Vacuum selection and collective quantum response in an octonionic matrix model: Paper P7 in a ten-part series P1-P10

Paper P7 of a ten part series P1-P10 on Interaction, Cohesive Emergence, and Fundamental Constants in Generalised Trace Dynamics P7 — Nonlinear instability and exact descent A useful benchmark for cohesive emergence must select its matrix background dynamically and retain the modes that remain light. We study these questions in a seven-matrix $G_2$-invariant mechanics with a cubic interaction and a positive radial quartic. At radial-to-commutator ratio $\lambda/g^2=1/2$, we prove that every positive-radius associative Pauli stationary configuration of multiplicity at least three, with nonnegative mass squared, fails to be a zero-charge classical local minimum. An exact rational deformation has lower energy on a uniform finite amplitude interval throughout this parameter family, despite a nonnegative benchmark Hessian. We then construct a competing irreducible $N=6$ stationary configuration from rank-three tensor operators on spin five-halves. Its benchmark normal Hessian is numerically positive. In an explicitly traceless canonical quantum model, we calculate the hard-mode radial response, the induced interaction on seven retained fermion modes, and a coupled rotor--fermion ordering operator in one specified charge representation. The distinction between exact identities, numerical stability and conditional quantum results is maintained throughout. These results sharpen a finite dynamical test for the GTD programme; they do not reconstruct physical spacetime, Standard Model colour or measured fundamental constants.