Model-level synthetic-flux control of hyperchaos order and matched-resource sensing in dissipative optomechanics

Within a normalized six-dimensional model of dissipative optomechanics (one cavity + two mechanical resonators), a synthetic-flux phase $Φ_{\rm syn}$ acts as a reproducible control coordinate that selects the \emph{order} of a drive- and coupling-gated hyperchaos transition---up to four simultaneously positive Lyapunov exponents, beyond any reported single-mode benchmark. A phase-consistent Floquet--Lyapunov protocol (cross-checked by monodromy multipliers, dissipative volume balance $\sumλ_i=\operatorname{Tr}(J)=-1.04$ and a 180-run three-seed audit) localizes the onset to a Neimark--Sacker bifurcation at $E^{*}=\num{1.060}$ ($θ=0$). As a secondary, model-level geometric clarification, the identical matched-resource force-sensing protocol returns a null gain on the chaotic attractor ($\mathcal{G}_{A/B}=\num{1.039}\pm\num{0.014}$), consistent with the matched-Fisher lemma: noise projected onto an unstable manifold is stretched by the same factor $e^{λt}$ as the deterministic signal. Truncated-Fock and truncated-Wigner checks support the mean-field description at selected points. All results remain strictly model-level: the strong-coupling sector lies $\num{2542}\times$ beyond anchored silicon optomechanical couplings. Closing that gap requires ultrasonic characterization of the mechanical degeneracy $ω_2$, a measured inter-resonator hopping $J_m$, and the emergence of a genuine gigahertz platform.