Everything, LiSSA, NTK diagonal, sharpness, all runs on one primitive: the Hessian-vector product.
One extra backward pass per call, no matrix ever stored. Four hard invariants every run, not guidelines, enforced, and the simulation fails loudly if any break. Pass 2 is the heavy lift, pass 3 is cheap, and everything downstream unlocks in parallel the moment the checkpoint saves.
Simulate, read, clean, repeat until you'd ship it.