Polycyclic aromatic hydrocarbons (PAHs) represent a family of organic compounds formed by the fusion of aromatic rings. In this work, we focus our attention on the open-shell subclass of PAHs with one/two unpaired electrons. A variety of studies show that the presence of unpaired electrons in these species leads to a number of interesting properties such as: two photon absorption enhancement, singlet fission, interesting chiroptical, or amphoteric redox behaviour. These properties make open-shell PAHs attractive for applications in the fields of materials science, spintronics, and quantum computing. Accordingly, the design and synthesis of openshell PAHs is an active field of research. Among the many open-shell PAHs synthesised to date, derivatives of Chichibabin's hydrocarbons stand out due to their stability under ambient conditions. Particular examples of such stable Chichibabin radicals are those bearing anthracene units as the central core. When it comes to characterising the properties of open-shell PAHs, electron spin resonance (ESR) is a valuable technique because it directly probes the electron spin density of paramagnetic molecules. In its most popular implementation, continuous-wave ESR (cwESR) is used as a simple analytical tool for ascertaining that a particular compound is paramagnetic. However, this question becomes more complicated when it comes to determining the spin states of compounds with more than one unpaired electron. For example, consider an organic diradical: the absence of cwESR signals is often attributed to the diamagnetic singlet state, while the presence of a cwESR signal is linked to the triplet state. However, the mere existence of a non-zero cwESR spectrum is not sufficient to conclude that the observed paramagnetic species is the triplet state of the diradical. In fact, from a quantum mechanical perspective, the situation is worse: if the spin Hamiltonian of the diradical does not commute with Ŝ2 (the square of the total electronic spin operator), the system may exist in a quantum state which is neither singlet nor triplet. Consider the uncertainty relation: