Datasets:
umarzein
/
wikipedia-headings-tree-7k

Dataset card Viewer Files Community
rootwards
stringlengths
8
109
direct_child
stringlengths
41
13.4k
/wiki/Tenthredo_scrophulariae
{"inner": "Tenthredo scrophulariae", "level": 1, "lower": [{"inner": "Distribution and habitat", "level": 2, "lower": []}, {"inner": "Description", "level": 2, "lower": []}, {"inner": "Biology", "level": 2, "lower": []}, {"inner": "Gallery", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Larva
{"inner": "Larva", "level": 1, "lower": [{"inner": "Selected types of larvae", "level": 2, "lower": []}, {"inner": "Insect larvae", "level": 2, "lower": []}]}
/wiki/Verbascum
{"inner": "Verbascum", "level": 1, "lower": [{"inner": "Description", "level": 2, "lower": []}, {"inner": "Cultivation", "level": 2, "lower": []}, {"inner": "Other uses", "level": 2, "lower": []}, {"inner": "Select species", "level": 2, "lower": []}]}
/wiki/Keila
{"inner": "Keila", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": []}, {"inner": "Military base", "level": 2, "lower": []}, {"inner": "Nature", "level": 2, "lower": []}, {"inner": "Education", "level": 2, "lower": []}, {"inner": "Population", "level": 2, "lower": []}, {"inner": "Demographics", "level": 2, "lower": []}, {"inner": "International relations", "level": 2, "lower": [{"inner": "Twin towns \u2014 sister cities", "level": 3, "lower": []}]}, {"inner": "Notable residents", "level": 2, "lower": []}]}
/wiki/Scrophularia
{"inner": "Scrophularia", "level": 1, "lower": [{"inner": "Selected species", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}]}
/wiki/Geoff_Bent
{"inner": "Geoff Bent", "level": 1, "lower": [{"inner": "Early life", "level": 2, "lower": []}, {"inner": "Manchester United career", "level": 2, "lower": []}, {"inner": "Munich air disaster", "level": 2, "lower": []}, {"inner": "Legacy", "level": 2, "lower": []}, {"inner": "Notes, citations and sources", "level": 2, "lower": [{"inner": "Notes", "level": 3, "lower": []}, {"inner": "Citations", "level": 3, "lower": []}, {"inner": "Sources", "level": 3, "lower": [{"inner": "Books", "level": 4, "lower": []}, {"inner": "Newspapers", "level": 4, "lower": []}, {"inner": "Online", "level": 4, "lower": []}]}]}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Matt_Landers
{"inner": "Matt Landers", "level": 1, "lower": [{"inner": "Early life", "level": 2, "lower": []}, {"inner": "College career", "level": 2, "lower": []}, {"inner": "Professional career", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}]}
/wiki/Republican_Palace_Museum
{"inner": "Republican Palace Museum", "level": 1, "lower": [{"inner": "Location", "level": 2, "lower": [{"inner": "Opening hours", "level": 3, "lower": []}]}, {"inner": "History", "level": 2, "lower": []}, {"inner": "Functionality", "level": 2, "lower": [{"inner": "Cultural and social activities", "level": 3, "lower": []}, {"inner": "Educational activities", "level": 3, "lower": []}]}, {"inner": "Departments", "level": 2, "lower": [{"inner": "Automobile suite", "level": 3, "lower": []}, {"inner": "Photographs and paintings suite", "level": 3, "lower": []}, {"inner": "Honours suite", "level": 3, "lower": []}, {"inner": "Gift suite", "level": 3, "lower": []}, {"inner": "Suite of musical instruments, utensils, and furniture", "level": 3, "lower": []}, {"inner": "Documentation suite", "level": 3, "lower": []}, {"inner": "Decoration suite", "level": 3, "lower": []}, {"inner": "Weapons suite", "level": 3, "lower": []}, {"inner": "Library", "level": 3, "lower": []}]}, {"inner": "Notes", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Russian_invasion_of_Ukraine
{"inner": "Russian invasion of Ukraine", "level": 1, "lower": [{"inner": "Background", "level": 2, "lower": [{"inner": "Ukrainian unrest, Russian activity in Crimea and Donbas", "level": 3, "lower": []}]}, {"inner": "Prelude", "level": 2, "lower": [{"inner": "Putin's invasion announcement", "level": 3, "lower": []}]}, {"inner": "Invasion", "level": 2, "lower": [{"inner": "Initial invasion of Ukraine (24 February \u2013 7 April)", "level": 3, "lower": [{"inner": "Kyiv and northern front", "level": 4, "lower": []}, {"inner": "North-eastern front", "level": 4, "lower": []}, {"inner": "Southern front", "level": 4, "lower": []}, {"inner": "Eastern front", "level": 4, "lower": []}]}, {"inner": "Southeastern front (8 April \u2013 5 September)", "level": 3, "lower": [{"inner": "Fall of Mariupol", "level": 4, "lower": []}, {"inner": "Fall of Sievierodonetsk and Lysychansk", "level": 4, "lower": []}, {"inner": "Kharkiv front", "level": 4, "lower": []}, {"inner": "Kherson-Mykolaiv front", "level": 4, "lower": []}, {"inner": "Zaporizhzhia front", "level": 4, "lower": []}]}, {"inner": "Russian annexations and Ukrainian counterattacks (6 September\u00a0\u2013 11 November 2022)", "level": 3, "lower": [{"inner": "Russian annexation of Donetsk, Kherson, Luhansk and Zaporizhzhia oblasts", "level": 4, "lower": []}, {"inner": "Zaporizhzhia front", "level": 4, "lower": []}, {"inner": "Kherson counteroffensive", "level": 4, "lower": []}, {"inner": "Kharkiv counteroffensive", "level": 4, "lower": []}]}, {"inner": "Winter stalemate, attrition campaign and military surge (12 November 2022\u00a0\u2013 present)", "level": 3, "lower": [{"inner": "Battle of Bakhmut", "level": 4, "lower": []}, {"inner": "Southern front", "level": 4, "lower": []}, {"inner": "Diplomatic developments", "level": 4, "lower": []}, {"inner": "Continued infrastructure attacks", "level": 4, "lower": []}]}, {"inner": "Events in Crimea", "level": 3, "lower": []}, {"inner": "Missile attacks and aerial warfare", "level": 3, "lower": []}, {"inner": "Naval blockade and engagements", "level": 3, "lower": []}, {"inner": "Command", "level": 3, "lower": []}, {"inner": "Nuclear threats", "level": 3, "lower": []}, {"inner": "Ukrainian resistance", "level": 3, "lower": []}]}, {"inner": "Reactions", "level": 2, "lower": []}, {"inner": "Foreign involvement", "level": 2, "lower": []}, {"inner": "Casualties", "level": 2, "lower": [{"inner": "Prisoners of war", "level": 3, "lower": []}]}, {"inner": "Impacts", "level": 2, "lower": [{"inner": "Humanitarian impact", "level": 3, "lower": []}, {"inner": "Refugee crisis", "level": 3, "lower": []}, {"inner": "Environmental impact", "level": 3, "lower": []}]}, {"inner": "Peace efforts", "level": 2, "lower": []}]}
/wiki/Wikipedia
{"inner": "Wikipedia", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": [{"inner": "Nupedia", "level": 3, "lower": []}, {"inner": "Launch and growth", "level": 3, "lower": []}, {"inner": "Milestones", "level": 3, "lower": []}]}, {"inner": "Openness", "level": 2, "lower": [{"inner": "Restrictions", "level": 3, "lower": []}, {"inner": "Review of changes", "level": 3, "lower": []}, {"inner": "Vandalism", "level": 3, "lower": []}, {"inner": "Edit warring", "level": 3, "lower": []}]}, {"inner": "Policies and laws", "level": 2, "lower": [{"inner": "Content policies and guidelines", "level": 3, "lower": []}]}, {"inner": "Governance", "level": 2, "lower": [{"inner": "Administrators", "level": 3, "lower": []}, {"inner": "Dispute resolution", "level": 3, "lower": [{"inner": "Arbitration Committee", "level": 4, "lower": []}]}]}, {"inner": "Community", "level": 2, "lower": [{"inner": "Studies", "level": 3, "lower": []}, {"inner": "Diversity", "level": 3, "lower": []}]}, {"inner": "Language editions", "level": 2, "lower": [{"inner": "English Wikipedia editor numbers", "level": 3, "lower": []}]}, {"inner": "Reception", "level": 2, "lower": [{"inner": "Accuracy of content", "level": 3, "lower": []}, {"inner": "Discouragement in education", "level": 3, "lower": [{"inner": "Medical information", "level": 4, "lower": []}]}, {"inner": "Coverage of topics and systemic bias", "level": 3, "lower": [{"inner": "Coverage of topics and bias", "level": 4, "lower": []}, {"inner": "Systemic biases", "level": 4, "lower": []}]}, {"inner": "Explicit content", "level": 3, "lower": []}, {"inner": "Privacy", "level": 3, "lower": []}, {"inner": "Sexism", "level": 3, "lower": []}]}, {"inner": "Operation", "level": 2, "lower": [{"inner": "Wikimedia Foundation and affiliate movements", "level": 3, "lower": []}, {"inner": "Software operations and support", "level": 3, "lower": []}, {"inner": "Automated editing", "level": 3, "lower": []}, {"inner": "Hardware operations and support", "level": 3, "lower": []}, {"inner": "Internal research and operational development", "level": 3, "lower": []}, {"inner": "Internal news publications", "level": 3, "lower": []}, {"inner": "The Wikipedia Library", "level": 3, "lower": []}]}, {"inner": "Access to content", "level": 2, "lower": [{"inner": "Content licensing", "level": 3, "lower": []}, {"inner": "Methods of access", "level": 3, "lower": [{"inner": "Mobile access", "level": 4, "lower": []}]}, {"inner": "Chinese access", "level": 3, "lower": []}]}, {"inner": "Cultural influence", "level": 2, "lower": [{"inner": "Trusted source to combat fake news", "level": 3, "lower": []}, {"inner": "Readership", "level": 3, "lower": [{"inner": "COVID-19 pandemic", "level": 4, "lower": []}]}, {"inner": "Cultural significance", "level": 3, "lower": [{"inner": "Awards", "level": 4, "lower": []}, {"inner": "Satire", "level": 4, "lower": []}]}, {"inner": "Sister projects\u00a0\u2013 Wikimedia", "level": 3, "lower": []}, {"inner": "Publishing", "level": 3, "lower": []}, {"inner": "Research use", "level": 3, "lower": []}]}, {"inner": "Related projects", "level": 2, "lower": []}]}
/wiki/Encyclopedia
{"inner": "Encyclopedia", "level": 1, "lower": [{"inner": "Etymology", "level": 2, "lower": []}, {"inner": "Characteristics", "level": 2, "lower": [{"inner": "Four major elements", "level": 3, "lower": []}, {"inner": "Encyclopedic dictionaries", "level": 3, "lower": []}, {"inner": "Differences between encyclopedias and dictionaries", "level": 3, "lower": []}]}, {"inner": "Pre-modern encyclopedias", "level": 2, "lower": []}, {"inner": "Printed encyclopedias", "level": 2, "lower": [{"inner": "Encyclop\u00e9die", "level": 3, "lower": []}, {"inner": "Encyclop\u00e6dia Britannica", "level": 3, "lower": []}, {"inner": "Brockhaus Enzyklop\u00e4die", "level": 3, "lower": []}, {"inner": "Encyclopedias in the US", "level": 3, "lower": []}]}, {"inner": "Digital encyclopedias", "level": 2, "lower": [{"inner": "Physical media", "level": 3, "lower": []}, {"inner": "Online", "level": 3, "lower": [{"inner": "Free encyclopedias", "level": 4, "lower": []}]}]}]}
/wiki/Catalecticant
{"inner": "Catalecticant", "level": 1, "lower": [{"inner": "Binary forms", "level": 2, "lower": []}, {"inner": "Catalecticants of quartic forms", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}]}
/wiki/Hermann_Hankel
{"inner": "Hermann Hankel", "level": 1, "lower": [{"inner": "Biography", "level": 2, "lower": []}, {"inner": "Selected publications", "level": 2, "lower": []}, {"inner": "Notes", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Square_matrix
{"inner": "Square matrix", "level": 1, "lower": [{"inner": "Main diagonal", "level": 2, "lower": []}, {"inner": "Special kinds", "level": 2, "lower": [{"inner": "Diagonal or triangular matrix", "level": 3, "lower": []}, {"inner": "Identity matrix", "level": 3, "lower": []}, {"inner": "Invertible matrix and its inverse", "level": 3, "lower": []}, {"inner": "Symmetric or skew-symmetric matrix", "level": 3, "lower": []}, {"inner": "Definite matrix", "level": 3, "lower": []}, {"inner": "Orthogonal matrix", "level": 3, "lower": []}, {"inner": "Normal matrix", "level": 3, "lower": []}]}, {"inner": "Operations", "level": 2, "lower": [{"inner": "Trace", "level": 3, "lower": []}, {"inner": "Determinant", "level": 3, "lower": []}, {"inner": "Eigenvalues and eigenvectors", "level": 3, "lower": []}]}]}
/wiki/Tropical_cyclone
{"inner": "Tropical cyclone", "level": 1, "lower": [{"inner": "Background", "level": 2, "lower": []}, {"inner": "Intensity", "level": 2, "lower": [{"inner": "Factors that influence intensity", "level": 3, "lower": []}, {"inner": "Formation", "level": 3, "lower": []}, {"inner": "Rapid intensification", "level": 3, "lower": []}, {"inner": "Dissipation", "level": 3, "lower": []}, {"inner": "Methods for assessing intensity", "level": 3, "lower": []}, {"inner": "Intensity metrics", "level": 3, "lower": []}]}, {"inner": "Classification and naming", "level": 2, "lower": [{"inner": "Classification", "level": 3, "lower": []}, {"inner": "Naming", "level": 3, "lower": []}]}, {"inner": "Structure", "level": 2, "lower": [{"inner": "Eye and center", "level": 3, "lower": []}, {"inner": "Size", "level": 3, "lower": []}]}, {"inner": "Movement", "level": 2, "lower": [{"inner": "Environmental steering", "level": 3, "lower": []}, {"inner": "Beta drift", "level": 3, "lower": []}, {"inner": "Multiple storm interaction", "level": 3, "lower": []}, {"inner": "Interaction with the mid-latitude westerlies", "level": 3, "lower": []}]}, {"inner": "Formation regions and warning centers", "level": 2, "lower": []}, {"inner": "Preparations", "level": 2, "lower": []}, {"inner": "Effects", "level": 2, "lower": [{"inner": "Natural phenomena caused or worsened by tropical cyclones", "level": 3, "lower": []}, {"inner": "Effect on property and human life", "level": 3, "lower": []}, {"inner": "Environmental effects", "level": 3, "lower": []}]}, {"inner": "Response", "level": 2, "lower": []}, {"inner": "Climatology", "level": 2, "lower": [{"inner": "Influence of climate change", "level": 3, "lower": []}]}, {"inner": "Observation and forecasting", "level": 2, "lower": [{"inner": "Observation", "level": 3, "lower": []}, {"inner": "Forecasting", "level": 3, "lower": []}, {"inner": "Geopotential height", "level": 3, "lower": []}]}, {"inner": "Related cyclone types", "level": 2, "lower": []}]}
