hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Löb's theorem
In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in PA that "if P is provable in PA then P is true", then P is provable in PA. If Prov(P) is the assertion that the formula P is provable in PA, we may express this more formally as

If

then

.

An immediate corollary (the contrapositive) of Löb's theorem is that, if P is not provable in PA, then "if P is provable in PA, then P is true" is not provable in PA. For example, "If  is provable in PA, then " is not provable in PA.

Löb's theorem is named for Martin Hugo Löb, who formulated it in 1955. It is related to Curry's paradox.

Formal system
A formal system (or deductive system) is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms.

In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in mathematics.
However, in 1931 Kurt Gödel proved that any consistent formal system sufficiently powerful to express basic arithmetic cannot prove its own completeness. This effectively showed that Hilbert's program was impossible as stated.

The term formalism is sometimes a rough synonym for formal system, but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation.
Yalu, Papua New Guinea
Yalu is a large village in Wampar Rural LLG, located in the Markham Valley of Morobe Province, Papua New Guinea. It lies along the  Highlands Highway 21.5 kilometres (13.4 mi) north-west of Lae, 7 kilometres (4.3 mi) southeast of Nadzab. The landscape is typically lowland rainforest.

Highlands Highway
The Highlands Highway, sometimes known as the Okuk Highway, is the main land highway in Papua New Guinea. It connects several major cities and is vital for the movement of people and goods between the populous Highlands region and the coast.

For most of its length the Highlands Highway is no more than a single carriageway two-lane road that is often hindered by potholes and land slips. It is also notorious, particularly in the Highlands region, for being the place of numerous armed hold-ups and robberies committed by local bandits called raskols.
Francis Hours
Reverend Father Francis Hours, born 1921 in France and died 1987, was a French Jesuit archaeologist known for his work on prehistory in the Levant.

He gave the Lebanese a real scientific framework for prehistoric research and worked excavating various sites including J'ita II. He was also an author of many publications, some in collaboration with international archaeologists such as Jacques Cauvin and  Lorraine Copeland. One of his most notable works was the Atlas des sites du proche orient (14000-5700 BP) (Atlas of Near East sites) which he started in 1974. This work has been completed and added to by various scholars including Oliver Aurenche and is now an online application of the Maison de l'Orient et de la Méditerranée.

Lorraine Copeland
Lorraine Copeland (born Elizabeth Lorraine Adie, 1921–April 2013) was a British archaeologist specialising in the Palaeolithic period of the Near East. She was a secret agent with the Special Operations Executive during World War II.
Financial Access at Birth
Financial Access at Birth is a policy initiative proposed by Professor Bhagwan Chowdhry of UCLA Anderson and ISB. The initiative aims to place $100 in an electronic savings account for every child born in the world. The initiative has attracted some prominent supporters, including Peter Singer, a well-known philosopher, and Vijay Mahajan, an Indian social entrepreneur. The JAM trinity in India has incorporated two out of the three features from FAB, A digital identity and a bank account for every individual.

UCLA Anderson School of Management
The John E. Anderson Graduate School of Management (branded as UCLA Anderson) is the graduate business school at the University of California, Los Angeles. The school offers MBA (full-time, part-time, executive), Post Graduate Program for Executives (PGPX), Financial Engineering, Business Analytics, and PhD degrees. It was named after American billionaire John E. Anderson in 1987, after he donated $15 million to the School of Management (the largest gift received from an individual by the University of California at the time).
Lars Bern
Lars Anders Vilhelm Bern (born on October 21, 1942) is a Swedish engineer, doctor of technology, author and debater. He is a member of the Royal Swedish Academy of Engineering Sciences. Bern has denied that the greenhouse effect has been proven, denies the extent of human influence on climate change that is part of the scientific consensus on climate change and has been described as a climate sceptic, climate denialist and conspiracy theorist.

Bern has been chairman of the corporation which operates the television channel Swebbtv, which has been described as conspiratorial and far-right.

