Scaling laws ask: given compute C, choose N and D. They assume the parameter count N is constant for the whole run — and never argued for it.
So: given compute C, choose the trajectory N(t). The answer is a shape, not a number.
Flat vs grown, identical LR schedule, identical FLOP budget, multiple seeds. The original result changed four things at once and ran one seed.
Both arms stop at the same FLOP budget. Lower is better.
The shape under test. Both arms end at the same architecture.
Six hand-run points is not a search. An autonomous agent proposes, runs and merges growth schedules against the objective.