/wiki/English_language
{"inner": "English language", "level": 1, "lower": [{"inner": "Classification", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": [{"inner": "Proto-Germanic to Old English", "level": 3, "lower": []}, {"inner": "Middle English", "level": 3, "lower": []}, {"inner": "Early Modern English", "level": 3, "lower": []}, {"inner": "Spread of Modern English", "level": 3, "lower": []}]}, {"inner": "Geographical distribution", "level": 2, "lower": [{"inner": "Three circles of English-speaking countries", "level": 3, "lower": []}, {"inner": "Pluricentric English", "level": 3, "lower": []}, {"inner": "English as a global language", "level": 3, "lower": []}]}, {"inner": "Phonology", "level": 2, "lower": [{"inner": "Consonants", "level": 3, "lower": []}, {"inner": "Vowels", "level": 3, "lower": []}, {"inner": "Phonotactics", "level": 3, "lower": []}, {"inner": "Stress, rhythm and intonation", "level": 3, "lower": []}, {"inner": "Regional variation", "level": 3, "lower": []}]}, {"inner": "Grammar", "level": 2, "lower": [{"inner": "Nouns and noun phrases", "level": 3, "lower": [{"inner": "Adjectives", "level": 4, "lower": []}, {"inner": "Determiners", "level": 4, "lower": []}, {"inner": "Pronouns, case, and person", "level": 4, "lower": []}, {"inner": "Prepositions", "level": 4, "lower": []}]}, {"inner": "Verbs and verb phrases", "level": 3, "lower": [{"inner": "Tense, aspect and mood", "level": 4, "lower": []}, {"inner": "Phrasal verbs", "level": 4, "lower": []}, {"inner": "Adverbs", "level": 4, "lower": []}]}, {"inner": "Syntax", "level": 3, "lower": [{"inner": "Basic constituent order", "level": 4, "lower": []}, {"inner": "Clause syntax", "level": 4, "lower": []}, {"inner": "Auxiliary verb constructions", "level": 4, "lower": []}, {"inner": "Questions", "level": 4, "lower": []}, {"inner": "Discourse level syntax", "level": 4, "lower": []}]}]}, {"inner": "Vocabulary", "level": 2, "lower": [{"inner": "Word formation processes", "level": 3, "lower": []}, {"inner": "Word origins", "level": 3, "lower": []}, {"inner": "English loanwords and calques in other languages", "level": 3, "lower": []}]}, {"inner": "Writing system", "level": 2, "lower": []}, {"inner": "Dialects, accents and varieties", "level": 2, "lower": [{"inner": "Britain and Ireland", "level": 3, "lower": []}, {"inner": "North America", "level": 3, "lower": []}, {"inner": "Australia and New Zealand", "level": 3, "lower": []}, {"inner": "Southeast Asia", "level": 3, "lower": []}, {"inner": "Africa, the Caribbean, and South Asia", "level": 3, "lower": []}, {"inner": "Non-native varieties", "level": 3, "lower": []}]}, {"inner": "Sample text", "level": 2, "lower": []}]}
/wiki/Michoac%C3%A1n
{"inner": "Michoac\u00e1n", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": []}, {"inner": "Geography", "level": 2, "lower": [{"inner": "Flora", "level": 3, "lower": []}, {"inner": "Fauna", "level": 3, "lower": []}, {"inner": "Protected areas", "level": 3, "lower": []}]}, {"inner": "Economy", "level": 2, "lower": [{"inner": "Agriculture", "level": 3, "lower": []}, {"inner": "Forestry", "level": 3, "lower": []}, {"inner": "Fishing", "level": 3, "lower": []}, {"inner": "Mining and minerals", "level": 3, "lower": []}, {"inner": "Manufacturing", "level": 3, "lower": []}]}, {"inner": "Infrastructure", "level": 2, "lower": [{"inner": "Transport", "level": 3, "lower": []}, {"inner": "Media", "level": 3, "lower": []}]}, {"inner": "Education", "level": 2, "lower": []}, {"inner": "Tourism", "level": 2, "lower": []}, {"inner": "Crime", "level": 2, "lower": [{"inner": "Killings", "level": 3, "lower": []}, {"inner": "Kidnappings and Ransoms", "level": 3, "lower": []}, {"inner": "Drug Cartels", "level": 3, "lower": []}, {"inner": "Police and Militia", "level": 3, "lower": []}]}, {"inner": "Demographics", "level": 2, "lower": [{"inner": "Largest cities", "level": 3, "lower": []}]}, {"inner": "Municipalities", "level": 2, "lower": [{"inner": "Major communities", "level": 3, "lower": []}]}]}
/wiki/Oaxaca
{"inner": "Oaxaca", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": [{"inner": "Name", "level": 3, "lower": []}, {"inner": "Prehistoric and pre-Hispanic period", "level": 3, "lower": []}, {"inner": "Spanish colonization", "level": 3, "lower": []}, {"inner": "Independence", "level": 3, "lower": []}, {"inner": "Late 19th century to present", "level": 3, "lower": []}]}, {"inner": "Geography", "level": 2, "lower": [{"inner": "Regions, districts and major communities", "level": 3, "lower": []}, {"inner": "Climate", "level": 3, "lower": []}, {"inner": "Nature and conservation", "level": 3, "lower": [{"inner": "Lagunas de Chacahua National Park", "level": 4, "lower": []}, {"inner": "Benito Ju\u00e1rez National Park", "level": 4, "lower": []}, {"inner": "Huatulco National Park", "level": 4, "lower": []}, {"inner": "Tehuac\u00e1n-Cuicatl\u00e1n Biosphere Reserve", "level": 4, "lower": []}]}]}, {"inner": "Demographics", "level": 2, "lower": [{"inner": "Largest cities", "level": 3, "lower": []}, {"inner": "Overview", "level": 3, "lower": []}, {"inner": "Indigenous peoples", "level": 3, "lower": [{"inner": "Zapotecs", "level": 4, "lower": []}, {"inner": "Mixtecs", "level": 4, "lower": []}, {"inner": "Mazatecos", "level": 4, "lower": []}, {"inner": "Mixe", "level": 4, "lower": []}, {"inner": "Other", "level": 4, "lower": []}]}, {"inner": "Afro-Mexicans", "level": 3, "lower": []}, {"inner": "Religion", "level": 3, "lower": []}]}, {"inner": "Government and political geography", "level": 2, "lower": []}, {"inner": "Economy", "level": 2, "lower": [{"inner": "Migration", "level": 3, "lower": []}, {"inner": "Agriculture", "level": 3, "lower": []}, {"inner": "Mining and industry", "level": 3, "lower": []}, {"inner": "Commerce", "level": 3, "lower": []}]}, {"inner": "Transport", "level": 2, "lower": [{"inner": "Road, rail and sea", "level": 3, "lower": []}, {"inner": "Air", "level": 3, "lower": []}, {"inner": "Local transportation services", "level": 3, "lower": []}]}, {"inner": "Media", "level": 2, "lower": []}, {"inner": "Culture", "level": 2, "lower": [{"inner": "Arts", "level": 3, "lower": []}, {"inner": "Food and drink", "level": 3, "lower": []}, {"inner": "Landmarks and tourist attractions", "level": 3, "lower": []}, {"inner": "Handicrafts", "level": 3, "lower": []}, {"inner": "Symbols", "level": 3, "lower": [{"inner": "Flag", "level": 4, "lower": []}, {"inner": "Coat of Arms", "level": 4, "lower": []}, {"inner": "State emblem", "level": 4, "lower": []}]}]}, {"inner": "Education", "level": 2, "lower": [{"inner": "Primary education", "level": 3, "lower": []}, {"inner": "Higher education", "level": 3, "lower": []}]}, {"inner": "Health", "level": 2, "lower": []}, {"inner": "Sports", "level": 2, "lower": []}, {"inner": "Notable people from Oaxaca", "level": 2, "lower": []}]}
/wiki/Veracruz
{"inner": "Veracruz", "level": 1, "lower": [{"inner": "Etymology", "level": 2, "lower": []}, {"inner": "Geography", "level": 2, "lower": [{"inner": "Political geography", "level": 3, "lower": []}, {"inner": "Natural geography", "level": 3, "lower": []}, {"inner": "Climate", "level": 3, "lower": []}, {"inner": "Ecosystems", "level": 3, "lower": []}]}, {"inner": "History", "level": 2, "lower": [{"inner": "Pre-Columbian", "level": 3, "lower": []}, {"inner": "Colonial period, 1519\u20131821", "level": 3, "lower": []}, {"inner": "Independence", "level": 3, "lower": []}, {"inner": "20th century to the present", "level": 3, "lower": []}]}, {"inner": "Economy", "level": 2, "lower": [{"inner": "Agriculture", "level": 3, "lower": []}, {"inner": "Natural resources", "level": 3, "lower": []}, {"inner": "Golden Lane Oil Fields", "level": 3, "lower": []}, {"inner": "Industry, transportation and commerce", "level": 3, "lower": []}, {"inner": "Handcrafts", "level": 3, "lower": []}]}, {"inner": "Culture", "level": 2, "lower": [{"inner": "Gastronomy", "level": 3, "lower": []}, {"inner": "Museums", "level": 3, "lower": []}, {"inner": "Fairs and festivals", "level": 3, "lower": []}, {"inner": "Dance and music", "level": 3, "lower": []}, {"inner": "Art and architecture", "level": 3, "lower": []}, {"inner": "Literature", "level": 3, "lower": []}, {"inner": "Religion", "level": 3, "lower": []}]}, {"inner": "Education", "level": 2, "lower": []}, {"inner": "Demographics", "level": 2, "lower": [{"inner": "Largest cities", "level": 3, "lower": []}]}, {"inner": "Tourism", "level": 2, "lower": []}, {"inner": "Archeological sites", "level": 2, "lower": []}, {"inner": "Government", "level": 2, "lower": []}, {"inner": "Infrastructure", "level": 2, "lower": [{"inner": "Transport", "level": 3, "lower": []}, {"inner": "Media", "level": 3, "lower": []}]}, {"inner": "Major communities", "level": 2, "lower": []}, {"inner": "Notable People", "level": 2, "lower": []}]}
/wiki/Chris_Kreider
{"inner": "Chris Kreider", "level": 1, "lower": [{"inner": "Early life", "level": 2, "lower": []}, {"inner": "Playing career", "level": 2, "lower": [{"inner": "Amateur", "level": 3, "lower": []}, {"inner": "Collegiate", "level": 3, "lower": []}, {"inner": "Professional", "level": 3, "lower": [{"inner": "Early years (2012\u20132015)", "level": 4, "lower": []}, {"inner": "Later years", "level": 4, "lower": []}]}]}, {"inner": "International play", "level": 2, "lower": []}, {"inner": "Personal life", "level": 2, "lower": []}, {"inner": "Career statistics", "level": 2, "lower": [{"inner": "Regular season and playoffs", "level": 3, "lower": []}, {"inner": "International", "level": 3, "lower": []}]}, {"inner": "Awards and honors", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Colima
{"inner": "Colima", "level": 1, "lower": [{"inner": "Geography", "level": 2, "lower": []}, {"inner": "Demographics", "level": 2, "lower": []}, {"inner": "Principal communities", "level": 2, "lower": []}, {"inner": "Economy", "level": 2, "lower": []}, {"inner": "Tourist attractions", "level": 2, "lower": []}, {"inner": "Culture", "level": 2, "lower": []}, {"inner": "Communications and transportation", "level": 2, "lower": [{"inner": "Transport", "level": 3, "lower": []}, {"inner": "Media", "level": 3, "lower": []}]}, {"inner": "History", "level": 2, "lower": [{"inner": "Name and seal", "level": 3, "lower": []}, {"inner": "Pre-Hispanic period", "level": 3, "lower": []}, {"inner": "Colonial era", "level": 3, "lower": []}, {"inner": "Independence to the present", "level": 3, "lower": []}]}, {"inner": "Archaeology", "level": 2, "lower": []}, {"inner": "Education", "level": 2, "lower": []}, {"inner": "Sister cities", "level": 2, "lower": []}]}
/wiki/Hidalgo_(state)
{"inner": "Hidalgo (state)", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": []}, {"inner": "Demographics", "level": 2, "lower": []}, {"inner": "Culture", "level": 2, "lower": []}, {"inner": "Native gastronomy", "level": 2, "lower": []}, {"inner": "Tourism", "level": 2, "lower": []}, {"inner": "Geography", "level": 2, "lower": [{"inner": "Mountains", "level": 3, "lower": []}, {"inner": "Valleys", "level": 3, "lower": []}, {"inner": "Water", "level": 3, "lower": []}, {"inner": "Climate", "level": 3, "lower": []}]}, {"inner": "Ecology", "level": 2, "lower": []}, {"inner": "Economy", "level": 2, "lower": []}, {"inner": "Education", "level": 2, "lower": []}, {"inner": "Infrastructure", "level": 2, "lower": []}, {"inner": "Major communities", "level": 2, "lower": []}]}
/wiki/Guerrero
