The frame
Here the site follows two pages of the Met's timeline, for 1000-1400 and for 1400-1600. On the first, the entry for ca. 1261-1310 names "dozens of independent regional principalities", among them "the Osmanli (Ottomans) in northwestern Anatolia", and describes the courts of these regional dynasties as multiple centers of artistic patronage; the name "beyliks" that the site gives them does not appear on the Met's pages. The chart lists the "Ottoman principality (later empire), ca. 1299-1922". The conquests of Bayezid I (r. 1389-1403), according to the second page, lead to the fatal battle of Ankara against Timur in 1402-1403, after which his sons fight for the throne; in 1413-1421 "Mehmet I reestablishes a unified Ottoman state". The period ends in 1453 with the conquest of Constantinople, "which puts an end to the Byzantine empire". Sources 1, 2.
Boundaries and overlaps
Neither end is sharp. In the chart the Ottoman principality begins ca. 1299, a year before the site's ca. 1300, and the Seljuq sultanate continues to 1307; the Kingdom of Armenian Cilicia runs to 1375 and the Artuqid dynasty to 1409. The empire of the Grand Komnenoi in Trebizond, 1204-1461, runs through this period and the previous one, and continues eight years after 1453. The end of fragmentation is not 1453 either: according to the entry for 1453-1481, it is "Mehmet's takeover of various lands, including the realms of Trebizond and Karaman", that "ends the long period of fragmentation", and the overview of the first page says that Anatolia "will not be reunified until the Ottoman conquests in the late fifteenth century". Sources 1, 2.
On this site, and what is missing
Two items are placed in this period. "Bursa and Cumalıkızık: how the first Ottoman capital was built" reads the UNESCO page on a city that grew from five kulliye foci and on the waqf village that supplied its hinterland, from the early 14th to the middle of the 15th century. "The Great Mosque of Bursa: the patronage of Bayezid I" deals with the date 1396-1400 that the Met gives the mosque, and with the fact that the sources do not describe it. Both items come from Bursa. What is missing is a dated site of this period outside Bursa. In the two timeline pages and the UNESCO page on Bursa that were checked, Trebizond appears with the marriage alliances of the Grand Komnenoi with Turkmen rulers in the east (ca. 1350), and Karaman by name, but with no dated monument in either; the only other dated monument of the period on the page for 1400-1600, Mehmet's convent-mosque and tomb complex, "begun 1419" and "popularly known as 'Green'", is given there without a location. The article on Ani mentions the earthquake of 1319, which falls within this period, but it is placed in the previous period, because the earthquake is a single event rather than a documented phase of the city. Sources 1, 2, 3.