Human cognition organizes continuous experience into bounded units while maintaining continuity across them. Linguistic elements are also organized into bounded structural units such as words and phrases, with sentence marking the final bound of a grammatical construction process. How do such boundaries emerge? We propose boundaries emerge from interacting demands to maintain unresolved dependencies, integrate completed relations, and update semantic context, with structural completion allowing but not determining closure. First, in a generative simulation without predefined boundary positions or constituent labels, these demands produced sentence-like segment-length distributions and distinct characteristic timescales, with structural completion allowing but not determining closure. Near boundaries, unresolved dependency load declined, integration cost peaked, and accumulated pressure reset. Then, we tested whether same demands predicted human listeners' boundary choices during comprehension. Listeners were more likely to mark boundaries with fewer unresolved dependencies, higher integration cost and semantic mismatch, and elevated preceding memory load, beyond syntactic and prosodic cues. Third, in naturalistic self-paced reading, sentence-final slowing coincided with declining memory load and increasing integration cost and semantic mismatch, broadly consistent with the simulation. Processing same narratives with a large language model revealed increased local intrinsic dimensionality and straighter hidden-state trajectories at sentence endings, followed by larger representational updates. Boundary explained additional variation in reading time and hidden-state geometry beyond processing demands, but considerably less in next-token surprisal. Together, these findings suggest linguistic boundaries emerge as discrete manifestations of transitions in continuous processing dynamics.

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