{"inner": "Guerrero", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": [{"inner": "Prehistoric and Pre-Columbian periods", "level": 3, "lower": []}, {"inner": "Colonial period", "level": 3, "lower": []}, {"inner": "Independence and the later nineteenth century", "level": 3, "lower": []}, {"inner": "Mexican Revolution to the present", "level": 3, "lower": []}]}, {"inner": "Demographics", "level": 2, "lower": [{"inner": "Major communities", "level": 3, "lower": []}]}, {"inner": "Culture", "level": 2, "lower": []}, {"inner": "Tourism", "level": 2, "lower": [{"inner": "Triangle of the Sun", "level": 3, "lower": []}, {"inner": "Archeological sites", "level": 3, "lower": []}, {"inner": "Outdoor activities", "level": 3, "lower": []}]}, {"inner": "Handcrafts", "level": 2, "lower": []}, {"inner": "Politics", "level": 2, "lower": []}, {"inner": "Geography", "level": 2, "lower": []}, {"inner": "Economy", "level": 2, "lower": []}, {"inner": "Education", "level": 2, "lower": []}, {"inner": "Infrastructure", "level": 2, "lower": [{"inner": "Media", "level": 3, "lower": []}, {"inner": "Transport", "level": 3, "lower": []}]}]}
/wiki/Zakir_Husain
{"inner": "Zakir Husain", "level": 1, "lower": [{"inner": "Early life and family", "level": 2, "lower": []}, {"inner": "Career", "level": 2, "lower": [{"inner": "Sheikh-ul-Jamia, Jamia Millia Islamia (1926\u20131948)", "level": 3, "lower": []}, {"inner": "Basic National Education Committee (1937)", "level": 3, "lower": []}, {"inner": "Vice-Chancellor, Aligarh Muslim University (1948\u20131956)", "level": 3, "lower": []}, {"inner": "Governor of Bihar (1957\u20131962)", "level": 3, "lower": []}, {"inner": "Vice President of India (1962\u20131967)", "level": 3, "lower": []}, {"inner": "President of India (1967\u20131969)", "level": 3, "lower": []}, {"inner": "Author", "level": 3, "lower": []}]}, {"inner": "Death and legacy", "level": 2, "lower": [{"inner": "Commemoration", "level": 3, "lower": []}]}, {"inner": "Notes", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Jalisco
{"inner": "Jalisco", "level": 1, "lower": [{"inner": "Geography", "level": 2, "lower": [{"inner": "Climate", "level": 3, "lower": []}]}, {"inner": "Demographics", "level": 2, "lower": [{"inner": "Largest cities", "level": 3, "lower": []}]}, {"inner": "Government and regions", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": [{"inner": "Nomenclature and seal", "level": 3, "lower": []}, {"inner": "Pre-Hispanic period", "level": 3, "lower": []}, {"inner": "Colonial period", "level": 3, "lower": []}, {"inner": "Independence", "level": 3, "lower": []}, {"inner": "Mexican Revolution to present", "level": 3, "lower": []}]}, {"inner": "Tourism", "level": 2, "lower": []}, {"inner": "Culture", "level": 2, "lower": [{"inner": "\"Jalisco is Mexico\"", "level": 3, "lower": []}, {"inner": "Mariachi and other music", "level": 3, "lower": []}, {"inner": "Traditional clothing and dance", "level": 3, "lower": [{"inner": "Dresses", "level": 4, "lower": []}]}, {"inner": "Tequila", "level": 3, "lower": []}, {"inner": "Cuisine", "level": 3, "lower": []}, {"inner": "Catholic faith", "level": 3, "lower": []}]}, {"inner": "Economy", "level": 2, "lower": []}, {"inner": "Education", "level": 2, "lower": []}, {"inner": "Communication", "level": 2, "lower": []}, {"inner": "Infrastructure", "level": 2, "lower": [{"inner": "Media", "level": 3, "lower": []}, {"inner": "Transport", "level": 3, "lower": []}]}, {"inner": "Sports", "level": 2, "lower": []}, {"inner": "Twinning and covenants", "level": 2, "lower": []}]}
/wiki/Sandy_Koufax
{"inner": "Sandy Koufax", "level": 1, "lower": [{"inner": "Early life", "level": 2, "lower": [{"inner": "Major League tryouts", "level": 3, "lower": []}]}, {"inner": "Professional career", "level": 2, "lower": [{"inner": "Early years (1955\u20131960)", "level": 3, "lower": []}, {"inner": "Domination (1961\u20131964)", "level": 3, "lower": [{"inner": "1961 season", "level": 4, "lower": []}, {"inner": "1962 season", "level": 4, "lower": []}, {"inner": "1963 season", "level": 4, "lower": []}, {"inner": "1964 season", "level": 4, "lower": []}]}, {"inner": "Playing in pain (1965\u201366)", "level": 3, "lower": [{"inner": "1965 season", "level": 4, "lower": []}, {"inner": "Perfection", "level": 4, "lower": []}, {"inner": "World Series and Yom Kippur", "level": 4, "lower": []}]}, {"inner": "Holdout", "level": 3, "lower": [{"inner": "1966 season", "level": 4, "lower": []}]}, {"inner": "Retirement", "level": 3, "lower": []}, {"inner": "Career overall", "level": 3, "lower": [{"inner": "Career statistics", "level": 4, "lower": []}]}]}, {"inner": "Pitching style", "level": 2, "lower": []}, {"inner": "Post-playing career", "level": 2, "lower": []}, {"inner": "Legacy", "level": 2, "lower": []}, {"inner": "Personal life", "level": 2, "lower": []}]}
/wiki/Manchester_United_F.C.
{"inner": "Manchester United F.C.", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": [{"inner": "Early years (1878\u20131945)", "level": 3, "lower": []}, {"inner": "Busby years (1945\u20131969)", "level": 3, "lower": []}, {"inner": "1969\u20131986", "level": 3, "lower": []}, {"inner": "Ferguson years (1986\u20132013)", "level": 3, "lower": []}, {"inner": "2013\u2013present", "level": 3, "lower": []}]}, {"inner": "Crest and colours", "level": 2, "lower": []}, {"inner": "Grounds", "level": 2, "lower": [{"inner": "1878\u20131893: North Road", "level": 3, "lower": []}, {"inner": "1893\u20131910: Bank Street", "level": 3, "lower": []}, {"inner": "1910\u2013present: Old Trafford", "level": 3, "lower": []}]}, {"inner": "Support", "level": 2, "lower": [{"inner": "Rivalries", "level": 3, "lower": []}]}, {"inner": "Global brand", "level": 2, "lower": [{"inner": "Sponsorship", "level": 3, "lower": []}]}, {"inner": "Ownership and finances", "level": 2, "lower": [{"inner": "Glazer ownership", "level": 3, "lower": []}]}, {"inner": "Players", "level": 2, "lower": [{"inner": "First-team squad", "level": 3, "lower": [{"inner": "Out on loan", "level": 4, "lower": []}]}, {"inner": "Reserves and academy", "level": 3, "lower": [{"inner": "Out on loan", "level": 4, "lower": []}]}]}, {"inner": "Player awards", "level": 2, "lower": []}, {"inner": "Coaching staff", "level": 2, "lower": [{"inner": "Managerial history", "level": 3, "lower": []}]}, {"inner": "Management", "level": 2, "lower": [{"inner": "Manchester United Limited", "level": 3, "lower": []}, {"inner": "Manchester United Football Club", "level": 3, "lower": []}]}, {"inner": "Honours", "level": 2, "lower": [{"inner": "Doubles and Trebles", "level": 3, "lower": []}]}, {"inner": "Manchester United Women", "level": 2, "lower": []}, {"inner": "Footnotes", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "Further reading", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Yiddish
{"inner": "Yiddish", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": [{"inner": "Origins", "level": 3, "lower": []}, {"inner": "Written evidence", "level": 3, "lower": []}, {"inner": "Printing", "level": 3, "lower": []}, {"inner": "Secularization", "level": 3, "lower": []}, {"inner": "20th century", "level": 3, "lower": []}]}, {"inner": "Phonology", "level": 2, "lower": [{"inner": "Consonants", "level": 3, "lower": []}, {"inner": "Vowels", "level": 3, "lower": []}, {"inner": "Dialectal variation", "level": 3, "lower": []}, {"inner": "Comparison with German", "level": 3, "lower": []}, {"inner": "Comparison with Hebrew", "level": 3, "lower": []}]}, {"inner": "Grammar", "level": 2, "lower": []}, {"inner": "Writing system", "level": 2, "lower": []}, {"inner": "Numbers of speakers", "level": 2, "lower": []}, {"inner": "Status as a language", "level": 2, "lower": [{"inner": "Israel and Zionism", "level": 3, "lower": []}, {"inner": "South Africa", "level": 3, "lower": []}, {"inner": "Former Soviet Union", "level": 3, "lower": [{"inner": "Russia", "level": 4, "lower": []}, {"inner": "Ukraine", "level": 4, "lower": []}]}, {"inner": "Council of Europe", "level": 3, "lower": []}, {"inner": "Sweden", "level": 3, "lower": []}, {"inner": "United States", "level": 3, "lower": [{"inner": "Present U.S. speaker population", "level": 4, "lower": []}]}, {"inner": "United Kingdom", "level": 3, "lower": []}, {"inner": "Canada", "level": 3, "lower": []}, {"inner": "Religious communities", "level": 3, "lower": []}, {"inner": "Modern Yiddish education", "level": 3, "lower": []}, {"inner": "Internet", "level": 3, "lower": []}]}, {"inner": "Influence on other languages", "level": 2, "lower": []}, {"inner": "Language examples", "level": 2, "lower": []}]}
/wiki/President_of_India
{"inner": "President of India", "level": 1, "lower": [{"inner": "Origin", "level": 2, "lower": []}, {"inner": "Powers and duties", "level": 2, "lower": [{"inner": "Duty", "level": 3, "lower": []}, {"inner": "Legislative powers", "level": 3, "lower": []}, {"inner": "Executive powers", "level": 3, "lower": []}, {"inner": "Judicial powers", "level": 3, "lower": []}, {"inner": "Appointment powers", "level": 3, "lower": []}, {"inner": "Financial powers", "level": 3, "lower": []}, {"inner": "Diplomatic powers", "level": 3, "lower": []}, {"inner": "Military powers", "level": 3, "lower": []}, {"inner": "Pardoning powers", "level": 3, "lower": []}, {"inner": "Emergency powers", "level": 3, "lower": [{"inner": "National emergency", "level": 4, "lower": []}, {"inner": "State emergency", "level": 4, "lower": []}, {"inner": "Financial emergency", "level": 4, "lower": []}]}]}, {"inner": "Selection process", "level": 2, "lower": [{"inner": "Eligibility", "level": 3, "lower": []}]}, {"inner": "Time of election", "level": 2, "lower": [{"inner": "Conditions for the presidency", "level": 3, "lower": []}, {"inner": "Election process", "level": 3, "lower": []}, {"inner": "Oath or affirmation", "level": 3, "lower": []}]}, {"inner": "Emoluments", "level": 2, "lower": []}, {"inner": "Impeachment", "level": 2, "lower": []}, {"inner": "Succession", "level": 2, "lower": []}, {"inner": "President vs Chief Justice", "level": 2, "lower": []}, {"inner": "President vs Prime minister", "level": 2, "lower": []}, {"inner": "Important presidential interventions in the past", "level": 2, "lower": [{"inner": "Proving majority in the parliament", "level": 3, "lower": []}, {"inner": "Proof of Majority to form a Government", "level": 3, "lower": []}, {"inner": "Vetoing of a Bill", "level": 3, "lower": []}, {"inner": "Rashtrapati Bhavan Communiqu\u00e9s", "level": 3, "lower": []}, {"inner": "Return of a Bill", "level": 3, "lower": []}, {"inner": "Sacking state governors", "level": 3, "lower": []}]}]}
/wiki/Plessy_v._Ferguson
{"inner": "Plessy v. Ferguson", "level": 1, "lower": [{"inner": "Background", "level": 2, "lower": [{"inner": "Legal background and incident", "level": 3, "lower": []}, {"inner": "Trial", "level": 3, "lower": []}, {"inner": "State appeal", "level": 3, "lower": []}, {"inner": "Supreme Court appeal", "level": 3, "lower": []}]}, {"inner": "Decision", "level": 2, "lower": [{"inner": "Opinion of the Court", "level": 3, "lower": []}, {"inner": "Harlan's dissent", "level": 3, "lower": []}]}, {"inner": "Aftermath", "level": 2, "lower": []}, {"inner": "Significance", "level": 2, "lower": [{"inner": "Plessy and Ferguson Foundation", "level": 3, "lower": []}, {"inner": "Pardon", "level": 3, "lower": []}]}]}
/wiki/Ancient_Greek_religion
{"inner": "Ancient Greek religion", "level": 1, "lower": [{"inner": "Beliefs", "level": 2, "lower": [{"inner": "Theology", "level": 3, "lower": []}, {"inner": "Afterlife", "level": 3, "lower": []}, {"inner": "Mythology", "level": 3, "lower": []}, {"inner": "Morality", "level": 3, "lower": []}, {"inner": "Sacred texts", "level": 3, "lower": []}]}, {"inner": "Practices", "level": 2, "lower": [{"inner": "Ceremonies", "level": 3, "lower": []}, {"inner": "Sacrifice", "level": 3, "lower": []}, {"inner": "Festivals", "level": 3, "lower": []}, {"inner": "Rites of passage", "level": 3, "lower": []}]}, {"inner": "Sanctuaries and temples", "level": 2, "lower": [{"inner": "Cult images", "level": 3, "lower": []}]}, {"inner": "Role of women", "level": 2, "lower": []}, {"inner": "Mystery religions", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": [{"inner": "Origins", "level": 3, "lower": []}, {"inner": "Archaic and classical periods", "level": 3, "lower": []}, {"inner": "Hellenistic period", "level": 3, "lower": []}, {"inner": "Roman Empire", "level": 3, "lower": []}, {"inner": "Suppression and decline", "level": 3, "lower": []}, {"inner": "Modern revivals", "level": 3, "lower": []}]}]}
/wiki/Khartoum
{"inner": "Khartoum", "level": 1, "lower": [{"inner": "Etymology", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": [{"inner": "19th century", "level": 3, "lower": []}, {"inner": "20th century", "level": 3, "lower": []}, {"inner": "21st century", "level": 3, "lower": []}]}, {"inner": "Geography", "level": 2, "lower": [{"inner": "Location", "level": 3, "lower": []}]}, {"inner": "Climate", "level": 2, "lower": []}, {"inner": "Demographics", "level": 2, "lower": []}, {"inner": "Economy", "level": 2, "lower": [{"inner": "Retailing", "level": 3, "lower": []}]}, {"inner": "Education", "level": 2, "lower": []}, {"inner": "Transportation", "level": 2, "lower": []}, {"inner": "Architecture", "level": 2, "lower": []}, {"inner": "Culture", "level": 2, "lower": [{"inner": "Museums", "level": 3, "lower": []}, {"inner": "Botanical gardens", "level": 3, "lower": []}, {"inner": "Clubs", "level": 3, "lower": []}, {"inner": "Places of worship", "level": 3, "lower": []}]}, {"inner": "References", "level": 2, "lower": []}, {"inner": "Bibliography", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Chennai_Super_Kings
