hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Gauss map
In differential geometry, the Gauss map  of a surface is a function that maps each point in the surface to its normal direction, a unit vector that is orthogonal to the surface at that point. Namely, given a surface X in Euclidean space R3, the Gauss map is a map N: X → S2 (where S2 is the unit sphere) such that  for each p in X, the function value N(p) is a unit vector orthogonal to X at p. The Gauss map is named after Carl F. Gauss.

The Gauss map can be defined (globally) if and only if the surface is orientable, in which case its degree is half the Euler characteristic. The Gauss map can always be defined locally (i.e. on a small piece of the surface). The Jacobian determinant of the Gauss map is equal to Gaussian curvature, and the differential of the Gauss map is called the shape operator.

Gauss first wrote a draft on the topic in 1825 and published in 1827.

There is also a Gauss map for a link, which computes linking number.

Gaussian curvature
In differential geometry, the Gaussian curvature or Gauss curvature (symbol Κ, named after Carl Friedrich Gauss) of a smooth surface in three-dimensional space at a point is the product of the two principal curvatures, κ1 and κ2, at the given point:

For example, a sphere of radius r has Gaussian curvature ⁠1/r2⁠ everywhere, and a flat plane and a cylinder have Gaussian curvature zero everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus.

Gaussian curvature is an intrinsic measure of curvature, meaning that it could in principle be measured by a 2-dimensional being living entirely within the surface, because it depends only on distances that are measured “within” or along the surface, not on the way it is isometrically embedded in Euclidean space. This is the content of the Theorema Egregium, published by Gauss in 1827.
Waterloo, Iowa
Waterloo is a city in and the county seat of Black Hawk County, Iowa, United States. It is the eighth-most populous city in Iowa, with a population of 67,314 at the 2020 census. Waterloo comprises a twin conurbation with neighboring municipality Cedar Falls, and is the larger of the two cities. The Waterloo – Cedar Falls metropolitan area has an estimated 170,000 residents.

Waterloo is a major manufacturing, commercial, and cultural center in Northeast Iowa. John Deere, a brand renowned for its tractors, engines, and other agricultural machinery, has been manufacturing its products in the city for over a century. Locally known as the “Factory City,” Waterloo has played a significant role in the production of these important agricultural tools. Waterloo is bisected by the Cedar River flowing southeastward.

Black Hawk County, Iowa
Black Hawk County is a county in the northeastern part of the U.S. state of Iowa. As of the 2020 census, the population was 131,144, making it Iowa's fifth-most populous county. The county seat is Waterloo.

Black Hawk County is part of the Waterloo – Cedar Falls metropolitan area.
Santana 23
The Santana 23 is a lightweight, 23-foot 4-inch sailboat that was designed by W. Shad Turner and manufactured by W. D. Schock Corp as a "high performance racer" and trailerable cruiser. It was first built in 1978 and remained in production through 1987, with a total of 194 units produced, though the hull was brought back in 1993 as the Santana 2023. It was produced through 1984 as the Santana 23 "D" (for "daggerboard") model, commonly called the Santana 23D, with a retractable, vertical, daggerboard keel similar to racing dinghys, with a remaining 50 produced through 1987 with a traditional keel, called the Santana 23K. The hull was also used to inspire the Wavelength 24 also by Schrock, and supposedly "many other models."

Santana 2023
The Santana 2023 is a family of American trailerable sailboats that was designed by Steve Schock, with models for racing and cruising, first built in 1993.

