Combined Threshold Function

The Combined Threshold Function is the single criterion that joins the density, coherence and information thresholds to decide when an oscillatory pulse field can crystallize into a stable form. The book builds it from three reference scales in its framework of critical transition thresholds: the Critical Density Threshold ρ⨶, approximately 10¹⁵ kg/m³ [𝕄·𝕃⁻³]; the critical coherence C⨶ of the Phase Coherence Condition, |⟨e^i(φ_j − φ_k)⟩| ≥ C⨶, approximately 0.8 [∅]; and the Information Threshold I⨶ of the Information Density Criterion, I⌂ = −sum_i p_i log_2(p_i) ≥ I⨶ [𝕃⁻³·1ᵇ]. Each normalizes its factor of Θ, and the one rule is Θ ≥ 1, which marks the transition from unstable to stable substrate configurations: a surplus in one criterion can make up a shortfall in another. The current definition combines them as Θ(ρ,C,I) = [ρ/ρ⨶]^α × [C/C⨶]^β × [I/I⨶]^γ, a product of each quantity divided by its threshold, each raised to its own exponent α, β, γ, equal to 2, 1 and 1/2. It connects to the Critical Density Threshold, Phase Coherence Condition, Information Density Criterion, Recursive Density Threshold, Thresholds of Recursion and Field-to-Form Transition.