{"inner": "Chennai Super Kings", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": [{"inner": "2008\u20132009: First seasons", "level": 3, "lower": []}, {"inner": "2010: IPL and CLT20 double", "level": 3, "lower": []}, {"inner": "2011\u20132015: Success and suspension", "level": 3, "lower": []}, {"inner": "2018\u2013present", "level": 3, "lower": [{"inner": "2018", "level": 4, "lower": []}, {"inner": "2019", "level": 4, "lower": []}, {"inner": "2020", "level": 4, "lower": []}, {"inner": "2021", "level": 4, "lower": []}, {"inner": "2022", "level": 4, "lower": []}, {"inner": "2023", "level": 4, "lower": []}]}]}, {"inner": "Home ground", "level": 2, "lower": []}, {"inner": "Players", "level": 2, "lower": []}, {"inner": "Identity", "level": 2, "lower": [{"inner": "Name, logo, crest and colors", "level": 3, "lower": []}, {"inner": "Theme song", "level": 3, "lower": []}]}, {"inner": "Kit and sponsors", "level": 2, "lower": []}, {"inner": "Support and fan following", "level": 2, "lower": []}, {"inner": "Brand value", "level": 2, "lower": []}, {"inner": "Controversies", "level": 2, "lower": [{"inner": "Ownership of N. Srinivasan", "level": 3, "lower": []}, {"inner": "2013 betting scandal", "level": 3, "lower": []}, {"inner": "IPL suspension", "level": 3, "lower": []}]}, {"inner": "Result summary", "level": 2, "lower": [{"inner": "Overall results", "level": 3, "lower": []}, {"inner": "By opposition", "level": 3, "lower": []}, {"inner": "Overall results in the Champions League T20", "level": 3, "lower": []}]}, {"inner": "Statistics", "level": 2, "lower": [{"inner": "Most runs", "level": 3, "lower": []}, {"inner": "Most wickets", "level": 3, "lower": []}]}, {"inner": "Rivalries", "level": 2, "lower": [{"inner": "Rivalry with Mumbai Indians", "level": 3, "lower": []}, {"inner": "Rivalry with Royal Challengers Bangalore", "level": 3, "lower": []}]}, {"inner": "Seasons", "level": 2, "lower": [{"inner": "Indian Premier League", "level": 3, "lower": []}, {"inner": "Champions League T20", "level": 3, "lower": []}]}, {"inner": "Current squad", "level": 2, "lower": []}, {"inner": "Administration and support staff", "level": 2, "lower": []}, {"inner": "In popular culture", "level": 2, "lower": []}]}
/wiki/2023_Turkish_presidential_election
{"inner": "2023 Turkish presidential election", "level": 1, "lower": [{"inner": "Background", "level": 2, "lower": [{"inner": "2018 elections", "level": 3, "lower": []}]}, {"inner": "Date", "level": 2, "lower": [{"inner": "Discussion on snap elections", "level": 3, "lower": []}, {"inner": "Discussion on postponing election date", "level": 3, "lower": []}, {"inner": "Election calendar", "level": 3, "lower": []}]}, {"inner": "Electoral system", "level": 2, "lower": []}, {"inner": "Candidates", "level": 2, "lower": [{"inner": "Candidates", "level": 3, "lower": []}, {"inner": "Nominations", "level": 3, "lower": []}]}, {"inner": "Endorsements", "level": 2, "lower": [{"inner": "Parties and alliances", "level": 3, "lower": []}]}, {"inner": "Second round", "level": 2, "lower": [{"inner": "Negotiations by O\u011fan and \u00d6zda\u011f", "level": 3, "lower": [{"inner": "Dissolution of ATA Alliance", "level": 4, "lower": []}, {"inner": "Endorsement of Erdo\u011fan by O\u011fan", "level": 4, "lower": []}, {"inner": "\u00d6zda\u011f's support for K\u0131l\u0131\u00e7daro\u011flu", "level": 4, "lower": []}]}, {"inner": "Erdo\u011fan's strategy", "level": 3, "lower": []}, {"inner": "K\u0131l\u0131\u00e7daro\u011flu's strategy", "level": 3, "lower": []}, {"inner": "Potential debate", "level": 3, "lower": []}]}, {"inner": "Controversies", "level": 2, "lower": [{"inner": "Erdo\u011fan's right to seek re-election", "level": 3, "lower": []}, {"inner": "Political violence", "level": 3, "lower": []}, {"inner": "Erdo\u011fan's photo on ballot paper", "level": 3, "lower": []}, {"inner": "Fake videos", "level": 3, "lower": []}, {"inner": "Block of Ek\u015fi S\u00f6zl\u00fck", "level": 3, "lower": []}, {"inner": "Reporting of the results", "level": 3, "lower": []}, {"inner": "Azerbaijani and Russian interference allegations", "level": 3, "lower": []}]}, {"inner": "Opinion polls", "level": 2, "lower": [{"inner": "First round", "level": 3, "lower": []}, {"inner": "Second round", "level": 3, "lower": []}]}, {"inner": "Results", "level": 2, "lower": [{"inner": "Analysis", "level": 3, "lower": []}]}, {"inner": "Aftermath", "level": 2, "lower": [{"inner": "Domestic", "level": 3, "lower": [{"inner": "International", "level": 4, "lower": []}]}]}]}
/wiki/2023_Indian_Premier_League
{"inner": "2023 Indian Premier League", "level": 1, "lower": [{"inner": "Administration", "level": 2, "lower": []}, {"inner": "Background", "level": 2, "lower": []}, {"inner": "Participating teams", "level": 2, "lower": []}, {"inner": "Personnel changes", "level": 2, "lower": []}, {"inner": "Rules", "level": 2, "lower": []}, {"inner": "Venues", "level": 2, "lower": []}, {"inner": "Format", "level": 2, "lower": []}, {"inner": "Points table", "level": 2, "lower": []}, {"inner": "Match summary", "level": 2, "lower": []}, {"inner": "League stage", "level": 2, "lower": []}, {"inner": "Playoffs", "level": 2, "lower": [{"inner": "Qualifier 1", "level": 3, "lower": []}, {"inner": "Eliminator", "level": 3, "lower": []}, {"inner": "Qualifier 2", "level": 3, "lower": []}, {"inner": "Final", "level": 3, "lower": []}]}, {"inner": "Broadcasting", "level": 2, "lower": []}, {"inner": "Criticism", "level": 2, "lower": [{"inner": "Slow over- rate", "level": 3, "lower": []}, {"inner": "Impact player rule", "level": 3, "lower": []}]}, {"inner": "Statistics and awards", "level": 2, "lower": [{"inner": "Most runs", "level": 3, "lower": []}, {"inner": "Most wickets", "level": 3, "lower": []}, {"inner": "End of the season awards", "level": 3, "lower": []}]}, {"inner": "Notes", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Plutonium
{"inner": "Plutonium", "level": 1, "lower": [{"inner": "Characteristics", "level": 2, "lower": [{"inner": "Physical properties", "level": 3, "lower": []}, {"inner": "Allotropes", "level": 3, "lower": []}, {"inner": "Nuclear fission", "level": 3, "lower": []}, {"inner": "Isotopes and nucleosynthesis", "level": 3, "lower": []}, {"inner": "Decay heat and fission properties", "level": 3, "lower": []}, {"inner": "Compounds and chemistry", "level": 3, "lower": [{"inner": "Electronic structure", "level": 4, "lower": []}]}, {"inner": "Alloys", "level": 3, "lower": []}]}, {"inner": "Occurrence", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": [{"inner": "Discovery", "level": 3, "lower": []}, {"inner": "Early research", "level": 3, "lower": []}, {"inner": "Production during the Manhattan Project", "level": 3, "lower": []}, {"inner": "Trinity and Fat Man atomic bombs", "level": 3, "lower": []}, {"inner": "Cold War use and waste", "level": 3, "lower": []}, {"inner": "Medical experimentation", "level": 3, "lower": []}]}, {"inner": "Applications", "level": 2, "lower": [{"inner": "Explosives", "level": 3, "lower": []}, {"inner": "Mixed oxide fuel", "level": 3, "lower": []}, {"inner": "Power and heat source", "level": 3, "lower": []}]}, {"inner": "Precautions", "level": 2, "lower": [{"inner": "Toxicity", "level": 3, "lower": []}, {"inner": "Marine toxicity", "level": 3, "lower": []}, {"inner": "Criticality potential", "level": 3, "lower": []}, {"inner": "Flammability", "level": 3, "lower": []}]}, {"inner": "Transportation", "level": 2, "lower": [{"inner": "Land and sea", "level": 3, "lower": []}, {"inner": "Air", "level": 3, "lower": []}]}, {"inner": "In popular culture", "level": 2, "lower": []}, {"inner": "Notes", "level": 2, "lower": [{"inner": "Footnotes", "level": 3, "lower": []}, {"inner": "Citations", "level": 3, "lower": []}]}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/White_supremacy
{"inner": "White supremacy", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": [{"inner": "United States", "level": 3, "lower": [{"inner": "Early history", "level": 4, "lower": []}, {"inner": "20th century", "level": 4, "lower": []}, {"inner": "21st century", "level": 4, "lower": []}, {"inner": "Patterns of influence", "level": 4, "lower": []}]}, {"inner": "British Commonwealth", "level": 3, "lower": [{"inner": "South Africa", "level": 4, "lower": []}, {"inner": "Rhodesia", "level": 4, "lower": []}]}, {"inner": "Germany", "level": 3, "lower": []}, {"inner": "Australia and New Zealand", "level": 3, "lower": []}]}, {"inner": "Ideologies and movements", "level": 2, "lower": [{"inner": "White nationalism", "level": 3, "lower": []}, {"inner": "White separatism", "level": 3, "lower": [{"inner": "Notable white separatists", "level": 4, "lower": []}, {"inner": "Aligned organizations and philosophies", "level": 4, "lower": []}]}]}, {"inner": "Academic use of the term", "level": 2, "lower": []}]}
/wiki/Israeli_Air_Force
{"inner": "Israeli Air Force", "level": 1, "lower": [{"inner": "Mission statement", "level": 2, "lower": []}, {"inner": "Insignia", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": [{"inner": "Early years (1948\u20131967)", "level": 3, "lower": []}, {"inner": "Suez Crisis (1956)", "level": 3, "lower": []}, {"inner": "Six-Day War (1967)", "level": 3, "lower": []}, {"inner": "War of Attrition", "level": 3, "lower": []}, {"inner": "Yom Kippur War (1973)", "level": 3, "lower": []}, {"inner": "Expansion (1973\u20131982)", "level": 3, "lower": []}, {"inner": "1982 Lebanon War and aftermath", "level": 3, "lower": []}, {"inner": "1990s and beyond", "level": 3, "lower": []}, {"inner": "2006 Lebanon War", "level": 3, "lower": []}, {"inner": "2007 Operation Outside the Box", "level": 3, "lower": []}, {"inner": "Against Hamas", "level": 3, "lower": []}, {"inner": "Incidents during the Syrian Civil War", "level": 3, "lower": []}]}, {"inner": "Organization", "level": 2, "lower": [{"inner": "Administrative organization", "level": 3, "lower": []}, {"inner": "Operational organization", "level": 3, "lower": []}]}, {"inner": "Aircraft", "level": 2, "lower": [{"inner": "Current inventory", "level": 3, "lower": []}, {"inner": "Historic", "level": 3, "lower": []}, {"inner": "Munitions and space systems", "level": 3, "lower": []}]}, {"inner": "Pilot selection and training", "level": 2, "lower": [{"inner": "Ranks", "level": 3, "lower": [{"inner": "Officers", "level": 4, "lower": []}, {"inner": "Enlisted", "level": 4, "lower": []}]}]}, {"inner": "List of IAF commanders", "level": 2, "lower": []}]}
/wiki/New_Orleans
{"inner": "New Orleans", "level": 1, "lower": [{"inner": "Etymology and nicknames", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": [{"inner": "French\u2013Spanish colonial era", "level": 3, "lower": []}, {"inner": "United States territorial era", "level": 3, "lower": []}, {"inner": "Battle of New Orleans", "level": 3, "lower": []}, {"inner": "Port", "level": 3, "lower": []}, {"inner": "Civil War\u2013Reconstruction era", "level": 3, "lower": []}, {"inner": "Jim Crow era", "level": 3, "lower": []}, {"inner": "20th century", "level": 3, "lower": [{"inner": "Civil Rights movement", "level": 4, "lower": []}, {"inner": "Drainage and flood control", "level": 4, "lower": []}]}, {"inner": "21st century", "level": 3, "lower": [{"inner": "Hurricane Katrina", "level": 4, "lower": []}, {"inner": "Hurricane Rita", "level": 4, "lower": []}, {"inner": "Post-disaster recovery", "level": 4, "lower": []}, {"inner": "Hurricane Ida", "level": 4, "lower": []}]}]}, {"inner": "Geography", "level": 2, "lower": [{"inner": "Elevation", "level": 3, "lower": []}, {"inner": "Cityscape", "level": 3, "lower": [{"inner": "Historic and residential architecture", "level": 4, "lower": []}, {"inner": "Tallest buildings", "level": 4, "lower": []}]}, {"inner": "Climate", "level": 3, "lower": []}, {"inner": "Threat from tropical cyclones", "level": 3, "lower": []}]}, {"inner": "Demographics", "level": 2, "lower": [{"inner": "Race and ethnicity", "level": 3, "lower": []}, {"inner": "Sexual orientation and gender identity", "level": 3, "lower": []}, {"inner": "Religion", "level": 3, "lower": []}]}, {"inner": "Economy", "level": 2, "lower": [{"inner": "Port", "level": 3, "lower": []}, {"inner": "Business", "level": 3, "lower": []}, {"inner": "Tourist and convention business", "level": 3, "lower": []}, {"inner": "Federal and military agencies", "level": 3, "lower": []}]}, {"inner": "Culture and contemporary life", "level": 2, "lower": [{"inner": "Tourism", "level": 3, "lower": []}, {"inner": "Entertainment and performing arts", "level": 3, "lower": []}, {"inner": "Cuisine", "level": 3, "lower": []}, {"inner": "Dialect", "level": 3, "lower": []}]}, {"inner": "Sports", "level": 2, "lower": []}, {"inner": "National protected areas", "level": 2, "lower": []}, {"inner": "Government", "level": 2, "lower": []}, {"inner": "Crime", "level": 2, "lower": []}, {"inner": "Education", "level": 2, "lower": [{"inner": "Colleges and universities", "level": 3, "lower": []}, {"inner": "Primary and secondary schools", "level": 3, "lower": []}, {"inner": "Libraries", "level": 3, "lower": []}]}, {"inner": "Media", "level": 2, "lower": []}, {"inner": "Transportation", "level": 2, "lower": [{"inner": "Public transportation", "level": 3, "lower": [{"inner": "Streetcars", "level": 4, "lower": []}, {"inner": "Buses", "level": 4, "lower": []}, {"inner": "Ferries", "level": 4, "lower": []}]}, {"inner": "Bicycling", "level": 3, "lower": []}, {"inner": "Roads", "level": 3, "lower": []}, {"inner": "Taxi service", "level": 3, "lower": []}, {"inner": "Airports", "level": 3, "lower": []}, {"inner": "Rail", "level": 3, "lower": []}, {"inner": "Modal characteristics", "level": 3, "lower": []}]}, {"inner": "Notable people", "level": 2, "lower": []}, {"inner": "Sister cities", "level": 2, "lower": []}]}
