(5/5 Changing the Geometry of Arithmetic) Suppose an arithmetic configuration is absent. Traditionally, that may look like a failure of construction: we searched for something and did not find it. But in a transport picture, persistent absence is much more demanding. If the geometry keeps providing admissible transport while the arithmetic never realizes the corresponding configuration, the discrepancy cannot simply disappear. It must be carried somewhere. So permanent absence requires a persistent obstruction. This suggests a different proof strategy: Assume the configuration never occurs beyond some point. Translate that absence into the obstruction required to sustain it. Then follow the obstruction through the geometry. Can it be recycled indefinitely? Can it remain confined? Can it cross scales without accumulating discrepancy? Or does the geometry eventually force it into a configuration that contradicts the assumed absence? The important shift is this: We are no longer trying to produce the desired arithmetic object directly. We are asking whether the geometry required for its permanent absence can exist. And different fibres may fail in different ways. Large additive width, fixed gaps, or rigid divisibility constraints need not share the same terminal mechanism. The geometry can be common. The obstruction does not have to be. This is where the viewpoint becomes a research program rather than a change of coordinates. More to come. #Mathematics #NumberTheory #Geometry #PrimeNumbers