Which suggests that reality—that me, you, Earth, universe, etc.—is fundamentally some sort of abstract object existing outside spacetime. Hm. — Art48
Yes, we humans are essentially "abstract mathematical objects"*1 in space-time. I have arrived at a similar conclusion, except I typically use a more general term for reference to both the subjective objects of minds, and the objective things of physical senses : Information. From a scientific perspective, Mathematics*2 may be the fundamental aspect (essence) of reality. But, for Philosophical purposes Information*3 may be more broadly applicable. Math seems to be the most abstract form of Generic Information*4, yet it is the logical structure of the physical world.
Abstract objects*1 are not knowable by physical senses, but only by mental introspection or by communication with other minds. So, they are in the space-time world, but not of the physical world. Space-time is itself an abstract concept, that we measure indirectly by observing physical changes in the environment. Even the causes of change, Energy & Forces, are abstract concepts, not material things. We only know them indirectly by their effects on matter.
In my personal thesis, I refer to the universal power-to-enform (causation) as EnFormAction*5. And the logically necessary First Cause (the Enformer, the Programmer, the Great Mathematician, etc) is the only abstract thing that exists prior-to and outside the evolving (self-enforming) space-time world. I assume that you lean toward Platonism instead of Nominalism. Can you see the connection between Enformationism and your own proposal of a Mathematical universe?
*1. Abstract Object :
One doesn’t go far in the study of what there is without encountering the view that every entity falls into one of two categories: concrete or abstract. . . . Though there is a pervasive appeal to abstract objects, philosophers have nevertheless wondered whether they exist. The alternatives are: platonism, which endorses their existence, and nominalism, which denies the existence of abstract objects across the board.
https://plato.stanford.edu/entries/abstract-objects/
Note : while Mathematical Objects are typically accepted as real, in some sense, by pragmatic physicists & mathematicians, their Ideal (abstract ; non-concrete) existence puts them in the same ontological category as Souls & Ghosts. Hence, philosophically controversial.
*2. Mathematical universe hypothesis :
The theory can be considered a form of Pythagoreanism or Platonism in that it proposes the existence of mathematical entities; a form of mathematicism in that it denies that anything exists except mathematical objects; and a formal expression of ontic structural realism.
https://en.wikipedia.org/wiki/Mathemati ... hypothesis
*3. Information :
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed.
https://en.wikipedia.org/wiki/Information
*4. Information :
Knowledge and the ability to know. Technically, it's the ratio of order to disorder, of positive to negative, of knowledge to ignorance. It's measured in degrees of uncertainty. Those ratios are also called "differences". So Gregory Bateson* defined Information as "the difference that makes a difference". The latter distinction refers to "value" or "meaning". Babbage called his prototype computer a "difference engine". Difference is the cause or agent of Change. In Physics it’s called "Thermodynamics" or "Energy". In Sociology it’s called "Conflict".
http://blog-glossary.enformationism.info/page11.html
Note -- Information (EnFormAction) is generic in the sense of causing all forms of being in the universe.
*5. EnFormAction : The creative act of enforming; to give form to the formless.
Ententional Causation. A proposed metaphysical law or principle of the universe that causes random interactions between forces and particles to produce novel & stable arrangements of matter & energy. It’s the creative force of the universe. AKA : The innovative power of Evolution; the power to enform; Logos; Change.
http://blog-glossary.enformationism.info/page8.html