/wiki/Royal_assent
{"inner": "Royal assent", "level": 1, "lower": [{"inner": "Usage", "level": 2, "lower": [{"inner": "United Kingdom", "level": 3, "lower": [{"inner": "Historical development", "level": 4, "lower": []}, {"inner": "Relationship to royal consent", "level": 4, "lower": []}]}, {"inner": "Other Commonwealth realms", "level": 3, "lower": [{"inner": "Canada", "level": 4, "lower": []}]}]}, {"inner": "Development", "level": 2, "lower": []}, {"inner": "Ceremony", "level": 2, "lower": [{"inner": "United Kingdom", "level": 3, "lower": []}, {"inner": "Australia and New Zealand", "level": 3, "lower": []}, {"inner": "Canada", "level": 3, "lower": []}]}, {"inner": "Other countries", "level": 2, "lower": [{"inner": "Belgium", "level": 3, "lower": []}, {"inner": "Japan", "level": 3, "lower": []}, {"inner": "Jordan", "level": 3, "lower": []}, {"inner": "Luxembourg", "level": 3, "lower": []}, {"inner": "Norway", "level": 3, "lower": []}, {"inner": "Spain", "level": 3, "lower": []}, {"inner": "Tonga", "level": 3, "lower": []}]}, {"inner": "Notes", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "Further reading", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/2023_Indianapolis_500
{"inner": "2023 Indianapolis 500", "level": 1, "lower": [{"inner": "Race background", "level": 2, "lower": [{"inner": "Sponsorship", "level": 3, "lower": []}, {"inner": "Rule changes", "level": 3, "lower": []}, {"inner": "2023 IndyCar Series", "level": 3, "lower": []}]}, {"inner": "Race schedules", "level": 2, "lower": []}, {"inner": "Entry list", "level": 2, "lower": []}, {"inner": "Testing and rookie orientation", "level": 2, "lower": [{"inner": "Open Test\u2014Thursday April 20", "level": 3, "lower": []}, {"inner": "Open test\u2014Friday April 21", "level": 3, "lower": []}]}, {"inner": "Practice", "level": 2, "lower": [{"inner": "Opening day\u2014Tuesday May 16", "level": 3, "lower": []}, {"inner": "Wednesday May 17", "level": 3, "lower": []}, {"inner": "Thursday May 18", "level": 3, "lower": []}, {"inner": "Fast Friday\u2014Friday May 19", "level": 3, "lower": []}]}, {"inner": "Time trials", "level": 2, "lower": [{"inner": "Saturday, May 20", "level": 3, "lower": []}, {"inner": "Sunday, May 21", "level": 3, "lower": [{"inner": "Top 12 qualifying", "level": 4, "lower": []}, {"inner": "Last Chance Qualifying", "level": 4, "lower": []}, {"inner": "Fast Six Qualifying", "level": 4, "lower": []}]}]}, {"inner": "Post-qualifying practice", "level": 2, "lower": [{"inner": "Post-qualifying practice\u2014Monday, May 22", "level": 3, "lower": []}, {"inner": "Special test\u2014Thursday, May 25", "level": 3, "lower": []}, {"inner": "Carb Day\u2014Friday, May 26", "level": 3, "lower": []}, {"inner": "Pit Stop Challenge", "level": 3, "lower": []}]}, {"inner": "Starting grid", "level": 2, "lower": []}, {"inner": "Race report", "level": 2, "lower": [{"inner": "First half", "level": 3, "lower": []}, {"inner": "Second half", "level": 3, "lower": [{"inner": "First red flag", "level": 4, "lower": []}, {"inner": "Second red flag", "level": 4, "lower": []}, {"inner": "Third red flag and finish", "level": 4, "lower": []}]}]}, {"inner": "Box score", "level": 2, "lower": []}, {"inner": "Broadcasting", "level": 2, "lower": [{"inner": "Television", "level": 3, "lower": []}, {"inner": "Radio", "level": 3, "lower": []}]}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/June_6
{"inner": "June 6", "level": 1, "lower": [{"inner": "Events", "level": 2, "lower": [{"inner": "Pre-1600", "level": 3, "lower": []}, {"inner": "1601\u20131900", "level": 3, "lower": []}, {"inner": "1901\u2013present", "level": 3, "lower": []}]}, {"inner": "Births", "level": 2, "lower": [{"inner": "Pre-1600", "level": 3, "lower": []}, {"inner": "1601\u20131900", "level": 3, "lower": []}, {"inner": "1901\u2013present", "level": 3, "lower": []}]}, {"inner": "Deaths", "level": 2, "lower": [{"inner": "Pre-1600", "level": 3, "lower": []}, {"inner": "1601\u20131900", "level": 3, "lower": []}, {"inner": "1901\u2013present", "level": 3, "lower": []}]}, {"inner": "Holidays and observances", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Iraq_and_weapons_of_mass_destruction
{"inner": "Iraq and weapons of mass destruction", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": [{"inner": "Program development 1960s\u20131980s", "level": 3, "lower": [{"inner": "Western help with Iraq's WMD program", "level": 4, "lower": []}, {"inner": "United States", "level": 4, "lower": []}, {"inner": "United Kingdom", "level": 4, "lower": []}]}, {"inner": "Iran\u2013Iraq War", "level": 3, "lower": [{"inner": "Chemical weapon attacks", "level": 4, "lower": []}]}, {"inner": "1991 Gulf War", "level": 3, "lower": []}, {"inner": "UN inspections", "level": 3, "lower": [{"inner": "UNSCOM inspections 1991\u20131998", "level": 4, "lower": []}, {"inner": "Between inspections: 1998\u20132003", "level": 4, "lower": []}]}, {"inner": "2003 Iraq War", "level": 3, "lower": [{"inner": "Prelude", "level": 4, "lower": []}, {"inner": "Legal justification", "level": 4, "lower": []}, {"inner": "Coalition expanded intelligence", "level": 4, "lower": []}, {"inner": "Iraq Survey Group", "level": 4, "lower": []}, {"inner": "Captured documents", "level": 4, "lower": []}, {"inner": "Post-war discoveries and incidents", "level": 4, "lower": []}, {"inner": "2005: Operation Avarice", "level": 4, "lower": []}, {"inner": "2006: House Armed Services Committee Hearing", "level": 4, "lower": []}, {"inner": "The New York Times investigative report", "level": 4, "lower": []}]}, {"inner": "2009 Declaration", "level": 3, "lower": []}]}, {"inner": "Public perception", "level": 2, "lower": []}]}
/wiki/Murder_of_James_Byrd_Jr.
{"inner": "Murder of James Byrd Jr.", "level": 1, "lower": [{"inner": "Background", "level": 2, "lower": []}, {"inner": "Murder", "level": 2, "lower": []}, {"inner": "Perpetrators", "level": 2, "lower": [{"inner": "Shawn Berry", "level": 3, "lower": []}, {"inner": "Lawrence Brewer", "level": 3, "lower": []}, {"inner": "John King", "level": 3, "lower": []}]}, {"inner": "Reactions", "level": 2, "lower": [{"inner": "Impact on US politics", "level": 3, "lower": []}, {"inner": "Musical and poetry tributes", "level": 3, "lower": []}]}]}
/wiki/Linear_algebra
{"inner": "Linear algebra", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": []}, {"inner": "Vector spaces", "level": 2, "lower": [{"inner": "Linear maps", "level": 3, "lower": []}, {"inner": "Subspaces, span, and basis", "level": 3, "lower": []}]}, {"inner": "Matrices", "level": 2, "lower": []}, {"inner": "Linear systems", "level": 2, "lower": []}, {"inner": "Endomorphisms and square matrices", "level": 2, "lower": [{"inner": "Determinant", "level": 3, "lower": []}, {"inner": "Eigenvalues and eigenvectors", "level": 3, "lower": []}]}, {"inner": "Duality", "level": 2, "lower": [{"inner": "Dual map", "level": 3, "lower": []}, {"inner": "Inner-product spaces", "level": 3, "lower": []}]}, {"inner": "Relationship with geometry", "level": 2, "lower": []}, {"inner": "Usage and applications", "level": 2, "lower": [{"inner": "Geometry of ambient space", "level": 3, "lower": []}, {"inner": "Functional analysis", "level": 3, "lower": []}, {"inner": "Study of complex systems", "level": 3, "lower": []}, {"inner": "Scientific computation", "level": 3, "lower": []}]}, {"inner": "Extensions and generalizations", "level": 2, "lower": [{"inner": "Module theory", "level": 3, "lower": []}, {"inner": "Multilinear algebra and tensors", "level": 3, "lower": []}, {"inner": "Topological vector spaces", "level": 3, "lower": []}]}]}
/wiki/June_8
{"inner": "June 8", "level": 1, "lower": [{"inner": "Events", "level": 2, "lower": [{"inner": "Pre-1600", "level": 3, "lower": []}, {"inner": "1601\u20131900", "level": 3, "lower": []}, {"inner": "1901\u2013present", "level": 3, "lower": []}]}, {"inner": "Births", "level": 2, "lower": [{"inner": "Pre-1600", "level": 3, "lower": []}, {"inner": "1601\u20131900", "level": 3, "lower": []}, {"inner": "1901\u2013present", "level": 3, "lower": []}]}, {"inner": "Deaths", "level": 2, "lower": [{"inner": "Pre-1600", "level": 3, "lower": []}, {"inner": "1601\u20131900", "level": 3, "lower": []}, {"inner": "1901\u2013present", "level": 3, "lower": []}]}, {"inner": "Holidays and observances", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Wikimedia_Foundation
{"inner": "Wikimedia Foundation", "level": 1, "lower": [{"inner": "Mission", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": []}, {"inner": "Projects and initiatives", "level": 2, "lower": [{"inner": "Wikimedia projects", "level": 3, "lower": []}, {"inner": "Affiliates", "level": 3, "lower": []}, {"inner": "Wikimania", "level": 3, "lower": []}]}, {"inner": "Technology", "level": 2, "lower": [{"inner": "Hardware", "level": 3, "lower": []}, {"inner": "Software", "level": 3, "lower": []}]}, {"inner": "Finances", "level": 2, "lower": [{"inner": "Wikimedia Endowment", "level": 3, "lower": []}, {"inner": "Financial development", "level": 3, "lower": []}, {"inner": "Expenses", "level": 3, "lower": []}, {"inner": "Grants", "level": 3, "lower": []}]}, {"inner": "Staff", "level": 2, "lower": [{"inner": "History", "level": 3, "lower": []}, {"inner": "Present department structure", "level": 3, "lower": []}, {"inner": "Board of trustees", "level": 3, "lower": []}]}, {"inner": "Independent contractors", "level": 2, "lower": []}, {"inner": "Disputes", "level": 2, "lower": [{"inner": "Excessive spending and fundraising", "level": 3, "lower": []}, {"inner": "Knowledge Engine project", "level": 3, "lower": []}]}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": [{"inner": "Organization", "level": 3, "lower": []}, {"inner": "Financials", "level": 3, "lower": []}, {"inner": "Charity status", "level": 3, "lower": []}, {"inner": "Community", "level": 3, "lower": []}]}]}
/wiki/Symmetric_matrix
{"inner": "Symmetric matrix", "level": 1, "lower": [{"inner": "Example", "level": 2, "lower": []}, {"inner": "Properties", "level": 2, "lower": [{"inner": "Basic properties", "level": 3, "lower": []}, {"inner": "Decomposition into symmetric and skew-symmetric", "level": 3, "lower": []}, {"inner": "Matrix congruent to a symmetric matrix", "level": 3, "lower": []}, {"inner": "Symmetry implies normality", "level": 3, "lower": []}, {"inner": "Real symmetric matrices", "level": 3, "lower": []}, {"inner": "Complex symmetric matrices", "level": 3, "lower": []}]}, {"inner": "Decomposition", "level": 2, "lower": []}, {"inner": "Hessian", "level": 2, "lower": []}, {"inner": "Symmetrizable matrix", "level": 2, "lower": []}]}
/wiki/Orthonormal_basis
{"inner": "Orthonormal basis", "level": 1, "lower": [{"inner": "Examples", "level": 2, "lower": []}, {"inner": "Basic formula", "level": 2, "lower": []}, {"inner": "Incomplete orthogonal sets", "level": 2, "lower": []}, {"inner": "Existence", "level": 2, "lower": []}, {"inner": "Choice of basis as a choice of isomorphism", "level": 2, "lower": []}, {"inner": "As a principal homogeneous space", "level": 2, "lower": []}]}
/wiki/Hilbert_matrix
{"inner": "Hilbert matrix", "level": 1, "lower": [{"inner": "Historical note", "level": 2, "lower": []}, {"inner": "Properties", "level": 2, "lower": []}, {"inner": "Applications", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "Further reading", "level": 2, "lower": []}]}
/wiki/Operator_(mathematics)
