Nothing. Stating that God gave the Torah to our Hebrew (Israelite) ancestors is not a claim, it is history. The same goes for the Exodus, for God's promise of giving us the land of Canaan (Israel), and the rest of the events in the Hebrew Bible.
See also:
http://www.academia.edu/1651319/Is_the_Exodus_Story_Possible
http://judaism.answers.com/hebrew/does-archaeology-support-the-hebrew-bible
They are called Jews today, and they claim the history of the Hebrews as their ancestry.Answer:We claim ancestry through Abraham and Sarah, (his son) Isaac and Rebecca, (and his son) Jacob (and his wives Rachel and Leah). The book of Genesis has further detail.
There is no mention in any text of encounters between the Ancient Hebrews and the Hyksos. There are some historians who claim that the Hebrews and the Hyksos are the same people, but this is a rare minority view.
Hebrews
The Jews. Muslims also claim lineage from Abraham.
It is unknown when Hebrews first appeared in History. Tradition holds that Abraham (the first Jew) lived in about the year 2000 BCE. However, it's possible that the Hebrews have been around a lot longer than that, possibly 12,000 years. Other theories claim that at some point, the Hebrews and Canaanites were the same people.
The Hebrews' military was an army composed of Hebrews.
No, although some black people are Jewish. There is no historical basis for the Black Israelite Churches which claim that the Hebrews are representative of Africa and that the 12 tribes refer to the various locations of the African communities in the New World. However, it serves as a good allegory for that story and as such is commonly used and believed.
Yes, there were Hebrews in the Book of Judges. The Book was also written by Hebrews.
David was one of the Kings of the Hebrews.
House in Hebrew is בַּיִת. The significance could reference the "house of Israel" which refers to the collective population of all those who claim to be Jewish or identify themselves with Israel.
The Hebrews are considered as Gods own people.
In the Hebrews time his nickname was "Father of the Hebrews"