CH3 v3: Nodes, Short Windows, and Inheritance A conditional path and effective pipeline towards the Strong Goldbach Conjecture

We present a consolidated version (v3) of the CH3 program that integrates: (i) thedefinition of an inherited prime (CH3) and its direct implication for the Strong GoldbachConjecture (SGC), (ii) a Node Lemma with a centered basal bound, (iii) the Short WindowHypothesis (SWH) around E/2, (iv) a support functional S(E) that formalizes the ternary–binary bridge, (v) an explicit conditional theorem that reduces SGC to a computationalthreshold under SWH, and (vi) the Double Equilibrium (DE) substructure with its arithmeticfailure families. We include a reproducible Python pipeline for effective verification andan appendix on an analytic path (bilinear sums on minor arcs) that connects to futureimprovements (circle method type).