Paper LIV: Vacuum Stability as Auxetic Shape Memory: Why the G2 Fano Truss with ν = −1 For- bids Vacuum Fluctuations, Resolves the Cosmological Constant Problem, and Enforces the Universality of Physical Constants

The G2-symmetric Fano re-entrant truss of the brane fabric has Poisson ratio ν = −1 (Paper XXV), giving an innite shear modulus Gshear = E/2(1 + ν) →∞. We show that this single geometric fact the auxetic shape memory of the brane fabric is the complete explanation for four problems that are usually treated as separate: (1) the stability of the vacuum against wild uctuations in vacuum energy; (2) the cosmological constant problem, resolved by identifying the 10122 oending modes as shear modes of the Fano lattice that do not exist as physical excitations; (3) the universality of physical constants why G, αem, me, and sin2 θW are identical in the Andromeda galaxy and the laboratory; and (4) the impossibility of false vacuum decay not merely exponentially suppressed but algebraically forbidden, because bubble nucleation is a domain wall which is a shear deformation, and shear deformations cost innite energy in a ν = −1 auxetic. A precise hierarchy of vacuum stability follows: algebraic constants (c, ℏ) are xed by the octonion algebra itself; topological constants (e, baryon number) are winding integers protected by innite shear cost; frozen gradient constants (G, me, αem) are held by the shape memory of the electroweak viscosity gradient; and only the cosmological evolution parameters (H0, a0) are permitted to change, on the T1 timescale Tsump ≈72.65 Gyr via the one permitted deformation mode isotropic Hubble breathing. We further apply this framework to metastable nuclei, deriving the properties of Tc-99m (the most widely used radioisotope in nuclear medicine) as a direct consequence of the ∆J = 4 winding mismatch between its isomeric and ground states, and show that the clinical perfection of Tc-99m its 6-hour half-life, 140 keV gamma, pure isomeric transition, chemical versatility, and generator production from Mo-99 are all inevitable consequences of the Z = 43 winding saddle point in the nuclear Fano lattice. Four new predictions follow (Predictions 7982). 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.