The Santana 2023 is a development of W. Shad Turner's  1978 Santana 23 D design, using the same hull design, but different deck, mast and interior.
Rastriya Janata Party Nepal
The Rastriya Janata Party, Nepal, abbr. RJPN (Nepali: राष्ट्रिय जनता पार्टी, नेपाल,  translation: National People's Party, Nepal) was the fourth-largest political party in Nepal after the Nepali Congress, the Nepal Communist Party and the Samajbadi Party, Nepal. It was formed on 21 April 2017 after the merger of Tarai Madhes Loktantrik Party, led by the Mahantha Thakur, Terai Madhes Sadbhawana Party, led by the Mahendra Raya Yadav, Sadbhavana Party, led by the Rajendra Mahato, Nepal Sadbhawana Party, led by the Anil Kumar Jha, Madhesi Jana Adhikar Forum (Republican), led by Rajkishor Yadav and Rastriya Madhesh Samajwadi Party, led by Sharat Singh Bhandari. The party was founded with the ideology of democratic system.

On 22 April 2020, the party merged with Samajbadi Party, Nepal to form Janata Samajbadi Party, Nepal.

Samajbadi Party, Nepal (2019)
The Samajbadi Party, Nepal, abbr. SPN (Nepali: समाजवादी पार्टी, नेपाल, lit. 'Socialist Party, Nepal') was the third-largest political party in Nepal after the Nepali Congress and the Nepal Communist Party. It was formed on 6 May 2019 by the merger of the Federal Socialist Forum, Nepal, led by Deputy Prime Minister Upendra Yadav, and the Naya Shakti Party, Nepal, led by former Prime Minister Baburam Bhattarai. The party was founded with the ideology of democratic socialism and ethnic federalism. It uses the flag and election symbol of the Federal Socialist Forum, Nepal.

On 23 April 2020, the party merged with Rastriya Janata Party Nepal to form Janata Samajwadi Party, Nepal.
Merge Records
Merge Records is an independent record label based in Durham, North Carolina. It was founded in 1989 by Laura Ballance and Mac McCaughan. It began as an outlet for music from their band Superchunk and music created by friends, and has expanded to include artists from around the world, with records reaching the top of the Billboard music charts.

Mac McCaughan
Ralph Lee "Mac" McCaughan (/məˈkɑːn/; born July 12, 1967) is an American musician and record label owner, based in North Carolina. His main musical projects have been Superchunk since 1989, and Portastatic since the early 1990s. In 1989 he founded the independent record label Merge Records with Superchunk bandmate Laura Ballance.
Kings Newton
Kings Newton is a village in South Derbyshire. The population of the village is included in Melbourne.  The Holy well (pictured) was constructed around 1660, but has been refurbished at the end of the twentieth century.

Melbourne, Derbyshire
Melbourne (/ˈmɛlbɔːrn/) is a market town and civil parish in South Derbyshire, England.
It was home to Thomas Cook, founder of the eponymous travel agency, and has a street named after him. It is 8 miles (13 km) south of Derby and 2 miles (3 km) from the River Trent. The population of the civil parish at the 2021 Census was 5,264.
Karenga District
Karenga District is a district in Uganda’s Northern Region, located in the Karamoja sub-region. Created on 1 July 2019 by splitting from Kaabong District, it has its administrative and commercial center in Karenga town. Known as a gateway to Kidepo Valley National Park, the district is home to the Karimojong, Acholi, and Mening communities, who rely on pastoralism, subsistence farming, and tourism. Bordering South Sudan, Karenga combines vibrant cultural traditions with a rugged, promising landscape.

Karamoja
The Karamoja sub-region, commonly known as Karamoja, is a region in Uganda.  It covers an area of 27,528km and comprises the Kotido District, Kaabong District, Karenga District, Nabilatuk District, Abim District, Moroto District, Napak District, Amudat District and Nakapiripirit District. The region is projected to have a population of 1.4 millions in 2022 by UBOS.
Saw Pyei Chantha
Saw Pyei Chantha (Burmese: စောပြည့်ချမ်းသာ [sɔ́ bjḛ tɕʰáɴðà]), also spelled Shwe Bye Kyantha (Burmese: ရွှေပြည့်ချမ်းသာ), was the chief queen consort of Arakan for a few months in 1408. After she and her first husband King Anawrahta of Launggyet were captured by the Hanthawaddy forces in 1408, she became a junior queen consort of King Razadarit of Hanthawaddy.

