Why a Genuine Field Cosmology Must Carry the Same Dynamics as Galaxy Rotation

This paper shows within Tensor Field Dynamics (TFD) and the Phoenix Axiom that cosmology, local gravitation, and galaxy rotation cannot form separate physical sectors. If the framework admits only one primary field, one field equation, one gradient law, and a single scale continuation, then cosmic dynamics must carry the same underlying structure as galaxy rotation. The paper develops this statement as a TFD-internal, audit-proof derivation. It shows that local gravitation, the flattening of galactic rotation, and cosmological tension are different scale manifestations of the same Yukawa and gradient dynamics. Cosmology therefore does not appear as an additional independent law, but as the large-scale continuation of the same field mechanics. The result is a clear TFD core statement: a genuine field cosmology is not an independent dynamics, but the cosmic continuation of the same mechanics that already operates locally and galactically.