Research · 26 Jun 2026
Silent lookup errors, counted rather than estimated
Roughly 6,100 in a billion queries at the current index width, and the arithmetic is on the page.
Specifics
The numbers, and where they come from
| Quantity | Value | Basis |
|---|---|---|
| Fingerprint width | 16 bits | Stated |
| Queries modelled | 10⁹ | Stated |
| Expected silent accepts | ~6,100 | Computed |
| At 24 bits | ~24 | Computed |
The problem
A lookup that fails without saying so
The index answers membership queries. At a finite fingerprint width it will occasionally accept a key it does not hold, and it will do so silently: the caller gets a plausible answer with no flag attached. This is the one failure in the system that does not raise a typed flag, which is precisely why it is stated here in full.
At sixteen bits and a billion queries, the expected number of silent false accepts is roughly 6,100. That figure is computed from the width, not measured on a corpus, and it is labelled computed wherever it appears.
The trade
Bits are the only currency that buys it down
Every additional bit of fingerprint halves the false accept rate and costs storage proportional to the number of keys. Going from sixteen to twenty-four bits reduces expected silent accepts from about 6,100 to about 24 per billion queries, and consumes most of what is left of a 16 MB budget.
That is the whole trade, and it is why Octavo carries a weaker guarantee than Quarto rather than merely less content. On Folio the constraint does not bind and fingerprints run at full width.
The one unflagged failure
Every other failure mode in the accounting raises a typed flag. This one does not. A regulated deployment should size the index for the query volume it actually expects, and the arithmetic to do that is in the specification.