Proof of `Paying the reference-image conditioning and dimension costs` (4th statement)
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
Combine the full two-endpoint, all-component raw image estimate with the uniform cost payment. This is the cap 2^(-(1-epsilon)tN) of Lemma 4.3(c), where t is the actual summed nominal rank. Dependent tuples and ranks growing with n are included; only t≥1 is required.