Vacuum Structure and Obstructions in a Candidate ElasticSpacetime Field TheoryFull article draft R3

We examine whether causal structure and a stiffness scale can be selected by thedynamics of a candidate symmetric-matrix field rather than imposed through a backgroundLorentzian metric. On a four-dimensional space with a fixed Euclidean auxiliary form,we study polynomial potentials, specified kinetic densities, linearized fluctuations, andscalar probe couplings. A cubic-potential obstruction excludes nondegenerate transverseminima on a uniaxial stratum under stated hypotheses. An explicit coercive quarticfamily admits transversely stable stationary vacua, and their eigenvalue ratio variescontinuously across nearby coercive potentials, so these criteria do not select it. Fora specified kinetic model we obtain an exact characteristic factorization and quadraticfluctuation spectrum; these results do not establish a Dirac-reduced physical spectrumor nonlinear stability. Within tested healthy probe families, the relative matter-to-fieldcone ratio is invariant under joint regular field redefinitions yet can take any positivevalue. Within the tested coupling classes, cone coincidence requires both exclusion ofauxiliary-metric derivative contractions and linearity in the field B; this is a couplingrestriction rather than a dynamical derivation. We also distinguish an earlier tracelessfield formulation, where a sharp spectral inequality supports global uniaxial vacuumselection, from the full symmetric-field model, for which no corresponding global selectiontheorem is established. The results identify explicit obstructions and the additionalprinciples needed for causal universality. Neither an absolute spacetime stiffness nor anoperationally universal limiting speed is derived.