{"inner": "Operator (mathematics)", "level": 1, "lower": [{"inner": "Linear operators", "level": 2, "lower": []}, {"inner": "Bounded operators", "level": 2, "lower": []}, {"inner": "Examples", "level": 2, "lower": [{"inner": "Geometry", "level": 3, "lower": []}, {"inner": "Probability theory", "level": 3, "lower": []}, {"inner": "Calculus", "level": 3, "lower": [{"inner": "Fourier series and Fourier transform", "level": 4, "lower": []}, {"inner": "Laplace transform", "level": 4, "lower": []}]}, {"inner": "Fundamental operators on scalar and vector fields", "level": 3, "lower": []}]}]}
/wiki/Hilbert_space
{"inner": "Hilbert space", "level": 1, "lower": [{"inner": "Definition and illustration", "level": 2, "lower": [{"inner": "Motivating example: Euclidean vector space", "level": 3, "lower": []}, {"inner": "Definition", "level": 3, "lower": []}, {"inner": "Second example: sequence spaces", "level": 3, "lower": []}]}, {"inner": "History", "level": 2, "lower": []}, {"inner": "Examples", "level": 2, "lower": [{"inner": "Lebesgue spaces", "level": 3, "lower": []}, {"inner": "Sobolev spaces", "level": 3, "lower": []}, {"inner": "Spaces of holomorphic functions", "level": 3, "lower": [{"inner": "Hardy spaces", "level": 4, "lower": []}, {"inner": "Bergman spaces", "level": 4, "lower": []}]}]}, {"inner": "Applications", "level": 2, "lower": [{"inner": "Sturm\u2013Liouville theory", "level": 3, "lower": []}, {"inner": "Partial differential equations", "level": 3, "lower": []}, {"inner": "Ergodic theory", "level": 3, "lower": []}, {"inner": "Fourier analysis", "level": 3, "lower": []}, {"inner": "Quantum mechanics", "level": 3, "lower": []}, {"inner": "Color perception", "level": 3, "lower": []}]}, {"inner": "Properties", "level": 2, "lower": [{"inner": "Pythagorean identity", "level": 3, "lower": []}, {"inner": "Parallelogram identity and polarization", "level": 3, "lower": []}, {"inner": "Best approximation", "level": 3, "lower": []}, {"inner": "Duality", "level": 3, "lower": []}, {"inner": "Weakly-convergent sequences", "level": 3, "lower": []}, {"inner": "Banach space properties", "level": 3, "lower": []}]}, {"inner": "Operators on Hilbert spaces", "level": 2, "lower": [{"inner": "Bounded operators", "level": 3, "lower": []}, {"inner": "Unbounded operators", "level": 3, "lower": []}]}, {"inner": "Constructions", "level": 2, "lower": [{"inner": "Direct sums", "level": 3, "lower": []}, {"inner": "Tensor products", "level": 3, "lower": []}]}, {"inner": "Orthonormal bases", "level": 2, "lower": [{"inner": "Sequence spaces", "level": 3, "lower": []}, {"inner": "Bessel's inequality and Parseval's formula", "level": 3, "lower": []}, {"inner": "Hilbert dimension", "level": 3, "lower": []}, {"inner": "Separable spaces", "level": 3, "lower": [{"inner": "In quantum field theory", "level": 4, "lower": []}]}]}, {"inner": "Orthogonal complements and projections", "level": 2, "lower": []}, {"inner": "Spectral theory", "level": 2, "lower": []}, {"inner": "In popular culture", "level": 2, "lower": []}]}
/wiki/Determinant
{"inner": "Determinant", "level": 1, "lower": [{"inner": "Two by two matrices", "level": 2, "lower": [{"inner": "First properties", "level": 3, "lower": []}]}, {"inner": "Geometric meaning", "level": 2, "lower": []}, {"inner": "Definition", "level": 2, "lower": [{"inner": "Leibniz formula", "level": 3, "lower": [{"inner": "3 \u00d7 3 matrices", "level": 4, "lower": []}, {"inner": "n \u00d7 n matrices", "level": 4, "lower": []}]}]}, {"inner": "Properties of the determinant", "level": 2, "lower": [{"inner": "Characterization of the determinant", "level": 3, "lower": []}, {"inner": "Immediate consequences", "level": 3, "lower": [{"inner": "Example", "level": 4, "lower": []}]}, {"inner": "Transpose", "level": 3, "lower": []}, {"inner": "Multiplicativity and matrix groups", "level": 3, "lower": []}, {"inner": "Laplace expansion", "level": 3, "lower": [{"inner": "Adjugate matrix", "level": 4, "lower": []}]}, {"inner": "Block matrices", "level": 3, "lower": []}, {"inner": "Sylvester's determinant theorem", "level": 3, "lower": []}, {"inner": "Sum", "level": 3, "lower": [{"inner": "Sum identity for 2\u00d72 matrices", "level": 4, "lower": []}]}]}, {"inner": "Properties of the determinant in relation to other notions", "level": 2, "lower": [{"inner": "Eigenvalues and characteristic polynomial", "level": 3, "lower": []}, {"inner": "Trace", "level": 3, "lower": []}, {"inner": "Upper and lower bounds", "level": 3, "lower": []}, {"inner": "Derivative", "level": 3, "lower": []}]}, {"inner": "History", "level": 2, "lower": []}, {"inner": "Applications", "level": 2, "lower": [{"inner": "Cramer's rule", "level": 3, "lower": []}, {"inner": "Linear independence", "level": 3, "lower": []}, {"inner": "Orientation of a basis", "level": 3, "lower": []}, {"inner": "Volume and Jacobian determinant", "level": 3, "lower": []}]}, {"inner": "Abstract algebraic aspects", "level": 2, "lower": [{"inner": "Determinant of an endomorphism", "level": 3, "lower": []}, {"inner": "Square matrices over commutative rings", "level": 3, "lower": []}, {"inner": "Exterior algebra", "level": 3, "lower": []}]}, {"inner": "Generalizations and related notions", "level": 2, "lower": [{"inner": "Determinants for finite-dimensional algebras", "level": 3, "lower": []}, {"inner": "Infinite matrices", "level": 3, "lower": []}, {"inner": "Operators in von Neumann algebras", "level": 3, "lower": []}, {"inner": "Related notions for non-commutative rings", "level": 3, "lower": []}]}, {"inner": "Calculation", "level": 2, "lower": [{"inner": "Decomposition methods", "level": 3, "lower": []}, {"inner": "Further methods", "level": 3, "lower": []}]}]}
/wiki/Binomial_transform
{"inner": "Binomial transform", "level": 1, "lower": [{"inner": "Definition", "level": 2, "lower": []}, {"inner": "Example", "level": 2, "lower": []}, {"inner": "Ordinary generating function", "level": 2, "lower": []}, {"inner": "Euler transform", "level": 2, "lower": []}, {"inner": "Exponential generating function", "level": 2, "lower": []}, {"inner": "Integral representation", "level": 2, "lower": []}, {"inner": "Generalizations", "level": 2, "lower": []}]}
/wiki/Eigenvalue
{"inner": "Eigenvalues and eigenvectors", "level": 1, "lower": [{"inner": "Formal definition", "level": 2, "lower": []}, {"inner": "Overview", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": []}, {"inner": "Eigenvalues and eigenvectors of matrices", "level": 2, "lower": [{"inner": "Eigenvalues and the characteristic polynomial", "level": 3, "lower": []}, {"inner": "Algebraic multiplicity", "level": 3, "lower": []}, {"inner": "Eigenspaces, geometric multiplicity, and the eigenbasis for matrices", "level": 3, "lower": []}, {"inner": "Additional properties of eigenvalues", "level": 3, "lower": []}, {"inner": "Left and right eigenvectors", "level": 3, "lower": []}, {"inner": "Diagonalization and the eigendecomposition", "level": 3, "lower": []}, {"inner": "Variational characterization", "level": 3, "lower": []}, {"inner": "Matrix examples", "level": 3, "lower": [{"inner": "Two-dimensional matrix example", "level": 4, "lower": []}, {"inner": "Three-dimensional matrix example", "level": 4, "lower": []}, {"inner": "Three-dimensional matrix example with complex eigenvalues", "level": 4, "lower": []}, {"inner": "Diagonal matrix example", "level": 4, "lower": []}, {"inner": "Triangular matrix example", "level": 4, "lower": []}, {"inner": "Matrix with repeated eigenvalues example", "level": 4, "lower": []}]}, {"inner": "Eigenvector-eigenvalue identity", "level": 3, "lower": []}]}, {"inner": "Eigenvalues and eigenfunctions of differential operators", "level": 2, "lower": [{"inner": "Derivative operator example", "level": 3, "lower": []}]}, {"inner": "General definition", "level": 2, "lower": [{"inner": "Eigenspaces, geometric multiplicity, and the eigenbasis", "level": 3, "lower": []}, {"inner": "Spectral theory", "level": 3, "lower": []}, {"inner": "Associative algebras and representation theory", "level": 3, "lower": []}]}, {"inner": "Dynamic equations", "level": 2, "lower": []}, {"inner": "Calculation", "level": 2, "lower": [{"inner": "Classical method", "level": 3, "lower": [{"inner": "Eigenvalues", "level": 4, "lower": []}, {"inner": "Eigenvectors", "level": 4, "lower": []}]}, {"inner": "Simple iterative methods", "level": 3, "lower": []}, {"inner": "Modern methods", "level": 3, "lower": []}]}, {"inner": "Applications", "level": 2, "lower": [{"inner": "Eigenvalues of geometric transformations", "level": 3, "lower": []}, {"inner": "Schr\u00f6dinger equation", "level": 3, "lower": []}, {"inner": "Wave transport", "level": 3, "lower": []}, {"inner": "Molecular orbitals", "level": 3, "lower": []}, {"inner": "Geology and glaciology", "level": 3, "lower": []}, {"inner": "Principal component analysis", "level": 3, "lower": []}, {"inner": "Vibration analysis", "level": 3, "lower": []}, {"inner": "Eigenfaces", "level": 3, "lower": []}, {"inner": "Tensor of moment of inertia", "level": 3, "lower": []}, {"inner": "Stress tensor", "level": 3, "lower": []}, {"inner": "Graphs", "level": 3, "lower": []}, {"inner": "Basic reproduction number", "level": 3, "lower": []}]}]}
/wiki/Real_number
{"inner": "Real number", "level": 1, "lower": [{"inner": "Characterizing properties", "level": 2, "lower": []}, {"inner": "Arithmetic", "level": 2, "lower": [{"inner": "Auxiliary operations", "level": 3, "lower": []}, {"inner": "Auxiliary order relations", "level": 3, "lower": []}, {"inner": "Integers and fractions as real numbers", "level": 3, "lower": []}]}, {"inner": "Dedekind completeness", "level": 2, "lower": []}, {"inner": "Decimal representation", "level": 2, "lower": []}, {"inner": "Topological completeness", "level": 2, "lower": [{"inner": "\"The complete ordered field\"", "level": 3, "lower": []}]}, {"inner": "Cardinality", "level": 2, "lower": []}, {"inner": "Other properties", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": []}, {"inner": "Formal definitions", "level": 2, "lower": [{"inner": "Axiomatic approach", "level": 3, "lower": []}, {"inner": "Construction from the rational numbers", "level": 3, "lower": []}]}, {"inner": "Applications and connections", "level": 2, "lower": [{"inner": "Physics", "level": 3, "lower": []}, {"inner": "Logic", "level": 3, "lower": []}, {"inner": "Computation", "level": 3, "lower": []}, {"inner": "Set theory", "level": 3, "lower": []}]}, {"inner": "Vocabulary and notation", "level": 2, "lower": []}, {"inner": "Generalizations and extensions", "level": 2, "lower": []}]}
/wiki/Hankel_transform
{"inner": "Hankel transform", "level": 1, "lower": [{"inner": "Definition", "level": 2, "lower": [{"inner": "Domain of definition", "level": 3, "lower": []}, {"inner": "Alternative definition", "level": 3, "lower": []}]}, {"inner": "Transforming Laplace's equation", "level": 2, "lower": []}, {"inner": "Orthogonality", "level": 2, "lower": []}, {"inner": "The Plancherel theorem and Parseval's theorem", "level": 2, "lower": []}, {"inner": "Relation to the multidimensional Fourier transform", "level": 2, "lower": [{"inner": "Special cases", "level": 3, "lower": [{"inner": "Fourier transform in two dimensions", "level": 4, "lower": []}, {"inner": "Fourier transform in three dimensions", "level": 4, "lower": []}, {"inner": "Fourier transform in d dimensions (radially symmetric case)", "level": 4, "lower": []}, {"inner": "2D functions inside a limited radius", "level": 4, "lower": []}]}]}, {"inner": "Relation to the Fourier and Abel transforms", "level": 2, "lower": []}, {"inner": "Numerical evaluation", "level": 2, "lower": []}, {"inner": "Some Hankel transform pairs", "level": 2, "lower": []}]}
/wiki/Sequence
{"inner": "Sequence", "level": 1, "lower": [{"inner": "Examples and notation", "level": 2, "lower": [{"inner": "Examples", "level": 3, "lower": []}, {"inner": "Indexing", "level": 3, "lower": []}, {"inner": "Defining a sequence by recursion", "level": 3, "lower": []}]}, {"inner": "Formal definition and basic properties", "level": 2, "lower": [{"inner": "Definition", "level": 3, "lower": []}, {"inner": "Finite and infinite", "level": 3, "lower": []}, {"inner": "Increasing and decreasing", "level": 3, "lower": []}, {"inner": "Bounded", "level": 3, "lower": []}, {"inner": "Subsequences", "level": 3, "lower": []}, {"inner": "Other types of sequences", "level": 3, "lower": []}]}, {"inner": "Limits and convergence", "level": 2, "lower": [{"inner": "Formal definition of convergence", "level": 3, "lower": []}, {"inner": "Applications and important results", "level": 3, "lower": []}, {"inner": "Cauchy sequences", "level": 3, "lower": []}, {"inner": "Infinite limits", "level": 3, "lower": []}]}, {"inner": "Series", "level": 2, "lower": []}, {"inner": "Use in other fields of mathematics", "level": 2, "lower": [{"inner": "Topology", "level": 3, "lower": [{"inner": "Product topology", "level": 4, "lower": []}]}, {"inner": "Analysis", "level": 3, "lower": [{"inner": "Sequence spaces", "level": 4, "lower": []}]}, {"inner": "Linear algebra", "level": 3, "lower": []}, {"inner": "Abstract algebra", "level": 3, "lower": [{"inner": "Free monoid", "level": 4, "lower": []}, {"inner": "Exact sequences", "level": 4, "lower": []}, {"inner": "Spectral sequences", "level": 4, "lower": []}]}, {"inner": "Set theory", "level": 3, "lower": []}, {"inner": "Computing", "level": 3, "lower": []}, {"inner": "Streams", "level": 3, "lower": []}]}]}
