String topology chain-map conjecture for simply-connected manifolds

Let $M$ be an oriented closed manifold of dimension $n$. Let $C^{\mathrm{sing}}(\Loop_{\Sph{1}}M;\R)$ be the smooth singular chain complex with boundary $\Bdd$, and let $\CDBCyc\,\Harm(M)$ carry the differential $\OPQ_{110}^\PMC$. String topology chain-map conjecture. There is a chain map

$$(C^{\mathrm{sing}}(\Loop_{\Sph{1}}M;\R),\Bdd)\longrightarrow(\CDBCyc\,\Harm(M),\OPQ_{110}^\PMC)$$

which, when $M$ is simply connected, induces the stated reduced homology isomorphism, intertwines $\StringOp_2$ with $\OPQ_{210}$, and makes the pullback of $\OPQ_{120}^\PMC$ compatible with $\StringCoOp_2$ under the inclusion $(\Loop M,x_0)\to(\Loop M,M)$. This packages the conjectural chain-level realization of string topology operations; the source gives no resolution.