The 15-Bit Word Divider Deriving Spinal Resonance as Binary Boundary Oscillator in 32-Bit Substrate Architecture 2^15 Harmonic; Word-Splitting Function; Hexagonal k=3 Correction; Brain-Body Interface; 73 cm Geometric Necessity We derive human spinal resonance (1027 Hz = 32,864 × 1/32 Hz from [@CKS-BIO-32-2026]) as geometric necessity for 15-bit word-divider function in 32-bit substrate architecture, proving spine evolved not for structural support but as binary boundary oscillator separating high-word (brain/cranial) from low-word (body/ground) processing domains. Operating with zero adjustable parameters, CKS demonstrates that the "magic numbers" of modern physics are not arbitrary constants, but mechanical requirements of hexagonal geometry. This paper extends the framework into the domain of Anomalous Magnetic Moments & Electroweak Symmetry, deriving the final three "hidden" constants—the electron g-factor anomaly, the Euler-Mascheroni constant, and the Weinberg mixing angle—from first principles. Empirical Falsification (The Kill-Switch):CKS is a locked and falsifiable theory. This paper is 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. If the derived ratios for the electroweak mixing angle (\( \sin^2\theta_w \approx 0.231 \)) or the poloidal phase-lead (\( g_e \approx 2.00232 \)) deviate from CODATA 2018 values by more than the derived geometric residue, the hypothesis of unitary computational completeness is mechanically invalidated. 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 quantum anomalies, harmonic friction, and topological tilt are unified as mechanical residues of toroidal impedance. In CKS, these constants are reframed from arbitrary measurements to the mandatory results of an 84-bit torus navigating a 32-bit substrate bus. The model represents a closed-loop pedagogical truth where the g-factor is understood as "motion blur" and the Euler constant as "buffer flush heat," revealing the inherent unity of the physical world and information architecture. Package Contents:* `manuscript.md`: Paper* `README.md`: Overview Motto: Axioms first. Axioms always. Status: Locked. Experimentally falsifiable.

CKS FRAMEWORK PAPER - Registry ID: CKS-0-2026. Dependencies: CKS foundation only. This is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework extending into 0. The paper is subject to the Global Falsification Protocol [CKS-TEST-1-2026]: if the 1/32 Hz substrate quantization is absent in relevant precision measurements, this derivation is invalidated.

Theoretical derivation from CKS axioms applied to 0. Dependencies: CKS foundation only. Computational validation and empirical comparison where applicable.