Reducing Gilbreath's Conjecture to a Local Condition: How much of the triangle do we really need to watch?

We present a reduction of Gilbreath’s Conjecture to an explicit local bound. Specifically, we show that the conjecture follows from the condition |Gᵣ[2] − Gᵣ[1]| ≤ 2 for all r ≥ 1. We state four supporting lemmas used by the reduction, describe a minimal preimage structure associated with a model minimal violating configuration, and report computational verification of the local bound through 100,000 rows. The full conjecture remains open, but the remaining target is now clearly isolated. For correspondence and updates: BMorgan007(at)protonmail.com