The Universal Abstract LLM Conjecture: Toward a Substrate-Independent Theory of Generative Systems and the Reconstruction of Individual Implementations

Recent advances in inverting large language models have demonstrated that the prompting context underlying a model’s textual output can be recovered with high fidelity through techniques such as previous-token prediction. This result raises a broader question: can any humanly meaningful text, regardless of its origin, be treated as the output of a generative process for which analogous reconstruction is conceivable? We propose the Universal Abstract LLM Conjecture, which holds that every such text is an output of some concrete implementation of a single substrate-independent abstract class of generative systems. Current digital large language models constitute one family of implementations of this class; human minds may be functionally modeled as another, without any claim that the mind is ontologically identical to a large language model. Under the conjecture, individual generative systems become recoverable in principle as data-constrained feasible sets rather than as uniquely determined objects. Because complete historical conditioning information is unavailable and generation exhibits sensitive dependence on initial conditions, exact recovery is impossible. We therefore shift attention to the mathematical characterization of feasible sets, the design of graded authenticity metrics, and the development of comparative heuristics for producing new texts that remain consistent with an observed generative signature at quantifiable confidence levels. The conjecture opens a research program at the intersection of inverse problems, statistical learning under partial observability, and the theory of generative models, with potential implications for literary analysis, cognitive modeling, and human–AI collaboration.