What is the relationship between a physical system and a computational simulation of that system? The naive answer is causal: the computer runs the simulation, the simulation depends on the computer, and the two are related by the execution process. This paper argues that the naive answer is wrong.
Starting from four axioms about the physical basis of observer — axioms that are individually modest and collectively difficult to reject — we derive that a computer running a simulation and the simulation itself are two arrangements of the same information. No causal relationship is primary. No substrate is privileged. The geometric description and the computational description of a physical process are representationally equivalent.
This conclusion, which we call substrate independence, has direct consequences for physics. If the two descriptions are equivalent, then any property of the physical system must appear in its computational proxy, the execution trace.
The present paper is organised as follows. Section 2 states the four axioms. Section 3 derives substrate independence and the internal nature of time through two thought experiments. Section 4 proves that simulated consciousness follows from the axioms. Section 5 states the numerical precision corollary. Section 6 discusses falsifiability. Section 9 states the conclusions and connects forward to the rest of the series.