Quark confinement—the observation that quarks are never found in isolation but only in color-neutral bound states—is a fundamental feature of quantum chromodynamics. Despite decades of effort, a rigorous analytic proof of confinement from the QCD Lagrangian remains elusive. Lattice QCD provides strong numerical evidence but no conceptual mechanism. This paper shows that confinement follows directly from the discrete structure of spacetime in the canvas model. What this paper provides: · A geometric mechanism for confinement. Color charge couples to all three spatial axes via the SU(3) gauge field. When a quark and antiquark separate, the voxel lattice between them is stretched into a flux tube—a chain of excited voxels. Each voxel in the chain must be excited above its vacuum state, and the energy per unit length (string tension) grows linearly with separation.· Derivation of the string tension. The energy to excite a single voxel is E_{\text{voxel}} = (T_{SU(3)}/T_{ST}) \cdot \hbar c / a, where a = \ell_P is the voxel spacing, T_{SU(3)} is the SU(3) threshold, and T_{ST} = 4 is the spacetime threshold. The string tension is \sigma = E_{\text{voxel}} / a. The observed string tension \sigma \approx 0.9 GeV/fm emerges after renormalization from the Planck scale to the QCD scale: \sigma_{\text{eff}} \sim \sigma \cdot (\Lambda_{\text{QCD}}/M_P)^2.· Flux tube breaking and pair creation. When the stored energy exceeds twice the quark mass, \sigma r_{\text{crit}} = 2 m_q c^2, a new quark-antiquark pair is nucleated from the canvas vacuum, fragmenting the flux tube into color-neutral hadrons. This is the mechanism of quark fragmentation observed in high-energy colliders.· Derivation of the Hagedorn temperature. The maximum temperature of hadronic matter is k_B T_H = E_{\text{voxel}}. At this temperature, thermal energy exceeds the voxel excitation energy, and the flux tube dissolves into a quark-gluon plasma. The renormalized Hagedorn temperature at the QCD scale is T_H^{\text{QCD}} \sim 100 MeV, consistent with lattice QCD estimates of the deconfinement transition temperature (150–170 MeV).· Comparison with lattice QCD. The static quark-antiquark potential V(r) = -4\alpha_s/(3r) + \sigma r + V_0 is reproduced. The Lüscher term (fluctuations of the flux tube) appears as the Casimir energy of the vibrating voxel chain. Glueballs are predicted as closed loops of excited voxels, with the lightest glueball mass m_{0^{++}} \sim 1.5-2 GeV, consistent with lattice QCD. Why this matters: Confinement is not a mysterious property of the QCD vacuum. It is a direct geometric consequence of the discrete structure of spacetime. The string tension is not a free parameter—it is determined by the threshold for voxel excitation. The Hagedorn temperature, flux tube breaking, and the deconfinement transition all follow from the same mechanism. The canvas model provides a conceptual explanation for confinement that has eluded analytic QCD for decades. Keywords: quark confinement, QCD, string tension, flux tube, voxel lattice, canvas model, Hagedorn temperature, deconfinement, flux tube breaking, glueballs, Lüscher term