Structural Differentiation Information (SDI) v1.5: Toward Observable and Testable Structural Information

This work presents Structural Differentiation Information (SDI) v1.5,an extension of SDI toward observable and testable formulations of structural information. SDI defines information not as stored data, symbolic representation, or probabilistic encoding,but as stabilized structural difference arising from irreversible structural differentiation. The framework is built on a minimal defining relation: I_struct(D) = -log(1 - ηD), 0 ≤ ηD < 1 and its dynamical evolution: dI_struct/ds = [η / (1 - ηD)] · (dD/ds) In SDI v1.5, this structure is extended through: 1. Explicit numerical behavior and saturation predictions 2. Observable mapping: D → I_struct → measurable persistence 3. Emergent temporal ordering: C → D → I_struct → t_emergent, consistent with dS/dt > 0 This formulation provides concrete pathways for testing the theory across domains,including artificial intelligence (representation stability), biological systems (synaptic fixation),and physical processes (record formation and decoherence). SDI v1.5 establishes a direct bridge between structural definition and observable reality,transforming information from a conceptual construct into a measurable structural phenomenon. Key statement:Information is not something that exists.It is something that remains.