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We present a new model for the basic double-pionic fusion reaction pn → d + (ππ)0 in the energy region Tp = 1.0–1.4 GeV. The model takes into account the production of the I(JP) = 0(3+) dibaryon resonance recently observed experimentally in the above reaction and the subsequent decay of this resonance into d + (ππ)0 channel by two ways: through generation of an intermediate σ-meson and through an isovector I(JP) = 1(2+) dibaryon production. The model explains a strong near-threshold enhancement in the ππ invariant-mass spectrum, i.e., the well-known ABC effect, as a consequence of a σ-meson production under conditions of partial chiral symmetry restoration in excited dibaryons.