Toda's Gepner conjecture for the quintic threefold

Theorem 1.1: every smooth complex quintic threefold has a numerical Bridgeland stability condition, with support property on $K_{\mathrm{num}}(X)_{\mathbb R}$, on which $\Phi$ acts by rotating the charge by $e^{2\pi i/5}$ and shifting phases by $2/5$, normalized by $Z(\mathcal O_x)=-1$. The construction is a double tilt starting at slope $-1/2$, refined to a periodic grid of aisles. It relies on Xu's 2026 inequality. It does not prove Toda's general strong Bogomolov-Gieseker conjecture, treat other Calabi-Yau hypersurfaces, or describe the full stability manifold near the Gepner point.

Theorem 1.1: every smooth complex quintic threefold has a numerical Bridgeland stability condition, with support property on $K_{\mathrm{num}}(X)_{\mathbb R}$, on which $\Phi$ acts by rotating the charge by $e^{2\pi i/5}$ and shifting phases by $2/5$, normalized by $Z(\mathcal O_x)=-1$. The construction is a double tilt starting at slope $-1/2$, refined to a periodic grid of aisles. It relies on Xu's 2026 inequality. It does not prove Toda's general strong Bogomolov-Gieseker conjecture, treat other Calabi-Yau hypersurfaces, or describe the full stability manifold near the Gepner point.