I have dedicated a few moments over the years to follow that ancestry.
The excellent collection in Genealogics *, presents the ancestry of the current monarch of Japan as follows (click attached link):
http://genealogics.org/pedigree.php?personID=I00436222&tree=LEO&parentset=0&display=standard&generations=5
(however, soon there will be a corrected and augmented version forthcoming, Genealogics update probably sometime during this month)
(* genealogical website of Leo van de Pas)
Fully historically, the Japanese monarchs' ancestry, in male line, can be followed to around the year 400 CE, and an archetypal maternal ancestry, Fujiwara ancestry (Ahihito tenno's paternal grandmother, the late Sadako kogo, has that male-line pedigree), can be followed historically to almost as early dates (lord Kamatari Nakatomi lived in 600s, and his great-grandfather obviously something like a century earlier).
These two lineages, Yamato dynasty and Fujiwara-no-Nakatomi pedigree, are -afaik- the longest historically attested Japanese lineages from the past.
These two male lines, afaik, are not basically problematic in light of historical verifiability in any other way than the possibility of occasional hidden adultery, which is always a caveat in male-line pedigrees.
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