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In materials science, the relationship between microstructure and material properties underpins rational design and performance optimization. Still, due to the complexity, heterogeneity, and multiscale nature of microstructural data, it is difficult to recognize. Electron microscopy provides rich visual access to microstructures. Still, existing analysis approaches rely heavily on manual interpretation or supervised machine learning, both of which are limited by the scarcity of annotations and limited generalizability. This paper presents the hierarchical invariant microstructure representation (HIMR) framework as a purely theoretical contribution to self-supervised representation learning for analyzing the microstructure of electron microscopy images. Rather than proposing an algorithm or empirical pipeline, HIMR provides a conceptual framework for learning, structuring, and relating microstructural information to material properties without labeled data. This framework conceptualizes microstructures as hierarchically organized latent representations, where physically meaningful features emerge through invariance-driven self-supervision and scale-aware aggregation. By integrating principles from representation learning, self-supervised paradigms, and materials physics, HIMR addresses foundational challenges, including imaging variability, scale entanglement, and the disconnect between the learned properties and physically interpretable property reasoning. Central to the framework is the alignment of the learned representation manifolds with property spaces governed by physical laws, enabling interpretable and theoretically grounded microstructure–property reasoning. By articulating explicit theoretical commitments regarding hierarchy, invariance, interpretability, and epistemic restraint, this work advances a framework-level understanding of self-supervised learning in materials science. As a result, HIMR provides a durable conceptual foundation for autonomous, data-efficient, and physically grounded analysis in AI-driven materials discovery and engineering.