The Expansion Freedom Principle v6.2: Hierarchical Effective Flux Areas, Generalized Inertial Motion, Natural Gravitational Boundaries, and the Hubble Tension

This paper extends the Expansion Freedom Principle (v6.1) with four major developments.

First, the effective flux area A_eff is generalised across a hierarchy of system geometries: spherical bodies (A_eff = 4π*r^2), spiral-galaxy disks (A_eff = 4π*H_eff*r, recovering flat rotation curves), filaments (cross-section A_eff = H_eff^2, giving constant g), and galaxy-cluster nodes (A_eff = n*H_eff^2). This replaces the single isotropic-propagation assumption with geometry-dependent flux distribution. Dark matter is shown to be the residual of applying spherical A_eff to non-spherical systems.

Second, inertial motion is generalised to the condition a_matter = const, a_relative_with_system = 0, unifying Galilean straight-line inertia with circular inertial motion at galactic outskirts, and clarifying that solar-system orbits (forced motion) and galactic flat rotation (inertial motion) are fundamentally different phenomena historically conflated under Keplerian dynamics.

Third, each mass is shown to possess a natural boundary of gravitational influence at r_balance = (GM/H^2)^(1/3), verified at both solar-system (Oort Cloud) and galactic (virial radius) scales. Beyond this boundary, matter joins the Hubble flow. This natural boundary, absent in Newtonian gravity, eliminates the need for dark energy or a cosmological constant. A minimum-a_matter principle is introduced to explain mass-centre selection, self-reinforcing structure formation, and the separation of stellar clumps without invoking repulsion.

Fourth, a two-component expansion model (H = f_void * H_void + f_matter * H_matter) quantifies the Hubble tension as a natural consequence of void-fraction evolution rather than unresolved physics, consistent with the observed directional anisotropy of H0 (Cosmicflows-4, 3.9 sigma). The light-deflection result 4GM/(c^2 b) is given a physical derivation as two equal effects of an expanding source body: its surface approaching the light ray, and its surface flattening as it expands, explaining for the first time, in elementary terms, why GR's prediction is exactly twice Newton's.

Throughout, spacetime is treated as a map constructed to interpret expansion, with dark matter, dark energy, and the Hubble tension identified as Mercator-type projection artefacts of that map.