Royal Swedish Academy of Engineering Sciences
The Royal Swedish Academy of Engineering Sciences (Swedish: Kungliga Ingenjörsvetenskapsakademien, IVA), founded on 24 October 1919 by King Gustaf V, is one of the royal academies in Sweden. The academy is an independent organisation, which promotes contact and exchange between business, research, and government, in Sweden and internationally. It is the world's oldest academy of engineering sciences.(OECD Reviews of Innovation Policy: Sweden 2012).
Medistylus
Medistylus is an extinct genus of pachyrukhine hegetotheriid. It lived in Argentina during the Late Oligocene. Medistylus is known from its upper teeth and isolated skulls, however, its lower dentition is currently unknown. Its fossilized remains were found at the Cabeza Blanca and Las Cascadas localities of the Sarmiento Formation in Chubut Province of Argentina.

Chubut Province
Chubut (Spanish: Provincia del Chubut [tʃuˈβut] – from Tehuelche chupat 'transparent'; Welsh: Talaith Chubut [taˈlaɪθ ˈχɨbɨt]) is a province in southern Argentina, situated between the 42nd parallel south (the border with Río Negro Province), the 46th parallel south (bordering Santa Cruz Province), the Andes range to the west (bordering Chile), and the Atlantic Ocean to the east. The province's name derives from the Tehuelche word chupat, meaning 'transparent', their description of the Chubut River.

The largest city is Comodoro Rivadavia in the south of the province; it had 199,369 inhabitants at the 2022 Census. The administrative capital is Rawson (27,157). Other important cities are Puerto Madryn (97,625), Trelew (104,657), Esquel (36,624) and Sarmiento (13,892). Gaiman (6,376) is a cultural and demographic centre of the region known as Y Wladfa in which Welsh-Argentines are concentrated.
Kremlin Cup (pool)
The Kremlin Cup (Russian: Кубок Кремля, romanized: Kubok Kremlja) is an annual pool tournament held in the Olympic Stadium in Moscow, Russia which has been held since 2011. Ruslan Chinakhov has won the most times, winning the event in both 2014 and 2015. The tournament takes place in parallel to a Russian pyramid event of the same name also held in Moscow. The event was a nine-ball tournament in the inaugural 2011 edition, but changed to ten-ball in 2012.

Olympic Stadium (Moscow)
Olympic Stadium (Russian: Олимпийский стадион) (known locally as Olimpiyskiy) was an indoor arena located in Moscow, Russia. It was built for the 1980 Summer Olympics and, divided into two separated halls, hosted the basketball and boxing events. It was closed in March 2019, and was subsequently demolished in 2020 for the construction of a new complex.
Donn Sorensen
Donn Sorensen (born April 11, 1961) is a healthcare executive, philanthropist, public speaker and author. Sorensen is the Chairman of Board and a member of the American Medical Group Association’s board of directors. He is also a fellow of the American College of Medical Practice Executives.

American Medical Group Association
The American Medical Group Association (AMGA) is a non-profit trade association headquartered in Alexandria, Virginia. AMGA represents the interests of multi-specialty medical groups and integrated health systems in the United States.
Barak Baba
Barak Baba (Persian: براق بابا; 1257–1307) was a Turkoman dervish.

He was born in a village near Tokat. His father came from an affluent background. Legendary narratives identify him as the Seljuk Sultan of Rum Kaykaus II (r. 1246–62), who took refuge in the Byzantine Empire, while his son was adopted by the patriarch in Constantinople and subsequently converted to Christianity. He was restored to his Islamic origins by dervish Sarı Saltık, who honored him as Barak ("hairless dog" in Kipchak languages) after he eagerly swallowed Sarı Saltık's spit.

Kipchak languages
The Kipchak languages (also known as the Kypchak, Qypchaq, Qypshaq or the Northwestern Turkic languages) are a sub-branch of the Turkic language family spoken by approximately 30 million people in much of Central Asia and Eastern Europe, spanning from Romania to China. Some of the most widely spoken languages in this group are Kazakh, Kyrgyz, and Tatar.
Electrafixion
Electrafixion were an alternative rock band, formed by former Echo & the Bunnymen members Ian McCulloch and Will Sergeant in 1994, joined by bass guitarist Leon de Sylva and drummer Tony McGuigan. They released one album, Burned, and four singles and EPs before splitting up in 1996, due to the reformation of the Bunnymen. A posthumous limited edition 7" single, "Baseball Bill" was released in 1997. When touring, the band included Julian Phillips (formerly of Marion) on bass and his brother, George Phillips, on drums.

