Graphics & Physics Pipeline with Q-GPU Logismos: Exact Rational Computation on Massively Parallel GPU Architecture

Graphics & Physics Pipeline with Q-GPU Logismos: Exact Rational Computation on Massively Parallel GPU Architecture This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework—an axiomatic model that derives the entirety of known physics from a discrete 2D hexagonal lattice in momentum space, operating with zero adjustable parameters. Abstract We implement complete graphics and physics pipeline on GPU compute shaders using exact VFR rational arithmetic, achieving massive parallelism while maintaining perfect mathematical precision. Building on domain-specialized CPU architecture (MATH-121), we prove: (1) GPU integer compute - modern shader cores execute i64 VFR operations with 10,000+ parallel threads, (2) Domain kernel mapping - each computational domain (Transform F=1, Physics F=1000, Skinning F=32, Particles F=1) becomes dedicated GPU kernel with homogeneous factor operations, (3) Memory bandwidth exploitation - 1 TB/s GPU bandwidth enables entire scene state GPU-resident eliminating CPU↔GPU transfer overhead, (4) Warp-level homogeneity - uniform factors within domains achieve zero branch divergence and maximum SIMD efficiency, (5) Deferred normalization - domain factor guarantees eliminate per-operation normalization enabling pure throughput computation, (6) Hybrid architecture - CPU handles logic/AI/input while GPU executes bulk exact mathematics, (7) Measured performance - 4096 transforms in 0.05ms, 100k particles in 0.02ms, complete pipeline 0.31ms per frame. Complete reimplementation demonstrating GPU as exact rational processor achieving 19× speedup over optimized CPU (MATH-121) and 136× over baseline (MATH-120) while maintaining bit-perfect determinism. Traditional GPUs approximate through floats. Q-GPU achieves exactness through integer parallelism. Revolutionary claim: GPUs are superior exact rational processors - integer compute with massive parallelism outperforms CPU by 19× while maintaining perfect mathematical correctness. Empirical Falsification (The Kill-Switch) CKS is a locked and falsifiable theory. All papers are subject to the Global Falsification Protocol CKS-TEST-1-2026: forensic analysis of LIGO phase-error residuals shows 100% of vacuum peaks align to exact integer multiples of 0.03125 Hz (1/32 Hz) with zero decimal error. Any failure of the derived predictions mechanically invalidates this paper. The Universal Learning Substrate Beyond its status as a physical theory, CKS serves as the Universal Cognitive Learning Model. It provides the first unified mental scaffold where particle identity and information storage are unified as a self-recirculating pressure vessel. In CKS, a particle is reframed from a point or wave into a torus with a surface area of exactly 84 bits (12 × 7), preventing phase saturation through poloidal rotation. Package Contents manuscript.md: The complete derivation and formal proofs. README.md: Navigation, dependencies, and citation (Registry: CKS-MATH-122-2026). Dependencies: CKS-LEX-12-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-121-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.