Synchronization Cost

The Synchronization Cost is the computational cost of phase alignment across the substrate, ⇔⚕, one of the two terms that set the Substrate Threshold T▱(⨶) at which recursive dimensional capacity forces a phase transition. Part 1.15 writes the threshold as T▱(⨶) = α▱ × log(ↁⓘ▱) + β⇔ × √(⇔⚕): the information term, the substrate's information capacity ↁⓘ▱ weighted by α▱, and the synchronization term, the cost of holding phases aligned weighted by β⇔. When the Recursive Dimensional Capacity ℜ◉(n) exceeds that threshold, computational overload forces a phase transition to a higher organizational level (Pulse Phase Transition Condition), which is how the book has particles combine into atoms, atoms into molecules and molecules into complex structures through computational necessity rather than external force. The name replaces the earlier "Synchronization Energy", since the quantity is dimensionless, a cost in the substrate's own count, not an energy. The book tags ⇔⚕ [∅], the phase-alignment computational cost, with α▱ and β⇔ [∅] the weighting constants, ↁⓘ▱ [∅] the Data Information Substrate capacity and T▱(⨶) [∅] the threshold: [∅] × log([∅]) + [∅] × √[∅] = [∅]. It connects to Pulse Phase Transition Condition, Substrate Threshold, Recursive Dimensional Capacity, Phase Transition Criterion and Sustainability Constraint.