Collapse Threshold Equation

The Collapse Threshold Equation is the relation, which the book writes in general form in chapter 4 and explicitly in chapter 5, giving the tension at which collapse occurs as a function of the substrate's capacity and the recursive correlation length; the threshold decides whether accumulated tension produces a contained Nova Within or a rupturing Nova Without. The book refers to it in two places. In chapter 4 the Critical Data Density Threshold is said to set the bifurcation point at which the Collapse Threshold Equation of chapter 5 (Part 5.1) selects the regime. In chapter 5's cyclical phase architecture, the Structural Emergence phase, at near-zero entropy and a recursive tension far above its baseline, draws its high recursive tension from this equation. The phases that follow are entropy accumulation, null convergence and renewal. Chapter 5 gives the function explicitly as the Collapse Energy Threshold Equation. T⦰ = f(C▱, Lℜ) = C▱ × ln(1 + Lℜ/L_0), where T⦰ is the collapse energy threshold [𝕄·𝕃²·𝕋⁻²], C▱ the substrate computational capacity [𝕄·𝕃²·𝕋⁻²], Lℜ the recursive correlation length [𝕃] and L_0 the characteristic substrate scale [𝕃]. It connects to Critical Data Density Threshold, Nova Within, Nova Without, Collapse Threshold, Structural Emergence and Data Gravity Collapse Threshold.