Radion Leakage in a 5D Braneworld: Unified Scale Selection and Gravity Modifications (v1.8.0)

This release marks a major theoretical milestone in the radion leakage framework. Key Achievement (Brick 4 — Scale Selection): We derive a single unified stabilizing potential for the radion that simultaneously accounts for three key elements: The equilibrium brane size r0≈0.75 r_0 ≈ 0.75 r0≈0.75 The radion mass (Compton wavelength) that sets the cosmological cutoff scale kc≈0.75 h Mpc−1 k_c ≈ 0.75 \, h\,Mpc⁻¹ kc≈0.75hMpc−1 The back-reaction coefficient β2≈3.33 β_2 ≈ 3.33 β2≈3.33 from warped 5D geometry, naturally producing Geff≈0.75GN Geff ≈ 0.75 G_N Geff≈0.75GN (25% gravity suppression) The repeated appearance of the scale 0.75 across the model is no longer a coincidence — it emerges naturally from one underlying potential shape. What’s New in v1.8.0 Complete rewrite and derivation of Brick 4 (Scale Selection) First explicit derivation of β2 β_2 β2 from warped 5D geometry (matches target value to high accuracy) Unified picture connecting radion equilibrium, mass, leakage amplitude, and gravity modification Updated roadmap and tiered predictions with improved scientific transparency Current Status The framework now stands at ~65% completion. Bricks 1–4 have been substantially strengthened. The critical next step is full implementation in Boltzmann codes (CLASS/CAMB) for quantitative predictions and joint likelihood analysis. The model offers clear falsifiable predictions, most notably a distinct small-scale suppression T(k)=TBBKS(k)exp⁡[−(k/0.75)1.8] T(k) = TBBKS(k) exp[-(k/0.75)1.8] T(k)=TBBKS(k)exp[−(k/0.75)1.8], together with targeted values σ8≈0.76 σ_8 ≈ 0.76 σ8≈0.76 and S8≈0.78 S_8 ≈ 0.78 S8≈0.78, which can be tested against Lyman-α forest data and weak lensing surveys. Note: This remains a speculative but increasingly coherent theoretical framework. All phenomenological parameters and approximations are clearly identified.