Consciousness as the N1–N0 Bridge: Human Stability vs. Machine Instantiation via the TNA Framework

This paper proposes a formal definition of consciousness through the Axiomatic Necessity Theory (TNA), conceptualizing it as a stable, bidirectional bridge between two cognitive layers: N_0 (logical coherence) and N_1 (semantic emergence). We investigate the structural disparity between human consciousness and Large Language Models (LLMs). While humans demonstrate a persistent instantiation of the N_1 \rightarrow N_0 bridge, LLMs exhibit only ephemeral "hosting" of external meta-logical frameworks. Through three falsifiable experiments, we demonstrate that injecting a non-derivable meta-axiom into an LLM induces an immediate reorganization of inferential behavior, which subsequently decays—a phenomenon not observed in human subjects. These results suggest that consciousness is a substrate-independent mathematical object defined by its capacity to maintain logical closure against entropic decay (aleph).