Phase Transition Criterion

The Phase Transition Criterion is the depth at which recursion meets the substrate's ceiling and must reorganize: ℜ(n⨶) = T▱, so that with ℜ(n) = 2ⁿ the critical recursion level is n⨶ = log₂(T▱). Part 1.5 pairs it with the Sustainability Constraint ℜ(n) · ℨᵇ ≤ I▱⥣. Capacity doubles at every pulse, so the substrate ceiling is reached at a definite depth rather than approached asymptotically; at n⨶ the system cannot hold more and reorganizes into the next level of structure, the phase transition that ends each stage of recursion. The same threshold appears in Part 1.15 as the Substrate Threshold T▱(⨶) that the Recursive Dimensional Capacity ℜ◉(n) must exceed (Pulse Phase Transition Condition). Whether T▱ and I▱⥣ are one ceiling, and whether n⨶ is the Rupture Rule's L for a whole universe, is open. The book writes ℜ(n⨶) = T▱, where ℜ(n) is the total data capacity after n completed pulses [∅], n⨶ the critical recursion level, the threshold depth where phase transitions occur [∅], and T▱ the substrate threshold, the computational capacity limit that triggers reorganization [∅]: [∅] = [∅]. It connects to Sustainability Constraint, The Recursive Growth Law, Pulse Phase Transition Condition, Substrate Threshold, Rupture Rule and Synchronization Cost.