Cancellation conjecture for nonsingular full Q-forms

Let $Q$ be a form parameter, and let a nonsingular full $Q$-form be a nonsingular $Q$-form whose linearisation is surjective. Write $H_{b\epsilon_Q}(\mathbb{Z}^m)$ for the standard hyperbolic form on $\mathbb{Z}^{2m}$, and let $\mathrm{g}(\underline \mu)$ denote the genus, namely the largest non-negative integer $r$ such that

$$\underline \mu\cong\underline \mu'\oplus H_{\epsilon_Q}(\mathbb{Z}^r)$$

for a nonsingular full $Q$-form $\underline \mu'$. Cancellation conjecture. Let $\underline \mu_0$ and $\underline \mu_1$ be nonsingular full $Q$-forms of the same rank with $[\underline \mu_0]=[\underline \mu_1]\in W_0(Q)$. Then: (a) for some non-negative integer $m$, $\underline \mu_0\oplus H_{\epsilon_Q}(\mathbb{Z}^m)$ is isomorphic to $\underline \mu_1\oplus H_{\epsilon_Q}(\mathbb{Z}^m)$; and (b) if $\epsilon_Q=1$ and $\mathrm{g}(\underline \mu_0)\geq1$, or if $\epsilon_Q=-1$, then $\underline \mu_0$ and $\underline \mu_1$ are isomorphic. This is motivated by Kreck’s stable diffeomorphism and cancellation theorems and proposes algebraic analogues for full nonsingular $Q$-forms; the source supplies no resolution, so the conjecture is treated as open.