/wiki/Complex_number
{"inner": "Complex number", "level": 1, "lower": [{"inner": "Definition", "level": 2, "lower": []}, {"inner": "Notation", "level": 2, "lower": []}, {"inner": "Visualization", "level": 2, "lower": [{"inner": "Cartesian complex plane", "level": 3, "lower": []}, {"inner": "Polar complex plane", "level": 3, "lower": [{"inner": "Modulus and argument", "level": 4, "lower": []}]}, {"inner": "Complex graphs", "level": 3, "lower": []}]}, {"inner": "History", "level": 2, "lower": []}, {"inner": "Relations and operations", "level": 2, "lower": [{"inner": "Equality", "level": 3, "lower": []}, {"inner": "Ordering", "level": 3, "lower": []}, {"inner": "Conjugate", "level": 3, "lower": []}, {"inner": "Addition and subtraction", "level": 3, "lower": []}, {"inner": "Multiplication and square", "level": 3, "lower": []}, {"inner": "Reciprocal and division", "level": 3, "lower": []}, {"inner": "Multiplication and division in polar form", "level": 3, "lower": []}, {"inner": "Square root", "level": 3, "lower": []}, {"inner": "Exponential function", "level": 3, "lower": [{"inner": "Functional equation", "level": 4, "lower": []}, {"inner": "Euler's formula", "level": 4, "lower": []}]}, {"inner": "Complex logarithm", "level": 3, "lower": []}, {"inner": "Exponentiation", "level": 3, "lower": [{"inner": "Integer and fractional exponents", "level": 4, "lower": []}]}]}, {"inner": "Properties", "level": 2, "lower": [{"inner": "Field structure", "level": 3, "lower": []}, {"inner": "Solutions of polynomial equations", "level": 3, "lower": []}, {"inner": "Algebraic characterization", "level": 3, "lower": []}, {"inner": "Characterization as a topological field", "level": 3, "lower": []}]}, {"inner": "Formal construction", "level": 2, "lower": [{"inner": "Construction as ordered pairs", "level": 3, "lower": []}, {"inner": "Construction as a quotient field", "level": 3, "lower": []}, {"inner": "Matrix representation of complex numbers", "level": 3, "lower": []}]}, {"inner": "Complex analysis", "level": 2, "lower": [{"inner": "Complex exponential and related functions", "level": 3, "lower": []}, {"inner": "Holomorphic functions", "level": 3, "lower": []}]}, {"inner": "Applications", "level": 2, "lower": [{"inner": "Geometry", "level": 3, "lower": [{"inner": "Shapes", "level": 4, "lower": []}, {"inner": "Fractal geometry", "level": 4, "lower": []}, {"inner": "Triangles", "level": 4, "lower": []}]}, {"inner": "Algebraic number theory", "level": 3, "lower": []}, {"inner": "Analytic number theory", "level": 3, "lower": []}, {"inner": "Improper integrals", "level": 3, "lower": []}, {"inner": "Dynamic equations", "level": 3, "lower": []}, {"inner": "Linear algebra", "level": 3, "lower": []}, {"inner": "In applied mathematics", "level": 3, "lower": [{"inner": "Control theory", "level": 4, "lower": []}, {"inner": "Signal analysis", "level": 4, "lower": []}]}, {"inner": "In physics", "level": 3, "lower": [{"inner": "Electromagnetism and electrical engineering", "level": 4, "lower": []}, {"inner": "Fluid dynamics", "level": 4, "lower": []}, {"inner": "Quantum mechanics", "level": 4, "lower": []}, {"inner": "Relativity", "level": 4, "lower": []}]}]}, {"inner": "Generalizations and related notions", "level": 2, "lower": []}]}
/wiki/Hamburger_moment_problem
{"inner": "Hamburger moment problem", "level": 1, "lower": [{"inner": "Characterization", "level": 2, "lower": [{"inner": "Uniqueness of solutions", "level": 3, "lower": []}]}, {"inner": "Further results", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}]}
/wiki/Inverse_matrix
{"inner": "Invertible matrix", "level": 1, "lower": [{"inner": "Properties", "level": 2, "lower": [{"inner": "The invertible matrix theorem", "level": 3, "lower": []}, {"inner": "Other properties", "level": 3, "lower": []}, {"inner": "In relation to its adjugate", "level": 3, "lower": []}, {"inner": "In relation to the identity matrix", "level": 3, "lower": []}, {"inner": "Density", "level": 3, "lower": []}]}, {"inner": "Examples", "level": 2, "lower": []}, {"inner": "Methods of matrix inversion", "level": 2, "lower": [{"inner": "Gaussian elimination", "level": 3, "lower": []}, {"inner": "Newton's method", "level": 3, "lower": []}, {"inner": "Cayley\u2013Hamilton method", "level": 3, "lower": []}, {"inner": "Eigendecomposition", "level": 3, "lower": []}, {"inner": "Cholesky decomposition", "level": 3, "lower": []}, {"inner": "Analytic solution", "level": 3, "lower": [{"inner": "Inversion of 2 \u00d7 2 matrices", "level": 4, "lower": []}, {"inner": "Inversion of 3 \u00d7 3 matrices", "level": 4, "lower": []}, {"inner": "Inversion of 4 \u00d7 4 matrices", "level": 4, "lower": []}]}, {"inner": "Blockwise inversion", "level": 3, "lower": []}, {"inner": "By Neumann series", "level": 3, "lower": []}, {"inner": "p-adic approximation", "level": 3, "lower": []}, {"inner": "Reciprocal basis vectors method", "level": 3, "lower": []}]}, {"inner": "Derivative of the matrix inverse", "level": 2, "lower": []}, {"inner": "Generalized inverse", "level": 2, "lower": []}, {"inner": "Applications", "level": 2, "lower": [{"inner": "Regression/least squares", "level": 3, "lower": []}, {"inner": "Matrix inverses in real-time simulations", "level": 3, "lower": []}, {"inner": "Matrix inverses in MIMO wireless communication", "level": 3, "lower": []}]}]}
/wiki/Method_of_moments_(statistics)
{"inner": "Method of moments (statistics)", "level": 1, "lower": [{"inner": "Method", "level": 2, "lower": []}, {"inner": "Advantages and disadvantages", "level": 2, "lower": []}, {"inner": "Examples", "level": 2, "lower": [{"inner": "Proving the central limit theorem", "level": 3, "lower": []}, {"inner": "Uniform distribution", "level": 3, "lower": []}]}]}
/wiki/Hidden_Markov_model
{"inner": "Hidden Markov model", "level": 1, "lower": [{"inner": "Definition", "level": 2, "lower": [{"inner": "Terminology", "level": 3, "lower": []}]}, {"inner": "Examples", "level": 2, "lower": [{"inner": "Drawing balls from hidden urns", "level": 3, "lower": []}, {"inner": "Weather guessing game", "level": 3, "lower": []}]}, {"inner": "Structural architecture", "level": 2, "lower": []}, {"inner": "Inference", "level": 2, "lower": [{"inner": "Probability of an observed sequence", "level": 3, "lower": []}, {"inner": "Probability of the latent variables", "level": 3, "lower": [{"inner": "Filtering", "level": 4, "lower": []}, {"inner": "Smoothing", "level": 4, "lower": []}, {"inner": "Most likely explanation", "level": 4, "lower": []}]}, {"inner": "Statistical significance", "level": 3, "lower": []}]}, {"inner": "Learning", "level": 2, "lower": []}, {"inner": "Applications", "level": 2, "lower": []}, {"inner": "History", "level": 2, "lower": []}, {"inner": "Extensions", "level": 2, "lower": []}]}
/wiki/Cauchy_matrix
{"inner": "Cauchy matrix", "level": 1, "lower": [{"inner": "Cauchy determinants", "level": 2, "lower": []}, {"inner": "Generalization", "level": 2, "lower": []}]}
/wiki/Masanao_Aoki
{"inner": "Masanao Aoki", "level": 1, "lower": [{"inner": "Selected publications", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Richard_P._Brent
{"inner": "Richard P. Brent", "level": 1, "lower": []}
/wiki/ISBN_(identifier)
{"inner": "ISBN", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": []}, {"inner": "Overview", "level": 2, "lower": [{"inner": "Issuing process", "level": 3, "lower": []}, {"inner": "Registration group element", "level": 3, "lower": []}, {"inner": "Registrant element", "level": 3, "lower": [{"inner": "English language pattern", "level": 4, "lower": []}]}]}, {"inner": "Check digits", "level": 2, "lower": [{"inner": "ISBN-10 check digits", "level": 3, "lower": []}, {"inner": "ISBN-10 check digit calculation", "level": 3, "lower": []}, {"inner": "ISBN-13 check digit calculation", "level": 3, "lower": []}, {"inner": "ISBN-10 to ISBN-13 conversion", "level": 3, "lower": []}, {"inner": "Errors in usage", "level": 3, "lower": []}, {"inner": "eISBN", "level": 3, "lower": []}]}, {"inner": "EAN format used in barcodes, and upgrading", "level": 2, "lower": []}]}
/wiki/Vandermonde_matrix
{"inner": "Vandermonde matrix", "level": 1, "lower": [{"inner": "Applications", "level": 2, "lower": []}, {"inner": "Determinant", "level": 2, "lower": [{"inner": "Proofs", "level": 3, "lower": []}, {"inner": "Using polynomial properties", "level": 3, "lower": []}, {"inner": "Using linear maps", "level": 3, "lower": []}, {"inner": "By row and column operations", "level": 3, "lower": []}, {"inner": "Resulting properties", "level": 3, "lower": []}]}, {"inner": "Confluent Vandermonde matrices", "level": 2, "lower": []}]}
/wiki/Society_for_Industrial_and_Applied_Mathematics
{"inner": "Society for Industrial and Applied Mathematics", "level": 1, "lower": [{"inner": "Membership", "level": 2, "lower": []}, {"inner": "Activity groups", "level": 2, "lower": []}, {"inner": "Publications", "level": 2, "lower": [{"inner": "Journals", "level": 3, "lower": []}, {"inner": "Books", "level": 3, "lower": []}, {"inner": "Conferences", "level": 3, "lower": []}]}, {"inner": "Prizes and recognition", "level": 2, "lower": [{"inner": "John von Neumann Lecture", "level": 3, "lower": []}, {"inner": "MathWorks Math Modeling (M3) Challenge", "level": 3, "lower": []}]}, {"inner": "Leadership", "level": 2, "lower": []}]}
/wiki/Birkh%C3%A4user
{"inner": "Birkh\u00e4user", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}]}
/wiki/Victor_Pan
{"inner": "Victor Pan", "level": 1, "lower": [{"inner": "Education and career", "level": 2, "lower": []}, {"inner": "Contributions", "level": 2, "lower": []}, {"inner": "Recognition", "level": 2, "lower": []}, {"inner": "Selected publications", "level": 2, "lower": [{"inner": "Research papers", "level": 3, "lower": []}, {"inner": "Books", "level": 3, "lower": []}]}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Matrix_(mathematics)
{"inner": "Matrix (mathematics)", "level": 1, "lower": [{"inner": "Definition", "level": 2, "lower": [{"inner": "Size", "level": 3, "lower": []}]}, {"inner": "Notation", "level": 2, "lower": []}, {"inner": "Basic operations", "level": 2, "lower": [{"inner": "Addition, scalar multiplication, and transposition", "level": 3, "lower": []}, {"inner": "Matrix multiplication", "level": 3, "lower": []}, {"inner": "Row operations", "level": 3, "lower": []}, {"inner": "Submatrix", "level": 3, "lower": []}]}, {"inner": "Linear equations", "level": 2, "lower": []}, {"inner": "Linear transformations", "level": 2, "lower": []}, {"inner": "Square matrix", "level": 2, "lower": [{"inner": "Main types", "level": 3, "lower": [{"inner": "Diagonal and triangular matrix", "level": 4, "lower": []}, {"inner": "Identity matrix", "level": 4, "lower": []}, {"inner": "Symmetric or skew-symmetric matrix", "level": 4, "lower": []}, {"inner": "Invertible matrix and its inverse", "level": 4, "lower": []}, {"inner": "Definite matrix", "level": 4, "lower": []}, {"inner": "Orthogonal matrix", "level": 4, "lower": []}]}, {"inner": "Main operations", "level": 3, "lower": [{"inner": "Trace", "level": 4, "lower": []}, {"inner": "Determinant", "level": 4, "lower": []}, {"inner": "Eigenvalues and eigenvectors", "level": 4, "lower": []}]}]}, {"inner": "Computational aspects", "level": 2, "lower": []}, {"inner": "Decomposition", "level": 2, "lower": []}, {"inner": "Abstract algebraic aspects and generalizations", "level": 2, "lower": [{"inner": "Matrices with more general entries", "level": 3, "lower": []}, {"inner": "Relationship to linear maps", "level": 3, "lower": []}, {"inner": "Matrix groups", "level": 3, "lower": []}, {"inner": "Infinite matrices", "level": 3, "lower": []}, {"inner": "Empty matrix", "level": 3, "lower": []}]}, {"inner": "Applications", "level": 2, "lower": [{"inner": "Graph theory", "level": 3, "lower": []}, {"inner": "Analysis and geometry", "level": 3, "lower": []}, {"inner": "Probability theory and statistics", "level": 3, "lower": []}, {"inner": "Symmetries and transformations in physics", "level": 3, "lower": []}, {"inner": "Linear combinations of quantum states", "level": 3, "lower": []}, {"inner": "Normal modes", "level": 3, "lower": []}, {"inner": "Geometrical optics", "level": 3, "lower": []}, {"inner": "Electronics", "level": 3, "lower": []}]}, {"inner": "History", "level": 2, "lower": [{"inner": "Other historical usages of the word \"matrix\" in mathematics", "level": 3, "lower": []}]}]}
/wiki/Cambridge_University_Press
