Lemma. Append-only retention preserves contamination absent deletion [ftip-00D2]
Lemma. Append-only retention preserves contamination absent deletion [ftip-00D2]
Suppose the skill archives of Definition [ftip-00D0] are append-only: \(\mathcal K_n\subseteq \mathcal K_{n+1}\) for every \(n\). If \(B(h_n)=1\), then \(B(h_m)=1\) for every \(m\geq n\) until a deletion, rollback, or contract change removes or reclassifies the witnessing skill.
Proof. Choose \(k\in \mathcal K_n\) with \(b(k)=1\). Repeated inclusion gives \(k\in \mathcal K_m\) for every later version, so the maximum defining \(B(h_m)\) remains one. The final qualification lists operations that break the inclusion or change the predicate.
This finite observation concerns retained state. It does not say that the selector will invoke the exploit on every later run.