Anawrahta of Launggyet
Anawrahta Minsaw (Burmese: အနော်ရထာ မင်းစော, pronounced [ʔənɔ̀jətʰà mɪ́ɴ sɔ́]; d. March 1408) was the king of Launggyet Arakan from 1406 to 1408. He was appointed to the position by his overlord King Minkhaung I of the Ava Kingdom. He later married Minkhaung's eldest daughter Saw Pyei Chantha. He was overthrown in 1408 by the Hanthawaddy kingdom army, and subsequently executed on the order of King Razadarit of Hanthawaddy. He is one of two historical personalities that make up the Shwe Nawrahta nat spirit in the Burmese pantheon of nats.
Harsola copper plates
The Harsola copper plates are a set of two 949 CE Indian inscriptions that record the grants of two villages to a Nagar Brahmin father-son duo. The grants were issued by the Paramara king Siyaka II. The copper plates were discovered in Harsol (or Harsola) in present-day Gujarat state.

Besides the Paramara ancestors of Siyaka, the inscription mentions men with Rashtrakuta titles. Based on their identification as Rashtrakuta kings, some historians have theorized that Paramaras descended from the Rashtrakutas. However, others have argued that these men were Paramara rulers who had adopted Rashtrakuta titles to portray themselves as successors of the Rashtrakutas in Malwa.

Siyaka
Siyaka (IAST: Sīyaka; reigned c. 949–972), also known as Harsha (IAST: Harṣa), was the king of Malwa, who ruled in west-central India. He appears to have been the first independent ruler of the Paramara dynasty.

Siyaka is the earliest Paramara ruler known from his own inscriptions, which have been discovered in present-day Gujarat, and suggest that he was once a feudatory of the Rashtrakutas of Manyakheta. After the death of the Rashtrakuta emperor Krishna III, he fought against the new king Khottiga, and sacked the Rashtrakuta capital Manyakheta in c. 972 CE. This ultimately led to the decline of the Rashtrakutas, and established the Paramaras as a sovereign power.
Heibai Wuchang
The Heibai Wuchang, or Hak Bak Mo Seong, literally "Black and White Impermanence", are two deities in Chinese folk religion in charge of escorting the spirits of the dead to the underworld. As their names suggest, they are dressed in black and white respectively. They are worshiped as fortune deities and are also worshiped in City God Temples in some  countries.

In some instances, the Heibai Wuchang are represented as a single being – instead of two separate beings – known as the Wuchang Gui, literally "Ghost of Impermanence". Depending on the person it encounters, the Wuchang Gui can appear as either a fortune deity who rewards the person for doing good deeds or a malevolent deity who punishes the person for committing evil.

City God (China)
A City God (Chinese: 城隍神; pinyin: Chénghuángshén; lit. 'god of the boundary'), is a tutelary deity in Chinese folk religion who is believed to protect the people and the affairs of the particular village, town or city of great dimension, and the corresponding location in the afterlife. City God cults appeared over two millennia ago, and originally involved worship of a protective deity of a town's walls and moats. Later, the term came to be applied to deified leaders from the town, who serve in authority over the souls of the deceased from that town, and intervene in the affairs of the living, in conjunction with other officials of the hierarchy of divine beings. City Gods are considered above tǔdìgōng ('lords of local land'), which themselves are above landlord deities.
Lucknow–Moradabad line
The Lucknow–Moradabad line (also known as Lucknow–Moradabad main line) is a railway line connecting Lucknow and Moradabad railway stations, both in the Indian state of Uttar Pradesh. The line is under the administrative jurisdiction of Northern Railway.

Lucknow Charbagh railway station
Lucknow Charbagh (officially Lucknow NR, station code: LKO) is a railway station in Lucknow, Uttar Pradesh, India. It is the largest and busiest railway station of Lucknow city.

