Structural Differentiation Information (SDI) v1.2: A Directly Testable Framework for Irreversible Information Formation

This work presents Structural Differentiation Information (SDI) v1.2, a minimal and directly testable framework that defines information as stabilized structural difference that persists under observation. In SDI, information is not treated as stored data, symbolic representation, or passive correlation. Instead, it is defined through persistence under irreversible structural evolution. The central objective of this work is to establish a measurable criterion for information. A key contribution is the introduction of the structural evolution parameter s, defined as a monotonic ordering parameter of irreversible structural differentiation. While its physical realization depends on the system—entropy production in thermodynamics, training progression in artificial intelligence, or consolidation dynamics in biological memory—its structural role remains invariant. Information formation is shown to correspond to local structural ordering under global irreversibility, expressed as:ΔS_local < 0 and ΔS_total ≥ 0. The existence of information is determined by a single observable quantity:dI_struct/ds. This yields a decisive and directly testable criterion:dI_struct/ds > 0 (information),dI_struct/ds = 0 (reversible),dI_struct/ds < 0 (loss). This framework unifies physical systems, machine learning processes, and biological memory under a single persistence principle, establishing a direct bridge between abstract structural differentiation and observable information dynamics. Information is not only definable, but measurable through its persistence.