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In this paper, a pervasive wireless channel modeling theory is first proposed, which uses a unified channel modeling method and a unified equation of channel impulse response (CIR), and can integrate important channel characteristics at different frequency bands and scenarios. Then, we apply the proposed theory to a three dimensional (3D) space-time-frequency (STF) non-stationary geometry-based stochastic model (GBSM) for the sixth generation (6G) wireless communication systems. The proposed 6G pervasive channel model (6GPCM) can characterize statistical properties of channels at all frequency bands from sub-6 GHz to visible light communication (VLC) bands and all scenarios such as unmanned aerial vehicle (UAV), maritime, (ultra-)massive multiple-input multiple-output (MIMO), reconfigurable intelligent surface (RIS), and industry Internet of things (IIoT) scenarios. By adjusting channel model parameters, the 6GPCM can be reduced to various simplified channel models for specific frequency bands and scenarios. Also, it includes standard fifth generation (5G) channel models as special cases. In addition, key statistical properties of the proposed 6GPCM are derived, simulated, and verified by various channel measurement results, which clearly demonstrates its accuracy, pervasiveness, and applicability.