Three recent results describe what look like unrelated LLM reliability problems.
Yin et al. (2026) show reasoning RL collapses tool-reliability representations.
Suleymanov et al. (2026) show that under safety-constrained generation, large models rewrite flagged spans while small models truncate.
Bastounis et al. (2024) prove any consistent-reasoning system without an implicit "I don't know" function must hallucinate infinitely often on broad problem classes.
We argue these findings converge on a single intervention: calibrated abstention is what each independently identifies as the missing capability, even though the unavailability they document, a capability gap, a policy gap, and a recursion-theoretic gap, has a different source in each case.
Honesty post-training has narrowed the gap in deployed models, but principled closure of the class Bastounis identifies requires a calibrated abstention function whose training signal at the leaderboard level is absent: dominant benchmarks assign zero reward to decline, so the leaderboard gradient that would select for the function does not exist.
We propose four changes to evaluation: triple-scoring, abstention-rate reporting, capability-stratified evaluation, and mandatory calibration metrics.
Benchmark reform is necessary, not sufficient, for closing the gap the theorem identifies.