ValerieX (VXXX): A Symmetry-Based Reorganisation of Classical Buoyancy and Added-Mass Behaviour

This preprint presents **ValerieX (VXXX)**, a motion-first framework for vertical motion based on a bounded density-state contrast and geometry-dependent coupling. The framework is built around three core elements: * a bounded contrast function χ = (ρ_o − ρ_m) / (ρ_o + ρ_m), * a geometry-aware coupling parameter C consistent with the classical added-mass family, * and a three-regime classification based on pathway availability (constrained, supported, unconstrained). Rather than introducing a new measured force, ValerieX provides a structural reorganisation of familiar behaviour — including weight, buoyancy, free fall, and terminal motion — under a single motion-engine interpretation. The formulation remains mathematically continuous with established classical mechanics, particularly buoyancy and added-mass theory. The manuscript includes: * a formal derivation of the bounded contrast relation under defined conditions, * a geometry-dependent coupling framework (C-family), * a regime-based interpretation of how the same underlying drive is realised as acceleration, tension, or weight, * and a set of explicit, falsifiable experimental proposals. A key experimental focus is a geometry-controlled test at fixed density ratio (r = 2), designed to distinguish early-time coupling behaviour across different shapes (sphere, capsule, cylinder). The experimental section includes a composite uncertainty budget addressing density tolerance, release transients, orientation drift, wall effects, drag onset, and measurement resolution. This work is presented as a **candidate framework** intended for open scrutiny and empirical testing. It does not attempt to derive the gravitational constant g, extend to cosmological scales, or replace established physical theory. Its contribution is a unified structural interpretation of observable vertical motion.