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In the field of pan-sharpening, existing deep methods are hindered in deepening cross-modal complementarity in the intermediate feature, and lack effective strategies to harness the network entirety for optimal solutions, exhibiting limited feasibility and interpretability due to their black-box designs. Besides, validating pan-sharpening performance in high-level semantic tasks is intractable for the absence of datasets. To tackle these issues, we propose a deep adaptive unfolded network via spatial morphology stripping and spectral filtration for pan-sharpening, which is conceptualized as a linear inverse problem regularized by spatial and spectral priors. Specifically, we incorporate phase-oriented constraints into the spatial prior to facilitate the extraction of modal-invariant spatial morphology by intrinsic decomposition and leverage a physics-driven spectral filtration attention mechanism aligned with the spectral prior to mine the inherent spectral correlation. After transparently unfolding the model into a multi-stage network, an adaptive stage-exiting mechanism is designed to capitalize on fusion diversity by aggregating optimal image patches across candidate stages. To systematically complete the assessment, we construct the first panoptic segmentation dataset as a semantic-level benchmark for pan-sharpening performance validation. Extensive experiments are conducted to verify the merits of our method with state-of-the-arts. Code is available at https://github.com/Baixuzx7/DAPNet.