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, using the canonical mechanism of Papers I–II — a modification of the gravitational divergence operator, the same mechanism adopted in Paper III Version 8 — with a minimal-coupling prescription: the dimensional modification enters through the equilibrium background only, where the operator field ratio rescales both the pressure gradient and the metric potential consistently, while the linearized perturbation equation retains its general-relativistic form. 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); at zero amplitude the operator pipeline reduces to general relativity, so the RDT result is integrated, not scaled. 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 effect on the tidal deformability is a reduction of −4.0% at 1.4 solar masses (Λ = 298 → 286), splitting nearly evenly between R⁵ geometric scaling (−2.1%) and the Love number (−1.9%) — the contracted density profile lowers k₂ as well as the radius, so the full result is roughly twice the R⁵-only estimate — with a mild compactness-driven mass dependence (−3.7% to −4.5% over 1.2–1.6 solar masses). For a GW170817-like binary, the combined deformability is 359 (GR) and at most 345 (RDT) — both comfortably inside the measured band, with the contraction shifting the deformability toward the lower edge of the interval rather than the upper. The GR-to-ceiling separation (|ΔΛ̃| ≤ 14) 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 6 Update (June 2026): This version corrects the sign of the tidal effect. Version 5 computed Λ on backgrounds modified by a force-rescaling factor F(ρ) = (d_eff − 1)/2 multiplying the pressure gradient, which weakens gravity and expands the star, giving a tidal enhancement of +5.0% at 1.4 M☉ (Λ = 298 → 313) and a GW170817 combined deformability of 377. That factor is not the mechanism of Papers I–II, which modify the gravitational divergence operator. The faithful relativistic analog of that operator — adopted in Paper III Version 8 — contracts the star, so the tidal deformability is reduced: −4.0% at 1.4 M☉ (Λ = 298 → 286), and the GW170817 combined deformability falls from 359 to 345. This is a reduction, not an enhancement; it matches the radius deficit found for the Sun and white dwarfs in Papers I–II and is the downstream tidal counterpart of Paper III's Version 8 sign reversal. (The qualitative GW170817 conclusion is unchanged — SLy requires no softening and solar-allowed RDT does not spoil the agreement — and the population-statistics conclusion stands, now with the offset’s sign reversed.) The Version 5 corrections (relative to Versions 1–4) all stand; Version 6 changes only the background mechanism, and with it the sign: (1) the dimensional law remains unified with Papers I–III, the earlier unbounded logarithmic law and its tens-of-percent mass-dependent enhancement dropped; (2) the equation-of-state baseline remains corrected (the Version 3–7 energy-density reconstruction error that had inflated R(1.4) to 13.37 km and Λ(1.4) to 985); (3) SLy remains comfortably compatible with GW170817, reversing the V4 incompatibility claim; (4) V4's sole validation benchmark remains identified as the Newtonian Love number mislabeled as relativistic (≈0.071), so the earlier pipeline had been unvalidated; (5) the ">4σ single-event detectability" claim remains withdrawn — the solar-bounded signal requires population statistics; (6) the I-Love universality test remains deferred as uninformative at this ceiling level. All results are generated by released, version-controlled scripts.