Proof of `Gradient residuals vanish on effective profiles and selected atoms` (1st statement)
groundedproofs/Lax342547Proofs/RecipeResiduals.lean · lax-342547
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
The effective equation agrees with the full contraction because the baseline extends the table. On selected atoms the binary gradient prescriptions agree with the frozen contraction values. Linearity makes the residual zero on the sum of those two subspaces.