Paper LI: Newton's Constant as Brane Viscosity: Spacetime as a Non-Newtonian Fluid, MOND as Shear-Thinning, and the T1/T2/T2* Hierarchy as the Burgers Constitutive Equa- tion of the Brane

Newton's constant G is identied as the compliance (inverse shear viscosity) of the brane fabric regarded as a crystalline uid. From Paper XVI, G = c4/τbrane, where τbrane is the brane tension; tension is a viscosity-like quantity for a 2D material, so G is literally how easily spacetime deforms under a shear load. The brane uid is Newtonian at high acceleration (a ≫a0) and non-Newtonian at low acceleration (a ≲a0), with a0 = cH0/2π acting as the gravitational Reynolds threshold separating laminar from non-Newtonian ow. MOND phenomenology is the Carreau-Yasuda shear-thinning limit of this uid: the eective gravitational viscosity Geff(a) diverges as a →0 exactly as a shear-thinning polymer viscosity diverges at zero shear rate. The T1/T2/T2* relax- ation hierarchy (Papers XXXIV, XXXV) is identied as the three-component Burgers viscoelastic constitutive model: T1 is the Newtonian dashpot (global sump ow), T2 is the Kelvin-Voigt spring (stellar cluster elastic dephasing), and T2* is the Maxwell elas- tic element (coherent BH focal zone). The SPARC rotation curve equation from Paper XXXIV is derived as the constitutive equation of the brane uid, not postulated phe- nomenologically. Two dimensionless numbers complete the unication: the gravitational Weissenberg number Wigrav = (rT2∗/c)(a/a0) governs the elastic-to-viscous transition at xed radius, and the gravitational Deborah number Degrav = Tsump/tobs governs the quantum-mechanical (De ≫1, elastic) to MOND (De ≪1, viscous) transition across observation timescales. The G2-symmetric viscosity tensor has exactly two independent components in ratio 2πRbulk, restating the hierarchy problem as a viscosity ratio. The KSS bound η/s ≥ℏ/(4πkB) is saturated by the brane uid, which is the minimum- viscosity uid consistent with quantum mechanics a consequence of the Fano truss minimality. Four new predictions follow (Predictions 6568).

Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.