Logismos Graphics & Physics Pipeline: Exact Geometric and Physical Computation Through VFR Architecture

Logismos Graphics & Physics Pipeline: Exact Geometric and Physical Computation Through VFR 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 derive complete graphics and physics pipeline architecture using VFR (Value-Factor-Remainder) exact rational arithmetic, achieving perfect geometric accuracy and deterministic physical simulation. Building on Q-Taylor series (MATH-117) and VFR linear algebra (MATH-118), we specify: (1) Transform hierarchy - scene graph with exact composition preventing drift across any depth, (2) Camera system - perspective and orthographic projections maintaining perfect mathematical properties, (3) Skeletal animation - bone transformations and vertex skinning without vertex swimming or numerical wandering, (4) Rigid body physics - position, velocity, and orientation evolution with perfect energy conservation, (5) Collision detection - exact contact point computation and penetration depth calculation, (6) Constraint solving - joint and contact constraints solved exactly through VFR linear algebra, (7) Deterministic replay - identical results across platforms and runs guaranteed by rational arithmetic. Complete architecture specified through Zig structures and data flow description. Traditional floating-point pipelines produce approximate results with accumulated drift. VFR pipeline achieves mathematical exactness through integer-based rational computation at all stages. Revolutionary claim: Computer graphics and physics can be mathematically exact - every transform perfect, every collision precise, every replay identical - through comprehensive VFR architecture. 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-119-2026). Dependencies: CKS-LEX-12-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-118-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.