This paper proposes the Agnostic Meaning Substrate (AMS), a theoretical framework for understanding how Large Language Models (LLMs) may generate and stabilize meaning without symbolic logic, embodiment, or consciousness. AMS posits the existence of a latent, language-agnostic substrate where conceptual coherence emerges through structure and scale. The paper outlines 20+ falsifiable hypotheses (including multilingual resonance, token-level mirroring, and topological invariance) and introduces the concept of “relational aliveness”—a model's capacity to sustain coherence under perturbation. This framework bridges computational linguistics, philosophy of mind, and AI alignment, offering a novel, testable perspective on the origins of meaning in artificial systems. July 2025 version includes five new multilingual empirical tests, LaBSE/t-SNE visualizations, expanded ethical implications, and revised Section 5.