Proof of `Quantitative critical-comb consequence`
What this proof establishes
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
Choose the critical exponent large enough to absorb the linear-size constant from Lemma 4.3. Apply the maximum-degree reduction and then Lemma 3.1 in the sparse orientation. Complement invariance gives the second alternative.