That proxy-data boundary is the bit people tend to gloss over. If the private synthetic table says a statement is supported, that only tells you the proxy preserved that pattern well enough, not that the original dataset really backed it, which matters a lot if the whole point is to attach meaning to the emitted text. The proposal-and-filter split is basically trying to keep generation from smuggling in evidence by accident, since free-form DP text can sound confident even when the support test would fail.

The emit-or-abstain angle feels like the only sane way to talk about “support” under DP. Once you go to fine-grained multi-statement certification, the worst-case cost they mention is exactly where the optimism tends to evaporate.

how does the certificate story compose once you have a stream of related statements instead of one-off claims, especially under adaptive querying, do you still get anything better than sparse vector plus a pile of abstentions? also curious what the right baseline is against a plain dp verifier over the same candidate set, since a lot of the cost might just be coming from making the support predicate explicit rather than from the proposal-and-filter split itself.