To address the difficulty of accurately predicting porosity parameters and permeability under the condition of continuous logging curves but discrete core measurements in the L-well series of Block N, Daqing Oilfield, a core-constrained porosity-parameter and permeability prediction method based on CCML-KAN is proposed. Using conventional logging curves, including GR, RT, DEN, CNL, and AC, the method jointly constructs point-wise logging responses, gradient features, local statistical features, and multi-scale energy features, while introducing sparse core-point constraints to strengthen the mapping between logging responses and true petrophysical parameters. On this basis, a collaborative CCML-KAN framework with shared representations and dual output branches is developed to achieve joint modeling and continuous prediction of porosity parameters and permeability. Comparative experiments are conducted against 1D-CNN, LSTM, BiLSTM, CNN-BiLSTM, and Transformer. The results show that the proposed method achieves superior predictive performance on the test set, with an R² of 0.926 for porosity prediction and 0.911 for permeability prediction. In addition, it demonstrates strong discriminative capability in the integrated porosity-permeability classification task. The study indicates that CCML-KAN can effectively integrate multi-scale logging information with core constraints, providing an effective approach for fine prediction and comprehensive evaluation of reservoir porosity and permeability parameters.