(3/5 Testing the Geometry) Goldbach: width as a resource Now impose an additive constraint on the multiplicative geometry: p + q = 2N. For fixed N, this selects a fibre of candidate configurations. What matters is that the fibre has width. As N grows, the additive condition leaves an expanding family of configurations through which multiplicative transport can be tested. Suppose the required prime configurations were permanently absent beyond some scale. Then every available channel in an increasingly wide fibre would have to fail. In a transport picture, that absence must leave an obstruction somewhere in the geometry. But increasing width creates a problem for such an obstruction: more channels and more configurations become available as the scale grows. So width becomes a resource. The question is no longer only: Can we find p and q? It becomes: Can a persistent obstruction exclude every admissible prime configuration while the fibre continues to widen? And can it do so without recycling the same obstruction indefinitely? Now remove the width. What survives? #Mathematics #NumberTheory #Goldbach #Geometry