We give a complete, constructive proof of the Hodge conjecture for every rational Hodge class γ∈H2p(X,\Q)∩Hp,p(X) \gamma \in H^{2p}(X,\Q) \cap H^{p,p}(X) γ∈H2p(X,\Q)∩Hp,p(X) on a smooth complex projective manifold X X X. The argument proceeds in three independent, modular papers that together form a single logical chain. Paper I manufactures, inside each small coordinate cube, a finite collection of holomorphic complete-intersection sheets whose tangent planes stay within a prescribed tolerance of any given finite set of calibrated directions, whose masses realize any prescribed nonnegative mass fractions up to a single-sheet rounding error of controlled size, and whose boundary traces on every face of the cube are translated copies of a fixed reference template plus an error of order O(εholsk−1) O(\varepsilon_{\mathrm{hol}} s^{k-1}) O(εholsk−1), where s s s is the Bergman scale. Paper II assembles these local packets across a mesh of cubes. Global coherence of the master templates across shared faces produces a raw integral current whose boundary has flat norm tending to zero uniformly over the final 0 0 0-1 1 1 rounding choices. Cube-wise control of mass and tangent-plane barycenter forces the fractional bookkeeping current to have periods arbitrarily close to the target integral periods; fixed-dimensional discrepancy rounding then selects the final on/off decisions for the marginal sheets, after which a Federer–Fleming filling current of vanishing mass closes the cycle in the exact target homology class. The resulting sequence is almost-calibrated (calibration defect →0 \to 0 →0) and lies in the fixed Poincaré-dual class PD(m[β]) \mathrm{PD}(m[\beta]) PD(m[β]). Paper III applies compactness of integral currents of bounded mass and zero boundary: any almost-calibrated sequence converges (after passing to a subsequence) to a ψ \psi ψ-calibrated integral cycle in the same homology class. Such a cycle is a positive sum of complex analytic subvarieties of codimension p p p (Harvey–Lawson/King). For cone-positive classes (those admitting a smooth closed cone-valued representative β \beta β) this already yields algebraicity. An elementary signed decomposition writes an arbitrary rational Hodge class as the difference of a cone-positive class and a positive rational multiple of [ωp] [\omega^p] [ωp]; the latter is algebraic by Bertini (complete intersections of hyperplane sections), so the general class is algebraic. Hard Lefschetz reduces the range p>n/2 p > n/2 p>n/2 to p≤n/2 p \le n/2 p≤n/2. The entire proof uses only classical tools: quantitative Bergman-kernel estimates, Federer–Fleming theory, Harvey–Lawson calibrated geometry, Chow’s theorem, and Serre GAGA. The global-assembly step isolates and repairs the single point where earlier long-form arguments were vulnerable (period control before rounding). No further assumptions are required.