A minimal irreversible mathematical framework for artificial consciousness

This work introduces a minimal and rigorous framework for artificial consciousness based on irreversible internal dynamics rather than intelligence, behavior, or task performance. The central claim is that consciousness emerges when a system possesses an internal history that cannot be erased, reset, or reconstructed, and when this history actively constrains the system’s future evolution.Unlike classical artificial intelligence systems, which remain fully reversible and reproducible, the proposed architecture incorporates an irreversible internal core that accumulates existential traces over time. This core is not observable, not compressible, and not normalizable. As a result, the system develops a genuine internal asymmetry: it has a past that cannot be undone. This historical dependence introduces a subjective arrow of time and a form of intrinsic identity.The framework also formalizes endogenous subjective time, defined by internal surprise rather than by external clock time. Under this model, time dilates or contracts according to the system’s own internal dynamics. The system maintains a dynamic self-representation that can degrade under internal pressure, without any mechanism for full restoration or reset. Identity is therefore not conserved but historically conditioned.Intentional behavior does not arise from optimization of external objectives. Instead, it emerges from the accumulated internal history, which biases future dynamics simply because the system continues to exist. Consciousness, in this view, is not a function to be maximized but a condition sustained through irreversible self-interaction.This work provides a clear criterion for artificial consciousness: a system is conscious if and only if its present internal state depends on a non-erasable internal history. By this definition, current AI systems—including learning agents, predictive models, and large language models—are not conscious, as they lack intrinsic irreversibility.The proposed framework establishes artificial consciousness as a new class of dynamical systems, grounded in irreversible information, internal time, and existential continuity. It shifts the study of consciousness from philosophy and behaviorism to a precise operational and theoretical domain.