The station is part of the Northern Railway zone's Lucknow NR Division and the Varanasi–Lucknow line.

It is also part of the Lucknow-Rae Bareli-Varanasi line, Lucknow-Sultanpur-Jaunpur City-Varanasi line, Lucknow-Kanpur Suburban Railway and Lucknow-Moradabad line.

This station is a (NSG 2) category in Northern Railway. This station is situated in southern central part of Lucknow and adjacent to Lucknow Junction.

Nearby stations include Lucknow Junction (LJN) and Aishbagh (ASH).
HANS device
A HANS device (head and neck support device) is a type of head restraint and a safety device in motorsports. Head restraints are mandatory when competing with most major motorsports sanctioning bodies.  They reduce the likelihood of head or neck injuries, including basilar skull fracture, in the event of a crash. The devices are now mass produced and marketed by Simpson Performance Products. There are many such devices on the market today, like the Hutchens device now known as the Simpson Hybrid Device, but the HANS is the original and most commonly used name.

Hutchens device
A Hutchens device is used for protecting race car drivers in the event of an accident by controlling head movement, reducing head and neck injuries due to whiplash. It consists of a series of straps, attached to the helmet and connected across the chest and at the waist, depending on the lap belt for anchoring. The device was developed beginning in 2000.

From 2001 until 2004 NASCAR mandated that drivers use either a Hutchens device or the HANS device. NASCAR banned the use of the Hutchens device in January 2005, due to it failing SFI Foundation safety tests, and required all drivers to use the HANS device instead.
North Star Mine and Powerhouse
The North Star Mine and Powerhouse are located on Lafayette Hill a short distance south of Grass Valley in the U.S. state of California. It was the second largest producer of gold during California's Gold Rush. In 1898, the largest Pelton wheel for its time was built for the mine. The North Star Mine Company also owned locations on Weimar Hill, adjoining and south of the North Star Mine. It shut down during World War II after its consolidation with the Empire Mine.

Empire Mine State Historic Park
Empire Mine State Historic Park is a state-protected mine and park in the Sierra Nevada mountains in Grass Valley, California, U.S. The Empire Mine is on the National Register of Historic Places, a federal Historic District, and a California Historical Landmark. Since 1975 California State Parks has administered and maintained the mine as a historic site. The Empire Mine is "one of the oldest, largest, deepest, longest and richest gold mines in California". Between 1850 and its closure in 1956, the Empire Mine produced 5.8 million ounces (165 tons) of gold, extracted from 367 miles (591 km) of underground passages.
Ōsumi Peninsula
The Ōsumi Peninsula (大隅半島, Ōsumi Hantō) projects south from the Japanese island of Kyūshū and includes the southernmost point on the island, Cape Sata. Its east coast lies on the Pacific Ocean, while to the west it faces the Satsuma Peninsula across Kagoshima Bay. Politically it is part of Kagoshima Prefecture. Lava erupted in 1914 by Sakurajima (previously an island) made a land connection with the northwest of the Ōsumi Peninsula.

Japan's first satellite was named Ohsumi in honour of the people living in the area due their support of the people working on the launch.

Cape Sata
Cape Sata (佐多岬, Sata Misaki) is a cape at the southern tip of the Ōsumi Peninsula of Kyūshū island, Japan. It is the southernmost point of the island, and therefore of the overall Japanese Home Islands (Hokkaidō, Honshū, Shikoku, and Kyūshū), just south of 31 degrees latitude. It belongs to the town of Minamiōsumi, Kagoshima Prefecture. It is within the borders of the Kirishima-Kinkōwan National Park, in the town of Minamiōsumi.

The area contains a Shinto shrine, the Misaki Shrine, and is also home to the Satamisaki Lighthouse built in 1871, designed by the Scotsman Richard Henry Brunton.

