official_claims.json

[
  "Theorem 3.1 proves that a hypothesis class is uniformly generatable with replay if and only if it is uniformly generatable in the standard no-replay setting, with identical sample complexity, showing replay is benign for the strongest notion of generation (Theorem 3.1).",
  "Theorem 4.1 exhibits a countable hypothesis class that is non-uniformly generatable without replay but not non-uniformly generatable with replay, establishing a strict separation caused by replay (Theorem 4.1).",
  "Theorem 5.1 shows a computable algorithm using only membership queries can generate in the limit any countable hypothesis class even under replay conditions (Theorem 5.1).",
  "Theorem 5.6 constructs an uncountable hypothesis class that is generatable in the limit without replay but becomes non-generatable in the limit once replay is permitted (Theorem 5.6).",
  "Theorem 6.1 proves no deterministic generator using only membership queries can properly generate in the limit for all countable hypothesis classes (Theorem 6.1).",
  "Theorem 6.3 shows that even some finite hypothesis classes that are properly generatable in the limit without replay become impossible to properly generate once replay is introduced (Theorem 6.3)."
]