(4/5 Testing the Geometry) Twin primes: remove the width The Goldbach fibre had a hidden resource: width. For p + q = 2N, the available additive range grows with the scale. Now replace it with q − p = 2. The situation changes abruptly. The separation remains fixed. There is no expanding additive region through which transport can spread. Any mechanism that fundamentally relied on increasing width should therefore fail here. And that failure is informative. A common geometry does not require every arithmetic fibre to behave in the same way. It should reveal which parts of an argument are structural and which depend on the fibre itself. So the question becomes: If width is unavailable, what can carry the contradiction? The obstruction can no longer be defeated merely by distributing transport across an expanding region. Something more local must replace that mechanism. Information has to survive and transfer through a fixed-gap configuration. Same multiplicative geometry. Same idea of persistent obstruction. Different terminal mechanism. Next we remove something else: abundance. #Mathematics #NumberTheory #TwinPrimes #Geometry