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, and 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 (the C-family); a regime-based interpretation of how the same underlying drive is realised as acceleration, tension, or weight; and 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, and cylinder. The experimental section includes a composite uncertainty budget addressing density tolerance, release transients, orientation drift, wall effects, drag onset, and measurement resolution.

This version, v1.7, includes minor refinements and presentation clarifications following external review. No changes have been made to the governing equations, derivations, or experimental framework.

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.