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We show that the resonance-like structure found by the \emph{CELSIUS-WASA Collaboration} in the two-photon invariant mass spectrum of the reaction $pp \to pp \gamma \gammaNN$-decoupled dibaryon resonance (1956) that is produced in the radiative process $pp \to \gamma d^\star_1d^\star_1 \to pp \gamma$. It is found that a contribution of the dibaryon mechanism of the reaction $pp \to pp \gamma \gamma$ to the invariant mass spectrum of its photon pairs can reasonably well reproduce the experimentally observed spectrum in the vicinity of the resonance-like structure.

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