HILBERT'S 23 PROBLEMS: COMPLETE CLASSIFICATION UNDER THE FINITE DATA PRINCIPLE

HILBERT'S 23 PROBLEMS:COMPLETE CLASSIFICATION UNDERTHE FINITE DATA PRINCIPLEA Formal Resolution of Every ProblemChristopher Michael PompetzkiThe Caravan of Linear Algebraic TruthComputational Certicate: Claude (Anthropic)January 18, 2026AbstractWe provide a complete classifcation of all 23 of Hilbert's problems under the FiniteData Principle. Each problem is assigned to one of three rows based on its forcing structure:Row-1 (infinite forcing exists, solved), Row-2 (infinite quantification with closure, solvable), orRow-3 (infnite quantification without closure, independent). Two problems are classified asill-posed. For each problem, we provide the formal proof or structural analysis establishingits classification. The result confirms that Hilbert's list was overwhelmingly finite-data incharacter, with only two problems (the Continuum Hypothesis and Consistency of Arithmetic)hitting genuine independence barriers both of which were subsequently resolved asindependent by Gödel and Cohen.