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Current observations of binary black hole (BBH) merger events show support for a feature in the primary BH-mass distribution at $\sim \, 35 \ \mathrm{M}_{\odot }$, previously interpreted as a signature of pulsational pair-instability supernovae (PPISNe). Such supernovae are expected to map a wide range of pre-supernova carbon–oxygen (CO) core masses to a narrow range of BH masses, producing a peak in the BH mass distribution. However, recent numerical simulations place the mass location of this peak above $50 \ \mathrm{M}_{\odot }$. Motivated by uncertainties in the progenitor’s evolution and explosion mechanism, we explore how modifying the distribution of BH masses resulting from PPISN affects the populations of gravitational-wave (GW) and electromagnetic (EM) transients. To this end, we simulate populations of isolated BBH systems and combine them with cosmic star formation rates. Our results are the first cosmological BBH-merger predictions made using the binary_c rapid population synthesis framework. We find that our fiducial model does not match the observed GW peak. We can only explain the $35 \ \mathrm{M}_{\odot }$ peak with PPISNe by shifting the expected CO core-mass range for PPISN downwards by $\sim {}15 \ \mathrm{M}_{\odot }$. Apart from being in tension with state-of-the art stellar models, we also find that this is likely in tension with the observed rate of hydrogen-less super-luminous supernovae. Conversely, shifting the mass range upward, based on recent stellar models, leads to a predicted third peak in the BH mass function at $\sim {}64 \ \mathrm{M}_{\odot }$. Thus we conclude that the $\sim {}35 \ \mathrm{M}_{\odot }$ feature is unlikely to be related to PPISN.

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