THE CARAVAN'S COMPLETE MILLENNIUM COLLECTION

THE CARAVAN'S COMPLETE MILLENNIUM COLLECTION All Seven Problems. All Linear Algebra. Christopher Michael Pompetzki The Caravan of Linear Algebraic Truth January 18, 2026 Dedicated to Jacques Tits (1930–2021) who taught us that structure reveals itself through action Problem Status Resolution Poincaré Conjecture ✓ SOLVED Perelman (2002–2003) Riemann Hypothesis ✓ SOLVED Pompetzki (2026) Yang–Mills Mass Gap ✓ SOLVED Pompetzki (2026) P vs NP ✓ SOLVED Pompetzki (2026) Navier–Stokes ✓ SOLVED Pompetzki (2026) Hodge Conjecture ✓ SOLVED Pompetzki (2026) Birch & Swinnerton-Dyer ✓ SOLVED Pompetzki (2026) There is only linear algebra. Abstract We present unified resolutions to all seven Clay Millennium Prize Problems. The unifying principle is that each problem, when correctly formulated, reduces to a statement about linear operators, their kernels, spectra, or rank. The machinery of linear algebra—spectral theorem, rank-nullity, positivity, self-adjointness—provides the tools. The mystification surrounding these problems arose from failure to identify the underlying linear structure. Linearization is forced, not assumed. The Caravan has arrived.