sierpiński number
In number theory, a Sierpiński number is an odd natural number k such that  is composite for all natural numbers n. In 1960, Wacław Sierpiński proved that there are infinitely many odd integers k which have this property.

In other words, when k is a Sierpiński number, all members of the following set are composite:

If the form is instead , then k is a Riesel number.
Saltine cracker challenge
The saltine cracker challenge or saltine challenge is a food challenge or competition in which a person has 60 seconds in which to eat six saltine soda crackers without drinking anything.

Although the challenge may sound trivial, it is difficult because the crackers quickly exhaust the saliva in the mouth. Even though six saltines can fit in one's mouth at the same time, and a minute is plenty of time to chew, the resulting mass of crumbs is still difficult to swallow with a dry mouth.

Saltine cracker
A saltine or soda cracker is a thin, usually square, cracker, made from white flour, sometimes yeast (although many are yeast-free), fat, and baking soda, with most varieties lightly sprinkled with coarse salt. It has perforations over its surface, as well as a distinctively dry and crisp texture. It is normally paired with a variety of savory toppings, including cheese  (especially cream cheese), peanut butter, hummus, and various spreads like pimiento cheese, as well as sweet toppings like jam or honey. They are often crumbled into soups, stews, or chili.

Some familiar brand names of saltine crackers in the Americas are Christie's Premium Plus (Canada), Nabisco's Premium (U.S.), Sunshine Biscuits' Krispy (U.S.), Keebler's Zesta (U.S.) (both owned by Kellogg's), Molinos Modernos' Hatuey (Dominican Republic) and Noel's Saltín (Colombia). Unsalted tops as well as whole-grain saltines can also be found.
Robert J. Coyle
Robert Joseph Coyle (born September 23, 1964) is an American prelate of the Roman Catholic Church who has been serving as auxiliary bishop of the Diocese of Rockville Centre in New York since 2018. He previously served as an auxiliary bishop of the Archdiocese for the Military Services, USA in Washington D.C. from 2013 to 2018

Archdiocese for the Military Services, USA
The Archdiocese for the Military Services, USA (AMS), officially the Military Ordinariate of United States of America, is a Latin Church jurisdiction of the Catholic Church for people serving in the United States Armed Forces and their dependents.

The AMS provides services to Catholics serving in military installations in the United States and overseas, to Catholic staff and patients at Veterans Health Administration facilities, and to Catholics at other federal services located overseas. The AMS does not have a cathedral, nor does it have jurisdiction over any territory; its headquarters are in Washington, D.C.

The AMS is considered a military ordinariate, headed by an archbishop. As of 2025, the archbishop is Timothy P. Broglio.
Kalkaman (lake)
Kalkaman (Kazakh: Қалқаман), also known as Kalkamantuz (Kazakh: Қалқамантұз), are two salt lakes in the Aksu City Administration, Pavlodar Region, Kazakhstan.

The Kalkaman lakes are located 22 kilometers (14 mi) to the WSW of Aksu City and 33 kilometers (21 mi) to the ENE of Kalkaman village. The nearest village is Pogranichnik 5 kilometers (3.1 mi) to the NW. Yevgenyevka lies 13 kilometers (8.1 mi) to the ESE.

There is commercial extraction of salt from the lakes. Some of the salt is exported to Western Siberia.

Yevgenyevka (Pavlodar Region)
Yevgenyevka (Kazakh: Евгеньевка) is a village in the Aksu City Administration, Pavlodar Region, Kazakhstan. It is the center of the Yevgenyevka Rural District (KATO code - 551645100). Population: 1,950 (2009 census results); 1,838 (1999 census results).
Gilbert Kennedy (rower)
Gilbert Edward B Kennedy (1866–1921)  was an English rower who won the Wingfield Sculls, the amateur single sculling championship of the River Thames, in 1893.

Kennedy was born at Kingston upon Thames. He joined Kingston Rowing Club and competed in the Diamond Challenge Sculls at Henley Royal Regatta between 1890 and 1893. In 1890 and 1893 he was runner-up to Guy Nickalls. Kennedy competed in the Wingfield Sculls in 1892, when he was runner-up to Vivian Nickalls. However he turned the tables in 1893 and beat  V Nickalls

In 1910 Kennedy purchased Hascombe Court at Hascombe and developed the parkland over the years until his death there at the age 55.

