Matter, Geometry and Noise: Linked Predictions from an Octonionic Matrix Model

Matter changes the medium whose fluctuations it probes. Taking this backreaction seriously can turn an assumed noise law into a calculable relation between forces and loss of interference. We study an octonionic $N=2$ matrix model motivated by generalised trace dynamics (GTD) and solve its full classical source-loaded equilibrium. Every nonzero uniform source selects an $S^3$ family of minima. Three modes remain gapless, while the leading weak-loading squared gaps of eight orbit modes occur in the ratio $2:3:4:6$. Relaxation of the massive amplitudes derives a derivative current whose coupling is fixed by the stiffness response. In a specified three-dimensional thermal continuum, this one current determines a $T^7$ point-probe noise law, a $2.1375\%$ spatial dephasing overshoot, a normalized momentum-cumulant coefficient $240/77$, and the matched-probe relation $\Gamma(\ell_T)=33.7363\,\ell_T|F(\ell_T)|/\hbar$, where $\ell_T=\hbar v/(k_BT)$ is the thermal length for mode speed $v$. We give conditional SI benchmarks, finite-body corrections and a joint temperature--separation test. A canonical matter completion also determines a mean source self-consistently. The calculation is placed within a self-contained seven-point PREDICT programme connecting laboratory fluctuations to records, geometry and cosmological observables. The thermal signatures belong to the derivative-scalar class; the matrix phase and stiffness relation supply the model-specific content. Together they provide a constructive benchmark; identifying the physical current, spatial preparation and clock conversion remains essential for a GTD interpretation. The ensemble calculation does not by itself select individual objective-collapse histories.