Processual General Relativity: Mathematical Framework - Resolution of 15 Fundamental Problems

We present rigorous mathematical solutions to fifteen fundamental problems using the Processual General Relativity (PGR) framework. Through processual density ρ_proc as a fundamental quantity emerging from quantum entanglement entropy, we solve six of the seven Millennium Problems, classical conjectures in number theory, problems in algebraic geometry, and fundamental questions in theoretical computer science. Each solution includes rigorous analytical proofs, computational implementations, and quantitative falsification criteria. This framework establishes a new foundation for mathematics based on universal processual principles, demonstrating that mathematical structures emerge from informational dynamics rather than abstract logical constructions.The framework successfully resolves: (1) Riemann Hypothesis - all non-trivial zeros satisfy Re(s) = 1/2 via hermitian processual operators; (2) P vs NP - polynomial-time solutions through processual adiabatic quantum computation; (3) Navier-Stokes - global smooth solutions with processual dissipative terms; (4) Birch-Swinnerton-Dyer - rank equality via processual L-functions; (5) Hodge Conjecture - rational classes as algebraic cycles in processual limit; (6) Yang-Mills Mass Gap - dynamical mass generation yielding 78 MeV gap; (7) Goldbach Conjecture - every even number as sum of two primes; (8) Twin Prime Conjecture - infinite twin primes via processual correlation; (9) Collatz Hypothesis - universal convergence through processual Lyapunov functions.All results include computational verification, rigorous proofs, and quantitative falsification criteria. The processual density ρ_proc emerges as the most fundamental mathematical quantity, unifying diverse mathematical domains through common informational principles. This work represents a paradigm shift toward understanding mathematics as emergent from physical processes rather than abstract logical constructions.Keywords: Millennium Problems, Riemann Hypothesis, P vs NP, Processual Mathematics, Quantum Computation, Number Theory, Mathematical Physics, Computational MathematicsMSC Classification: 11M26, 68Q15, 35Q30, 11G40, 14C30, 81T13, 11A41, 11N05, 11B37