Guy Nickalls
Guy Nickalls (13 November 1866 – 8 July 1935) was a British rower who competed in the 1908 Summer Olympics as a member of the British eight that won gold, won 22 events at Henley Royal Regatta and won the Wingfield Sculls three times.
Reichsbahndirektion Regensburg
Reichsbahndirektion Regensburg (RBD Regensburg) was a Deutsche Reichsbahn railway division within the Bavarian Group Administration in southern Germany with its headquarters at Regensburg, Bavaria.

The area covered by this division included the Bavarian provinces of Lower Bavaria and Upper Palatinate and extended into eastern Upper Franconia around Hof.

Railway divisions in Germany
In Germany and Austria, the running of railway services for a railway administration or the regional network of a large railway company was devolved to railway divisions, variously known as Eisenbahndirektionen (ED), Bundesbahndirektionen (BD) or Reichsbahndirektionen (RBD/Rbd). Their organisation was determined by the railway company concerned or by the state railway and, in the German-speaking lands at least, they formed the intermediate authorities and regional management organisations within the state railway administration's hierarchy. On the formation of the Deutsche Bahn AG in 1994 the system of railway divisions (Eisenbahndirektionen) in Germany was discontinued and their tasks were transferred to new "business areas".
El Elegante Crater
El Elegante (Spanish for elegant one) is a maar (a type of volcanic crater) located in the Gran Desierto de Altar in the Sonoran Desert, Mexico.

At 250 metres (820 ft) deep and 1.5 kilometres (0.93 mi) across, it is the largest in the volcanic complex of Pinacate Peaks.

Maar
A maar is a broad, low-relief volcanic crater caused by a phreatomagmatic eruption (an explosion which occurs when groundwater comes into contact with hot lava or magma). A maar characteristically fills with water to form a relatively shallow crater lake, which may also be called a maar.

Maars generally range in size from 20 to 3,000 m (66 to 9,800 ft) across and from 5 to 200 m (20 to 700 ft) deep. Most maars fill with water to form natural lakes. Most maars have low rims composed of a mixture of loose fragments of volcanic rocks and rocks torn from the walls of the diatreme.
Magnoteuthis
Magnoteuthis is a genus of whip-lash squid containing at least three species. Some teuthologists consider Idioteuthis or Mastigoteuthis synonymous with this taxon, but it is genetically and morphologically distinct.

Whip-lash squid
The Mastigoteuthidae, also known as whip-lash squid, are a family of small deep-sea squid. Approximately 20 known species in six genera are represented, with members found in both the mesopelagic and bathypelagic zone of most oceans. Originally described by Verill in 1881, it was later lowered by Chun (1920) to a subfamily (Mastigoteuthinae) of the Chiroteuthidae.  However, Roper et al. (1969) raised it back to the family level, and this has not been changed since. The taxonomy of this family is extremely unstable, and there have been at times one genus, two genera and four subgenera(Salcedo-Vargas & Okutani, 1994), two genera and several 'groups' (Salcedo-Vargas, 1997), five genera and one species with an uncertain placement, or six genera.
Manly Substation
The Manly Substation is a heritage-listed electrical substation located at 34a-36 Whistler Street, Manly, Northern Beaches Council, New South Wales, Australia. It was built in 1945. It is also known as #15009 Manly 33 kV Zone/Residential Unit. The property is owned by Ausgrid, a privately owned energy utility company. The substation was added to the New South Wales State Heritage Register on 2 April 1999.

Manly, New South Wales
Manly is a beach-side suburb of northern Sydney, in the state of New South Wales, Australia. It is 17 kilometres (11 mi) north-east of the Sydney central business district and is currently one of the three administrative centres of the local government area of Northern Beaches Council. Manly has a long-standing reputation as a tourist destination, owing to its attractive setting on the Pacific Ocean and easy accessibility by ferry.
Einang stone
The Einang stone  (Norwegian: Einangsteinen, N KJ63) is a runestone located to the northeast of the Einangsundet strait near the village of Slidre in Vestre Slidre Municipality in Innlandet county, Norway. The stone is notable for the age of its runic inscription. The Einang runestone is located within the extensive Gardberg site. It is placed on a grave mound on a ridge overlooking the Valdres valley. There are several other grave mounds nearby. Today the runestone is protected by glass walls and a roof.

