We formalize a necessity law for proof-theoretic telomere protocols in self-modifying agents.Let Tlife be an ordinal-valued life counter and Hayflick = ε0 the boundary. We prove that onceTlife reaches (or exceeds) ε , sustainability cannot be maintained by any internally generated procedure: either self-modification must freeze (entering a non-adaptive regime), or an externally anchored event bound to an unpredictable external challenge is required to reset the counter and restore adaptive capability. This theorem isolates the irreducible role of external anchoring at the boundary, and provides audit-ready triggers and evidence-leaf schemas for protocol stacks.