Radial Dimensionality Theory II: White Dwarf Structure under Solar-Constrained Density-Dependent Dimensionality

This paper computes the white dwarf signatures of Radial Dimensionality Theory (RDT) under the solar constraints derived in Paper I. The density-dependent opening law d_eff(ρ) = 3·Ω(ρ), with Ω(ρ) = 1 − A·x/(1+x) and x = (ρ/ρ₀)^α, is applied unchanged — no parameters retuned — to non-relativistic n=1.5 polytropic white dwarfs with the physical degenerate-electron equation of state (μ_e = 2), using the exact modified Lane–Emden equation of Paper I with the modification confined to the gravitational divergence operator. Because Paper I finds no detection and instead bounds the law's amplitude (A < 0.0087 at 95% confidence for all transition exponents 0.02 ≤ α ≤ 0.5), the white dwarf results are presented as the maximum signatures still allowed by solar data, evaluated along the solar exclusion boundary. Across the validity range (M ≈ 0.16–0.86 solar masses), the maximum allowed effect is a radius deficit at fixed mass of |ΔR/R| ≤ 9.5×10⁻³, nearly mass-independent. This ceiling sits at the precision frontier of eclipsing-binary mass–radius measurements: a precise sample consistent with standard models at the few ×10⁻³ level would tighten the dimensional bound below the solar one, making white dwarfs the leading constraint. The included Python code (MIT licensed) provides the modified structure solver with validation gates, the prediction pipeline along the solar exclusion boundary, and reproduces every number quoted in the paper. Version 3 Update (June 2026): This version supersedes the results of Versions 1–2. The earlier numerical implementation was invalid: it used a dimensionless polytropic constant in cgs units (making its model stars ~10-meter objects) and began integration outside the stellar surface, inflating masses by factors of 9–79 and breaking the analytic n=1.5 mass–radius scalings. In addition, the earlier force-rescaling ansatz differed from the divergence-operator modification on which the series has standardized; the corrected equations reverse the sign of the predicted effect (a radius deficit, not an excess). The Chandrasekhar-mass claims are withdrawn entirely — an n=1.5 polytrope has no maximum mass, so the earlier "shifts" measured the edge of a scan grid rather than physics; relativistic compact-object predictions are deferred to Paper III. Finally, the solar calibration point this paper inherited (d_eff ≈ 2.95) was superseded by Paper I Version 3, which excludes it at more than 8σ; predictions are now bounded by Paper I's 95% confidence limit rather than anchored to a fitted value. The qualitative conclusion — that a single density-dependent law links solar and white dwarf regimes with no retuning — is unchanged and is now on a sound numerical footing.