Thought persists through time
Consciousness can not be time sliced through a CPU, thoughts that took place in the past have a bearing on thoughts that take place in the present. If this did not happen the brain would need to grow expediently to accommodate more advanced though processes. I believe these kind of through time anomalies have been observed in sub atomic particle physics.
What comprises you is every thought you had from the moment you were born to the moment you die, all of which work together as a whole to give you conscious thought. Without that persistence through time all you have is lump of gray goo that is capable of very little.
Can I have my award now for solving the mystery of conscious thought please?
I guess not as philosophers will only accept that you are capable of having ideas if you reach level 3 in their club.