Phenomenal Velocity Geometry

The paper constructs an algebraic–geometric framework around the “phenomenological ve-<br>locity” expression v = pN/D that arose in previous informal work. We introduce (i) the<br>energy-number field E, (ii) a non-commutative velocity-string algebra V, (iii) a curvature scalar<br>KPV defined from a “PV–Hessian”, and (iv) a curved A∞ category Fukv (M ) obtained from an<br>ordinary Fukaya category by multiplication with v. Basic structural results are proved; several<br>phenomena are left as conjectures to stimulate further study.