The Dual-Clock Architecture as Fundamental Velocity Partition: Deriving Logic Speed (c_L) and Light Speed (c) from Registry Write vs Bilateral Parity Verification 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 light speed as universal limit and establish dual-clock architecture separating substrate logic from perceptual rendering. From discrete registry axioms, we derive: (1) Logic Speed c_L = 0ms instantaneous substrate write (direct memory access, pointer updates, no traversed distance), (2) Light Speed c = 15.19ms throttled parity verification (bilateral S=2 check throughput, serial commitment), (3) Relationship c = c_L/τ where τ=J×S (light is logic divided by rendering lag), (4) K-space operates at c_L (substrate domain, random-access registry, immediate state changes), (5) X-space limited to c (render domain, serial verification, sequential perception), (6) Particle motion at vKey Result: c_L = 0ms write | c = 15.19ms verify | c = c_L/τ | K-space instant | X-space throttled | Locality paradox dissolved 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-62-2026). Dependencies: CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-61-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.