Radial Dimensionality Theory III: Neutron Star Structure under Solar-Constrained Density-Dependent Dimensionality

This paper computes the neutron-star signatures of Radial Dimensionality Theory (RDT) using the canonical mechanism of Papers I–II: a modification of the gravitational divergence operator, with matter and the mass integral kept three-dimensional. Promoted to general relativity, the radial gravitational field obeys a (3+δ)-dimensional Gauss law (δ = d_eff − 3 ≤ 0). At nuclear densities the opening law is saturated (δ → −3A, constant), so the modification is a constant operator correction throughout the star; EOS-insensitivity and parameter saturation are built-in structural properties, not findings.

On a GR baseline validated to ~0.1% against the published SLy mass–radius relation (full crust-to-core CompOSE equation of state: M_max = 2.050 solar masses, R(1.4) = 11.69 km), the maximum solar-allowed effect (amplitude A < 0.0087 from Paper I) is a contraction: at most −0.71% in the maximum mass (2.050 → 2.035 solar masses), −0.42% in R(1.4), and a reduction of the tidal deformability Λ(1.4). RDT makes neutron stars smaller and lowers the maximum mass — the same direction as the radius deficit found for the Sun and white dwarfs in Papers I–II. Because RDT lowers the maximum mass, it cannot help support heavy pulsars: standard SLy already sits above the 2.01-solar-mass floor (no rescue needed), and RDT moves it the wrong way, slightly worsening the soft-equation-of-state problem rather than rescuing it. The sign is read off the calculation, not assumed — the modified solver reduces to general relativity linearly as the amplitude goes to zero, and two inequivalent relativistic embeddings of the operator agree in sign (−0.57% to −0.71%), their ~0.15-percentage-point spread being the residual non-uniqueness of the relativistic embedding. The surviving falsifiable content is a uniform sub-percent contraction of neutron-star radii and tidal deformabilities, probed by next-generation measurements. Complete reproducible code (MIT licensed), validation gates, and data tables are included.

Version 8 Update (June 2026):

This version corrects the sign of the neutron-star effect and supersedes the quantitative results of Versions 1–7. Version 7 modified the Tolman–Oppenheimer–Volkoff pressure gradient by a force-rescaling factor F(ρ) = (d_eff − 1)/2 < 1, which weakens gravity and expands the star, giving +0.9% in maximum mass and the conclusion that RDT eases heavy-pulsar tension. That factor is not the mechanism of Papers I–II, which modify the gravitational divergence operator; the faithful relativistic analog of that operator contracts the star, giving −0.71% (−0.57% under the alternative embedding). The corrected sign matches the radius deficit of Papers I–II and reverses Version 7's conclusion: RDT lowers the maximum mass and does not help support heavy pulsars — it tightens, rather than eases, the soft-equation-of-state tension. The sign is established by the modified solver reducing to general relativity linearly as the amplitude vanishes (so the contraction is a genuine response of the modified equations, not an artifact of a fallback path), and by two inequivalent embeddings agreeing in sign. With this correction the whole series is sign-consistent: the canonical mechanism contracts compact objects in every regime — Sun, white dwarfs, and neutron stars. This is the third self-correction in the neutron-star line, after the radius bug of Versions 1–2 and the energy-density fix of Version 7; the residual tidal-deformability value is computed in Paper IV rather than scaled.

Prior corrections (Version 7, retained):

Version 7 superseded Versions 1–6 by taking the equation-of-state energy density directly from the published tables (ε = ρc²) rather than "reconstructing" it — the reconstruction double-counted internal energy by up to 40% at core densities and was the single error behind both the 35–40% radius error of V1–V2 and the residual 5–6% radius error and spurious 1.79-solar-mass maximum-mass cap of V3–V6 (wrongly attributed to table truncation; the same table with the correct convention yields the full 2.05). It also replaced the crust-truncated implementation with the full crust-to-core CompOSE table, validated the solver to ~0.1%, withdrew the irreproducible V6 "rescue" of SLy from 1.79 to 2.141 solar masses and the defective APR results, bounded the RDT amplitude by Paper I's solar constraint (A < 0.0087) rather than the superseded "solar-calibrated" value, and moved all figures and tables to released, version-controlled scripts.