Rectifiability and backward uniqueness conjecture for the top Ricci flow singular stratum

From papers

Let (Z,dZ,t)(Z,d_Z,\mathfrak{t}) be a noncollapsed Ricci flow limit space arising as the pointed Gromov--Hausdorff limit of a sequence in M(n,Y,T)\mathcal{M}(n,Y,T). Let SFn2\mathcal{S}_{\mathrm{F}}^{n-2} denote the F\mathrm{F}-stratum of the singular set of dimension n2n-2, and let Γ\Gamma be the finite group appearing in the corresponding tangent flow. Rectifiability and backward uniqueness conjecture. The set SFn2\mathcal{S}_{\mathrm{F}}^{n-2} is vertically parabolic (n2)(n-2)-rectifiable with respect to the dZd_Z-distance. Moreover, for Hn2\mathscr{H}^{n-2}-almost every xSFn2x\in\mathcal{S}_{\mathrm{F}}^{n-2}, the tangent flow at xx is backward unique, and its negative part is given by

Rn4×(R4/Γ)×R.\mathbb{R}^{n-4}\times(\mathbb{R}^4/\Gamma)\times\mathbb{R}_-.

If true, then together with the paper's rectifiability theorem for the other singular strata, this would imply that the entire singular set S\mathcal{S} is parabolic (n2)(n-2)-rectifiable. The claim is proposed in general dimension; the supplied text gives no resolution, so its status remains open.

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Primary source

Hanbing Fang and Yu Li, “Singular sets in noncollapsed Ricci flow limit spaces”, arXiv:2510.26317 (2026).

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