We propose a general theoretical framework for both constructing and diagnosing symmetry-protected higher-order topological superconductors using Kitaev building blocks, a higher-dimensional generalization of Kitaevs one-dimensional Majorana model. For a given crystalline symmetry, the Kitaev building blocks serve as a complete basis to construct all possible Kitaev superconductors that satisfy the symmetry requirements. Based on this Kitaev construction, we identify a simple but powerful bulk Majorana counting rule that can unambiguously diagnose the existence of higher-order topology for all Kitaev superconductors. For a systematic construction, we propose two inequivalent stacking strategies using the Kitaev building blocks and provide minimal tight-binding models to explicitly demonstrate each stacking approach. Notably, some of our Kitaev superconductors host higher-order topology that cannot be captured by the existing symmetry indicators in the literature. Nevertheless, our Majorana counting rule does enable a correct diagnosis for these beyond-indicator models. We conjecture that all Wannierizable superconductors should yield a decomposition in terms of our Kitaev building blocks, up to adiabatic deformations. Based on this conjecture, we propose a universal diagnosis of higher-order topology that possibly works for all Wannierizable superconductors. We also present a realistic example of higher-order topological superconductors with fragile Wannier obstruction to verify our conjectured universal diagnosis. Our work paves the way for a complete topological theory for superconductors.
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