Calculations on the Continuity of 60 Days Counts
Assuming the above dates, we can calculate their runs through the ancient periods up to present.
December 24 113 BC to December 24 105 BC covers 8 years.

If the years are multiplied by 365.2421644 days, there will be 2921.9373152 days.
If these days are divided by 60, there will be 48.6989552533333 cycles of sexagenary signs. The fraction involves 0.69896 x 60 = 41.9373 day.
If December 24 113 BC was a hsin ssu (xin si  18), then the calculations show that December 24 105 BC should 42 signs later, a gui hai sign (60), not jia zi (1) as noted.
May 17, 110 BC was a imao day (52). December 24 110 BC to December 24 105 BC covers 5 years.

If the years are multiplied by 365.2421644 days, there will be 1826.210822 days.
With the rest of December in 110 BC, the days in months June to November and May 17 to 31, the days are 2047.210822.
If these days are divided by 60, there will be 34.1201803666667 cycles. The fraction involves 0.1202 x 60 = 7.2108 day.
If May 17 110 BC was a imao day (52), then the calculations show that December 24 105 BC should 7 signs later, a ren xu sign (59) or gui hai (60) not jia zi as noted.
Both historical dates of December 24, 113 BC and May 17, 119 BC show that December 24 105 BC was either a ren xu (59) or more likely a gui hai (60) day. This indicates that for the Han Grand Inception calendar the emperor had purposefully and artificially reset December 24, 105 BC, a ren xu or gui hai day, to become a jia zi day.
Han Kao Tsu had broken the continuity by forcing the winter solstice of December 24 105 BC to assume the jia zi sign which actually was that of December 25. Thus, the historical evidence is that by Han Kao Tsu time the 60 cycle counts were no longer continuous.
Another historical tampering of the 60 cycle count occurred in the Tang dynasty. December 24 105 BC to December 24 AD 640 covers 744 years.
 If the years are multiplied by 365.2421644 days, there will be 271740.1703136 days.
If these days are divided by 60, there will be 4529.00283856 cycles. The fraction involves 0.168 day.
Hence, if December 24 was a jiazi day, then the calculations show that December 24 AD 640 should also be a jiazi day.
However, the Wu Lin calendar actually noted that it was December 25 AD 640 which was a jia zi day. Evidently, the creator of the Wu Lin calendar was aware that the December 24 105 BC jia zi sign for the Han Grand Inception calendar was a shift and corrected it back. Only, during the Tang dynasty, the Tang court decided that for calendrical purposes, the jiz zi sign for the Han Grand Inception should be accepted and December 24 AD 640 became a jia zi day when it should be a gui hai day.
Consider June 12 AD 618, which was supposed to be a jiazi day.
 December 24 AD 618 to December 24 AD 640 covers 22 years.
If the years are multiplied by 365.2421644 days, there will be 8035.3276168 days.
If these days are divided by 60, there will be 133.922126946667 cycles. The fraction involves 55.3278 days.
The rest of December AD 618 back to June 12 covers 195 days. With the 55.3278 days this totaled to 250.3278 days. If June 12 AD 618 was a jiazi day, December 24 AD 640 should not be a jiazi day but at least 10 signs ahead! So, between June 12 AD 618 to December 24 AD 640 there was a slip of at least 10 signs!
The historical evidence is that considerable arbitrary breaks and shifts in the 60 cycle counts for the day occurred since the Han dynasty.
Now, let us take December 24 AD 640 as a jia zi day. Look at the recent Chinese calendar. January 10, 1965 was a jiazi day.
 December 24 AD 640 to December 24 AD 1965 covers 483580.6256656 days.
The duration involves 8059.67709442667 cycles. The fraction has 40.674 days.
The rest of December 1964 and the next 10 days of January 1965 totaled 17 days.
Hence, 10 January 1965 should not be a jiazi day but at least 3 signs back!
The calculations shows that there were repeated discontinuities in the 60 cycle day counts between the Han dynasty to the present.