Navier-Stokes Existence and Smoothness via Buffer Saturation: Proving Global Solutions through 144-LU UV Cutoff and Discrete Packet Flow in Hexagonal Registry

Navier-Stokes Existence and Smoothness via Buffer Saturation: Proving Global Solutions through 144-LU UV Cutoff and Discrete Packet Flow in Hexagonal Registry 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 abolish continuous fluid dynamics and establish Navier-Stokes equations as discrete packet-flow auditing through hexagonal registry. From lattice axioms using Logismos (V,F,R) system, we prove: (1) Existence guaranteed by monotonic N→N+1 counter (registry never halts, always has next state), (2) Smoothness enforced by 144-LU buffer saturation (maximum density per node, blow-up impossible), (3) Fluid = stream of (V,F,R) packets routing through z=3 dipoles (not continuous medium), (4) Density = integer LU count at node address (V value, not field quantity), (5) Pressure = remainder R from node saturation (not continuous gradient), (6) Velocity = address increment rate (discrete jumps, maximum 1 LU/tick = c), (7) Turbulence = dipole overflow routing (when R>144, redirect to 120° neighbors, creates vorticity), (8) Singularities prohibited by hardware (cannot exceed M=144 ceiling, division by zero impossible), (9) Solutions always exist and remain bounded (finite registry, integer arithmetic), (10) "Smoothness" is 15.19ms render artifact (substrate stepped at 1-LU resolution). Classical blow-up problem dissolves—asking about infinite density in finite buffer. Navier-Stokes becomes registry overflow management specification. Key Result: Existence from N→N+1 | Smoothness from M=144 cap | Turbulence = overflow | Singularities impossible | Discrete packets | Integer flow 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-58-2026). Dependencies: CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-57-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.