Radial Dimensionality Theory IV: Tidal Deformability Ceilings under Solar-Constrained Density-Dependent Dimensionality

This paper computes the tidal deformability of neutron stars in Radial Dimensionality Theory (RDT) under the solar constraints of Paper I, completing the series' bound-propagation chain for the gravitational-wave inspiral observable. The relativistic tidal perturbation equations (Hinderer 2008, in the Postnikov–Prakash–Lattimer formulation) are solved on stellar backgrounds validated to ~0.1% against the published SLy mass–radius relation, with a minimal-coupling prescription: the dimensional modification enters through the equilibrium background only. The pipeline is gated before use — it reproduces the analytic Newtonian Love number for an n=1 polytrope (k₂ → 0.2594 vs 0.2599) and the published SLy value Λ(1.4 M☉) = 298 (literature ≈ 297).

Because Paper I bounds the dimensional law's amplitude (A < 0.0087 at 95% confidence) rather than detecting it, results are reported as ceilings — the largest signatures not excluded by solar data. The maximum allowed enhancement of the tidal deformability is +5.0% at 1.4 solar masses (Λ = 298 → 313), splitting nearly evenly between R⁵ geometric scaling (+2.6%) and the Love number (+2.3%), with a mild compactness-driven mass dependence (+4.4% to +5.6% over 1.0–1.6 solar masses). For a GW170817-like binary, the combined deformability is 359 (GR) and at most 377 (RDT) — both comfortably inside the measured band. The GR-to-ceiling separation is below the single-event precision forecast for third-generation detectors; the realistic test is statistical, across populations of mergers, where the EOS-independent, nearly mass-independent offset is a clean target. Complete reproducible code (MIT licensed) with validation gates is included.

Version 5 Update (June 2026):

This version supersedes all quantitative results of Versions 1–4. The corrections: (1) The dimensional law is unified with Papers I–III — the earlier logarithmic law, active only above nuclear saturation, evaded the solar and white-dwarf constraints by construction and is dropped; with it goes the earlier headline of tens-of-percent, strongly mass-dependent enhancements, which were features of that unbounded law at an unconstrained parameter value. (2) The equation-of-state baseline is corrected: V4 inherited the energy-density reconstruction error documented in Paper III Version 7, inflating R(1.4) to 13.37 km and Λ(1.4) to 985 (~3.3× the published value); its claimed agreement with "literature values ~950–1000" was incorrect, as published SLy values are ≈297. (3) V4's conclusion that SLy exceeds the GW170817 bound in both GR and RDT is reversed — it was an artifact of the inflated baseline; correctly computed, SLy is comfortably compatible. (4) V4's sole validation benchmark ("k₂ = 0.26 at C = 0.15") is shown to have been the Newtonian Love number mislabeled as a relativistic one (the true relativistic value is ≈0.071), so the earlier pipeline was never actually validated. (5) The claimed ">4σ single-event detectability at Einstein Telescope" is withdrawn; the solar-bounded signal requires population statistics. (6) The I-Love universality test is deferred: at the ≤5.6% ceiling level it is uninformative under the Lattimer–Schutz approximation used earlier. All results are generated by released, version-controlled scripts.