Coherence-Preserving Bifurcation Lemma

Introduces the Coherence-Preserving Bifurcation Lemma for discrete-time contracting systems with bounded integration capacity. The result shows that when a coherent attractor approaches its coherence boundary under increasing forcing, there exists a finite computable horizon k∗ after which bifurcation into admissible coherent sub-basins is strictly cheaper than sustaining an incoherent state. The crossover occurs at k∗=⌈Cb/cinc⌉+1 under a simple cost model. This lemma extends the Integration Capacity framework for recursive systems and provides a general structural principle for contracting dynamics. A brief heuristic interpretation relating the result to confinement-like behavior in physical systems is included.