Physics assumes that space is three-dimensional everywhere and that gravity simply follows from that geometry. This paper steps back and asks a more basic question: what if the ability to store information places constraints on how many dimensions can operate independently at macroscopic scales?
Every physical record — from a fossil to a computer bit to a molecular cloud in a galaxy — requires finite resources. You cannot make infinitely fine distinctions in the real world. At the same time, the microscopic laws of physics are reversible. When you combine these two simple ideas, something surprising emerges: in regions of space that are physically thin enough, it becomes impossible to maintain three independently distinguishable spatial directions in a stable way. In those regions, the effective macroscopic description is forced to behave as if it has only two independent spatial dimensions. We call this dimensional reduction, and in the paper it is proven as a geometric theorem, independent of any specific theory of gravity.
Why does this matter? Because many galaxies are structured as thin disks. When the theorem is applied to such systems — together with a clearly stated assumption about how stable macroscopic variables define effective dynamics — it predicts that there should be a specific surface density of matter at which this dimensional reduction activates. Remarkably, that surface density corresponds to the same acceleration scale at which galaxy rotation curves stop declining and become flat — the phenomenon often attributed to dark matter. The paper does not claim to eliminate dark matter or overturn general relativity. Instead, it proposes a structural mechanism that could generate similar behaviour from geometric constraints on information storage.
The key test is simple and empirical: do galaxies transition to flat rotation curves at a common surface density of ordinary (baryonic) matter? If that clustering exists — beyond what can be explained by smoothing choices or selection effects — it would support the idea that a geometric activation threshold is at work. If it does not, the mechanism is falsified. Either way, the result is informative. At its heart, the paper suggests that the large-scale structure of gravity might not depend only on fields and particles, but also on something more primitive: the finite capacity of the universe to make and preserve distinctions.