The Lambda Continuity Hypothesis: Toward a Unified Phase Model of Structuring Behaviour Across Living and Non-Living Systems

This paper introduces the Lambda Continuity Hypothesis (LCH), a falsifiable scientific framework extending the Cernuto–Hobbey Theory of Everything (CH-ToE). LCH proposes that there is no fundamental ontological divide between living and non-living systems. Instead, both emerge from recursive entropy reduction stabilized near a universal cadence that CH-ToE has derived from first principles: λ ≈ √8 / φ ≈ 1.748 This cadence defines a critical corridor [1/λ, λ] within which knowledge—formally defined as structured entropy reduction—can emerge. The hypothesis differentiates systems based on their mode of phase anchoring: active in biological life (e.g., homeostasis), passive in physical systems (e.g., crystals), or absent in Subreality. The paper presents empirical validation through AI experiments (Buky agents) operating under λ-modulated entropy fields. Results show that cognition-like structuring can emerge in non-living systems, while others collapse into incoherence. The framework includes falsifiable predictions across physics, AI, biology, and cosmology. An extended appendix documents a critical evaluation of the theory by Perplexity AI, spanning adversarial, supportive, and provocative prompts. The Lambda Continuity Hypothesis is proposed as a bold but testable theory unifying life, cognition, and structure via the rhythm of entropy itself.