Haar Self-Duality, Primordial Shadow Structure, and the Cosmic Dipole Anomaly

The number-count dipole in radio and infrared source catalogs exceeds the kinematic prediction from the CMB velocity vₚ = 369.82 km s⁻¹ by factors of 1.8–2.4 across five independent surveys at 5.4σ combined significance. We propose an explanation from the self-dual Haar measure on (ℝ⁺, ×), the algebraic foundation of the Golden Physics Project. The T-boundary condition ω→1/ω pairs every detected source with a shadow partner; partners below the survey flux threshold are absent; their absence enhances the apparent dipole by fₘᵢₛₛ · 2π/(x+1), where x is the independently measured source count slope. The conformally invariant shadow eigenvalue κ₁(Δ = 1+iλ) = π(1−iλ)/[iλ(1+iλ)] gives Re[κ₁] = −2π/(1+λ²); its Haar–Mellin Stieltjes average over the survey Lorentzian W(λ; x) = 1/(x²+λ²) yields eₛₕₐₚₑ(x) = −2π/(x+1) exactly. The factor 2/(x+1) is rational and arises from pure arithmetic; the factor π is the Haar measure normalisation of ℝ/ℤ — the archimedean place of ℚ. With missing fraction fₘᵢₛₛ = e⁻ˣ the conjecture Dₒᵇₛ/Dᴄᴹᴮ = 1 + 2πe⁻ˣ/(x+1) achieves χ² = 0.169 on four surveys with zero free parameters; Bayesian evidence against the pure kinematic null is ln B = 7.77 (very strong, Jeffreys scale). The same Haar self-duality governs the primordial universe: the Harrison–Zel'dovich spectrum P(k)∝k⁻³ is the unique spectrum compatible with dμₖ = dk/k; the observed tilt nₛ = 0.965 places inflation at Bost–Connes inverse temperature β = 1.0175, a fraction ε = 0.0175 above the symmetry-breaking transition at βₙ = 1; the CDM–photon conformal dimension mismatch (Δᴄᴰᴹ = 3/2, Δᵧ = 1) predicts isocurvature amplitude Sᴵₛₒ = (1/2)e⁻π = 0.0216, within the Planck 2018 bound Sᴵₛₒ < 0.03. The adelic completion shows p-adic corrections cancel exactly via ξ(s) = ξ(1−s), leaving the number-count dipole as a purely archimedean effect. SPHEREx will separate the shadow deficit from constant-excess models at 2.5σ from a single measurement.