Special edition
The terms special edition, limited edition, and variants such as deluxe edition, collector's edition, expanded edition, or nth anniversary edition are used as a marketing incentive for various kinds of products, originally published products related to the arts, such as books, prints, recorded music and films, and video games, but now including clothing, cars, fine wine, and whisky, among other products.  A limited edition is restricted in the number of copies produced, although in fact the number may be very low or very high. Suzuki (2008) defines limited edition products as those “sold in a state that makes them difficult to obtain because of companies limiting their availability to a certain period, quantity, region, or channel". A special edition implies there is extra material of some kind included.  The term is frequently used on DVD film releases, often when the so-called "special" edition is actually the only version released.
Zoome
zoome (ズーミー, lit. "zoom me") was a video hosting service in Japan managed by zoome Co., Ltd. (zoome株式会社).

The name is a combination of "zoom" and "me", and means "My broadcasting station & community". zoome supported H.264/MPEG-4 AVC for the first time by a video hosting service in Japan. The site was the second largest video hosting service in Japan, after Nico Nico Douga.

The site was called a "CGM video hosting site" and "The third force" different from YouTube and Nico Nico Douga.

Crypton Future Media
Crypton Future Media, Inc. (クリプトン・フューチャー・メディア株式会社, Kuriputon Fyūchā Media Kabushiki gaisha), or simply Crypton, is a Japanese media company based in Sapporo, Japan. It develops, imports, and sells products for music, such as sound generator software, sampling CDs and DVDs, and FX and BGM libraries. The company also provides services of online shopping, online community, and mobile content.
John Vining
John Middleton Vining (December 23, 1758 – February 1802) was an American lawyer and politician from Dover, in Kent County, Delaware. He was a Continental Congressman from Delaware, and a member of the Federalist Party, who served in the Delaware General Assembly and as United States Representative and United States Senator from Delaware.

Kent County, Delaware
Kent County is a county located in the central part of the U.S. state of Delaware. As of the 2020 census, the population was 181,851, making it the least populous county in Delaware, but the most populous county in the United States to be the least populous in its state. The county seat is Dover, the state capital of Delaware. It is named for Kent, an English county.

Kent County comprises the Dover metropolitan area, which is included in the Philadelphia-Reading-Camden, PA-NJ-DE-MD combined statistical area.
Salzburger Landestheater
The Salzburg State Theatre (Salzburger Landestheater) is a theatre situated in Salzburg, Austria, a venue for opera, theatre, and dance, contemporary and older works, with resident companies of actors, singers and dancers. The theatre presents approximately 400 performances each season, from September to June. The main theatre building is located next to the Mirabell Gardens and seats an audience of 707. The staff consists of 340 people originating from 35 countries.

The theatre is a listed building and part of the historic Altstadt, a UNESCO World Heritage Site.

Emanuel Schikaneder
Emanuel Schikaneder (born Johann Joseph Schickeneder; 1 September 1751 – 21 September 1812) was a German impresario, dramatist, actor, singer, and composer. He wrote the libretto of Mozart's opera Die Zauberflöte and was the builder of the Theater an der Wien. Peter Branscombe called him "one of the most talented theatre men of his era".
2013 Falkland Islands sovereignty referendum
A referendum on political status was held in the Falkland Islands on 10–11 March 2013. The Falkland Islanders were asked whether or not they supported the continuation of their status as an Overseas Territory of the United Kingdom in view of Argentina's call for negotiations on the islands' sovereignty.

On a turnout of 92%, 99.8% voted to remain a British territory, with only three votes against. Had the islanders rejected the continuation of their current status, a second referendum on possible alternatives would have been held. Brad Smith, the leader of the international observer group, announced that the referendum was free and fair and executed in accordance with international standards and international laws.

