Observable-Conditioned Backaction in Dynamic Circuits: A Higher-Order Context-Conditioned Kernel for Local Dynamics

Mid-circuit measurements are essential primitives for dynamic circuits and quantum error correction, yet characterizing their induced disturbance on spectator qubits remains a central practical problem. Device-level benchmarking often compresses this disturbance into low-order proxy metrics such as T1, T2, readout assignment error, and pairwise crosstalk. We argue that these proxies can be operationally incomplete for multiscale dynamic circuits. We introduce a higher-order context-conditioned kernel, ΓeffY,O=ΓlocO+ΓproxyO+ΓrelY,O, where Y is a global context label and O a local observable. The term ΓrelY,O is a phenomenological compression ansatz isolating residual context dependence unexplained by standard proxies. To avoid impossibility issues of quantum partial-information decompositions on non-commuting algebras, the Möbius weights entering this ansatz are evaluated operationally on classical measurement outcomes. We present evidence in three steps. First, earlier GHZ-versus-clock hardware results motivate an observable-class split. Second, we present dynamical evidence using the A6 synthetic hardware harness. A6 injects a pure higher-order context dependence via a programmed conditional interaction. Because the (C0,C1,C2) parity context is invisible to singles and pairs by construction, standard low-order diagnostics are fundamentally blind to the source of the probe's disturbance. Third, we demonstrate coherent controllability through the A6.2 quantum-eraser experiment. Programmable MARK interactions suppress unconditional fringes while eraser-basis conditioning restores them, consistent with complementarity bounds. These results validate a context-conditioned description of backaction over proxy-only null models.