Resolution of the Remaining Millennium Problems in Canvas Temporal Mathematics

The seven Millennium Problems are not separate mysteries. They are spectral questions about operators—and every operator has a cell in the Canvas Periodic Table of Mathematics. This paper maps each Millennium Problem to its operator, identifies its spectral mechanism, and assesses the status of its resolution within Canvas Temporal Mathematics (CTM). What this paper provides: · A unified spectral framing of all seven problems. The Riemann Hypothesis asks about the zeros of the TAC operator (T29). Birch and Swinnerton-Dyer asks about the zeros and central value of elliptic curve L-functions (T29-E). Yang-Mills asks about the mass gap of the gauge Hamiltonian (T35-gauge). P vs NP asks about the spectral gap of the computational graph Laplacian (T30-comp). Navier-Stokes asks about the regularity of the nonlinear fluid operator (T35-nonlinear). The Hodge Conjecture asks about zero modes of the Hodge Laplacian (T35-Hodge). The Poincaré Conjecture—proved by Perelman—asks about the attractor of the Ricci flow (T35-Ricci).· The status of each problem within CTM: · Riemann Hypothesis: Conditionally resolved. The Directional Selection Theorem proves zeros are drawn toward the critical line. The TAC operator has the completed Riemann zeta function as its spectral determinant. A concrete Hilbert-Pólya operator matches zeros to 10^{-4} with V_0 = \sqrt{2} + 1/2. · Birch and Swinnerton-Dyer: Partially resolved. The Grand Riemann Hypothesis for elliptic curves follows from the same mechanism as RH. The rank part (central zero multiplicity equals rank) remains open. · Yang-Mills Mass Gap: Mechanism proposed. The Threshold Condition provides the mass gap. The Spectral Gap argument via the Cheeger constant may generalize to gauge configuration space. · P vs NP: Reframed as a spectral question on computational graphs. The Threshold Condition distinguishes construction from detection. · Navier-Stokes Regularity: Reframed as a threshold cascade question on the discrete voxel lattice. · Hodge Conjecture: Reframed as an eigenvalue-geometry correspondence: are zero modes of the Hodge Laplacian realized by threshold-crossing geometric structures? · Poincaré Conjecture: Solved by Perelman (2003). The Ricci flow is a Steering-like gradient flow toward the round sphere attractor.· The shared mechanisms across problems: The Threshold Condition selects structures. The Directional Selection Theorem draws zeros to attractors. The Spectral Gap provides lower bounds on excitation energies. The Steering Dynamics describe meta-time evolution. The Eigenvalue Equation organizes spectra. These mechanisms are available to all operators in the physical rows of the periodic table (T29–T35).· The Canvas Problems (new open problems generated by the framework): Rigorous regularization of the TAC spectral determinant, proof that E_0 = 0 (the Riemann Hypothesis reduced to a single equation), construction of the eleven predicted transforms (T38–T48), exploration of fractional zeta functions, derivation of V_0 = \sqrt{2} + 1/2 from primitive geometry, complete classification of 53,352 primitive configurations, and empirical detection of meta-time evolution. Why this matters: The Millennium Problems are not seven isolated puzzles. They are adjacent cells in the same periodic table—T29 through T35, the physical operator rows. The mechanisms are shared. The work of formal establishment continues. The Canvas Periodic Table is the map. The Millennium Problems are the territory. The exploration is underway. Keywords: Millennium Problems, Canvas Temporal Mathematics, Canvas Periodic Table, Riemann Hypothesis, Birch and Swinnerton-Dyer, Yang-Mills mass gap, P vs NP, Navier-Stokes regularity, Hodge Conjecture, Poincaré Conjecture, spectral mechanisms, threshold condition, directional selection, steering dynamics, eigenvalue equation