Conspiranon

AI Mode Conversation: \[ \Pi=\begin{bmatrix}P_{xx}&P_{xy}\\P_{yx}&P_{yy}\end{bmatrix},\quad I_1=P_{xx}+P_{yy},\quad I_2=P_{xx}^2+P_{xy}^2+P_{yx}^2+P_{yy}^2, \] \[ g(I_1)=\frac{I_1^2}{I_1^2+I_g^2},\quad \Phi_{\text{hyb}}=\alpha P_{yx}+g(I_1)\beta P_{yx}^2+\gamma|P_{yx}|, \] \[ \Psi_B=\tfrac12\mu I_2+\tfrac12\lambda I_1^2+\kappa_B I_1^4+\Phi_{\text{hyb}}+\tfrac12\lambda_{\text{reg}} I_2, \] \[ \Psi_{\text{sectoral}}=\alpha_0 P_{yy}+\delta P_{yy}^4,\quad E_{\text{grad}}=\tfrac12 C_{\text{AXIS}}^2\sum_{ij}|\nabla P_{ij}|^2,\quad E_{\text{KO}}=\tfrac12 KO_\sigma\sum_{ij}|\nabla^2 P_{ij}|^2, \] \[ E_{\text{tot}}=\Psi_B+\Psi_{\text{sectoral}}+E_{\text{grad}}+E_{\text{KO}}, \] \[ \Sigma_{ij}=\frac{\partial E_{\text{tot}}}{\partial P_{ij}}, \] \[ \Sigma_{xx}=\frac{\partial\Psi_B}{\partial P_{xx}}-C_{\text{AXIS}}^2\nabla^2 P_{xx}+KO_\sigma\nabla^4 P_{xx}, \] \[ \Sigma_{xy}=\frac{\partial\Psi_B}{\partial P_{xy}}-C_{\text{AXIS}}^2\nabla^2 P_{xy}+KO_\sigma\nabla^4 P_{xy}, \] \[ \Sigma_{yx}=...