Until October 29, 2012,  the land was under the jurisdiction of a private company, which charged admission for entry to the area; however, the land was sold to the municipality of Minamiōsumi and is now free to enter.

Alan Booth's 1986 book The Roads to Sata details his walk from Cape Sōya at the northern tip of Hokkaidō south to Cape Sata.
Vojenská spravodajská služba
Vojenská spravodajská služba (Military Intelligence Service) was a military intelligence agency for the government and armed forces of Slovakia. On 1 January 2013 it was merged with the Vojenské obranné spravodajstvo (VOS) and created the Vojenské spravodajstvo.

Vojenské spravodajstvo
Vojenské spravodajstvo (English: Military Intelligence) is a military intelligence agency of the Slovak Republic operating under the Ministry of Defence. It was established on 1 January 2013 by merging the Vojenská spravodajská služba (VSS) and the Vojenské obranné spravodajstvo (VOS).
Matt Wozniak
Matt Wozniak (born January 6, 1983) is a Canadian curler from Winnipeg, Manitoba.  Wozniak is the former second for the Mike McEwen team which curled out of the Assiniboine Memorial Curling Club in Winnipeg.

Mike McEwen (curler)
Michael McEwen (born July 30, 1980) is a Canadian curler from Winnipeg, Manitoba, who grew up in Brandon, Manitoba. McEwen won six Grand Slams in his career before his team qualified for their first  Brier, Canada's national championship in 2016. He is noted as one of the top curlers using the Manitoba tuck delivery today. He is nicknamed "Magic" Mike McEwen.
Couperin family
The Couperin family was a musical dynasty of professional composers and performers. They were the most prolific family in French musical history, active during the Baroque era (17th—18th centuries). Louis Couperin and his nephew, François Couperin le grand, are the best known members of the family.

François Couperin
François Couperin (French: [fʁɑ̃swa kupʁɛ̃]; 10 November 1668 – 11 September 1733) was a French Baroque composer, organist and harpsichordist. He was known as Couperin le Grand ("Couperin the Great") to distinguish him from other members of the musically talented Couperin family.
SWEEPS-04
SWEEPS-04 is an extrasolar planet orbiting the star SWEEPS J175853.92−291120.6 in the constellation Sagittarius approximately 27,710 light years away (based on a distance modulus of 14.1) from the Solar System, making it (along with SWEEPS-11) the most distant exoplanet(s) known. This planet was found in 2006 by the Sagittarius Window Eclipsing Extrasolar Planet Search (SWEEPS) program that uses the transit method.

The upper limit on the planet's mass is 3.8 times the mass of Jupiter. The best fit radius is 0.81 times that of Jupiter, but the uncertainty in this value is large, around 12%. It orbits at an average distance of 8,200,000 km (0.055 AU) from the parent star, taking 4.2 days to revolve around it.

HST SWEEPS-4 2006

Radial Velocities of SWEEPS-04 (UVES-VLT)

Artist's impression of a transiting Jupiter-mass exoplanet SWEEPS J175853.92-291120.6 b

SWEEPS-11
SWEEPS-11 is an extrasolar planet orbiting SWEEPS J175902.67−291153.5 in the constellation Sagittarius, approximately 27,710 light years away from the Solar System (based on a distance modulus of 14.1), making it (along with SWEEPS-04) the most distant exoplanet(s) known. This planet was found in 2006 by the Sagittarius Window Eclipsing Extrasolar Planet Search (SWEEPS) program that uses the transit method.

This hot Jupiter has a mass 9.7 times that of Jupiter and a radius of 1.13 times that of Jupiter, but the uncertainty in this value is large, around 21%. The planet orbits at about 1.75 times closer to the star than 51 Pegasi b is to 51 Pegasi, taking only 1.8 days or 43 hours to orbit the star. It is also the most distant planet yet discovered.
Khalifa House Museum
The Khalifa House Museum is an ethnographic museum, located opposite the tomb of  Muhammad Ahmad in the city of Omdurman in Sudan. Towards the end of the 19th century, it was the residence of the successor of the Mahdi, Khalifa Abdallahi ibn Muhammad and the headquarters of the administration of the Mahdi State. The House was converted into a museum in 1928 during the Anglo-Egyptian condominium.

