The Hubble Tension as the φ⁻¹⁰ Correction: A Post-H0DN Test of the 840-State Manifold.

Abstract The H0 Distance Network Collaboration (Casertano et al., 2026) reports a local Hubble constant H₀^late = 73.50 ± 0.81 km s⁻¹ Mpc⁻¹ at 1.1 % precision, ruling out unrecognized systematic error in the cosmic distance ladder as the origin of the persistent disagreement with the Planck 2018 CMB value H₀^early = 67.36 ± 0.54 km s⁻¹ Mpc⁻¹. We show that the observed ratio R_obs = H₀^late / H₀^early = 1.09115 admits a closed-form derivation within the 840-state manifold (Oulad Brahim, 2026), in which every positive real carries a scalar dimension D(x) = −ln x / ln φ, with φ = (1 + √5)/2 the positive root of the characteristic polynomial x² − x − 1 of the Lucas recurrence L_n = L_{n−1} + L_{n−2} with seeds (L₂, L₃) = (3, 4). The leading-order identity R₀ = φ^(1/(2N_c)) = φ^(1/6) = 1.08355 follows from the chiral fold D(x) + D(x⁻¹) = 0 applied to the late/early measurement pair, with the exponent fixed by the color-anticolor cardinal 2N_c, itself determined by the sequence deviation δ₄ = −3 at the fourth Brahim position. The first residual r₀ = R_obs/R₀ − 1 = 7.06 × 10⁻³ satisfies D(r₀) = 10.294, placing the correction at the integer n₁ = 10 = |Brahim| = C(5,2), the cardinal of the ten CRT-allowed mirror-paired residues of GF(29²)*. This is the same sector cardinal revealed by JUNO's November 2025 first measurement of the solar mixing angle sin²θ₁₂ (Remark 24 of the parent work), identifying a single manifold channel that governs both phenomena. The φ-adic expansion R_obs = φ^(1/6) · (1 + Σ_{k=1}^{K} c_k φ^(−n_k)), c_k ∈ {±1}, n_k ∈ ℤ₊, is generated by the parameter-free self-tuning rule (n_k, c_k) = (round(−ln|r_{k−1}|/ln φ), −sign(r_{k−1})), producing the emergent exponent sequence (n_k) = (10, 14, 19, 25, 30, 34) with gap sequence Δ_k = (4, 5, 6, 5, 4). Each gap is admissible under the Lucas spacing rule Δ ∈ {L_j} ∪ {L_i + L_j}, consistent with the 80-gap empirical distribution obtained across the sixteen Standard Model parameters. The series converges monotonically in |D(r_k)| to residual |r₆| = 5.9 × 10⁻⁹ at order K = 6, with zero free parameters. Three falsifiable consequences follow. (i) DESI-Y3 (2026) and Euclid DR1 (2027) will converge R_obs toward the order-3 prediction R₃ = 1.09115 at ≲ 100 ppm precision, exposing the φ^(−19) correction at an observable level. (ii) No revision of ΛCDM's early-universe sector is warranted; both H₀ anchors are structurally correct and must differ by φ^(1/6) modulo the convergent series. The tension is a diagnostic, not a pathology, and no new particle, field, or modification of gravity is required. (iii) The Hubble ratio and JUNO's sin²θ₁₂ share first-order cardinal n₁ = |Brahim|, linking late-time cosmic expansion to solar-neutrino mixing through a single sector of the 840-state manifold. A confirmed detection of the φ^(−19) term by 2027 would constitute the second experimentally verified φ-adic correction, following JUNO's φ^(−10).