One-Octonion Brane-Bulk Framework — Paper CCCV: The Auxetic Flow — The Fifth-Force Desert as an IR Fixed Point (nu=-1, betaₙu=- (1+nu) ) and the Three Scalars as Endpoints of One Coarse-Graining

Paper CCCIV predicted a fifth-force desert (no Yukawa deviation from Newtonian gravity in the Bonanno-Glaviano window, Phys. Rev. Lett. 136, 201501, 2026) but rested on ENUMERATING the framework's three curvature-coupled scalars rather than deriving their absence from a flow, as asymptotic safety does. This paper closes that gap. The brane is an auxetic elastic medium with a coarse-graining flow whose control parameter is the 2D Poisson ratio nu= (K-mu) / (K+mu). We show nu=-1 is an INFRARED-ATTRACTIVE fixed point with beta function betaₙu = dnu/dln (l) = - (1+nu) + O ( (1+nu) ²) and eigenvalue -1, at which the area modulus vanishes (K*=0). A curvature-coupled scalar is a phonon with mₛ² proportional to stiffness, so the fixed point dynamically gaps the spectrum: the dilational scalar couples to K->0 and is driven massless (lifted only by the global Hubble pre-stress to m ~ hbar H0 = the sump/dark-energy field), while the shear scalar couples to the finite shear modulus mu and stays at the electroweak condensate scale (the Higgs viscosity wave). The three scalars of CCCIV are thus NOT an inventory but the two fixed-point endpoints (UV-stiff Planck mass = metric-signature/Thangavelu mode; IR-floppy hbar H0 = sump field) plus the shear branch (electroweak Higgs) of a SINGLE flow. The fifth-force desert is the gap between the two endpoints: intermediate masses are not fixed points (betaₙu != 0), so no curvature-coupled scalar can settle there - exactly as asymptotic safety's excluded region is where no UV-complete trajectory lands. The absence is now an attractor property, not an assumption. Two contrasts with asymptotic safety: the OOB fixed point is in the IR (where fifth forces are measured), and it is an attractor (generic trajectories funnel to it) rather than reached by fine-tuned trajectories. Honest status: nu*=-1 and its attractive character are robust (symmetry-forced, two verified routes), but the quantitative beta function uses a leading-order coarse-graining ansatz (K (l) ~ 1/l) ; a full functional treatment of the elastic kernel is the natural next step (the exponent may shift, the fixed point will not). The 'no in-gap states' phonon property is cited from the framework's verified Fano-truss band computation and the Maxwell-Calladine isostatic theorem. Zero new free parameters. verify 16/16.