Information Density Criterion

The Information Density Criterion sets the reference information density I⨶ at which the information factor (I/I⨶)^γ of the Combined Threshold Function reaches 1; the local information density, measured as a Shannon entropy in bits, enters stable form emergence through Θ ≥ 1 rather than as a requirement on its own. It is the third of the reference scales that normalize Θ, after the Critical Density Threshold and the Phase Coherence Condition, and it ties form emergence to Information Conservation. The Information Threshold is set at approximately 10 bits/m³. The three criteria are joined in the Combined Threshold Function Θ(ρ,C,I) = [ρ/ρ⨶]^α × [C/C⨶]^β × [I/I⨶]^γ with α = 2, β = 1, γ = 1/2, and form emerges when Θ ≥ 1. The formal statement is I⌂ = −sum_i p_i log_2(p_i) ≥ I⨶, where I⌂ is the local information density, p_i the probability of state i, log_2 the base-2 logarithm and I⨶ the Information Threshold. Dimensions from the book's Where-list: I⌂ and I⨶ [𝕃⁻³·1ᵇ], p_i and i [∅]. It connects to the Information Threshold, Combined Threshold Function, Form Emergence Condition, Critical Density Threshold, Phase Coherence Condition and Information Conservation.