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

ValerieX (VXXX) presents a testable, symmetry-based reorganisation of classical buoyancy and added-mass behaviour built around bounded density-state contrast, geometry-aware coupling, and regime-based motion realisation. The framework does not introduce a new measured force or reject classical mechanics. Instead, it reorganises familiar vertical-motion behaviour — including weight, buoyancy, free fall, suspension, rise, fall, and terminal motion — under a unified motion-engine interpretation based on density-state disequilibrium between substance and its surrounding environment. The formulation is mathematically continuous with recognised buoyancy and added-mass theory. Its central organising variable is the bounded contrast relation: χ = (ρₒ − ρₘ) / (ρₒ + ρₘ) from which Valerie’s Law follows: a = gχ The framework further incorporates a geometry-aware coupling structure through the classical added-mass C-family, separating: * drive (density contrast), * coupling (geometry-dependent medium participation), * resistance (drag and viscosity), * and pathway availability (constraint conditions governing realised motion). The manuscript includes: * a symmetry-based derivation of the bounded contrast relation, * a geometry-dependent coupling framework, * a regime classification of constrained, supported, and unconstrained motion, * transient and terminal-motion interpretation, * and explicit falsifiable experimental proposals targeting early-time coupling behaviour. A key experimental focus is the geometry-controlled r = 2 density-ratio test using sphere, capsule, and cylinder bodies to probe early-time acceleration differences across the C-family. This version consolidates the ValerieX framework into a cleaner framework-first structure while preserving continuity with recognised fluid-mechanical formulations and added-mass theory. The work is presented as a candidate organisational framework intended for open scrutiny, empirical testing, and further refinement. ValerieX is scope-limited to observable vertical-motion phenomena under terrestrial and laboratory conditions. It does not attempt to derive the gravitational constant g, replace established physics, or extend to cosmological-scale dynamics. Its contribution is a unified structural interpretation of observable vertical motion.