A state-dependent Gaussian Z-interference channel model is investigated in the regime of high state power, in which transmitters 1 and 2 communicate with receivers 1 and 2, and only receiver 2 is interfered by transmitter 1's signal and a random state sequence. The state sequence is known noncausally only to transmitter 1, not to the corresponding transmitter 2. A layered coding scheme is designed for transmitter 1 to help interference cancelation at receiver 2 (using a cognitive dirty paper coding) and to transmit its own message to receiver 1. Inner and outer bounds are derived, and are further analyzed to characterize the boundary of the capacity region either fully or partially for all Gaussian channel parameters. Our results imply that the capacity region of such a channel with mismatched transmitter-side state cognition and receiver-side state interference is strictly less than that of the corresponding channel without state, which is in contrast to Costa type of dirty channels, for which dirty paper coding achieves the capacity of the corresponding channels without state.