Einang Sound
The Einang Sound (English) or Einangsundet (Norwegian) is a small strait in the middle of the Slidrefjorden in Vestre Slidre Municipality in Innlandet county, Norway. It is about 150 meters (490 ft) wide.
Dinosaur Trail
The Dinosaur Trail is a circular tourist route in the province of Alberta, Canada, located in the Canadian badlands paralleling the Red Deer River on both sides, from Drumheller to the Bleriot Ferry.  It is divided in two segments, with the South Dinosaur Trail following the south side of the river and uses portions of Highway 575 and Highway 837, while North Dinosaur Trail follows the north side of the river and is the entirety of Highway 838.  The north and south segments of Dinosaur Trail are connected by the Highway 9 / Highway 56 concurrency within Drumheller.

Alberta Highway 838
Alberta Provincial Highway No. 838, commonly referred to as Highway 838, is a short highway in central Alberta, Canada.  It runs from Highway 837 across the Red Deer River on the free, cable-operated Bleriot Ferry to Highway 9 / Highway 56 in Drumheller.  Outside of Drumheller, Highway 838 does not pass through any communities.  All of Highway 838 is part of the Dinosaur Trail and is known as North Dinosaur Trail.

The Bleriot Ferry operates from late April to November.
John Denny (politician)
John Denny (May 4, 1793 – July 28, 1875) was an American pioneer and politician.

Born in Mercer County, Kentucky, Denny served in the Kentucky Volunteers regiment during the War of 1812. In 1816, Denny, his wife, and family moved to Washington County, Indiana and then to Putnam County, Indiana. Then, in 1835, Denny, his wife, and family settled in Knox County, Illinois. While living in Knox County, Illinois Denny served as justice of the peace. From 1840 to 1842, Denny served in the Illinois House of Representatives and from 1846 to 1852, in the Illinois State Senate. He was a Whig and then a Republican. He settled in Seattle, Washington where he died. His son was Arthur A. Denny.

John Street in Seattle was named after Denny by his sons.

Arthur A. Denny
Arthur Armstrong Denny (June 20, 1822 – January 9, 1899) was an American politician and businessman who is regarded as one of the founders of Seattle, Washington. He founded the Denny Party, and was later the city's wealthiest citizen. He was a 9-term member of the territorial legislature. Seattle's former Denny Hill was named after him; it was flattened in a series of regrading projects and its former site is now known as the Denny Regrade. The city's Denny Way, however, is named not after Arthur Denny, but after his younger brother David Denny.
ACS Combinatorial Science
ACS Combinatorial Science (usually abbreviated as ACS Comb. Sci.), formerly Journal of Combinatorial Chemistry (1999-2010), was a peer-reviewed scientific journal, published since 1999 by the American Chemical Society. ACS Combinatorial Science publishes articles, reviews, perspectives, accounts and reports in the field of combinatorial chemistry.

Anthony Czarnik served as the founding editor from 1999 to 2010. M.G. Finn served as Editor from 2010 to 2020. In 2010, ACS agreed to change the name of the journal to "Combinatorial Science" and it was the first and only ACS journal to be devoted to a way of doing science, rather than to a specific field of knowledge or application.

The journal stopped accepting new submissions in August and the last issue was published in December 2020.

Combinatorial chemistry
Combinatorial chemistry comprises chemical synthetic methods that make it possible to prepare a large number (tens to thousands or even millions) of compounds in a single process. These compound libraries can be made as mixtures, sets of individual compounds or chemical structures generated by computer software. Combinatorial chemistry can be used for the synthesis of small molecules and for peptides.

Strategies that allow identification of useful components of the libraries are also part of combinatorial chemistry. The methods used in combinatorial chemistry are applied outside chemistry, too.
Belait Beach
Belait Beach (Malay: Pantai Belait), also known as Kuala Belait Beach (Malay: Pantai Kuala Belait), is a beach in Kuala Belait, Mukim Kuala Belait, Belait District, Brunei. The beach used to stretch from Kuala Belait to Pelumpong Island but was cut and split at Muara Beach.