{"inner": "Cambridge University Press", "level": 1, "lower": [{"inner": "History", "level": 2, "lower": []}, {"inner": "Print and typographic heritage", "level": 2, "lower": [{"inner": "People", "level": 3, "lower": []}, {"inner": "Publications", "level": 3, "lower": []}]}, {"inner": "Current publications", "level": 2, "lower": []}, {"inner": "Open access", "level": 2, "lower": []}, {"inner": "Nobel prize winners published by Cambridge University Press", "level": 2, "lower": []}, {"inner": "Organisational governance and operational structure", "level": 2, "lower": [{"inner": "Relationship with the University of Cambridge", "level": 3, "lower": []}, {"inner": "Operational structure", "level": 3, "lower": []}]}, {"inner": "Cambridge University Press partnerships and acquisitions", "level": 2, "lower": []}, {"inner": "Digital developments", "level": 2, "lower": []}, {"inner": "Controversies", "level": 2, "lower": [{"inner": "Tax exemption controversy", "level": 3, "lower": []}, {"inner": "Alms for Jihad", "level": 3, "lower": []}, {"inner": "Cambridge University Press v. Patton", "level": 3, "lower": []}, {"inner": "The China Quarterly", "level": 3, "lower": []}, {"inner": "The Cambridge Handbook of Privatization", "level": 3, "lower": []}]}, {"inner": "Corporate social responsibility", "level": 2, "lower": [{"inner": "Community", "level": 3, "lower": []}, {"inner": "Environment", "level": 3, "lower": []}]}, {"inner": "References", "level": 2, "lower": [{"inner": "Citations", "level": 3, "lower": []}, {"inner": "Sources", "level": 3, "lower": []}]}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Alternant_matrix
{"inner": "Alternant matrix", "level": 1, "lower": [{"inner": "Properties", "level": 2, "lower": []}, {"inner": "Applications", "level": 2, "lower": []}]}
/wiki/Jonathan_Partington
{"inner": "Jonathan Partington", "level": 1, "lower": [{"inner": "Education", "level": 2, "lower": []}, {"inner": "Career", "level": 2, "lower": []}, {"inner": "Books", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Skew-Hermitian_matrix
{"inner": "Skew-Hermitian matrix", "level": 1, "lower": [{"inner": "Example", "level": 2, "lower": []}, {"inner": "Properties", "level": 2, "lower": []}, {"inner": "Decomposition into Hermitian and skew-Hermitian", "level": 2, "lower": []}]}
/wiki/Skew-symmetric_matrix
{"inner": "Skew-symmetric matrix", "level": 1, "lower": [{"inner": "Example", "level": 2, "lower": []}, {"inner": "Properties", "level": 2, "lower": [{"inner": "Vector space structure", "level": 3, "lower": []}, {"inner": "Determinant", "level": 3, "lower": []}, {"inner": "Cross product", "level": 3, "lower": []}, {"inner": "Spectral theory", "level": 3, "lower": []}]}, {"inner": "Skew-symmetric and alternating forms", "level": 2, "lower": []}, {"inner": "Infinitesimal rotations", "level": 2, "lower": []}, {"inner": "Coordinate-free", "level": 2, "lower": []}, {"inner": "Skew-symmetrizable matrix", "level": 2, "lower": []}]}
/wiki/Band_matrix
{"inner": "Band matrix", "level": 1, "lower": [{"inner": "Band matrix", "level": 2, "lower": [{"inner": "Bandwidth", "level": 3, "lower": []}]}, {"inner": "Examples", "level": 2, "lower": []}, {"inner": "Applications", "level": 2, "lower": []}, {"inner": "Band storage", "level": 2, "lower": []}, {"inner": "Band form of sparse matrices", "level": 2, "lower": []}]}
/wiki/Bidiagonal_matrix
{"inner": "Bidiagonal matrix", "level": 1, "lower": [{"inner": "Usage", "level": 2, "lower": [{"inner": "Bidiagonalization", "level": 3, "lower": []}]}]}
/wiki/Arrowhead_matrix
{"inner": "Arrowhead matrix", "level": 1, "lower": [{"inner": "Real symmetric arrowhead matrices", "level": 2, "lower": []}, {"inner": "Eigenvalues and eigenvectors", "level": 2, "lower": []}, {"inner": "Inverses", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}]}
/wiki/Anti-diagonal_matrix
{"inner": "Anti-diagonal matrix", "level": 1, "lower": [{"inner": "Formal definition", "level": 2, "lower": []}, {"inner": "Example", "level": 2, "lower": []}, {"inner": "Properties", "level": 2, "lower": []}]}
/wiki/Block_tridiagonal_matrix
{"inner": "Block matrix", "level": 1, "lower": [{"inner": "Example", "level": 2, "lower": []}, {"inner": "Block matrix multiplication", "level": 2, "lower": []}, {"inner": "Block matrix inversion", "level": 2, "lower": []}, {"inner": "Block matrix determinant", "level": 2, "lower": []}, {"inner": "Block diagonal matrices", "level": 2, "lower": []}, {"inner": "Block tridiagonal matrices", "level": 2, "lower": []}, {"inner": "Block Toeplitz matrices", "level": 2, "lower": []}, {"inner": "Block transpose", "level": 2, "lower": []}, {"inner": "Direct sum", "level": 2, "lower": []}, {"inner": "Application", "level": 2, "lower": []}]}
/wiki/Block-diagonal_matrix
{"inner": "Block matrix", "level": 1, "lower": [{"inner": "Example", "level": 2, "lower": []}, {"inner": "Block matrix multiplication", "level": 2, "lower": []}, {"inner": "Block matrix inversion", "level": 2, "lower": []}, {"inner": "Block matrix determinant", "level": 2, "lower": []}, {"inner": "Block diagonal matrices", "level": 2, "lower": []}, {"inner": "Block tridiagonal matrices", "level": 2, "lower": []}, {"inner": "Block Toeplitz matrices", "level": 2, "lower": []}, {"inner": "Block transpose", "level": 2, "lower": []}, {"inner": "Direct sum", "level": 2, "lower": []}, {"inner": "Application", "level": 2, "lower": []}]}
/wiki/Complex_Hadamard_matrix
{"inner": "Complex Hadamard matrix", "level": 1, "lower": [{"inner": "Equivalency", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Centrosymmetric_matrix
{"inner": "Centrosymmetric matrix", "level": 1, "lower": [{"inner": "Examples", "level": 2, "lower": []}, {"inner": "Algebraic structure and properties", "level": 2, "lower": []}, {"inner": "Related structures", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "Further reading", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Boolean_matrix
{"inner": "Boolean matrix", "level": 1, "lower": [{"inner": "References", "level": 2, "lower": []}, {"inner": "Further reading", "level": 2, "lower": []}]}
/wiki/Block_matrix
{"inner": "Block matrix", "level": 1, "lower": [{"inner": "Example", "level": 2, "lower": []}, {"inner": "Block matrix multiplication", "level": 2, "lower": []}, {"inner": "Block matrix inversion", "level": 2, "lower": []}, {"inner": "Block matrix determinant", "level": 2, "lower": []}, {"inner": "Block diagonal matrices", "level": 2, "lower": []}, {"inner": "Block tridiagonal matrices", "level": 2, "lower": []}, {"inner": "Block Toeplitz matrices", "level": 2, "lower": []}, {"inner": "Block transpose", "level": 2, "lower": []}, {"inner": "Direct sum", "level": 2, "lower": []}, {"inner": "Application", "level": 2, "lower": []}]}
/wiki/Equivalent_matrix
{"inner": "Matrix equivalence", "level": 1, "lower": [{"inner": "Properties", "level": 2, "lower": []}, {"inner": "Canonical form", "level": 2, "lower": []}]}
/wiki/Bisymmetric_matrix
{"inner": "Bisymmetric matrix", "level": 1, "lower": [{"inner": "Properties", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}]}
/wiki/Elementary_matrix
{"inner": "Elementary matrix", "level": 1, "lower": [{"inner": "Elementary row operations", "level": 2, "lower": [{"inner": "Row-switching transformations", "level": 3, "lower": [{"inner": "Properties", "level": 4, "lower": []}]}, {"inner": "Row-multiplying transformations", "level": 3, "lower": [{"inner": "Properties", "level": 4, "lower": []}]}, {"inner": "Row-addition transformations", "level": 3, "lower": [{"inner": "Properties", "level": 4, "lower": []}]}]}]}
/wiki/DFT_matrix
{"inner": "DFT matrix", "level": 1, "lower": [{"inner": "Definition", "level": 2, "lower": []}, {"inner": "Examples", "level": 2, "lower": [{"inner": "Two-point", "level": 3, "lower": []}, {"inner": "Four-point", "level": 3, "lower": []}, {"inner": "Eight-point", "level": 3, "lower": []}]}, {"inner": "Unitary transform", "level": 2, "lower": []}, {"inner": "Other properties", "level": 2, "lower": []}, {"inner": "A limiting case: The Fourier operator", "level": 2, "lower": []}]}
/wiki/Hessenberg_matrix
{"inner": "Hessenberg matrix", "level": 1, "lower": [{"inner": "Definitions", "level": 2, "lower": [{"inner": "Upper Hessenberg matrix", "level": 3, "lower": []}, {"inner": "Lower Hessenberg matrix", "level": 3, "lower": []}]}, {"inner": "Examples", "level": 2, "lower": []}, {"inner": "Computer programming", "level": 2, "lower": []}, {"inner": "Reduction to Hessenberg matrix", "level": 2, "lower": []}, {"inner": "Properties", "level": 2, "lower": []}, {"inner": "Hessenberg operator", "level": 2, "lower": []}]}
/wiki/Hermitian_matrix
{"inner": "Hermitian matrix", "level": 1, "lower": [{"inner": "Alternative characterizations", "level": 2, "lower": [{"inner": "Equality with the adjoint", "level": 3, "lower": []}, {"inner": "Reality of quadratic forms", "level": 3, "lower": []}, {"inner": "Spectral properties", "level": 3, "lower": []}]}, {"inner": "Applications", "level": 2, "lower": []}, {"inner": "Examples and solutions", "level": 2, "lower": []}, {"inner": "Properties", "level": 2, "lower": [{"inner": "Main diagonal values are real", "level": 3, "lower": []}, {"inner": "Symmetric", "level": 3, "lower": []}, {"inner": "Normal", "level": 3, "lower": []}, {"inner": "Diagonalizable", "level": 3, "lower": []}, {"inner": "Sum of Hermitian matrices", "level": 3, "lower": []}, {"inner": "Inverse is Hermitian", "level": 3, "lower": []}, {"inner": "Associative product of Hermitian matrices", "level": 3, "lower": []}, {"inner": "ABA Hermitian", "level": 3, "lower": []}, {"inner": "vHAv is real for complex v", "level": 3, "lower": []}, {"inner": "Complex Hermitian forms vector space over R", "level": 3, "lower": []}, {"inner": "Eigendecomposition", "level": 3, "lower": []}, {"inner": "Singular values", "level": 3, "lower": []}, {"inner": "Real determinant", "level": 3, "lower": []}]}, {"inner": "Decomposition into Hermitian and skew-Hermitian matrices", "level": 2, "lower": []}, {"inner": "Rayleigh quotient", "level": 2, "lower": []}]}
/wiki/Diagonally_dominant_matrix
{"inner": "Diagonally dominant matrix", "level": 1, "lower": [{"inner": "Variations", "level": 2, "lower": []}, {"inner": "Examples", "level": 2, "lower": []}, {"inner": "Applications and properties", "level": 2, "lower": []}, {"inner": "Notes", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "External links", "level": 2, "lower": []}]}
/wiki/Copositive_matrix
{"inner": "Copositive matrix", "level": 1, "lower": [{"inner": "References", "level": 2, "lower": []}]}
/wiki/Hadamard_matrix
{"inner": "Hadamard matrix", "level": 1, "lower": [{"inner": "Properties", "level": 2, "lower": []}, {"inner": "Sylvester's construction", "level": 2, "lower": [{"inner": "Alternative construction", "level": 3, "lower": []}]}, {"inner": "Hadamard conjecture", "level": 2, "lower": []}, {"inner": "Equivalence and uniqueness", "level": 2, "lower": []}, {"inner": "Special cases", "level": 2, "lower": [{"inner": "Skew Hadamard matrices", "level": 3, "lower": []}, {"inner": "Regular Hadamard matrices", "level": 3, "lower": []}, {"inner": "Circulant Hadamard matrices", "level": 3, "lower": []}]}, {"inner": "Generalizations", "level": 2, "lower": []}, {"inner": "Practical applications", "level": 2, "lower": []}]}
/wiki/Generalized_permutation_matrix
{"inner": "Generalized permutation matrix", "level": 1, "lower": [{"inner": "Structure", "level": 2, "lower": [{"inner": "Group structure", "level": 3, "lower": []}, {"inner": "Subgroups", "level": 3, "lower": []}]}, {"inner": "Properties", "level": 2, "lower": []}, {"inner": "Generalizations", "level": 2, "lower": []}, {"inner": "Signed permutation group", "level": 2, "lower": [{"inner": "Properties", "level": 3, "lower": []}]}, {"inner": "Applications", "level": 2, "lower": [{"inner": "Monomial representations", "level": 3, "lower": []}]}, {"inner": "References", "level": 2, "lower": []}]}
/wiki/Conference_matrix
{"inner": "Conference matrix", "level": 1, "lower": [{"inner": "Symmetric conference matrices", "level": 2, "lower": [{"inner": "Example", "level": 3, "lower": []}]}, {"inner": "Antisymmetric conference matrices", "level": 2, "lower": []}, {"inner": "Generalizations", "level": 2, "lower": []}, {"inner": "Telephone conference circuits", "level": 2, "lower": []}, {"inner": "Notes", "level": 2, "lower": []}, {"inner": "References", "level": 2, "lower": []}, {"inner": "Further reading", "level": 2, "lower": []}]}
/wiki/Frobenius_matrix
{"inner": "Frobenius matrix", "level": 1, "lower": []}
/wiki/Hollow_matrix
{"inner": "Hollow matrix", "level": 1, "lower": [{"inner": "Definitions", "level": 2, "lower": [{"inner": "Sparse", "level": 3, "lower": []}, {"inner": "Block of zeroes", "level": 3, "lower": []}, {"inner": "Diagonal entries all zero", "level": 3, "lower": [{"inner": "Properties", "level": 4, "lower": []}]}]}, {"inner": "References", "level": 2, "lower": []}]}