The atlas gave way to transport.
The proof began as an atlas: escape regions, collision cones, boxes, charts, and the joins between them. Its decisive moment was realizing that the atlas itself was the wrong object. In a curvature coordinate, the difficult sign could travel through one positive crossing mechanism. The resulting theorem and the exact failure beyond it now meet in a checked formal release.
- Everyone assumed
- A global positivity theorem required an expanding map of local cases and regional joins.
- I asked
- Could the cases be replaced by one transport object whose geometry already carries the sign?
- I changed
- Move to a curvature coordinate, turn the obstruction into a positive crossing transport, and meet the universal result with an exact finite counterexample at the next order.
- Now there is
- A finished exact-order classification of the global Riemann kernel, assembled in Lean and published with a reproducibility repository and archival release.