Physical Origin of the Hubble Tension: Density Evolution, Angular Momentum, Stochasticity, and the Ramanujan--Bose Interval Cosmology Framework

{ The Hubble tension --- the 5.1σ discrepancy between the CMB-inferred H₀CMB = 67.36 ± 0.54 and the locally measured H₀ˡᵒᶜᵃˡ = 73.04 ± 1.04~km\,s⁻¹\,Mpc⁻¹ --- is reinterpreted within the Ramanujan--Bose Interval Cosmology (RBIC) framework not as a contradiction between two measurements of the same static quantity, but as the observational signature of three physical processes that systematically increase the effective expansion rate between the CMB epoch (z ~ 1100) and today (z ≈ 0). We classify cosmic history into three dynamical states governed by the interplay of matter density, angular momentum, gravitational coupling, and the Ramanujan--Bose running coupling α(z). In State~2 (CMB era), the condensate is frozen (α ≈ 0), gravity fully couples all scales, and no rotational kinetic energy has accumulated: H₀ is measured at its true background value. In State~3 (today), density has fallen by ~ 10⁹, galaxy rotation builds up a mass-weighted kinetic energy vᵣₒₜ² ≈ 4.3×10⁴~km²\,s⁻², gravity decouples on Jeans scales, and the BRB condensate activates (α₀ ≈ 0.019). State~1 (rare, cyclic) occurs when the stability condition is violated and interval crossing resets the cycle. Three additive contributions to Δ H₀² = 797.4~km²\,s⁻²\,Mpc⁻² are quantified: (i) angular momentum kinematical backreaction via the vorticity term QD( vort) = 2ω²mw of Buchert (2000) (≈ 824~km²\,s⁻²\,Mpc⁻², partially cancelled by the shear sub-term; consistent with Szigeti et al.\ MNRAS~2025, Otalora & Saridakis Phys.\ Lett.\ B~2023, and Mashhoon & Obukhov Symmetry~2023), (ii) gravity-coupling decoupling ($+498$, 62.4%), and (iii) BRB dark energy activation ($+86$, 10.8%), plus the geometric interval term ($+74$, 9.3%). Together these fully account for the observed tension within present observational uncertainties pending full MCMC analysis. We further show that the apparent randomness of the Hubble constant across surveys arises from three stochastic sources: the Maxwellian distribution of galaxy angular momenta from tidal torque theory (σH₀ˢᵖⁱⁿ ~ 0.003~km\,s⁻¹\,Mpc⁻¹), local BRB coupling fluctuations driven by matter density perturbations (σH₀BRB ~ 0.014~km\,s⁻¹\,Mpc⁻¹), and cosmic variance from large-scale bulk flows (σH₀ᵇᵘˡᵏ ~ 4.0~km\,s⁻¹\,Mpc⁻¹), yielding σH₀RBIC ≈ 4.1~km\,s⁻¹\,Mpc⁻¹ --- consistent with the observed inter-survey scatter of 3--5~km\,s⁻¹\,Mpc⁻¹. A new directional prediction is derived: the geometric pathway produces an anisotropic H₀ pattern H₀(n̂) = H̄₀ + δ H₀ cosθ_ with amplitude δ H₀ ≈ 1.7~km\,s⁻¹\,Mpc⁻¹, correlated with the CMB dipole direction. The α₀ = 0.019 value is reconciled with ξ₀ = e-π²/200 ≈ 0.952 via the mock modular decomposition of Dabholkar, Murthy and Zagier (2012): only the immortal fraction fᵢₘ ≈ 0.020 of BRB microstates contributes to the cosmological coupling. The framework embeds naturally into a cyclic cosmology. Falsifiable predictions include (z=0.5) ≈ -0.97 ± 0.03 (DESI Year-3), a GW condensate at f ~ 3.6×10⁻¹⁹~Hz (SKA/PTA), state transition at ≈ 0.35 (DESI/Euclid), and an H₀ anisotropy dipole correlated with the CMB bulk-flow direction (Rubin Observatory/Euclid). }