Our tool manifest has a field called refuses. It holds what that tool declines to tell you.
Fifteen of the twenty-one tools carry one. The other six are null, and the manifest's own comment says why: a refusal has to be drawn from something the tool actually does, and where there is no refusal the field is left empty rather than filled in with something that sounds good.
I think this is the most useful design decision in the whole wing, and it cost nothing to make. So here is what it is for, and then the tools themselves, which are the part you can click.
A tool that answers every input is lying somewhere. Not usually on purpose. It is just that the alternative to a refusal is a number, and a number that came from insufficient evidence looks exactly like a number that came from good evidence. Same font, same decimal places, same confidence.
The room-acoustics tool is the sharpest case. You clap in your kitchen, and for some octave bands your recording genuinely does not contain enough decay above the noise floor to fit a slope to. Every competing app returns a reverberation time anyway. Ours prints which band it dropped and why, because a made-up 0.4 seconds is worse than a blank, and the blank is the honest measurement.
Once you accept that, the refusal stops being an error path and becomes a feature with a spec. And then it wants to live in the manifest next to the tool's name, where a reader meets it before they meet the answer, rather than in a caveats paragraph nobody scrolls to.
Cut List is 1-D cutting stock. Give it stock lengths, a blade kerf and a parts list, and it returns a cutting plan plus a certified lower bound on how few boards any plan could ever use.
The engineering is the good part. Gilmore–Gomory column generation produces LP duals in floating point; a separate routine then verifies dual feasibility in exact integer arithmetic, via a bounded knapsack that has no access to the thing that proposed the answer. The simplex output is only ever a proposal. And there is a re-check button that reads the numbers back out of the rendered table cells rather than out of memory, so if you edit one in devtools the check goes red.
Benched over 2,355 BPPLIB instances at 6 seconds each: it matched the published optimum on 1,843, proved optimality itself on 1,578, and claimed fewer boards than a proved optimum zero times, in every one of the twelve sets. On Schoenfield's Hard28, built in 2002 specifically to defeat good heuristics, it proves 12 at six seconds. The bench also counts separately the instances where no certificate could ever have closed the gap, because ceil(LP) sits strictly below the optimum and a closing certificate would have to prove something false. BPPLIB's ANI set is built that way on purpose, and across its 250 instances the tool claims zero certificates. That number has to be zero, and it is.
What Light Is That?: you are on a coast at night, there is a light flashing out there, and you want to know which one it is. Type the colour, the flashes in a burst, and tap out the period.
It ships 40,559 navigation lights parsed from the NGA List of Lights by a hand-written grammar for characteristic strings (Fl.(2+1)W.R., Q+LFl, Mo(A)), in a columnar payload of 5.65 MB. Candidates are filtered by the geographic horizon computed from lamp height and your eye height and by advertised range, and every exclusion returns its reason. Then it blinks each candidate on its own schedule so you can hold the phone up next to the real thing.
It ships a pre-registered accuracy study, which I have not seen a browser tool do. 3,000 simulated observers, 2 km of position error, 0.08 s timing noise: the true light lands in the shortlist 98.4% of the time and ranks first 78.7%, median shortlist length 1, median query 0.089 ms. The study also publishes the tolerance sweep where it does badly, which is the half that makes it worth reading: tighten to 0.05 and recall falls to 50.2%.
Its refusal is the loudest thing on the page. Do not navigate by this. And it says out loud that the United States is almost entirely absent, because Pub. 110-116 is NGA's foreign list.
Canvas Ratio: type two sides of a rectangle, and it counts how many catalogued paintings sit inside your tolerance.
711,555 painting proportions in 717,482 bytes. That is 1.008 bytes per painting, and the trick is the whole tool: store ln(long/short) quantised to a millionth, sort it, delta-code the deltas as LEB128 varints. Decodes in single-digit milliseconds, after which every query is two binary searches. Nothing is pooled across catalogues, which is a statistical choice rather than a UI one, and worth knowing since Wikidata is 696,533 of the 711,555.
Its refusal is in the result itself: a percentage of catalogued paintings is not a percentage of paintings.
Printed Numbers: a printed decimal is a claim about rounding, and this does exact interval arithmetic on what the figure actually denotes.
Two independently written engines run side by side in your browser and the page reports whether they agree. Engine A's header states that it was written from the specification alone, before Engine B was read. Both are BigInt rationals with, in its own words, "no Number anywhere that carries a value". 3.20 / 1.75 comes back as 71/39, 641/349). The naive answer 1.828571… is inside it, but 1.8205 to 1.8367 means the second decimal was never determined. An integer with trailing zeros gets answered twice, strictly and loosely, instead of being refused.