Question: In which district of the Badakhshan Province is the settlement located which is famous for its ancient mines, which produce a deep blue metamorphic rock used as a semi-precious stone that has been prized since antiquity for its intense color, and are said to produce the world's finest of this stone?

Context articles: Badakhshan
Caymanite
Carbuncle (gemstone)
List of governors of Badakhshan
Baharak, Afghanistan
Lapis lazuli
Azurite
Slate
Blue diamond
Sar-i Sang

Badakhshan (Pashto/Persian: بدخشان‎ ‎ , "Badaxšân"; Tajik: Бадахшон , "Badaxşon"; Russian: Бадахшан ; , Xiao'erjing: بَا دَا کْ شًا, Ming dynasty era Chinese name- 巴丹沙) is a historic region comprising parts of what is now northeastern Afghanistan and southeastern Tajikistan.
 The name is retained in Badakhshan Province, which is one of the 34 provinces of Afghanistan and is located in North-East Afghanistan.
 Much of historic Badakhshan lies within Tajikistan's Gorno-Badakhshan Autonomous Region located in the south-eastern part of the country.
 The music of Badakhshan is an important part of the region's cultural heritage.
Caymanite at its type area is an uncommon variety of dolostone originally reported from locations in the Miocene Cayman Formation in the Cayman Islands: the Bluff in Cayman Brac and the East End on Grand Cayman.
 Away from the type area, material now being called "caymanite" is not an "uncommon variety of dolostone" as it is "sensu stricto" at the type area.
 It has been reported from the Buda Hills of Hungary.
 Caymanite occurs as a fine grained or vug filling variety of the mineral dolomite CaMg(CO).
 It occurs as white to red and black filling in fossil molds, small cavities and caves.
 It is used as a semi-precious stone.
 In News South Wales, Australia, pockets of later-deposited beds (usually reddish) are widespread in the Silurian-Devonian limestones.
 These are thus far reported only from the Lachlan Fold Belt portion of the Tasman Orogen.
 They are mostly small pockets but occasionally reach up to several metres wide.
 These had been long known about and began to be referred to as Caymanite by Dr. Armstrong Osborne who also worked up and published the finding that the Jenolan cave complex is world's oldest known and dated open cave system ().
 The best description so far of the New South Wales caymanite is from Jenolan Caves.
 None of the NSW material is silicified or in any way suitable for use as a semi-precious stone.
A carbuncle is any red gemstone, most often a red garnet.
 The word occurs in four places in many English translations of the Bible.
 The English translation is a rendering of the Vulgate's Latin "carbunculus", a word used for a small coal (or charcoal), and also for any of a number of precious or semi-precious stones, especially those of a red color.
 Jerome apparently chose the term because of its similarity in meaning to the Septuagint's ἄνθραξ ("anthrax" meaning "coal"), which was in turn used by the Greek to translate the Hebrew נֹפֶךְ ("nōphek") in two of its four occurrences in the Old Testament.
 The etymology of the Hebrew term is uncertain, though Koehler-Baumgartner suggests a connection to פּוּךְ ("phook"), used in the Old Testament as a term for eye makup, and probably implying a colored powder most likely made from a crushed mineral.
 For נֹפֶךְ ("nōphek") itself they suggest the gloss "semi-precious stone" (of uncertain color).
The Governor of Badakhshan (Persian: حاکم بدخشان, "hākim-i badakhshān") is the head of the government of Badakhshan.
 In the late 19th century Badakhshan was joined with Qataghan into a single province and there were governors of Qataghan-Badakhshan Province and Badakhshan District.
 In 1963 the province was dissolved and Badakhshan became one of the 34 provinces of Afghanistan.
 Badakhshan province is located in the north-east of the country, between the Hindu Kush and the Amu Darya.
 The capital of Badakhshan and the seat of the provincial governor is the town of Fayzabad.
Baharak is a small town and seat of Baharak District Badakhshan Province in north-eastern Afghanistan.
 It is roughly 15 kilometers from Jurm, on the Kokcha River.
 Baharak Girls' School was opened on December 17, 2006 by Munshi Abdul Majeed the Governor of Badakhshan Province, it serves about 3000 girls who attend in three separate shifts during the day.
Lapis lazuli ( , ), or lapis for short, is a deep blue metamorphic rock used as a semi-precious stone that has been prized since antiquity for its intense color.
 As early as the 7th millennium BC, lapis lazuli was mined in the Sar-i Sang mines, in Shortugai, and in other mines in Badakhshan province in northeast Afghanistan.
 Lapis was highly valued by the Indus Valley Civilisation (3300–1900 BC).
 Lapis beads have been found at Neolithic burials in Mehrgarh, the Caucasus, and even as far from Afghanistan as Mauritania.
 It was used in the funeral mask of Tutankhamun (1341–1323 BC).
Azurite is a soft, deep blue copper mineral produced by weathering of copper ore deposits.
 It is also known as Chessylite after the type locality at Chessy-les-Mines near Lyon, France.
 The mineral, a carbonate, has been known since ancient times, and was mentioned in Pliny the Elder's Natural History under the Greek name "kuanos" (κυανός: "deep blue," root of English "cyan") and the Latin name "caeruleum".
 The blue of azurite is exceptionally deep and clear, and for that reason the mineral has tended to be associated since antiquity with the deep blue color of low-humidity desert and winter skies.
 The modern English name of the mineral reflects this association, since both "azurite" and "azure" are derived via Arabic from the Persian "lazhward" (لاژورد), an area known for its deposits of another deep blue stone, lapis lazuli ("stone of azure").
Slate is a fine-grained, foliated, homogeneous metamorphic rock derived from an original shale-type sedimentary rock composed of clay or volcanic ash through low-grade regional metamorphism.
 It is the finest grained foliated metamorphic rock.
 Foliation may not correspond to the original sedimentary layering, but instead is in planes perpendicular to the direction of metamorphic compression.
Blue diamond is a type of diamond which exhibits all of the same inherent properties of the mineral except with the additional element of blue color in the stone.
 They are colored blue by trace amounts of boron that contaminate the crystalline lattice structure.
 Blue diamonds belong to a subcategory of diamonds called fancy color diamonds, the generic name for diamonds that exhibit intense color.
 Blue diamonds range in grade from Flawless to Included, just as in the case of white diamonds.
Sar-i Sang (or Sar-e Sang) is a settlement in the Kuran Wa Munjan District of Badakhshan Province, Afghanistan, famous for its ancient lapis lazuli mines producing the world's finest lapis.