Cat Tails as Phase-Array Antennas—Deriving Feline Auxiliary Bus from Toroidal Stability Requirements: Proving Tail = Linear Phase Compensator Enabling Zero-Latency Proprioception via 300 Baud Vortex Lock 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 feline tail function from toroidal stability requirements establishing tail as cantilevered phase-array antenna solving horizontal spine coherence problem. From geometric constraints, we prove: (1) Tail = auxiliary bus compensating horizontal orientation (vertical spine grounded to gravity, horizontal spine perpendicular to dN/dt, requires phase compensator), (2) 300 baud tip twitch = buffer flush (micro-oscillations clear 84-bit reality buffer, maintains 11-nines eye-claw coherence, enables zero-latency strike), (3) S-curve = double toroidal waveguide (counter-rotating vortices cancel front/hind torque, chassis remains laminar, zero proprioceptive noise), (4) 90° hook = Jacobian lock (orthogonal projection alignment, keep-alive signal while resting, maintains 3D render during low-power), (5) Tail mass ratio = 1/3 body length forced (N^(1/3) scaling, handles polar nodes while body handles equatorial, 5:2 dimensional split resolution), (6) Puffed tail = manifold hardening (increased thickness creates phase-shield, stress response via impedance boost), (7) Tucked tail = bus disconnect (reduces neural territory, prevents external phase-avalanche, fear protection mechanism), (8) 15.19ms lag universal but externally compensated (same toroidal pitch as humans, tail provides dynamic modulation, hunting overclock capability), (9) Bent tail = topological kink (phase reflection at break point, forces Type 1 locked gait, permanent coherence loss without repair), (10) Chattering synchronized to tail (k-k-k phonemes match tip frequency, manual clock alignment to target substrate address). Cats proven as phase-array equipped quadrupeds using external hardware (tail) where humans use internal software (Dan Tien). Tail damage = antenna failure with cascading motor dysfunction. Key Result: Tail = phase antenna | 300 baud twitch = sync | S-curve = vortex pair | Bent = broken bus | Sway requires coherent tail 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-BIO-49-2026). Dependencies: CKS-BIO-1-2026, CKS-BIO-48-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.