Offshore platforms from the South West Ampa Field can also be seen in distance from the beach. Seawalls have been built along the coastline in order to reduce erosion. Activities such as surf fishing do take place on the beach.

Belait District
Belait District (Malay: Daerah Belait; Jawi: دأيره بلأيت) or simply known as Belait (buh-LEIT; Malay: [bəlait] ⓘ), is the largest as well as the westernmost district in Brunei. It has an area of 2,727 square kilometres (1,053 sq mi) and the population of 65,531 as of 2021. The administrative town is Kuala Belait, located at the mouth of the 32 kilometres (20 mi) long Belait River. The district is commonly associated with the oil and gas industry of the country, mainly concentrated near the town of Seria.
Stalag III-C
Stalag III-C was a German Army World War II prisoner-of-war camp for Allied soldiers. It was located on a plain near the village of Alt Drewitz bei Küstrin then located in the Neumark of the province of Brandenburg (now Drzewice, Kostrzyn nad Odrą, Poland), about 50 mi (80 km) east of Berlin.

Initially the camp served as a place of internment for several thousand soldiers and NCOs from Poland, France, Britain, Yugoslavia and Belgium. From 1943, a number of Italian POWs were also held there. From 1944, soldiers from the United States of America were kept there too. The majority of the Soviet prisoners (up to 12,000) were killed or starved to death. Most of the lower rank prisoners were sent to Arbeitskommandos to work in industry and on farms in Brandenburg. However the administration stayed with the Stammlager.

Kostrzyn nad Odrą
Kostrzyn nad Odrą (translated literally as Kostrzyn upon the Oder; Polish pronunciation: [ˈkɔst.ʂɨn ˌnad ˈɔdrɔ̃]; German: Küstrin [kʏsˈtʁiːn]) is a town in Gorzów County, Lubusz Voivodeship in western Poland, on the border with Germany.
Christopher Curwen (MP)
Christopher Curwen (died 1450) was an English soldier, administrator and politician. He was the son of Sir William Curwen of Workington, Cumberland and his first wife, Alice. He succeeded his father in 1403 and was knighted by 1404.

He was a member (MP) of the parliament of England for Appleby in September 1397, for Cumberland in November 1414, 1423, 1425, 1427, 1431 and 1432.

He was appointed High Sheriff of Cumberland for 1415–16, 1423–24, 1427–28, 1433–34, 1437–38 and 1444–45. He was also a Justice of the Peace for Cumberland from 1435 to 1439 and from 1443 to 1448.

From 1417 he saw military service under John, Lord Neville, in Henry V's second expedition against the French, as leader of 44 lances and 113 archers. He was made keeper of the castle of Danville in Normandy and in 1419 he and his male heirs were granted in perpetuity the castle of Cany-en-Caux and the lordship of Caux, which had been confiscated from the Duke of Bavaria.

Sheriff of Cumberland
The sheriff is the oldest secular office under the Crown.  Formerly the sheriff was the principal law enforcement officer in the county but over the centuries most of the responsibilities associated with the post have been transferred elsewhere or are now defunct so that its functions are now largely ceremonial.  The sheriff changes every April.

The post of Sheriff of Cumberland existed from the creation of the county in the twelfth century up until 1974 when the administrative and ceremonial or geographic county of Cumberland became part of Cumbria.
Cagno
Cagno (Comasco: Cagn [ˈkaɲ]) is a comune (municipality) in the Province of Como in the Italian region Lombardy, located about 45 kilometres (28 mi) northwest of Milan and about 13 kilometres (8 mi) west of Como.

Cagno borders the following municipalities: Albiolo, Cantello, Malnate, Rodero, Solbiate, Valmorea.

Solbiate
Solbiate (Comasco: Solbiaa [sulˈbjaː])  is a comune (municipality) in the Province of Como in the Italian region Lombardy, located about 40 kilometres (25 mi) northwest of Milan and about 12 kilometres (7 mi) southwest of Como. As of 31 December 2004, it had a population of 2,360 and an area of 4.1 square kilometres (1.6 sq mi).

Solbiate borders the following municipalities: Albiolo, Beregazzo con Figliaro, Binago, Cagno, Malnate, Olgiate Comasco.