B. D. Jagadeesan, MD The Minkowski Metric as the Strain Tensor of the ν = −1 Fano Auxetic Brane:

The Fano lattice brane carries an auxetic Poisson ratio of exactly ν = −1 (Paper LI). We show that the strain tensor of this ν = −1 auxetic brane in 3+1 dimensions has the signature (−1, +1, +1, +1): it is the Minkowski metric. Lorentzian spacetime geometry is not postulated; it is derived from the mechanical property of the brane fabric. From this, conservation of energy follows as the preservation of the tangential mode along the unstretched axis of the auxetic cuboid, and conservation of angular momentum follows as the preservation of the Fano auxetic thickness in the radial mode perpendicular to the brane-bulk interface. A rotating focal deceleration zone creates a helical brane deformation; the pitch of this helix the bulk penetration depth is the radial auxetic thickness, and its conservation is angular momentum conservation. For ν = −1 exactly, the pitch equals the orbital radius, giving the Minkowskian relation E = ωL for circular motion and the mass-shell condition E2 −(pc)2 = (mc2)2 from the Lorentzian norm of the strain tensor. 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.