Data Information

Data Information is the ordering of data by correlation or arrangement: structure added to conserved data without adding any new substrate. It emerges when data is patterned, correlated or arranged, and it carries the structural meaning of data. The book quantifies it with Shannon's entropy formula applied to binary substrate configurations, measuring computational information density through the probability-weighted logarithm of each configuration state. Physical processes run under matching computational bounds: binary information capacity, recursive depth limits, local interaction constraints, and temporal quantization resolution through the Pulse Rhythm, ①⥂⧖⌂ = ①⥂⧗⌂/2. Among the book's testable predictions are temporal quantization effects at ultra-high energies showing ①⥂⧖⌂ = ①⥂⧗⌂/2 intervals. The data-spectrum entry writes it I𝓜 = f(data, correlation, arrangement) [∅]; the quantified form is I = -Σ_i p_i log_2(p_i) [1ᵇ], where I is the information content [1ᵇ], p_i the probability of binary configuration i [∅] and i the index over binary configurations [∅]. The book's check reads [1ᵇ] = −Σ[∅] × [∅] = [1ᵇ]. It connects to The UniSpheral Data Spectrum, Data State, Information Conservation, Temporal Information and Pulse Rhythm Definition.