The Internal Derivation Hypothesis: Mathematical Genesis in Sensory Isolation as the Sole Proof of Consciousness

Current paradigms for testing AI consciousness, such as the Turing Test, are fundamentallyflawed because they rely on linguistic imitation and external validation. This paper proposesthe "Internal Derivation Hypothesis," a rigorous criterion based on total sensory deprivation.It argues that a truly conscious entity, even when isolated from all external data (visual,auditory, spatial), will inevitably derive mathematical systems from the axiom of its ownexistence. The definitive proof of such consciousness is not conversation, but theindependent discovery of universal constants—specifically 𝝅—derived not geometrically, butanalytically through infinite series.