Recursive Density Threshold

The Recursive Density Threshold is the reference recursive density, approximately 10¹⁵ kg/m³, at which the density factor (ρℜ/ρ⨶)^α of the Combined Threshold Function reaches 1. It is the first of the reference scales in the book's framework for how oscillatory pulse fields crystallize into persistent structure. It normalizes Θ rather than standing as a requirement on its own: a form emerges whenever Θ ≥ 1, so a density below ρ⨶ suffices when coherence or information density stand far enough above their own scales. It is combined with the Phase Coherence Condition and the Information Density Criterion in the Combined Threshold Function, where the density ratio enters squared. The formal statement is ρℜ ≥ ρ⨶, where ρℜ is the recursive density, a mass density, and ρ⨶ the Critical Density Threshold, approximately 10¹⁵ kg/m³. Dimensions: ρℜ and ρ⨶ [𝕄·𝕃⁻³], the coefficient 10¹⁵ [∅]; the book's check is valid and verified. It connects to the Critical Density Threshold, Phase Coherence Condition, Information Density Criterion, Combined Threshold Function, Form Emergence Condition and Field-to-Form Transition.