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The author constructed a spectral sequence strongly converging to h_*(Omega^nSigma^n X) for any homology theory in [Topology 33 (1994) 631-662]. In thisnote, we prove that the E^1-term of the spectral sequence is isomorphic to thecobar construction, and hence the spectral sequence is isomorphic to theclassical cobar-type Eilenberg-Moore spectral sequence based on the geometriccobar construction from the E^1-term. Similar arguments can be also applied toits variants constructed in [Contemp Math 293 (2002) 299-329].

On the E^1-term of the gravity spectral sequence