Special Relativity in Twistor-EBIKK-β Gravity: Modified Formulas and Experimental Tests

We present a systematic derivation of modified Special Relativity (SR) formulas within the Twistor-Entropic-Born-Infeld-Kaluza-Klein β-gravity framework. The model predicts: (1) energy-dependent corrections to Lorentz transformations, (2) modified dispersion relation, and (3) cumulative velocity-dependent effects testable with ultra-high-energy cosmic rays. All standard SR results are recovered at energies E ≪ EPlanck.