Proof of `Walsh operator bounds with explicit bilinear rank` (6th statement)
groundedproofs/Lax342547Proofs/BilinearWalsh.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
Bound each weight's squared energy by the number of inputs. Rank-nullity cancels the inactive coordinates after normalization, leaving squared correlation at most 2^(-rank), hence the claimed square-root bound.