Can a single local measurement detect a quantum phase transition?

In open quantum systems, detecting the point where quantum behavior sharply shifts usually requires probing the entire system. This work shows that purely local measurements — specifically local quantum Fisher information and the Bloch vector of a single qubit — capture these crossover signatures just as well. A previously proposed geometric measure called 'quantum obesity' fails as a universal indicator, revealing a fundamental gap between local and global geometric pictures of quantum transitions.