Bootstrap Theory of Representational Emergence (TBER): Explanatory Insufficiency, Transition Regimes, and the Emergence of New Representational Levels

Representation learning is central to modern machine learning, yet most research focuses on optimizing representations after a framework has been selected. The Bootstrap Theory of Representational Emergence (TBER) addresses a prior question: when does a new representational level become necessary? Version 4 identifies explanatory insufficiency as a positive epistemic signal for representational transition. A representation may remain useful while becoming unable to make relevant relations, transformations, distinctions, or organizational properties intelligible. TBER distinguishes two dimensions. Explanatory insufficiency may be descriptive, transformational, or related to generalization. The resulting response may belong to a local-corrective, representationally resolutive, or structurally recurrent regime. The bootstrap process is recursive: stabilized representations enable observation; anomalies expose persistent insufficiencies; candidate re-representations are generated; discriminating tests constrain them; surviving representations undergo provisional stabilization and closure assessment. Formal cases such as Kaprekar's routine and G"odelian incompleteness are used only as boundary examples of distinct transition regimes, not as proofs of TBER or models of physical or biological dynamics. The framework concerns transitions between scientific, mathematical, or computational representations. It has implications for representation learning, latent spaces, foundation models, world models, adaptive biological systems, scientific discovery, and autonomous AI. TBER suggests that future intelligent systems should not only learn representations, but also diagnose their limits, determine when re-representation is warranted, test alternatives, and recognize whether a limitation is locally resolved or structurally recurrent.