Length-filtration conjecture for complex K-theory of manifolds

Let $(Q,q_0)$ and $(Q',q'_0)$ be compact pointed Riemannian manifolds. For each $t\in\mathbf{R}$, let $F_{<t}C_*(\Omega_{q_0}Q;\mathbf{C})$ denote the subcomplex generated by loops of length less than $t$, and similarly for $Q'$. Suppose there is a quasi-isomorphism of dg algebras

$$C_*(\Omega_{q_0}Q;\mathbf{C})\simeq C_*(\Omega_{q'_0}Q';\mathbf{C})$$

that carries the filtered subcomplex for every $t$ quasi-isomorphically to the corresponding filtered subcomplex. Length-filtration conjecture. Then

$$\mathbf{K}_*(Q)\cong\mathbf{K}_*(Q').$$

The claim is an explicit string-topology-style proposal relating the exact length filtration on based loop chains to complex $K$-theory; the source states that it has no evidence and gives no resolution.