Time Field Theory (TFT): Rigorous Axiomatic Derivation of the Velocity Composition Formula

This paper presents the only correct, rigorous, first-principles derivation of the inertial frame transformation and velocity composition formula in Time Field Theory (TFT). The full derivation is self-contained, mathematically consistent, and does not rely on special relativity or any external framework. Important version notice:All previous drafts, earlier versions, or non-rigorous derivations on TFT velocity composition contain incomplete or incorrect steps and are hereby fully retracted and superseded.Only this present paper constitutes the valid, citable, and officially correct version of the TFT velocity composition derivation.