Quantum physicists have identified a distinct spectral signature of non-invertible symmetries within the entanglement spectrum of quantum many-body states. A recent study, published on arXiv, details how the categorical data of the Kramers--Wannier (KW) duality defect, a canonical example from the critical Ising chain, is directly encoded within this spectrum 1. This specific defect, characterized by an irrational quantum dimension of d_sigma = sqrt(2), leaves a unique "fingerprint" resolved at the spectral level. While non-invertible symmetries were previously known via their topological defects, their precise manifestation within the entanglement spectrum remained unresolved. This work clarifies how these complex symmetries manifest beyond abstract characterization, providing a tangible spectral representation. This breakthrough offers a crucial diagnostic tool for detecting and analyzing non-invertible symmetries in complex quantum systems, advancing quantum information theory and potentially informing next-generation fault-tolerant quantum computation.