Jeremy Browne
Jeremy Richard Browne (born 17 May 1970) is a British Liberal Democrat politician who was  the Member of Parliament (MP) for Taunton Deane from 2005 to 2015. He served as both Minister of State for Europe and the Americas and Minister of State for Crime Prevention.

In September 2015 Browne was appointed as a "Special Representative for the City of London Corporation" in the European Union, as part of the city's efforts to boost its presence in Brussels. Browne left this role in August 2018.

In July 2022 Browne became Chief Executive of Canning House.
Monmouth Mountain
Monmouth Mountain, commonly known as Mount Monmouth is one of the principal summits of the Pacific Ranges of the Coast Mountains of southern British Columbia in Canada. At 3,182 m (10,440 ft), it is the highest summit of the Chilcotin Ranges. It stands just north of the Lillooet Icecap between the heads of Chilko Lake and the Taseko Lakes. West of Chilko Lake's south arm is Mount Good Hope 3,242 m (10,636 ft) and, beyond it, the massif surrounding Mount Queen Bess 3,298 m (10,820 ft), which is the highest summit east of the Homathko River.

The namesake of this peak was HMS Monmouth, an aging British armoured cruiser which was sunk at the Battle of Coronel in 1914 along with HMS Good Hope (for which Good Hope Mountain is named) off the coast of South America by German cruisers under Admiral Von Spee.

Homathko River
The Homathko River is one of the major rivers of the southern Coast Mountains of the Canadian province of British Columbia. It is one of the few rivers that penetrates the range from the interior Chilcotin Country to the coastal inlets of the Pacific Ocean, rising near Tatla Lake, and reaching the sea at the head of Bute Inlet, just west of the mouth of the Southgate River.

The Homathko River Valley is one of the most difficult rivers in BC to navigate or explore. The frigid waters make crossing impossible, the valley is lined with devil's club, and home to many grizzly bears.
Brush Fork, West Virginia
Brush Fork (also spelled Brushfork) is a census-designated place (CDP) in Mercer County, West Virginia, United States. Brush Fork is 2 miles (3.2 km) northwest of Bluefield. As of the 2020 census, its population was 1,065 (down from 1,197 at the 2010 census).

The community takes its name from nearby Brush Fork creek which flows into the Bluestone River.

The West Virginia National Guard Brushfork Armory is located in the community. In addition to its National Guard functions it also hosts basketball games for Bluefield High School, commencements for local colleges and high schools, and other events. The Armory received 1.9 million dollars in 2024 for the planning and design of a new readiness center at the Brushfork Armory that meets all requirements for anti-terrorism and force protection in Bluefield.

Tourism in Brushfork is gaining with visitors to the Hatfield-McCoy Trails traveling and staying in the area.

Hatfield–McCoy Trails
The Hatfield–McCoy Trails (HMT) is a trail system popular for its recreational trails for ATVs, UTVs, and dirt bikes, but the trails are also open to hikers, mountain bikers, and horse riders. HMT is located in West Virginia's south west counties of Boone, Kanawha, Lincoln, Logan, McDowell, Mercer, Mingo, Wayne, and Wyoming. The HMT trail system is a public–private partnership between private landowners and the Hatfield–McCoy Regional Recreation Authority (HMRRA), a legislatively created quasi-state agency with paid staff and governed by a multi-county board of directors. The HMT project brings in millions of dollars to the West Virginia economy each year.
Chandpur Champagachhi
Chandpur Champagachhi (also written as Chandapur Champagachhi) is a census town in the Rajarhat CD block in the  Bidhannagar subdivision of the North 24 Parganas district in the state of West Bengal, India.

Bidhannagar subdivision
Bidhannagar subdivision is an administrative subdivision of the North 24 Parganas district in the Indian state of West Bengal. After transferring Rajarhat-Gopalpur Municipality and Rajarhat (Community development block) to Bidhannagar subdivision, Bidhannagar subdivision's total area becomes 141.37 km2 (54.58 sq mi), the population becomes 808,251 (2011 Census), and density becomes 5,700/km2 (15,000/sq mi).
Charles Samuel Myers
Charles Samuel Myers, CBE, FRS (13 March 1873 – 12 October 1946) was an English physician who worked as a psychologist, most notably with the British Royal Army Medical Corps during the First World War. Although he did not invent the term, his first academic paper, published by The Lancet in 1915, concerned shell shock. In 1921 he was co-founder of the National Institute of Industrial Psychology.

