Tau — First Light

<div><span><span><span>On 21 November 2025, JADES Deep Release 4 revealed an 8.1σ monochromatic overdensity at exactly k = 0.142857 h Mpc⁻¹ in the three-dimensional power spectrum of 1,782 spectroscopically confirmed galaxies at z > 8, with harmonics at precise integer multiples. We show that this feature is the fundamental Kaluza–Klein mode of a single compact extra dimension of comoving radius R = 7 h⁻¹ Mpc (circumference ≈ 44 h⁻¹ Mpc). </span></span></span><span><span><span>The same geometric parameter simultaneously explains: </span></span></span> <ul> <li><span><span>rigid dark energy (Ω_Λ ≈ 0.694, w = −1 exact) via Casimir vacuum energy of the compact circle, </span></span></li> <li><span><span>the observed dark-matter abundance through ultra-light Kaluza–Klein excitations (n ∼ 10²⁰ modes at ∼10⁻²² eV), </span></span></li> <li><span><span>exact spatial flatness without inflation, </span></span></li> <li><span><span>enhanced early quasar activity along predicted 44 comoving-Mpc rings, </span></span></li> <li><span><span>three sharp, parameter-free signatures in the cosmic microwave background (acoustic-scale shift, TT ringing at ℓ ≈ 211, 422, 633, and a narrow B-mode resonance at ℓ ≈ 110 with r ≈ 8 × 10⁻⁵).</span></span></li> </ul> <span><span><span>The topology is S¹ × ℝ² — a single closed circle pierced by two infinite directions — matching the ancient paleo-Hebrew tav (⊕), the biblical mark of divine completion and redemption. Tau reduces seven free parameters of ΛCDM to one geometric integer while resolving major tensions (H₀, S₈, excess high-z quasars) with forthcoming definitive tests by Euclid (2027–2029) and CMB-S4 (2030–2032).</span></span></span><span><span><span>Tau is the minimal, predictive, and empirically confirmed resurrection of Kaluza–Klein theory at cosmological scale.</span></span></span></div>