Proof of `Gram-conditioned columns and their rank-failure probability` (2nd statement)
groundedproofs/Lax342547Proofs/GramColumns.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
Apply the affine extension-dependence estimate to the independent annihilator columns of a fixed Gram fiber. When both old frames have d columns and the channel has h, this is exactly 2^(2d+h-N), the conditional channel-rank failure bound in Lemma 4.3(a).