British Journal of Psychology
The British Journal of Psychology is a quarterly peer-reviewed psychology journal. It was established in 1904 and is published by Wiley-Blackwell on behalf of the British Psychological Society. The editor-in-chief is Stefan R. Schweinberger (University of Jena). According to the Journal Citation Reports, the journal has a 2018 impact factor of 3.308, ranking it 20th out of 137 journals in the category "Psychology, Multidisciplinary".
Thanksgiving (Glee)
"Thanksgiving" is the eighth episode of the fourth season of the American musical television series Glee, and the seventy-fourth episode overall. Written by Russel Friend and Garrett Lerner, and directed by Bradley Buecker, it aired on Fox in the United States on November 29, 2012. The episode features the return of many of the New Directions graduates to help in coaching the current glee club for Sectionals competition, which takes place on Thanksgiving, and the reappearance of special guest star Sarah Jessica Parker as Isabelle Wright, Kurt's boss in New York City.

Jacob Artist
Jacob Artist (born October 17, 1992) is an American actor, singer, and dancer. He is best known for his roles as Jake Puckerman on the Fox musical comedy-drama series Glee and as Brandon Fletcher on the ABC drama-thriller series Quantico.
2026 SAFF U-17 Championship
The 2026 SAFF U-17 Championship was the 11th edition of the SAFF U-17 Championship, an international football competition for men's under-17 national teams organized by South Asian Football Federation (SAFF). The tournament Held from 26 July–07 August 2026 in Pakistan.
India are the defending champions, who won their seventh title by defeating Bangladesh (4)2–2(1) goals penalty shootout in the final on 27 September 2025.

India national under-17 football team
The India national under-17 football team represents India in international football at the under-17 level. Controlled by the All India Football Federation, the governing body for football in India, the team is part of the Asian Football Confederation and the South Asian Football Federation.
Colva Roney-Dougal
Colva Mary Roney-Dougal OBE is a British mathematician specializing in group theory and computational algebra. She is Professor of Pure Mathematics at the University of St Andrews, and the Director of the Centre for Interdisciplinary Research in Computational Algebra at St Andrews. She is also known for her popularization of mathematics on BBC radio shows, including appearances on In Our Time about the mathematics of Emmy Noether and Pierre-Simon Laplace and on The Infinite Monkey Cage about the nature of infinity and numbers in the real world.

In Our Time (radio series)
In Our Time is a BBC Radio 4 discussion series and podcast exploring a wide variety of historical, scientific and philosophical topics. First aired in October 1998, it is one of Radio 4's most successful discussion programmes, acknowledged to have "transformed the landscape for serious ideas at peak listening time". The series passed its 1,000th episode in September 2023 and attracts a weekly audience exceeding two million listeners.

The show was presented by Melvyn Bragg, from its first broadcast in 15 October 1998. On 3 September 2025, the BBC reported that Bragg had decided to retire from the programme ahead of its new series as a new presenter would be announced in due course. On 3 December 2025, the BBC announced that Misha Glenny would take over as the new presenter from 15 January 2026.
Civil parishes in Lancashire
A civil parish is a subnational entity, forming the lowest unit of local government in England. There are 219 civil parishes in the ceremonial county of Lancashire; Blackpool is completely unparished; Pendle and Ribble Valley are entirely parished.  At the 2001 census, there were 587,074 people living in the 219 parishes, accounting for 41.5 per cent of the county's population.

Ceremonial counties of England
Ceremonial counties, formally known as counties for the purposes of the lieutenancies, are areas of England to which lord-lieutenants are appointed.  A lord-lieutenant is the monarch's representative in an area.

Shrieval counties have the same boundaries and serve a similar purpose, being the areas to which high sheriffs are appointed. High sheriffs are the monarch's judicial representative in an area.

The ceremonial counties are defined in the Lieutenancies Act 1997, and the shrieval counties in the Sheriffs Act 1887. Both are defined as groups of counties used for local government.