10. THE CORNER THEOREM

Every other document in this exhibition carries the caveat CF CONSISTENT not PASS — consistent with what is known, but not claimed as proof. The Corner Theorem is the single exception: it is proved, in the strict mathematical sense, both directions, confirmed in March 2026. The proof rests on one fact about fluids that nobody disputes — that incompressible fluids cannot change their own volume — and follows its consequences with mathematical rigour. That one constraint forces the three numbers describing any fluid deformation to always sum to exactly zero, which in turn collapses the full three-dimensional symmetry of space into something smaller and more specific: a hexagon, with exactly six corners, present in every incompressible fluid, at every scale, in every domain, from a water droplet to Saturn's atmosphere. The hexagon itself is revealed as the intersection of two equilateral triangles — the positive (cyclonic) and negative (anticyclonic) bulbs, each independently selected by maximum plastic dissipation — whose intersection is uniquely the regular Tresca hexagon, and this bulb intersection structure was the key insight that closed the only-if direction of the proof. The consequence is the Trojan Horse: the hexagonal geometry is not something turbulence creates over time, it is latent in the equations from the first instant, waiting to be activated. Before March 2026, this was a computational observation. After March 2026, it is a theorem.