UniSpheral Pulse Closure Conditions

The UniSpheral Pulse Closure Conditions are the tests that decide whether a structure persists or collapses, by comparing the time it needs to resolve recursively with the temporal bound of one Local Pulse Rate. The endurance of any structure in the UniSphere depends on whether it can complete its recursive resolution within that bound, so the stability of matter is reduced to a computational test. Structures whose resolution completes within the Pulse Rate limit achieve successful recursive closure and are stable; structures that need longer exceed the closure threshold and collapse, which the book ties to gravitational breakdown and the Null Well. The same test is restated in dimensionless form through the closure parameter χ. The conditions are τ(m) ≤ ⥂⌂ for stability and τ(m) > ⥂⌂ for collapse, where τ(m) is the time required to recursively resolve a structure of mass m [𝕋], ⥂⌂ is the maximum allowed closure interval, the Pulse Tempo bound [𝕋], and m is the mass parameter [𝕄]. In dimensionless form χ = ⥂⌂ / τ(m), with χ ≥ 1 stable, χ < 1 collapse and χ = 1 critical. By the Where-list the conditions read [𝕋] ≤ [𝕋] and [𝕋] > [𝕋], and χ is [∅]. It connects to the UniSpheral Law of Pulse Recursion, Pulse Stability Condition, Pulse Collapse Condition, Dimensionless Pulse Closure Parameter, Pulse Critical Threshold and Null Well.