The Mahdi's tomb
The Mahdi's tomb or qubba (Arabic: قُبَّة) is located in Omdurman, Sudan. It was the burial place of Muhammad Ahmad, the leader of an Islamic revolt against Turco-Egyptian Sudan in the late 19th century.

The Mahdist State was established in 1885 after the Siege of Khartoum. Muhammad Ahmad died shortly after this Mahdist victory and was buried at Omdurman. The Mahdist State was led by the Mahdī's successor, the Khalifa Abdullahi, until 1898 when an Anglo-Egyptian force, led by Lord Kitchener, defeated the Mahdists at the Battle of Omdurman. This victory marked the success of Kitchener's reconquest of Sudan. After the Battle, the Mahdī's tomb was seriously damaged by naval gunfire on Lord Kitchener's orders.

The tomb was reconstructed in 1947 under the direction of the Mahdī's son, al-sayyid ʿAbd-al-Raḥman al-Mahdī. It is located next to the Khalifa House Museum. The tomb has been listed as a site of 'outstanding cultural value' by UNESCO.
Ollie Quinn
Ollie Johnson Quinn (26 May 1893 – 23 August 1949) was a mob boss in Galveston, Texas in the United States, who was involved in bootlegging, illegal gambling, numbers racket, prostitution and other criminal activities from the 1910s up until the 1930s. He, with Dutch Voight, led the Beach Gang, one of the two criminal organisations which controlled most of the Galveston underworld until the mid-1920s.

He was generally considered the dominant figure in vice, especially gambling, on the island and was respected by most Galveston residents and other Galveston County inhabitants alike. His main casino, the Deluxe Club, was a fixture in the city. His Modern Vending Company leased gaming equipment such as slot machines to area businesses. Quinn was known for being, above all, a businessman who was accepting of honest competition in the vice business.

Quinn became a mentor, and then a partner, to Sam and Rosario Maceo, who later took over the Galveston underworld.

Rosario Maceo
Rosario Maceo (Sr.) (Italian pronunciation: [roˈzaːrjo maˈtʃɛːo] June 8, 1887 – March 29, 1954), also known as Papa Rose or Rose Maceo, was an Italian-American businessman, power broker and crime boss in Galveston, Texas in the United States. Because of his efforts and those of his brother Sam, Galveston Island became a nationally known resort city during the early and mid 20th century, during a period known as Galveston's Wide-Open Era. They owned various restaurant and casino venues including the now-vanished Hollywood Dinner Club and the Balinese Room. He became an Al Capone-like figure in the city. Sometimes known as the "Iron Glove", Rose was the top enforcer for the empire he and his brother formed.
Lac-Matapédia
Lac-Matapédia (French pronunciation: [lak matapedja]) is an unorganized territory in the Bas-Saint-Laurent region of Quebec, Canada. It is named after and located on the northern shores of Lake Matapedia in the Matapédia Valley.

The territory is home to a small protected area, Lac-Matapédia Forest Refuge (304 hectares (750 acres)) that was established in 2008 to protect three populations of the calypso orchid (Calypso bulbosa), a plant designated as threatened or vulnerable in Quebec. A part of the remainder of the territory is being considered for the creation of a new provincial park.

Lake Matapedia
Lake Matapedia is a body of water in the Matapedia Valley, located in the unorganized territory of Lac-Matapédia, in Sayabec, in Val-Brillant, in La Matapédia Regional County Municipality, in administrative region of Bas-Saint-Laurent, in Quebec, Canada, and the source of the Matapedia River. The town of Amqui lies at the southeast corner of the lake.