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From 1310.6×106 J/ψ and 448.1×106 ψ(3686) events collected with the BESIII experiment, we report the first observation of Σ+ and Σ¯− spin polarization in e+e−→J/ψ(ψ(3686))→Σ+Σ¯− decays. The relative phases of the form factors ΔΦ have been measured to be (−15.5±0.7±0.5)∘ and (21.7±4.0±0.8)∘ with J/ψ and ψ(3686) data, respectively. The non-zero value of ΔΦ allows for a direct and simultaneous measurement of the decay asymmetry parameters of Σ+→pπ0 (α0=−0.998±0.037±0.009) and Σ¯−→p¯π0 (α¯0=0.990±0.037±0.011), the latter value being determined for the first time. The average decay asymmetry, (α0−α¯0)/2, is calculated to be −0.994±0.004±0.002. The CP asymmetry ACP,Σ=(α0+α¯0)/(α0−α¯0)=−0.004±0.037±0.010 is extracted for the first time, and is found to be consistent with CP conservation.