“Time is a mathematical structure invented to categorize change.”
I’ll agree that the language, terms, units and tools we use to measure time are mathematical structures invented to categorize change.
We started out by dividing known astronomical cycles of change into units of time. Earth’s orbit around the sun, earth’s rotation (the sun’s position in the sky).
Then we refined these units by inventing machines that measured time (change) in smaller increments - hourglasses, mechanical clocks, electrical clocks, digital clocks.
Note that in all of these, something is changing: the sand is flowing into the lower chamber, the spring is unwinding, gears are turning - even in the electric and digital clocks there is change - electrical pulses throw micro switches to advance the seconds, minutes and hours being displayed.
But time itself is not a man-made mathematical structure - only the tools and language we have invented to measure it.
I do think you nailed it.
You are equating change with time. They are not the same. Time is a construct. Change is the nature of a thing.
We create time out of the revolution of the earth around the sun and a rotation of the earth. It is earth specific. The same period of time does not occur in any other celestial body. Thus, time is a construct of this place in this solar system.
The planet Uranus takes 84 earth years to circumvent the sun. A day is equal to our 17 hours. Time is relative, as such it has no singularity. It is a construct.