The Origin and Necessity of the Quantization of the Universe ——The Universe Exists Only in the Present Moment, and the Adjacent Yuanke Transition Is the Origin and Necessity of Quantization

Previous work (Chen, 2026b) established that the universe exists only in thepresent moment (the previous moment is inaccessible, and the next moment hasnot yet arrived), and introduced the concept of Yuanke — a discrete transitionfrom state Uk to Uk+1 that is physically indivisible (Axiom 6). On this basis, we define Yuanliang: the formal difference of any quantity between two adjacent Yuankesteps. Yuanliang is an objective mathematical relation, but its measurability depends on the observational position — an external observer with external storagecan directly measure it, while the system’s interior (without external storage) canonly treat it as a theoretical analytical tool. We prove three core theorems:Theorem 1 (Discreteness and nonzero infimum of Yuanliang values):From the finiteness of the total information capacity N of the universe (Axiom 4), itfollows that the attainable value set V of each lattice site is finite, and hence the setΛstep of the magnitudes of any Yuanliang ∆q is a finite discrete set with a nonzeroinfimum ϵmin > 0. Any difference smaller than ϵmin would require a continuumstate space, violating finite information capacity.Theorem 2 (Indivisibility of Yuanliang as a single whole): Any Yuanliang ∆q(k)jis a single complete event in the physical semantics. Even if its magnitude has a multiple relation with ϵmin, this multiple is merely a ratio on the real axisand does not imply that the physical process consists of multiple sub-transitions.Λstep does not possess additive closure.Theorem 3 (Positive/negative/zero three states form a complete spectrum of change): Under any observational projection, the sign of any Yuanliangmust be one of positive, negative, or zero, and these three jointly constitute a closedand complete classification of changes.Final conclusion: The universe is quantized at the fundamental level — themagnitudes of changes of all observables form a discrete spectrum, and there existsa nonzero minimum scale of change ϵmin. This quantization does not arise fromany external physical hypothesis, but stems from the fundamental fact already established in previous work: the universe exists only in the present moment.Since every state transition of the universe is an independent, irreversible overwriting event (a Yuanke), the transition itself is quantized; and Yuanliang, as thedescription of the difference of this transition, also necessarily takes discrete values.Macroscopic continuity arises from coarse-grained averaging.Correspondence to: [email protected]