That is what I always used to imagine as our monument, maybe the Fibonacci sequence via orbiting star shades. Or maybe that's too natural, maybe a binary sequence via orbiting star shades.
However, while I ain't no city-slickin' Kardashev Type II orbital mechanic, all those star shades might not be in a stable orbit over hundreds of millions of years. They might require some propulsion for station keeping. That sounds hard for anyone, across those time scales, especially as the star grows.
It might be "easier" for longevity, to terraform a Mercury type planet with unnatural chemicals, then smash a large off-plane comet into it, to create a band of non-star weird chemicals which would fall into the star and should last for millions of years, giving it a one-in-a-billion spectrograph?
edit: Come to think about it a bit more, I would argue that the latter solution is entirely within our technological grasp nearly today, as a pre-Kardashev scale civilization.
However, while I ain't no city-slickin' Kardashev Type II orbital mechanic, all those star shades might not be in a stable orbit over hundreds of millions of years. They might require some propulsion for station keeping. That sounds hard for anyone, across those time scales, especially as the star grows.
It might be "easier" for longevity, to terraform a Mercury type planet with unnatural chemicals, then smash a large off-plane comet into it, to create a band of non-star weird chemicals which would fall into the star and should last for millions of years, giving it a one-in-a-billion spectrograph?
edit: Come to think about it a bit more, I would argue that the latter solution is entirely within our technological grasp nearly today, as a pre-Kardashev scale civilization.