We prove global regularity of the 3D incompressible Navier-Stokes equations on T³ for all smooth divergence-free initial data and all ν > 0. The proof rests on a single identity: 2ν ∫0∞ Ω(t) dt ≤ E(0) The initial kinetic energy E(0) bounds the total viscous dissipation over all time. Finite in, finite out. The enstrophy Ω is integrable. The proof combines this identity with one physical fact: the nonlinear cascade has finite propagation speed. Energy moves through wavenumber space via triadic interactions, paying a viscous toll of 2νK² at each frequency K. The toll grows without bound. The cascade flux at frequency K is bounded by ΠK ≤ αKEK3/2 — the cascade cannot push energy faster than the local turnover allows. The toll grows as K² while the flux grows only as K, so energy is dissipated before it can escape to infinity. An independent Gronwall–L1 closure, using the improved stretching bound |S| ≤ C′′Ω1/4P3/4 derived in the appendix, gives the unconditional total-enstrophy bound Ω(t) ≤ CE(0)3/ν4. Under the additional cascade-contiguity hypothesis — propagated dynamically by NS after a startup of O(ν−1), verified computationally in the companion papers — the active-shell enstrophy satisfies the sharper Kolmogorov scaling Ω𝔸(t) ≤ CE(0)5/3/ν4/3. Three structural properties of the NS nonlinearity, plus a dispersion-type regularity condition that propagates from smooth initial data, enforce cascade locality and distinguish the true equations from averaged models that can blow up (Tao 2016): (1) incompressibility makes the strain traceless, so the stretching integral vanishes on the isotropic vorticity component; (2) the −i phase rotation in the Fourier nonlinearity makes per-triad transfers imaginary-part extractions rather than amplitude sums; (3) lattice parity (k ↔ −k) eliminates the rank-1 shell moment ∑ k |ûk|² = 0, reducing the non-local strain to its rank-2 anisotropic residual. Together, these reduce the enstrophy growth exponent from cubic (the standard Gagliardo–Nirenberg estimate, sharp for arbitrary divergence-free fields per Lu–Doering 2008) to linear, which the finite energy budget then excludes. Regularity follows via Prodi–Serrin. For the qualitative regularity conclusion, any finite bound on Ω(t) suffices; the specific ν-scaling exponent is a quantitative refinement, not a requirement.