AbstractAngle-resolved photoemission spectroscopy, visualizing the superconducting gap in k-space, plays a pivotal role in research on cuprates and other high-T_c superconducting materials. However, there has always been an imminent doubt whether this technique truly represents the intrinsic bulk spectral function, whose response can be distorted by energy- and k-dependence of the photoexcitation matrix element, and by a small photoelectron escape depth of few surface atomic layers. Here, we address this fundamental question with soft-X-ray photoemission measurements of the superconducting gap in the paradigm high-T_c cuprate Bi₂Sr₂CaCu₂O₈. We vary the matrix element by spanning a dense k-space grid, formed by the lattice superstructure, and the probing depth by changing the emission angle. The measured gap appears independent of the matrix element effects, probing depth or photoexcitation energy. This fact proves the relevance of photoemission studies for the bulk superconductivity in Bi₂Sr₂CaCu₂O₈, and calls for similar verification experiments on other high-T_c compounds, in particular more three-dimensional ones. Bi₂Sr₂CaCu₂O₈ shows an anomalously fast decay of the coherent spectral weight with photon energy, tracing back to strong electron–phonon interaction or relaxation of the lattice coherence.