Newton and General Relativity, Reread in the Language of Expansion Freedom: A Unified Classification of Motion, the Derivation of Gravitational Time Dilation, and the Diagnosis of Dark Matter and Dark Energy

This paper rereads central results of Newtonian mechanics and General Relativity in the language of the Expansion Freedom Principle introduced in v6. 0-v6. 2. A single inequality, comparing the expansion-deficit term GM/Aₑff (r) to the expansion term H² r, is shown to classify all motion in the universe: bound orbital motion, inertial motion, and recession into the Hubble flow are simply the three signs of aₘatter (r). Inertial motion turns out to be the measure-zero boundary between the other two, not an independent category. Kepler's second law and the vis-viva equation are rederived as expressions of a single conserved quantity, r² v² = L² (suppression area times expressed freedom), with the sign of the orbital energy E providing the same three-way classification as the first result. The natural boundary rbalance = (GM/H²) ^ (1/3) introduced in v6. 2 is reinterpreted: it is not a cause (a boundary condition imposed on the dynamics) but a result, the attractor of the expansion/suppression dynamics, populated by whatever survives after unbound matter joins the Hubble flow and bound matter falls inward. The apparent tension between the minimum-aₘatter principle (a particle selects the mass centre that most suppresses its own expansion) and the axiom that everything seeks maximal expansion is resolved: local sacrifice of expansion freedom produces a larger total, so structure formation is the axiom's optimal solution, not a departure from it. Gravitational time dilation is derived directly: the dimensionless quantity GM/ (r c²) = Phi (r) /c² (accumulated expansion deficit divided by the universal rate c²) reproduces the General-Relativistic weak-field result d (tau) /dt ~ 1 - GM/ (r c²) exactly, verified numerically to a ratio of 1. 0000 using Earth-surface vs GPS-altitude data. The result is summarised as: where mass suppresses expansion, both space and time are correspondingly diminished, with no separate geometric object (curvature) required to link the two. We then diagnose why dark matter and dark energy became necessary in General Relativity: GR removed the Newtonian force of gravity but retained a force-isomorphic mediator structure (mass -> curvature -> motion). When this mediator's magnitude fails to match observation, additional invisible mass or energy must be posited to correct it. The Expansion Freedom Principle has no such mediator: mass is a record of local expansion lag, not an agent of influence, so there is nothing to correct. Finally, we show that the axiom's word "everything" applies literally to radiation as well: the Eddington luminosity limit is the same balance condition (aₑff = 0) that produces rbalance at cosmological scales, with radiation pressure, the expansion freedom of photons, playing the role that H² r plays for galaxies. A short opening section also establishes that the appearance of a mass M is what makes "distance r" a meaningful quantity in the first place (a sharpened form of Mach's principle): the same equation that defines the expansion deficit also defines the only r with respect to which that deficit makes sense.