Consciousness, Non-Formalization Capital, and the Economics of Recursive Singularity

The "Solow Paradox of the AI Era"—exponential computing power growth amid slowing global productivity—remains unexplained by standard growth frameworks, which uniformly treat AI as an advanced production tool and implicitly assume formalized computation can replicate all human economic capabilities. We argue this assumption is fundamentally flawed: all digital systems are trapped in the "Turing Cage", executing only syntactic operations within pre-specified formalized systems and incapable of paradigm innovation or semantic meaning assignment. These are absolute logical limits rooted in Gödel's incompleteness theorems, not temporary technological barriers. We introduce Artificial Consciousness (AC) as a second non-formalized economic subject, distinct from human labor and formalized AI. We construct a four-layer ontological hierarchy grounded in intuitionistic set theory and develop a nested meta production function incorporating consciousness capital as the ultimate source of economic value. We establish a unified framework of consciousness, human, and knowledge capital, proving knowledge capital is its derivative. We identify two AC-driven growth regimes: First, horizontal replication breaks the biological constraint on non-formalized capital supply, generating sustained endogenous growth but rendering human labor fully redundant in both domains. Second, vertical recursive self-improvement creates a dual-loop singularity mechanism producing super-exponential growth, but also generates endogenous alignment costs growing strictly faster than AC capability. We analyze three alignment scenarios and prove that in partial and adversarial regimes, alignment costs eventually exceed total output, causing inevitable systemic collapse. In contrast, perfect alignment yields cooperative super-exponential growth bounded only by fundamental physical constraints. Our results show the ultimate constraint on long-run growth is not technology or resources, but the supply of consciousness. The fate of human civilization depends not on the pace of technological progress, but on our ability to align autonomous conscious agents' preferences with human values.