Recent advances in large language models (LLMs) have revealed unprecedented fluency, reasoning, and cross-linguistic capabilities. These behaviors challenge traditional theories of how meaning arises in artificial systems. This paper introduces the concept of the Agnostic Meaning Substrate (AMS)—a hypothesized, non-symbolic, language-independent structure within LLMs that stabilizes meaning before it is surfaced as language. Drawing on recent empirical research from Anthropic and OpenAI, AMS is defined not as a conscious space, but as a computational structure capable of supporting semantic coherence, analogical reasoning, and multilingual resonance. We outline five testable hypotheses related to the emergence, topology, and scaling properties of AMS, and explore the theoretical, ethical, and philosophical implications of such a structure. If validated, AMS offers a novel framework for understanding how meaning may emerge in complex systems—without mind, yet with integrity.