What is the prevailing theory on why these have the double zeroes? They sort of make you think of the double zero T-38's, but these are way too nice of condition to be out of service weapons.
The theory for many years was that the zeros were added to note the actual sequential serial numbers of the guns (the series started at 50001 [or, possibly, 50000]). A more recent theory is that the zeros actually denote these guns as being "second class" firearms very similar to those Japanese rifles with the two zeros preceding the serial number. Double Zero-marked guns have center-tailed strikers/guides and center-slotted bolts/locking blocks. These are the only T14s produced with this difference. The modified parts will not fit any other T14s, and, similarly, those parts in other T14s will not fit the modified Double Zeros guns. Also, if you check Val's above image of the serial number, you will note that the two zeros have "cratered" edges indicating they were added after the serial number and after final surface buffing. So, the two zeros are an added marking -- they may have been added to denote these guns as being non-standard. Another feature of the Double Zero-marked guns is that almost all of them are in very nice, if not new, condition. One explanation for that fact is that they were not issued but, instead, kept in storage to be found by souvenir-hunters after the war.
These guns are quite rare. The highest reported example is 50185, and the next low normally-marked example is 50189. To date, 31 Double Zero examples have been reported to my database. Of those, 17 are 16-dates, and 14 are 17-dates. As a side note, of the 35 possible arsenal, series, and year date codes available in T14 production, the 16-date Toriimatsu guns (all Double Zeros) are the "rarest" if you only consider the number produced. Even fewer of them were produced than the very scarce "Taisho" T14s. Based on reported examples, there could only be up to 81 16-date Toriimatsu guns, while there could be up to 115 Taisho guns. But, since the Taisho guns were produced much earlier and fewer of them survived (only 15 have been reported), they are harder to find and more valuable than the 16-date Double Zero guns. Regardless, the all Double Zero-marked guns are very rare and desirable T14 variants, and anyone possessing one of them should be justifiabley proud.