In a joint experimental and theoretical endeavor, photoionization of metastable C4+(1s2sS13) ions via intermediate levels with hollow, double-K-vacancy configurations 2s2p, 2s3p, 2p3s, 2p3d, 2s4p, 2p4s, and 2p4d has been investigated. High-resolution photon-ion merged-beams measurements were carried out with the resolving power reaching up to 25 800 which is sufficient to separate the leading fine-structure components of the 2s2pP3 term. Many-body perturbation theory was employed to determine level-to-level cross sections for K-shell excitation with subsequent autoionization. The resonance energies were calculated with inclusion of electron correlation and radiative contributions. Their uncertainties are estimated to be below ±1 meV. Detailed balance confirms the present photoionization cross-section results by comparison with previous dielectronic-recombination measurements. The high accuracy of the theoretical transition energies together with the present experimental results qualify photoabsorption resonances in heliumlike ions as new, greatly improved energy-reference standards at synchrotron radiation facilities.